LMFDB - Embedded newform 147.3.f.c.31.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [147,3,Mod(19,147)]

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, 5]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("147.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	147.f (of order $6$, 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:	$4.00545988610$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	147.31
Dual form			147.3.f.c.19.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(1.50000 - 2.59808i) q^{4} +(4.50000 - 2.59808i) q^{5} +1.73205i q^{6} -7.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(1.50000 - 2.59808i) q^{4} +(4.50000 - 2.59808i) q^{5} +1.73205i q^{6} -7.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(-4.50000 - 2.59808i) q^{10} +(5.50000 - 9.52628i) q^{11} +(-4.50000 + 2.59808i) q^{12} +6.92820i q^{13} -9.00000 q^{15} +(-2.50000 - 4.33013i) q^{16} +(-21.0000 - 12.1244i) q^{17} +(1.50000 - 2.59808i) q^{18} +(3.00000 - 1.73205i) q^{19} -15.5885i q^{20} -11.0000 q^{22} +(-14.0000 - 24.2487i) q^{23} +(10.5000 + 6.06218i) q^{24} +(1.00000 - 1.73205i) q^{25} +(6.00000 - 3.46410i) q^{26} -5.19615i q^{27} +25.0000 q^{29} +(4.50000 + 7.79423i) q^{30} +(28.5000 + 16.4545i) q^{31} +(-16.5000 + 28.5788i) q^{32} +(-16.5000 + 9.52628i) q^{33} +24.2487i q^{34} +9.00000 q^{36} +(29.0000 + 50.2295i) q^{37} +(-3.00000 - 1.73205i) q^{38} +(6.00000 - 10.3923i) q^{39} +(-31.5000 + 18.1865i) q^{40} +3.46410i q^{41} +26.0000 q^{43} +(-16.5000 - 28.5788i) q^{44} +(13.5000 + 7.79423i) q^{45} +(-14.0000 + 24.2487i) q^{46} +(66.0000 - 38.1051i) q^{47} +8.66025i q^{48} -2.00000 q^{50} +(21.0000 + 36.3731i) q^{51} +(18.0000 + 10.3923i) q^{52} +(-15.5000 + 26.8468i) q^{53} +(-4.50000 + 2.59808i) q^{54} -57.1577i q^{55} -6.00000 q^{57} +(-12.5000 - 21.6506i) q^{58} +(7.50000 + 4.33013i) q^{59} +(-13.5000 + 23.3827i) q^{60} +(-12.0000 + 6.92820i) q^{61} -32.9090i q^{62} +13.0000 q^{64} +(18.0000 + 31.1769i) q^{65} +(16.5000 + 9.52628i) q^{66} +(26.0000 - 45.0333i) q^{67} +(-63.0000 + 36.3731i) q^{68} +48.4974i q^{69} +64.0000 q^{71} +(-10.5000 - 18.1865i) q^{72} +(-6.00000 - 3.46410i) q^{73} +(29.0000 - 50.2295i) q^{74} +(-3.00000 + 1.73205i) q^{75} -10.3923i q^{76} -12.0000 q^{78} +(-8.50000 - 14.7224i) q^{79} +(-22.5000 - 12.9904i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(3.00000 - 1.73205i) q^{82} +53.6936i q^{83} -126.000 q^{85} +(-13.0000 - 22.5167i) q^{86} +(-37.5000 - 21.6506i) q^{87} +(-38.5000 + 66.6840i) q^{88} +(69.0000 - 39.8372i) q^{89} -15.5885i q^{90} -84.0000 q^{92} +(-28.5000 - 49.3634i) q^{93} +(-66.0000 - 38.1051i) q^{94} +(9.00000 - 15.5885i) q^{95} +(49.5000 - 28.5788i) q^{96} +91.7987i q^{97} +33.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - 3 q^{3} + 3 q^{4} + 9 q^{5} - 14 q^{8} + 3 q^{9}+O(q^{10}) $ 2 * q - q^2 - 3 * q^3 + 3 * q^4 + 9 * q^5 - 14 * q^8 + 3 * q^9	$ 2 q - q^{2} - 3 q^{3} + 3 q^{4} + 9 q^{5} - 14 q^{8} + 3 q^{9} - 9 q^{10} + 11 q^{11} - 9 q^{12} - 18 q^{15} - 5 q^{16} - 42 q^{17} + 3 q^{18} + 6 q^{19} - 22 q^{22} - 28 q^{23} + 21 q^{24} + 2 q^{25} + 12 q^{26} + 50 q^{29} + 9 q^{30} + 57 q^{31} - 33 q^{32} - 33 q^{33} + 18 q^{36} + 58 q^{37} - 6 q^{38} + 12 q^{39} - 63 q^{40} + 52 q^{43} - 33 q^{44} + 27 q^{45} - 28 q^{46} + 132 q^{47} - 4 q^{50} + 42 q^{51} + 36 q^{52} - 31 q^{53} - 9 q^{54} - 12 q^{57} - 25 q^{58} + 15 q^{59} - 27 q^{60} - 24 q^{61} + 26 q^{64} + 36 q^{65} + 33 q^{66} + 52 q^{67} - 126 q^{68} + 128 q^{71} - 21 q^{72} - 12 q^{73} + 58 q^{74} - 6 q^{75} - 24 q^{78} - 17 q^{79} - 45 q^{80} - 9 q^{81} + 6 q^{82} - 252 q^{85} - 26 q^{86} - 75 q^{87} - 77 q^{88} + 138 q^{89} - 168 q^{92} - 57 q^{93} - 132 q^{94} + 18 q^{95} + 99 q^{96} + 66 q^{99}+O(q^{100}) $ 2 * q - q^2 - 3 * q^3 + 3 * q^4 + 9 * q^5 - 14 * q^8 + 3 * q^9 - 9 * q^10 + 11 * q^11 - 9 * q^12 - 18 * q^15 - 5 * q^16 - 42 * q^17 + 3 * q^18 + 6 * q^19 - 22 * q^22 - 28 * q^23 + 21 * q^24 + 2 * q^25 + 12 * q^26 + 50 * q^29 + 9 * q^30 + 57 * q^31 - 33 * q^32 - 33 * q^33 + 18 * q^36 + 58 * q^37 - 6 * q^38 + 12 * q^39 - 63 * q^40 + 52 * q^43 - 33 * q^44 + 27 * q^45 - 28 * q^46 + 132 * q^47 - 4 * q^50 + 42 * q^51 + 36 * q^52 - 31 * q^53 - 9 * q^54 - 12 * q^57 - 25 * q^58 + 15 * q^59 - 27 * q^60 - 24 * q^61 + 26 * q^64 + 36 * q^65 + 33 * q^66 + 52 * q^67 - 126 * q^68 + 128 * q^71 - 21 * q^72 - 12 * q^73 + 58 * q^74 - 6 * q^75 - 24 * q^78 - 17 * q^79 - 45 * q^80 - 9 * q^81 + 6 * q^82 - 252 * q^85 - 26 * q^86 - 75 * q^87 - 77 * q^88 + 138 * q^89 - 168 * q^92 - 57 * q^93 - 132 * q^94 + 18 * q^95 + 99 * q^96 + 66 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$50$	$52$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.500000	−	0.866025i	−0.250000	−	0.433013i	0.713525	−	0.700629i	$-0.247097\pi$
$2$	−0.500000	−	0.866025i	−0.250000	−	0.433013i	−0.963525	+	0.267617i	$0.913764\pi$
$3$	−1.50000	−	0.866025i	−0.500000	−	0.288675i
$3$	−1.50000	−	0.866025i	−0.500000	−	0.288675i
$4$	1.50000	−	2.59808i	0.375000	−	0.649519i
$5$	4.50000	−	2.59808i	0.900000	−	0.519615i	0.0227998	−	0.999740i	$-0.492742\pi$
$5$	4.50000	−	2.59808i	0.900000	−	0.519615i	0.877200	+	0.480125i	$0.159409\pi$
$6$			1.73205i			0.288675i
$7$		0			0
$7$		0			0
$8$	−7.00000			−0.875000
$9$	1.50000	+	2.59808i	0.166667	+	0.288675i
$10$	−4.50000	−	2.59808i	−0.450000	−	0.259808i
$11$	5.50000	−	9.52628i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$11$	5.50000	−	9.52628i	0.500000	−	0.866025i	1.00000			$0$
$12$	−4.50000	+	2.59808i	−0.375000	+	0.216506i
$13$			6.92820i			0.532939i	0.963843	+	0.266469i	$0.0858571\pi$
$13$			6.92820i			0.532939i	−0.963843	+	0.266469i	$0.914143\pi$
$14$		0			0
$15$	−9.00000			−0.600000
$16$	−2.50000	−	4.33013i	−0.156250	−	0.270633i
$17$	−21.0000	−	12.1244i	−1.23529	−	0.713197i	−0.267165	−	0.963651i	$-0.586087\pi$
$17$	−21.0000	−	12.1244i	−1.23529	−	0.713197i	−0.968129	+	0.250453i	$0.919420\pi$
$18$	1.50000	−	2.59808i	0.0833333	−	0.144338i
$19$	3.00000	−	1.73205i	0.157895	−	0.0911606i	−0.418971	−	0.908000i	$-0.637609\pi$
$19$	3.00000	−	1.73205i	0.157895	−	0.0911606i	0.576865	+	0.816839i	$0.304276\pi$
$20$		−	15.5885i		−	0.779423i
$21$		0			0
$22$	−11.0000			−0.500000
$23$	−14.0000	−	24.2487i	−0.608696	−	1.05429i	−0.991456	−	0.130444i	$-0.958360\pi$
$23$	−14.0000	−	24.2487i	−0.608696	−	1.05429i	0.382760	−	0.923848i	$-0.374974\pi$
$24$	10.5000	+	6.06218i	0.437500	+	0.252591i
$25$	1.00000	−	1.73205i	0.0400000	−	0.0692820i
$26$	6.00000	−	3.46410i	0.230769	−	0.133235i
$27$		−	5.19615i		−	0.192450i
$28$		0			0
$29$	25.0000			0.862069			0.431034	−	0.902335i	$-0.358149\pi$
$29$	25.0000			0.862069			0.431034	+	0.902335i	$0.358149\pi$
$30$	4.50000	+	7.79423i	0.150000	+	0.259808i
$31$	28.5000	+	16.4545i	0.919355	+	0.530790i	0.883429	−	0.468565i	$-0.155229\pi$
$31$	28.5000	+	16.4545i	0.919355	+	0.530790i	0.0359257	+	0.999354i	$0.488562\pi$
$32$	−16.5000	+	28.5788i	−0.515625	+	0.893089i
$33$	−16.5000	+	9.52628i	−0.500000	+	0.288675i
$34$			24.2487i			0.713197i
$35$		0			0
$36$	9.00000			0.250000
$37$	29.0000	+	50.2295i	0.783784	+	1.35755i	0.929723	+	0.368260i	$0.120046\pi$
$37$	29.0000	+	50.2295i	0.783784	+	1.35755i	−0.145939	+	0.989294i	$0.546620\pi$
$38$	−3.00000	−	1.73205i	−0.0789474	−	0.0455803i
$39$	6.00000	−	10.3923i	0.153846	−	0.266469i
$40$	−31.5000	+	18.1865i	−0.787500	+	0.454663i
$41$			3.46410i			0.0844903i	0.999107	+	0.0422451i	$0.0134510\pi$
$41$			3.46410i			0.0844903i	−0.999107	+	0.0422451i	$0.986549\pi$
$42$		0			0
$43$	26.0000			0.604651			0.302326	−	0.953205i	$-0.402237\pi$
$43$	26.0000			0.604651			0.302326	+	0.953205i	$0.402237\pi$
$44$	−16.5000	−	28.5788i	−0.375000	−	0.649519i
$45$	13.5000	+	7.79423i	0.300000	+	0.173205i
$46$	−14.0000	+	24.2487i	−0.304348	+	0.527146i
$47$	66.0000	−	38.1051i	1.40426	−	0.810747i	0.409429	−	0.912342i	$-0.365728\pi$
$47$	66.0000	−	38.1051i	1.40426	−	0.810747i	0.994826	+	0.101595i	$0.0323945\pi$
$48$			8.66025i			0.180422i
$49$		0			0
$50$	−2.00000			−0.0400000
$51$	21.0000	+	36.3731i	0.411765	+	0.713197i
$52$	18.0000	+	10.3923i	0.346154	+	0.199852i
$53$	−15.5000	+	26.8468i	−0.292453	+	0.506543i	−0.974389	−	0.224868i	$-0.927805\pi$
$53$	−15.5000	+	26.8468i	−0.292453	+	0.506543i	0.681936	+	0.731412i	$0.261138\pi$
$54$	−4.50000	+	2.59808i	−0.0833333	+	0.0481125i
$55$		−	57.1577i		−	1.03923i
$56$		0			0
$57$	−6.00000			−0.105263
$58$	−12.5000	−	21.6506i	−0.215517	−	0.373287i
$59$	7.50000	+	4.33013i	0.127119	+	0.0733920i	0.562211	−	0.826994i	$-0.309951\pi$
$59$	7.50000	+	4.33013i	0.127119	+	0.0733920i	−0.435092	+	0.900386i	$0.643284\pi$
$60$	−13.5000	+	23.3827i	−0.225000	+	0.389711i
$61$	−12.0000	+	6.92820i	−0.196721	+	0.113577i	−0.595125	−	0.803633i	$-0.702898\pi$
$61$	−12.0000	+	6.92820i	−0.196721	+	0.113577i	0.398404	+	0.917210i	$0.369564\pi$
$62$		−	32.9090i		−	0.530790i
$63$		0			0
$64$	13.0000			0.203125
$65$	18.0000	+	31.1769i	0.276923	+	0.479645i
$66$	16.5000	+	9.52628i	0.250000	+	0.144338i
$67$	26.0000	−	45.0333i	0.388060	−	0.672139i	−0.604129	−	0.796887i	$-0.706479\pi$
$67$	26.0000	−	45.0333i	0.388060	−	0.672139i	0.992189	+	0.124748i	$0.0398121\pi$
$68$	−63.0000	+	36.3731i	−0.926471	+	0.534898i
$69$			48.4974i			0.702861i
$70$		0			0
$71$	64.0000			0.901408			0.450704	−	0.892673i	$-0.351173\pi$
$71$	64.0000			0.901408			0.450704	+	0.892673i	$0.351173\pi$
$72$	−10.5000	−	18.1865i	−0.145833	−	0.252591i
$73$	−6.00000	−	3.46410i	−0.0821918	−	0.0474534i	0.458341	−	0.888777i	$-0.348444\pi$
$73$	−6.00000	−	3.46410i	−0.0821918	−	0.0474534i	−0.540533	+	0.841323i	$0.681777\pi$
$74$	29.0000	−	50.2295i	0.391892	−	0.678777i
$75$	−3.00000	+	1.73205i	−0.0400000	+	0.0230940i
$76$		−	10.3923i		−	0.136741i
$77$		0			0
$78$	−12.0000			−0.153846
$79$	−8.50000	−	14.7224i	−0.107595	−	0.186360i	0.807200	−	0.590277i	$-0.200982\pi$
$79$	−8.50000	−	14.7224i	−0.107595	−	0.186360i	−0.914795	+	0.403917i	$0.867648\pi$
$80$	−22.5000	−	12.9904i	−0.281250	−	0.162380i
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$	3.00000	−	1.73205i	0.0365854	−	0.0211226i
$83$			53.6936i			0.646911i	0.946243	+	0.323455i	$0.104845\pi$
$83$			53.6936i			0.646911i	−0.946243	+	0.323455i	$0.895155\pi$
$84$		0			0
$85$	−126.000			−1.48235
$86$	−13.0000	−	22.5167i	−0.151163	−	0.261822i
$87$	−37.5000	−	21.6506i	−0.431034	−	0.248858i
$88$	−38.5000	+	66.6840i	−0.437500	+	0.757772i
$89$	69.0000	−	39.8372i	0.775281	−	0.447609i	−0.0594743	−	0.998230i	$-0.518942\pi$
$89$	69.0000	−	39.8372i	0.775281	−	0.447609i	0.834755	+	0.550621i	$0.185609\pi$
$90$		−	15.5885i		−	0.173205i
$91$		0			0
$92$	−84.0000			−0.913043
$93$	−28.5000	−	49.3634i	−0.306452	−	0.530790i
$94$	−66.0000	−	38.1051i	−0.702128	−	0.405374i
$95$	9.00000	−	15.5885i	0.0947368	−	0.164089i
$96$	49.5000	−	28.5788i	0.515625	−	0.297696i
$97$			91.7987i			0.946378i	0.880961	+	0.473189i	$0.156897\pi$
$97$			91.7987i			0.946378i	−0.880961	+	0.473189i	$0.843103\pi$
$98$		0			0
$99$	33.0000			0.333333
$100$	−3.00000	−	5.19615i	−0.0300000	−	0.0519615i
$101$	18.0000	+	10.3923i	0.178218	+	0.102894i	0.586455	−	0.809982i	$-0.300523\pi$
$101$	18.0000	+	10.3923i	0.178218	+	0.102894i	−0.408237	+	0.912876i	$0.633856\pi$
$102$	21.0000	−	36.3731i	0.205882	−	0.356599i
$103$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$103$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$104$		−	48.4974i		−	0.466321i
$105$		0			0
$106$	31.0000			0.292453
$107$	−15.5000	−	26.8468i	−0.144860	−	0.250905i	0.784461	−	0.620178i	$-0.212940\pi$
$107$	−15.5000	−	26.8468i	−0.144860	−	0.250905i	−0.929321	+	0.369274i	$0.879606\pi$
$108$	−13.5000	−	7.79423i	−0.125000	−	0.0721688i
$109$	68.0000	−	117.779i	0.623853	−	1.08055i	−0.364908	−	0.931043i	$-0.618900\pi$
$109$	68.0000	−	117.779i	0.623853	−	1.08055i	0.988761	−	0.149502i	$-0.0477670\pi$
$110$	−49.5000	+	28.5788i	−0.450000	+	0.259808i
$111$		−	100.459i		−	0.905036i
$112$		0			0
$113$	−74.0000			−0.654867			−0.327434	−	0.944874i	$-0.606184\pi$
$113$	−74.0000			−0.654867			−0.327434	+	0.944874i	$0.606184\pi$
$114$	3.00000	+	5.19615i	0.0263158	+	0.0455803i
$115$	−126.000	−	72.7461i	−1.09565	−	0.632575i
$116$	37.5000	−	64.9519i	0.323276	−	0.559930i
$117$	−18.0000	+	10.3923i	−0.153846	+	0.0888231i
$118$		−	8.66025i		−	0.0733920i
$119$		0			0
$120$	63.0000			0.525000
$121$		0			0
$122$	12.0000	+	6.92820i	0.0983607	+	0.0567886i
$123$	3.00000	−	5.19615i	0.0243902	−	0.0422451i
$124$	85.5000	−	49.3634i	0.689516	−	0.398092i
$125$			119.512i			0.956092i
$126$		0			0
$127$	−1.00000			−0.00787402			−0.00393701	−	0.999992i	$-0.501253\pi$
$127$	−1.00000			−0.00787402			−0.00393701	+	0.999992i	$0.501253\pi$
$128$	59.5000	+	103.057i	0.464844	+	0.805133i
$129$	−39.0000	−	22.5167i	−0.302326	−	0.174548i
$130$	18.0000	−	31.1769i	0.138462	−	0.239822i
$131$	−157.500	+	90.9327i	−1.20229	+	0.694142i	−0.961064	−	0.276326i	$-0.910883\pi$
$131$	−157.500	+	90.9327i	−1.20229	+	0.694142i	−0.241226	+	0.970469i	$0.577550\pi$
$132$			57.1577i			0.433013i
$133$		0			0
$134$	−52.0000			−0.388060
$135$	−13.5000	−	23.3827i	−0.100000	−	0.173205i
$136$	147.000	+	84.8705i	1.08088	+	0.624048i
$137$	−44.0000	+	76.2102i	−0.321168	+	0.556279i	−0.980729	−	0.195372i	$-0.937409\pi$
$137$	−44.0000	+	76.2102i	−0.321168	+	0.556279i	0.659561	+	0.751651i	$0.270742\pi$
$138$	42.0000	−	24.2487i	0.304348	−	0.175715i
$139$		−	190.526i		−	1.37069i	−0.728220	−	0.685344i	$-0.759652\pi$
$139$		−	190.526i		−	1.37069i	0.728220	−	0.685344i	$-0.240348\pi$
$140$		0			0
$141$	−132.000			−0.936170
$142$	−32.0000	−	55.4256i	−0.225352	−	0.390321i
$143$	66.0000	+	38.1051i	0.461538	+	0.266469i
$144$	7.50000	−	12.9904i	0.0520833	−	0.0902110i
$145$	112.500	−	64.9519i	0.775862	−	0.447944i
$146$			6.92820i			0.0474534i
$147$		0			0
$148$	174.000			1.17568
$149$	115.000	+	199.186i	0.771812	+	1.33682i	0.936569	+	0.350484i	$0.113983\pi$
$149$	115.000	+	199.186i	0.771812	+	1.33682i	−0.164757	+	0.986334i	$0.552684\pi$
$150$	3.00000	+	1.73205i	0.0200000	+	0.0115470i
$151$	−113.500	+	196.588i	−0.751656	+	1.30191i	0.195364	+	0.980731i	$0.437411\pi$
$151$	−113.500	+	196.588i	−0.751656	+	1.30191i	−0.947020	+	0.321175i	$0.895922\pi$
$152$	−21.0000	+	12.1244i	−0.138158	+	0.0797655i
$153$		−	72.7461i		−	0.475465i
$154$		0			0
$155$	171.000			1.10323
$156$	−18.0000	−	31.1769i	−0.115385	−	0.199852i
$157$	42.0000	+	24.2487i	0.267516	+	0.154450i	0.627758	−	0.778408i	$-0.283973\pi$
$157$	42.0000	+	24.2487i	0.267516	+	0.154450i	−0.360242	+	0.932859i	$0.617306\pi$
$158$	−8.50000	+	14.7224i	−0.0537975	+	0.0931799i
$159$	46.5000	−	26.8468i	0.292453	−	0.168848i
$160$			171.473i			1.07171i
$161$		0			0
$162$	9.00000			0.0555556
$163$	−106.000	−	183.597i	−0.650307	−	1.12636i	−0.983048	−	0.183346i	$-0.941307\pi$
$163$	−106.000	−	183.597i	−0.650307	−	1.12636i	0.332742	−	0.943018i	$-0.392026\pi$
$164$	9.00000	+	5.19615i	0.0548780	+	0.0316839i
$165$	−49.5000	+	85.7365i	−0.300000	+	0.519615i
$166$	46.5000	−	26.8468i	0.280120	−	0.161728i
$167$			96.9948i			0.580807i	0.956904	+	0.290404i	$0.0937896\pi$
$167$			96.9948i			0.580807i	−0.956904	+	0.290404i	$0.906210\pi$
$168$		0			0
$169$	121.000			0.715976
$170$	63.0000	+	109.119i	0.370588	+	0.641878i
$171$	9.00000	+	5.19615i	0.0526316	+	0.0303869i
$172$	39.0000	−	67.5500i	0.226744	−	0.392732i
$173$	−186.000	+	107.387i	−1.07514	+	0.620735i	−0.929582	−	0.368614i	$-0.879832\pi$
$173$	−186.000	+	107.387i	−1.07514	+	0.620735i	−0.145562	+	0.989349i	$0.546499\pi$
$174$			43.3013i			0.248858i
$175$		0			0
$176$	−55.0000			−0.312500
$177$	−7.50000	−	12.9904i	−0.0423729	−	0.0733920i
$178$	−69.0000	−	39.8372i	−0.387640	−	0.223804i
$179$	−23.0000	+	39.8372i	−0.128492	+	0.222554i	−0.923092	−	0.384578i	$-0.874347\pi$
$179$	−23.0000	+	39.8372i	−0.128492	+	0.222554i	0.794601	+	0.607132i	$0.207680\pi$
$180$	40.5000	−	23.3827i	0.225000	−	0.129904i
$181$		−	31.1769i		−	0.172248i	−0.996284	−	0.0861241i	$-0.972552\pi$
$181$		−	31.1769i		−	0.172248i	0.996284	−	0.0861241i	$-0.0274481\pi$
$182$		0			0
$183$	24.0000			0.131148
$184$	98.0000	+	169.741i	0.532609	+	0.922505i
$185$	261.000	+	150.688i	1.41081	+	0.814532i
$186$	−28.5000	+	49.3634i	−0.153226	+	0.265395i
$187$	−231.000	+	133.368i	−1.23529	+	0.713197i
$188$		−	228.631i		−	1.21612i
$189$		0			0
$190$	−18.0000			−0.0947368
$191$	−104.000	−	180.133i	−0.544503	−	0.943106i	−0.998638	−	0.0521735i	$-0.983385\pi$
$191$	−104.000	−	180.133i	−0.544503	−	0.943106i	0.454135	−	0.890933i	$-0.349948\pi$
$192$	−19.5000	−	11.2583i	−0.101562	−	0.0586371i
$193$	−119.500	+	206.980i	−0.619171	+	1.07244i	0.370466	+	0.928846i	$0.379198\pi$
$193$	−119.500	+	206.980i	−0.619171	+	1.07244i	−0.989637	+	0.143590i	$0.954135\pi$
$194$	79.5000	−	45.8993i	0.409794	−	0.236595i
$195$		−	62.3538i		−	0.319763i
$196$		0			0
$197$	−26.0000			−0.131980			−0.0659898	−	0.997820i	$-0.521020\pi$
$197$	−26.0000			−0.131980			−0.0659898	+	0.997820i	$0.521020\pi$
$198$	−16.5000	−	28.5788i	−0.0833333	−	0.144338i
$199$	210.000	+	121.244i	1.05528	+	0.609264i	0.924122	−	0.382098i	$-0.124798\pi$
$199$	210.000	+	121.244i	1.05528	+	0.609264i	0.131155	+	0.991362i	$0.458132\pi$
$200$	−7.00000	+	12.1244i	−0.0350000	+	0.0606218i
$201$	−78.0000	+	45.0333i	−0.388060	+	0.224046i
$202$		−	20.7846i		−	0.102894i
$203$		0			0
$204$	126.000			0.617647
$205$	9.00000	+	15.5885i	0.0439024	+	0.0760413i
$206$		0			0
$207$	42.0000	−	72.7461i	0.202899	−	0.351431i
$208$	30.0000	−	17.3205i	0.144231	−	0.0832717i
$209$		−	38.1051i		−	0.182321i
$210$		0			0
$211$	−52.0000			−0.246445			−0.123223	−	0.992379i	$-0.539323\pi$
$211$	−52.0000			−0.246445			−0.123223	+	0.992379i	$0.539323\pi$
$212$	46.5000	+	80.5404i	0.219340	+	0.379907i
$213$	−96.0000	−	55.4256i	−0.450704	−	0.260214i
$214$	−15.5000	+	26.8468i	−0.0724299	+	0.125452i
$215$	117.000	−	67.5500i	0.544186	−	0.314186i
$216$			36.3731i			0.168394i
$217$		0			0
$218$	−136.000			−0.623853
$219$	6.00000	+	10.3923i	0.0273973	+	0.0474534i
$220$	−148.500	−	85.7365i	−0.675000	−	0.389711i
$221$	84.0000	−	145.492i	0.380090	−	0.658336i
$222$	−87.0000	+	50.2295i	−0.391892	+	0.226259i
$223$		−	22.5167i		−	0.100972i	−0.998725	−	0.0504858i	$-0.983923\pi$
$223$		−	22.5167i		−	0.100972i	0.998725	−	0.0504858i	$-0.0160770\pi$
$224$		0			0
$225$	6.00000			0.0266667
$226$	37.0000	+	64.0859i	0.163717	+	0.283566i
$227$	−58.5000	−	33.7750i	−0.257709	−	0.148789i	0.365580	−	0.930780i	$-0.380871\pi$
$227$	−58.5000	−	33.7750i	−0.257709	−	0.148789i	−0.623289	+	0.781991i	$0.714204\pi$
$228$	−9.00000	+	15.5885i	−0.0394737	+	0.0683704i
$229$	27.0000	−	15.5885i	0.117904	−	0.0680719i	−0.439888	−	0.898053i	$-0.644982\pi$
$229$	27.0000	−	15.5885i	0.117904	−	0.0680719i	0.557792	+	0.829981i	$0.311649\pi$
$230$			145.492i			0.632575i
$231$		0			0
$232$	−175.000			−0.754310
$233$	−131.000	−	226.899i	−0.562232	−	0.973814i	−0.997301	−	0.0734171i	$-0.976610\pi$
$233$	−131.000	−	226.899i	−0.562232	−	0.973814i	0.435070	−	0.900397i	$-0.356724\pi$
$234$	18.0000	+	10.3923i	0.0769231	+	0.0444116i
$235$	198.000	−	342.946i	0.842553	−	1.45934i
$236$	22.5000	−	12.9904i	0.0953390	−	0.0550440i
$237$			29.4449i			0.124240i
$238$		0			0
$239$	160.000			0.669456			0.334728	−	0.942315i	$-0.391356\pi$
$239$	160.000			0.669456			0.334728	+	0.942315i	$0.391356\pi$
$240$	22.5000	+	38.9711i	0.0937500	+	0.162380i
$241$	−409.500	−	236.425i	−1.69917	−	0.981016i	−0.946548	−	0.322564i	$-0.895455\pi$
$241$	−409.500	−	236.425i	−1.69917	−	0.981016i	−0.752622	−	0.658452i	$-0.771211\pi$
$242$		0			0
$243$	13.5000	−	7.79423i	0.0555556	−	0.0320750i
$244$			41.5692i			0.170366i
$245$		0			0
$246$	−6.00000			−0.0243902
$247$	12.0000	+	20.7846i	0.0485830	+	0.0841482i
$248$	−199.500	−	115.181i	−0.804435	−	0.464441i
$249$	46.5000	−	80.5404i	0.186747	−	0.323455i
$250$	103.500	−	59.7558i	0.414000	−	0.239023i
$251$		−	67.5500i		−	0.269123i	−0.990905	−	0.134562i	$-0.957037\pi$
$251$		−	67.5500i		−	0.269123i	0.990905	−	0.134562i	$-0.0429626\pi$
$252$		0			0
$253$	−308.000			−1.21739
$254$	0.500000	+	0.866025i	0.00196850	+	0.00340955i
$255$	189.000	+	109.119i	0.741176	+	0.427918i
$256$	85.5000	−	148.090i	0.333984	−	0.578478i
$257$	351.000	−	202.650i	1.36576	−	0.788521i	0.375376	−	0.926873i	$-0.377514\pi$
$257$	351.000	−	202.650i	1.36576	−	0.788521i	0.990383	+	0.138352i	$0.0441804\pi$
$258$			45.0333i			0.174548i
$259$		0			0
$260$	108.000			0.415385
$261$	37.5000	+	64.9519i	0.143678	+	0.248858i
$262$	157.500	+	90.9327i	0.601145	+	0.347071i
$263$	−53.0000	+	91.7987i	−0.201521	+	0.349044i	−0.949019	−	0.315220i	$-0.897922\pi$
$263$	−53.0000	+	91.7987i	−0.201521	+	0.349044i	0.747498	+	0.664264i	$0.231255\pi$
$264$	115.500	−	66.6840i	0.437500	−	0.252591i
$265$			161.081i			0.607852i
$266$		0			0
$267$	−138.000			−0.516854
$268$	−78.0000	−	135.100i	−0.291045	−	0.504104i
$269$	−376.500	−	217.372i	−1.39963	−	0.808076i	−0.405275	−	0.914195i	$-0.632824\pi$
$269$	−376.500	−	217.372i	−1.39963	−	0.808076i	−0.994353	+	0.106119i	$0.966158\pi$
$270$	−13.5000	+	23.3827i	−0.0500000	+	0.0866025i
$271$	−109.500	+	63.2199i	−0.404059	+	0.233284i	−0.688234	−	0.725489i	$-0.741614\pi$
$271$	−109.500	+	63.2199i	−0.404059	+	0.233284i	0.284175	+	0.958772i	$0.408280\pi$
$272$			121.244i			0.445748i
$273$		0			0
$274$	88.0000			0.321168
$275$	−11.0000	−	19.0526i	−0.0400000	−	0.0692820i
$276$	126.000	+	72.7461i	0.456522	+	0.263573i
$277$	−118.000	+	204.382i	−0.425993	+	0.737841i	−0.996513	−	0.0834427i	$-0.973408\pi$
$277$	−118.000	+	204.382i	−0.425993	+	0.737841i	0.570520	+	0.821284i	$0.306742\pi$
$278$	−165.000	+	95.2628i	−0.593525	+	0.342672i
$279$			98.7269i			0.353860i
$280$		0			0
$281$	−116.000			−0.412811			−0.206406	−	0.978466i	$-0.566177\pi$
$281$	−116.000			−0.412811			−0.206406	+	0.978466i	$0.566177\pi$
$282$	66.0000	+	114.315i	0.234043	+	0.405374i
$283$	321.000	+	185.329i	1.13428	+	0.654874i	0.945007	−	0.327051i	$-0.106055\pi$
$283$	321.000	+	185.329i	1.13428	+	0.654874i	0.189269	+	0.981925i	$0.439388\pi$
$284$	96.0000	−	166.277i	0.338028	−	0.585482i
$285$	−27.0000	+	15.5885i	−0.0947368	+	0.0546963i
$286$		−	76.2102i		−	0.266469i
$287$		0			0
$288$	−99.0000			−0.343750
$289$	149.500	+	258.942i	0.517301	+	0.895992i
$290$	−112.500	−	64.9519i	−0.387931	−	0.223972i
$291$	79.5000	−	137.698i	0.273196	−	0.473189i
$292$	−18.0000	+	10.3923i	−0.0616438	+	0.0355901i
$293$			19.0526i			0.0650258i	0.999471	+	0.0325129i	$0.0103510\pi$
$293$			19.0526i			0.0650258i	−0.999471	+	0.0325129i	$0.989649\pi$
$294$		0			0
$295$	45.0000			0.152542
$296$	−203.000	−	351.606i	−0.685811	−	1.18786i
$297$	−49.5000	−	28.5788i	−0.166667	−	0.0962250i
$298$	115.000	−	199.186i	0.385906	−	0.668409i
$299$	168.000	−	96.9948i	0.561873	−	0.324397i
$300$			10.3923i			0.0346410i
$301$		0			0
$302$	227.000			0.751656
$303$	−18.0000	−	31.1769i	−0.0594059	−	0.102894i
$304$	−15.0000	−	8.66025i	−0.0493421	−	0.0284877i
$305$	−36.0000	+	62.3538i	−0.118033	+	0.204439i
$306$	−63.0000	+	36.3731i	−0.205882	+	0.118866i
$307$		−	457.261i		−	1.48945i	−0.667371	−	0.744725i	$-0.732580\pi$
$307$		−	457.261i		−	1.48945i	0.667371	−	0.744725i	$-0.267420\pi$
$308$		0			0
$309$		0			0
$310$	−85.5000	−	148.090i	−0.275806	−	0.477711i
$311$	−285.000	−	164.545i	−0.916399	−	0.529083i	−0.0339143	−	0.999425i	$-0.510797\pi$
$311$	−285.000	−	164.545i	−0.916399	−	0.529083i	−0.882484	+	0.470342i	$0.844131\pi$
$312$	−42.0000	+	72.7461i	−0.134615	+	0.233161i
$313$	−475.500	+	274.530i	−1.51917	+	0.877093i	−0.519424	+	0.854517i	$0.673854\pi$
$313$	−475.500	+	274.530i	−1.51917	+	0.877093i	−0.999745	+	0.0225763i	$0.992813\pi$
$314$		−	48.4974i		−	0.154450i
$315$		0			0
$316$	−51.0000			−0.161392
$317$	−93.5000	−	161.947i	−0.294953	−	0.510873i	0.680021	−	0.733192i	$-0.261971\pi$
$317$	−93.5000	−	161.947i	−0.294953	−	0.510873i	−0.974974	+	0.222319i	$0.928637\pi$
$318$	−46.5000	−	26.8468i	−0.146226	−	0.0844239i
$319$	137.500	−	238.157i	0.431034	−	0.746574i
$320$	58.5000	−	33.7750i	0.182812	−	0.105547i
$321$			53.6936i			0.167270i
$322$		0			0
$323$	−84.0000			−0.260062
$324$	13.5000	+	23.3827i	0.0416667	+	0.0721688i
$325$	12.0000	+	6.92820i	0.0369231	+	0.0213175i
$326$	−106.000	+	183.597i	−0.325153	+	0.563182i
$327$	−204.000	+	117.779i	−0.623853	+	0.360182i
$328$		−	24.2487i		−	0.0739290i
$329$		0			0
$330$	99.0000			0.300000
$331$	8.00000	+	13.8564i	0.0241692	+	0.0418623i	0.877857	−	0.478923i	$-0.158973\pi$
$331$	8.00000	+	13.8564i	0.0241692	+	0.0418623i	−0.853688	+	0.520785i	$0.825639\pi$
$332$	139.500	+	80.5404i	0.420181	+	0.242591i
$333$	−87.0000	+	150.688i	−0.261261	+	0.452518i
$334$	84.0000	−	48.4974i	0.251497	−	0.145202i
$335$		−	270.200i		−	0.806567i
$336$		0			0
$337$	83.0000			0.246291			0.123145	−	0.992389i	$-0.460702\pi$
$337$	83.0000			0.246291			0.123145	+	0.992389i	$0.460702\pi$
$338$	−60.5000	−	104.789i	−0.178994	−	0.310027i
$339$	111.000	+	64.0859i	0.327434	+	0.189044i
$340$	−189.000	+	327.358i	−0.555882	+	0.962816i
$341$	313.500	−	180.999i	0.919355	−	0.530790i
$342$		−	10.3923i		−	0.0303869i
$343$		0			0
$344$	−182.000			−0.529070
$345$	126.000	+	218.238i	0.365217	+	0.632575i
$346$	186.000	+	107.387i	0.537572	+	0.310367i
$347$	−179.000	+	310.037i	−0.515850	+	0.893479i	0.483981	+	0.875079i	$0.339191\pi$
$347$	−179.000	+	310.037i	−0.515850	+	0.893479i	−0.999831	+	0.0183999i	$0.994143\pi$
$348$	−112.500	+	64.9519i	−0.323276	+	0.186643i
$349$			678.964i			1.94546i	0.231950	+	0.972728i	$0.425489\pi$
$349$			678.964i			1.94546i	−0.231950	+	0.972728i	$0.574511\pi$
$350$		0			0
$351$	36.0000			0.102564
$352$	181.500	+	314.367i	0.515625	+	0.893089i
$353$	558.000	+	322.161i	1.58074	+	0.912639i	0.994752	+	0.102317i	$0.0326255\pi$
$353$	558.000	+	322.161i	1.58074	+	0.912639i	0.585985	+	0.810322i	$0.300708\pi$
$354$	−7.50000	+	12.9904i	−0.0211864	+	0.0366960i
$355$	288.000	−	166.277i	0.811268	−	0.468386i
$356$		−	239.023i		−	0.671413i
$357$		0			0
$358$	46.0000			0.128492
$359$	142.000	+	245.951i	0.395543	+	0.685101i	0.993170	−	0.116673i	$-0.0372230\pi$
$359$	142.000	+	245.951i	0.395543	+	0.685101i	−0.597627	+	0.801774i	$0.703890\pi$
$360$	−94.5000	−	54.5596i	−0.262500	−	0.151554i
$361$	−174.500	+	302.243i	−0.483380	+	0.837238i
$362$	−27.0000	+	15.5885i	−0.0745856	+	0.0430620i
$363$		0			0
$364$		0			0
$365$	−36.0000			−0.0986301
$366$	−12.0000	−	20.7846i	−0.0327869	−	0.0567886i
$367$	−238.500	−	137.698i	−0.649864	−	0.375199i	0.138540	−	0.990357i	$-0.455759\pi$
$367$	−238.500	−	137.698i	−0.649864	−	0.375199i	−0.788404	+	0.615158i	$0.789092\pi$
$368$	−70.0000	+	121.244i	−0.190217	+	0.329466i
$369$	−9.00000	+	5.19615i	−0.0243902	+	0.0140817i
$370$		−	301.377i		−	0.814532i
$371$		0			0
$372$	−171.000			−0.459677
$373$	−25.0000	−	43.3013i	−0.0670241	−	0.116089i	0.830566	−	0.556920i	$-0.188017\pi$
$373$	−25.0000	−	43.3013i	−0.0670241	−	0.116089i	−0.897590	+	0.440831i	$0.854684\pi$
$374$	231.000	+	133.368i	0.617647	+	0.356599i
$375$	103.500	−	179.267i	0.276000	−	0.478046i
$376$	−462.000	+	266.736i	−1.22872	+	0.709404i
$377$			173.205i			0.459430i
$378$		0			0
$379$	458.000			1.20844			0.604222	−	0.796816i	$-0.293484\pi$
$379$	458.000			1.20844			0.604222	+	0.796816i	$0.293484\pi$
$380$	−27.0000	−	46.7654i	−0.0710526	−	0.123067i
$381$	1.50000	+	0.866025i	0.00393701	+	0.00227303i
$382$	−104.000	+	180.133i	−0.272251	+	0.471553i
$383$	−351.000	+	202.650i	−0.916449	+	0.529112i	−0.882501	−	0.470311i	$-0.844142\pi$
$383$	−351.000	+	202.650i	−0.916449	+	0.529112i	−0.0339486	+	0.999424i	$0.510808\pi$
$384$		−	206.114i		−	0.536755i
$385$		0			0
$386$	239.000			0.619171
$387$	39.0000	+	67.5500i	0.100775	+	0.174548i
$388$	238.500	+	137.698i	0.614691	+	0.354892i
$389$	349.000	−	604.486i	0.897172	−	1.55395i	0.0660793	−	0.997814i	$-0.478951\pi$
$389$	349.000	−	604.486i	0.897172	−	1.55395i	0.831093	−	0.556134i	$-0.187716\pi$
$390$	−54.0000	+	31.1769i	−0.138462	+	0.0799408i
$391$			678.964i			1.73648i
$392$		0			0
$393$	315.000			0.801527
$394$	13.0000	+	22.5167i	0.0329949	+	0.0571489i
$395$	−76.5000	−	44.1673i	−0.193671	−	0.111816i
$396$	49.5000	−	85.7365i	0.125000	−	0.216506i
$397$	498.000	−	287.520i	1.25441	−	0.724233i	0.282426	−	0.959289i	$-0.408861\pi$
$397$	498.000	−	287.520i	1.25441	−	0.724233i	0.971982	+	0.235056i	$0.0755274\pi$
$398$		−	242.487i		−	0.609264i
$399$		0			0
$400$	−10.0000			−0.0250000
$401$	142.000	+	245.951i	0.354115	+	0.613345i	0.986966	−	0.160929i	$-0.0514489\pi$
$401$	142.000	+	245.951i	0.354115	+	0.613345i	−0.632851	+	0.774273i	$0.718116\pi$
$402$	78.0000	+	45.0333i	0.194030	+	0.112023i
$403$	−114.000	+	197.454i	−0.282878	+	0.489960i
$404$	54.0000	−	31.1769i	0.133663	−	0.0771706i
$405$			46.7654i			0.115470i
$406$		0			0
$407$	638.000			1.56757
$408$	−147.000	−	254.611i	−0.360294	−	0.624048i
$409$	181.500	+	104.789i	0.443765	+	0.256208i	0.705193	−	0.709015i	$-0.250860\pi$
$409$	181.500	+	104.789i	0.443765	+	0.256208i	−0.261428	+	0.965223i	$0.584193\pi$
$410$	9.00000	−	15.5885i	0.0219512	−	0.0380206i
$411$	132.000	−	76.2102i	0.321168	−	0.185426i
$412$		0			0
$413$		0			0
$414$	−84.0000			−0.202899
$415$	139.500	+	241.621i	0.336145	+	0.582219i
$416$	−198.000	−	114.315i	−0.475962	−	0.274797i
$417$	−165.000	+	285.788i	−0.395683	+	0.685344i
$418$	−33.0000	+	19.0526i	−0.0789474	+	0.0455803i
$419$		−	131.636i		−	0.314167i	−0.987585	−	0.157083i	$-0.949791\pi$
$419$		−	131.636i		−	0.314167i	0.987585	−	0.157083i	$-0.0502091\pi$
$420$		0			0
$421$	−28.0000			−0.0665083			−0.0332542	−	0.999447i	$-0.510587\pi$
$421$	−28.0000			−0.0665083			−0.0332542	+	0.999447i	$0.510587\pi$
$422$	26.0000	+	45.0333i	0.0616114	+	0.106714i
$423$	198.000	+	114.315i	0.468085	+	0.270249i
$424$	108.500	−	187.928i	0.255896	−	0.443225i
$425$	−42.0000	+	24.2487i	−0.0988235	+	0.0570558i
$426$			110.851i			0.260214i
$427$		0			0
$428$	−93.0000			−0.217290
$429$	−66.0000	−	114.315i	−0.153846	−	0.266469i
$430$	−117.000	−	67.5500i	−0.272093	−	0.157093i
$431$	−59.0000	+	102.191i	−0.136891	+	0.237102i	−0.926318	−	0.376742i	$-0.877044\pi$
$431$	−59.0000	+	102.191i	−0.136891	+	0.237102i	0.789427	+	0.613844i	$0.210378\pi$
$432$	−22.5000	+	12.9904i	−0.0520833	+	0.0300703i
$433$		−	561.184i		−	1.29604i	−0.761624	−	0.648019i	$-0.775598\pi$
$433$		−	561.184i		−	1.29604i	0.761624	−	0.648019i	$-0.224402\pi$
$434$		0			0
$435$	−225.000			−0.517241
$436$	−204.000	−	353.338i	−0.467890	−	0.810409i
$437$	−84.0000	−	48.4974i	−0.192220	−	0.110978i
$438$	6.00000	−	10.3923i	0.0136986	−	0.0237267i
$439$	640.500	−	369.793i	1.45900	−	0.842353i	0.460036	−	0.887900i	$-0.347837\pi$
$439$	640.500	−	369.793i	1.45900	−	0.842353i	0.998962	+	0.0455478i	$0.0145033\pi$
$440$			400.104i			0.909327i
$441$		0			0
$442$	−168.000			−0.380090
$443$	77.5000	+	134.234i	0.174944	+	0.303011i	0.940142	−	0.340784i	$-0.110692\pi$
$443$	77.5000	+	134.234i	0.174944	+	0.303011i	−0.765198	+	0.643795i	$0.777359\pi$
$444$	−261.000	−	150.688i	−0.587838	−	0.339388i
$445$	207.000	−	358.535i	0.465169	−	0.805696i
$446$	−19.5000	+	11.2583i	−0.0437220	+	0.0252429i
$447$		−	398.372i		−	0.891212i
$448$		0			0
$449$	−368.000			−0.819599			−0.409800	−	0.912176i	$-0.634401\pi$
$449$	−368.000			−0.819599			−0.409800	+	0.912176i	$0.634401\pi$
$450$	−3.00000	−	5.19615i	−0.00666667	−	0.0115470i
$451$	33.0000	+	19.0526i	0.0731707	+	0.0422451i
$452$	−111.000	+	192.258i	−0.245575	+	0.425349i
$453$	340.500	−	196.588i	0.751656	−	0.433969i
$454$			67.5500i			0.148789i
$455$		0			0
$456$	42.0000			0.0921053
$457$	−170.500	−	295.315i	−0.373085	−	0.646203i	0.616953	−	0.787000i	$-0.288367\pi$
$457$	−170.500	−	295.315i	−0.373085	−	0.646203i	−0.990038	+	0.140797i	$0.955033\pi$
$458$	−27.0000	−	15.5885i	−0.0589520	−	0.0340359i
$459$	−63.0000	+	109.119i	−0.137255	+	0.237732i
$460$	−378.000	+	218.238i	−0.821739	+	0.474431i
$461$		−	55.4256i		−	0.120229i	−0.998191	−	0.0601146i	$-0.980853\pi$
$461$		−	55.4256i		−	0.120229i	0.998191	−	0.0601146i	$-0.0191466\pi$
$462$		0			0
$463$	−178.000			−0.384449			−0.192225	−	0.981351i	$-0.561570\pi$
$463$	−178.000			−0.384449			−0.192225	+	0.981351i	$0.561570\pi$
$464$	−62.5000	−	108.253i	−0.134698	−	0.233304i
$465$	−256.500	−	148.090i	−0.551613	−	0.318474i
$466$	−131.000	+	226.899i	−0.281116	+	0.486907i
$467$	−570.000	+	329.090i	−1.22056	+	0.704689i	−0.965037	−	0.262115i	$-0.915580\pi$
$467$	−570.000	+	329.090i	−1.22056	+	0.704689i	−0.255520	+	0.966804i	$0.582247\pi$
$468$			62.3538i			0.133235i
$469$		0			0
$470$	−396.000			−0.842553
$471$	−42.0000	−	72.7461i	−0.0891720	−	0.154450i
$472$	−52.5000	−	30.3109i	−0.111229	−	0.0642180i
$473$	143.000	−	247.683i	0.302326	−	0.523643i
$474$	25.5000	−	14.7224i	0.0537975	−	0.0310600i
$475$		−	6.92820i		−	0.0145857i
$476$		0			0
$477$	−93.0000			−0.194969
$478$	−80.0000	−	138.564i	−0.167364	−	0.289883i
$479$	−441.000	−	254.611i	−0.920668	−	0.531548i	−0.0368199	−	0.999322i	$-0.511723\pi$
$479$	−441.000	−	254.611i	−0.920668	−	0.531548i	−0.883848	+	0.467774i	$0.845056\pi$
$480$	148.500	−	257.210i	0.309375	−	0.535853i
$481$	−348.000	+	200.918i	−0.723493	+	0.417709i
$482$			472.850i			0.981016i
$483$		0			0
$484$		0			0
$485$	238.500	+	413.094i	0.491753	+	0.851740i
$486$	−13.5000	−	7.79423i	−0.0277778	−	0.0160375i
$487$	420.500	−	728.327i	0.863450	−	1.49554i	−0.00512864	−	0.999987i	$-0.501633\pi$
$487$	420.500	−	728.327i	0.863450	−	1.49554i	0.868578	−	0.495552i	$-0.165034\pi$
$488$	84.0000	−	48.4974i	0.172131	−	0.0993800i
$489$			367.195i			0.750910i
$490$		0			0
$491$	−959.000			−1.95316			−0.976578	−	0.215162i	$-0.930972\pi$
$491$	−959.000			−1.95316			−0.976578	+	0.215162i	$0.930972\pi$
$492$	−9.00000	−	15.5885i	−0.0182927	−	0.0316839i
$493$	−525.000	−	303.109i	−1.06491	−	0.614825i
$494$	12.0000	−	20.7846i	0.0242915	−	0.0420741i
$495$	148.500	−	85.7365i	0.300000	−	0.173205i
$496$		−	164.545i		−	0.331744i
$497$		0			0
$498$	−93.0000			−0.186747
$499$	59.0000	+	102.191i	0.118236	+	0.204792i	0.919069	−	0.394097i	$-0.128943\pi$
$499$	59.0000	+	102.191i	0.118236	+	0.204792i	−0.800832	+	0.598889i	$0.795609\pi$
$500$	310.500	+	179.267i	0.621000	+	0.358535i
$501$	84.0000	−	145.492i	0.167665	−	0.290404i
$502$	−58.5000	+	33.7750i	−0.116534	+	0.0672809i
$503$			363.731i			0.723123i	0.932348	+	0.361561i	$0.117756\pi$
$503$			363.731i			0.723123i	−0.932348	+	0.361561i	$0.882244\pi$
$504$		0			0
$505$	108.000			0.213861
$506$	154.000	+	266.736i	0.304348	+	0.527146i
$507$	−181.500	−	104.789i	−0.357988	−	0.206685i
$508$	−1.50000	+	2.59808i	−0.00295276	+	0.00511432i
$509$	−382.500	+	220.836i	−0.751473	+	0.433863i	−0.826226	−	0.563339i	$-0.809517\pi$
$509$	−382.500	+	220.836i	−0.751473	+	0.433863i	0.0747526	+	0.997202i	$0.476183\pi$
$510$		−	218.238i		−	0.427918i
$511$		0			0
$512$	305.000			0.595703
$513$	−9.00000	−	15.5885i	−0.0175439	−	0.0303869i
$514$	−351.000	−	202.650i	−0.682879	−	0.394261i
$515$		0			0
$516$	−117.000	+	67.5500i	−0.226744	+	0.130911i
$517$		−	838.313i		−	1.62149i
$518$		0			0
$519$	372.000			0.716763
$520$	−126.000	−	218.238i	−0.242308	−	0.419689i
$521$	843.000	+	486.706i	1.61804	+	0.934177i	0.987426	+	0.158082i	$0.0505311\pi$
$521$	843.000	+	486.706i	1.61804	+	0.934177i	0.630616	+	0.776095i	$0.282802\pi$
$522$	37.5000	−	64.9519i	0.0718391	−	0.124429i
$523$	408.000	−	235.559i	0.780115	−	0.450399i	−0.0563562	−	0.998411i	$-0.517948\pi$
$523$	408.000	−	235.559i	0.780115	−	0.450399i	0.836471	+	0.548011i	$0.184615\pi$
$524$			545.596i			1.04121i
$525$		0			0
$526$	106.000			0.201521
$527$	−399.000	−	691.088i	−0.757116	−	1.31136i
$528$	82.5000	+	47.6314i	0.156250	+	0.0902110i
$529$	−127.500	+	220.836i	−0.241021	+	0.417460i
$530$	139.500	−	80.5404i	0.263208	−	0.151963i
$531$			25.9808i			0.0489280i
$532$		0			0
$533$	−24.0000			−0.0450281
$534$	69.0000	+	119.512i	0.129213	+	0.223804i
$535$	−139.500	−	80.5404i	−0.260748	−	0.150543i
$536$	−182.000	+	315.233i	−0.339552	+	0.588122i
$537$	69.0000	−	39.8372i	0.128492	−	0.0741847i
$538$			434.745i			0.808076i
$539$		0			0
$540$	−81.0000			−0.150000
$541$	−403.000	−	698.016i	−0.744917	−	1.29023i	−0.950234	−	0.311538i	$-0.899156\pi$
$541$	−403.000	−	698.016i	−0.744917	−	1.29023i	0.205317	−	0.978696i	$-0.434178\pi$
$542$	109.500	+	63.2199i	0.202030	+	0.116642i
$543$	−27.0000	+	46.7654i	−0.0497238	+	0.0861241i
$544$	693.000	−	400.104i	1.27390	−	0.735485i
$545$		−	706.677i		−	1.29665i
$546$		0			0
$547$	−154.000			−0.281536			−0.140768	−	0.990043i	$-0.544957\pi$
$547$	−154.000			−0.281536			−0.140768	+	0.990043i	$0.544957\pi$
$548$	132.000	+	228.631i	0.240876	+	0.417209i
$549$	−36.0000	−	20.7846i	−0.0655738	−	0.0378590i
$550$	−11.0000	+	19.0526i	−0.0200000	+	0.0346410i
$551$	75.0000	−	43.3013i	0.136116	−	0.0785867i
$552$		−	339.482i		−	0.615004i
$553$		0			0
$554$	236.000			0.425993
$555$	−261.000	−	452.065i	−0.470270	−	0.814532i
$556$	−495.000	−	285.788i	−0.890288	−	0.514008i
$557$	425.500	−	736.988i	0.763914	−	1.32314i	−0.176905	−	0.984228i	$-0.556609\pi$
$557$	425.500	−	736.988i	0.763914	−	1.32314i	0.940819	−	0.338910i	$-0.110058\pi$
$558$	85.5000	−	49.3634i	0.153226	−	0.0884650i
$559$			180.133i			0.322242i
$560$		0			0
$561$	462.000			0.823529
$562$	58.0000	+	100.459i	0.103203	+	0.178753i
$563$	−370.500	−	213.908i	−0.658082	−	0.379944i	0.133464	−	0.991054i	$-0.457390\pi$
$563$	−370.500	−	213.908i	−0.658082	−	0.379944i	−0.791546	+	0.611110i	$0.790723\pi$
$564$	−198.000	+	342.946i	−0.351064	+	0.608060i
$565$	−333.000	+	192.258i	−0.589381	+	0.340279i
$566$		−	370.659i		−	0.654874i
$567$		0			0
$568$	−448.000			−0.788732
$569$	409.000	+	708.409i	0.718805	+	1.24501i	0.961474	+	0.274897i	$0.0886439\pi$
$569$	409.000	+	708.409i	0.718805	+	1.24501i	−0.242669	+	0.970109i	$0.578023\pi$
$570$	27.0000	+	15.5885i	0.0473684	+	0.0273482i
$571$	−142.000	+	245.951i	−0.248687	+	0.430738i	−0.963162	−	0.268923i	$-0.913332\pi$
$571$	−142.000	+	245.951i	−0.248687	+	0.430738i	0.714475	+	0.699661i	$0.246666\pi$
$572$	198.000	−	114.315i	0.346154	−	0.199852i
$573$			360.267i			0.628737i
$574$		0			0
$575$	−56.0000			−0.0973913
$576$	19.5000	+	33.7750i	0.0338542	+	0.0586371i
$577$	655.500	+	378.453i	1.13605	+	0.655898i	0.945449	−	0.325770i	$-0.105623\pi$
$577$	655.500	+	378.453i	1.13605	+	0.655898i	0.190599	+	0.981668i	$0.438957\pi$
$578$	149.500	−	258.942i	0.258651	−	0.447996i
$579$	358.500	−	206.980i	0.619171	−	0.357479i
$580$		−	389.711i		−	0.671916i
$581$		0			0
$582$	−159.000			−0.273196
$583$	170.500	+	295.315i	0.292453	+	0.506543i
$584$	42.0000	+	24.2487i	0.0719178	+	0.0415218i
$585$	−54.0000	+	93.5307i	−0.0923077	+	0.159882i
$586$	16.5000	−	9.52628i	0.0281570	−	0.0162564i
$587$			947.432i			1.61402i	0.590535	+	0.807012i	$0.298917\pi$
$587$			947.432i			1.61402i	−0.590535	+	0.807012i	$0.701083\pi$
$588$		0			0
$589$	114.000			0.193548
$590$	−22.5000	−	38.9711i	−0.0381356	−	0.0660528i
$591$	39.0000	+	22.5167i	0.0659898	+	0.0380993i
$592$	145.000	−	251.147i	0.244932	−	0.424235i
$593$	−354.000	+	204.382i	−0.596965	+	0.344658i	−0.767847	−	0.640634i	$-0.778672\pi$
$593$	−354.000	+	204.382i	−0.596965	+	0.344658i	0.170882	+	0.985292i	$0.445338\pi$
$594$			57.1577i			0.0962250i
$595$		0			0
$596$	690.000			1.15772
$597$	−210.000	−	363.731i	−0.351759	−	0.609264i
$598$	−168.000	−	96.9948i	−0.280936	−	0.162199i
$599$	−278.000	+	481.510i	−0.464107	+	0.803857i	−0.999161	−	0.0409613i	$-0.986958\pi$
$599$	−278.000	+	481.510i	−0.464107	+	0.803857i	0.535054	+	0.844818i	$0.320291\pi$
$600$	21.0000	−	12.1244i	0.0350000	−	0.0202073i
$601$			580.237i			0.965453i	0.875771	+	0.482726i	$0.160353\pi$
$601$			580.237i			0.965453i	−0.875771	+	0.482726i	$0.839647\pi$
$602$		0			0
$603$	156.000			0.258706
$604$	340.500	+	589.763i	0.563742	+	0.976429i
$605$		0			0
$606$	−18.0000	+	31.1769i	−0.0297030	+	0.0514471i
$607$	−571.500	+	329.956i	−0.941516	+	0.543584i	−0.890435	−	0.455110i	$-0.849600\pi$
$607$	−571.500	+	329.956i	−0.941516	+	0.543584i	−0.0510805	+	0.998695i	$0.516267\pi$
$608$			114.315i			0.188019i
$609$		0			0
$610$	72.0000			0.118033
$611$	264.000	+	457.261i	0.432079	+	0.748382i
$612$	−189.000	−	109.119i	−0.308824	−	0.178299i
$613$	−160.000	+	277.128i	−0.261011	+	0.452085i	−0.966511	−	0.256625i	$-0.917389\pi$
$613$	−160.000	+	277.128i	−0.261011	+	0.452085i	0.705500	+	0.708710i	$0.250723\pi$
$614$	−396.000	+	228.631i	−0.644951	+	0.372363i
$615$		−	31.1769i		−	0.0506942i
$616$		0			0
$617$	652.000			1.05673			0.528363	−	0.849019i	$-0.322806\pi$
$617$	652.000			1.05673			0.528363	+	0.849019i	$0.322806\pi$
$618$		0			0
$619$	558.000	+	322.161i	0.901454	+	0.520455i	0.877672	−	0.479262i	$-0.159096\pi$
$619$	558.000	+	322.161i	0.901454	+	0.520455i	0.0237823	+	0.999717i	$0.492429\pi$
$620$	256.500	−	444.271i	0.413710	−	0.716566i
$621$	−126.000	+	72.7461i	−0.202899	+	0.117144i
$622$			329.090i			0.529083i
$623$		0			0
$624$	−60.0000			−0.0961538
$625$	335.500	+	581.103i	0.536800	+	0.929765i
$626$	475.500	+	274.530i	0.759585	+	0.438546i
$627$	−33.0000	+	57.1577i	−0.0526316	+	0.0911606i
$628$	126.000	−	72.7461i	0.200637	−	0.115838i
$629$		−	1406.43i		−	2.23597i
$630$		0			0
$631$	−97.0000			−0.153724			−0.0768621	−	0.997042i	$-0.524490\pi$
$631$	−97.0000			−0.153724			−0.0768621	+	0.997042i	$0.524490\pi$
$632$	59.5000	+	103.057i	0.0941456	+	0.163065i
$633$	78.0000	+	45.0333i	0.123223	+	0.0711427i
$634$	−93.5000	+	161.947i	−0.147476	+	0.255437i
$635$	−4.50000	+	2.59808i	−0.00708661	+	0.00409146i
$636$		−	161.081i		−	0.253272i
$637$		0			0
$638$	−275.000			−0.431034
$639$	96.0000	+	166.277i	0.150235	+	0.260214i
$640$	535.500	+	309.171i	0.836719	+	0.483080i
$641$	−350.000	+	606.218i	−0.546022	+	0.945738i	0.452520	+	0.891754i	$0.350525\pi$
$641$	−350.000	+	606.218i	−0.546022	+	0.945738i	−0.998542	+	0.0539833i	$0.982808\pi$
$642$	46.5000	−	26.8468i	0.0724299	−	0.0418174i
$643$		−	325.626i		−	0.506416i	−0.967412	−	0.253208i	$-0.918514\pi$
$643$		−	325.626i		−	0.506416i	0.967412	−	0.253208i	$-0.0814857\pi$
$644$		0			0
$645$	−234.000			−0.362791
$646$	42.0000	+	72.7461i	0.0650155	+	0.112610i
$647$	312.000	+	180.133i	0.482226	+	0.278413i	0.721344	−	0.692577i	$-0.243525\pi$
$647$	312.000	+	180.133i	0.482226	+	0.278413i	−0.239118	+	0.970991i	$0.576858\pi$
$648$	31.5000	−	54.5596i	0.0486111	−	0.0841969i
$649$	82.5000	−	47.6314i	0.127119	−	0.0733920i
$650$		−	13.8564i		−	0.0213175i
$651$		0			0
$652$	−636.000			−0.975460
$653$	−186.500	−	323.027i	−0.285605	−	0.494682i	0.687151	−	0.726515i	$-0.258861\pi$
$653$	−186.500	−	323.027i	−0.285605	−	0.494682i	−0.972756	+	0.231833i	$0.925528\pi$
$654$	204.000	+	117.779i	0.311927	+	0.180091i
$655$	−472.500	+	818.394i	−0.721374	+	1.24946i
$656$	15.0000	−	8.66025i	0.0228659	−	0.0132016i
$657$		−	20.7846i		−	0.0316356i
$658$		0			0
$659$	−818.000			−1.24127			−0.620637	−	0.784098i	$-0.713126\pi$
$659$	−818.000			−1.24127			−0.620637	+	0.784098i	$0.713126\pi$
$660$	148.500	+	257.210i	0.225000	+	0.389711i
$661$	−327.000	−	188.794i	−0.494705	−	0.285618i	0.231819	−	0.972759i	$-0.425532\pi$
$661$	−327.000	−	188.794i	−0.494705	−	0.285618i	−0.726524	+	0.687141i	$0.758866\pi$
$662$	8.00000	−	13.8564i	0.0120846	−	0.0209311i
$663$	−252.000	+	145.492i	−0.380090	+	0.219445i
$664$		−	375.855i		−	0.566047i
$665$		0			0
$666$	174.000			0.261261
$667$	−350.000	−	606.218i	−0.524738	−	0.908872i
$668$	252.000	+	145.492i	0.377246	+	0.217803i
$669$	−19.5000	+	33.7750i	−0.0291480	+	0.0504858i
$670$	−234.000	+	135.100i	−0.349254	+	0.201642i
$671$			152.420i			0.227154i
$672$		0			0
$673$	1205.00			1.79049			0.895245	−	0.445574i	$-0.147000\pi$
$673$	1205.00			1.79049			0.895245	+	0.445574i	$0.147000\pi$
$674$	−41.5000	−	71.8801i	−0.0615727	−	0.106647i
$675$	−9.00000	−	5.19615i	−0.0133333	−	0.00769800i
$676$	181.500	−	314.367i	0.268491	−	0.465040i
$677$	466.500	−	269.334i	0.689069	−	0.397834i	−0.114194	−	0.993458i	$-0.536429\pi$
$677$	466.500	−	269.334i	0.689069	−	0.397834i	0.803263	+	0.595624i	$0.203095\pi$
$678$		−	128.172i		−	0.189044i
$679$		0			0
$680$	882.000			1.29706
$681$	58.5000	+	101.325i	0.0859031	+	0.148789i
$682$	−313.500	−	180.999i	−0.459677	−	0.265395i
$683$	−474.500	+	821.858i	−0.694729	+	1.20331i	0.275543	+	0.961289i	$0.411142\pi$
$683$	−474.500	+	821.858i	−0.694729	+	1.20331i	−0.970272	+	0.242017i	$0.922191\pi$
$684$	27.0000	−	15.5885i	0.0394737	−	0.0227901i
$685$			457.261i			0.667535i
$686$		0			0
$687$	−54.0000			−0.0786026
$688$	−65.0000	−	112.583i	−0.0944767	−	0.163639i
$689$	−186.000	−	107.387i	−0.269956	−	0.155859i
$690$	126.000	−	218.238i	0.182609	−	0.316288i
$691$	267.000	−	154.153i	0.386397	−	0.223086i	−0.294201	−	0.955744i	$-0.595054\pi$
$691$	267.000	−	154.153i	0.386397	−	0.223086i	0.680598	+	0.732657i	$0.261720\pi$
$692$			644.323i			0.931102i
$693$		0			0
$694$	358.000			0.515850
$695$	−495.000	−	857.365i	−0.712230	−	1.23362i
$696$	262.500	+	151.554i	0.377155	+	0.217751i
$697$	42.0000	−	72.7461i	0.0602582	−	0.104370i
$698$	588.000	−	339.482i	0.842407	−	0.486364i
$699$			453.797i			0.649209i
$700$		0			0
$701$	−413.000			−0.589158			−0.294579	−	0.955627i	$-0.595179\pi$
$701$	−413.000			−0.589158			−0.294579	+	0.955627i	$0.595179\pi$
$702$	−18.0000	−	31.1769i	−0.0256410	−	0.0444116i
$703$	174.000	+	100.459i	0.247511	+	0.142900i
$704$	71.5000	−	123.842i	0.101562	−	0.175911i
$705$	−594.000	+	342.946i	−0.842553	+	0.486448i
$706$		−	644.323i		−	0.912639i
$707$		0			0
$708$	−45.0000			−0.0635593
$709$	−445.000	−	770.763i	−0.627645	−	1.08711i	−0.988023	−	0.154306i	$-0.950686\pi$
$709$	−445.000	−	770.763i	−0.627645	−	1.08711i	0.360379	−	0.932806i	$-0.382648\pi$
$710$	−288.000	−	166.277i	−0.405634	−	0.234193i
$711$	25.5000	−	44.1673i	0.0358650	−	0.0621200i
$712$	−483.000	+	278.860i	−0.678371	+	0.391658i
$713$		−	921.451i		−	1.29236i
$714$		0			0
$715$	396.000			0.553846
$716$	69.0000	+	119.512i	0.0963687	+	0.166916i
$717$	−240.000	−	138.564i	−0.334728	−	0.193255i
$718$	142.000	−	245.951i	0.197772	−	0.342550i
$719$	−579.000	+	334.286i	−0.805285	+	0.464932i	−0.845316	−	0.534267i	$-0.820588\pi$
$719$	−579.000	+	334.286i	−0.805285	+	0.464932i	0.0400307	+	0.999198i	$0.487254\pi$
$720$		−	77.9423i		−	0.108253i
$721$		0			0
$722$	349.000			0.483380
$723$	409.500	+	709.275i	0.566390	+	0.981016i
$724$	−81.0000	−	46.7654i	−0.111878	−	0.0645931i
$725$	25.0000	−	43.3013i	0.0344828	−	0.0597259i
$726$		0			0
$727$		−	417.424i		−	0.574174i	−0.957905	−	0.287087i	$-0.907313\pi$
$727$		−	417.424i		−	0.574174i	0.957905	−	0.287087i	$-0.0926868\pi$
$728$		0			0
$729$	−27.0000			−0.0370370
$730$	18.0000	+	31.1769i	0.0246575	+	0.0427081i
$731$	−546.000	−	315.233i	−0.746922	−	0.431236i
$732$	36.0000	−	62.3538i	0.0491803	−	0.0851828i
$733$	−171.000	+	98.7269i	−0.233288	+	0.134689i	−0.612088	−	0.790790i	$-0.709670\pi$
$733$	−171.000	+	98.7269i	−0.233288	+	0.134689i	0.378800	+	0.925479i	$0.376337\pi$
$734$			275.396i			0.375199i
$735$		0			0
$736$	924.000			1.25543
$737$	−286.000	−	495.367i	−0.388060	−	0.672139i
$738$	9.00000	+	5.19615i	0.0121951	+	0.00704086i
$739$	155.000	−	268.468i	0.209743	−	0.363285i	−0.741891	−	0.670521i	$-0.766071\pi$
$739$	155.000	−	268.468i	0.209743	−	0.363285i	0.951633	+	0.307236i	$0.0994040\pi$
$740$	783.000	−	452.065i	1.05811	−	0.610899i
$741$		−	41.5692i		−	0.0560988i
$742$		0			0
$743$	−812.000			−1.09287			−0.546433	−	0.837503i	$-0.684015\pi$
$743$	−812.000			−1.09287			−0.546433	+	0.837503i	$0.684015\pi$
$744$	199.500	+	345.544i	0.268145	+	0.464441i
$745$	1035.00	+	597.558i	1.38926	+	0.802091i
$746$	−25.0000	+	43.3013i	−0.0335121	+	0.0580446i
$747$	−139.500	+	80.5404i	−0.186747	+	0.107818i
$748$			800.207i			1.06980i
$749$		0			0
$750$	−207.000			−0.276000
$751$	537.500	+	930.977i	0.715712	+	1.23965i	0.962684	+	0.270628i	$0.0872312\pi$
$751$	537.500	+	930.977i	0.715712	+	1.23965i	−0.246972	+	0.969023i	$0.579435\pi$
$752$	−330.000	−	190.526i	−0.438830	−	0.253358i
$753$	−58.5000	+	101.325i	−0.0776892	+	0.134562i
$754$	150.000	−	86.6025i	0.198939	−	0.114857i
$755$			1179.53i			1.56229i
$756$		0			0
$757$	−484.000			−0.639366			−0.319683	−	0.947525i	$-0.603576\pi$
$757$	−484.000			−0.639366			−0.319683	+	0.947525i	$0.603576\pi$
$758$	−229.000	−	396.640i	−0.302111	−	0.523271i
$759$	462.000	+	266.736i	0.608696	+	0.351431i
$760$	−63.0000	+	109.119i	−0.0828947	+	0.143578i
$761$	−144.000	+	83.1384i	−0.189225	+	0.109249i	−0.591620	−	0.806217i	$-0.701511\pi$
$761$	−144.000	+	83.1384i	−0.189225	+	0.109249i	0.402395	+	0.915466i	$0.368178\pi$
$762$		−	1.73205i		−	0.00227303i
$763$		0			0
$764$	−624.000			−0.816754
$765$	−189.000	−	327.358i	−0.247059	−	0.427918i
$766$	351.000	+	202.650i	0.458225	+	0.264556i
$767$	−30.0000	+	51.9615i	−0.0391134	+	0.0677464i
$768$	−256.500	+	148.090i	−0.333984	+	0.192826i
$769$			594.093i			0.772553i	0.922383	+	0.386277i	$0.126239\pi$
$769$			594.093i			0.772553i	−0.922383	+	0.386277i	$0.873761\pi$
$770$		0			0
$771$	−702.000			−0.910506
$772$	358.500	+	620.940i	0.464378	+	0.804327i
$773$	−894.000	−	516.151i	−1.15653	−	0.667725i	−0.206062	−	0.978539i	$-0.566065\pi$
$773$	−894.000	−	516.151i	−1.15653	−	0.667725i	−0.950471	+	0.310814i	$0.899398\pi$
$774$	39.0000	−	67.5500i	0.0503876	−	0.0872739i
$775$	57.0000	−	32.9090i	0.0735484	−	0.0424632i
$776$		−	642.591i		−	0.828081i
$777$		0			0
$778$	−698.000			−0.897172
$779$	6.00000	+	10.3923i	0.00770218	+	0.0133406i
$780$	−162.000	−	93.5307i	−0.207692	−	0.119911i
$781$	352.000	−	609.682i	0.450704	−	0.780643i
$782$	588.000	−	339.482i	0.751918	−	0.434120i
$783$		−	129.904i		−	0.165905i
$784$		0			0
$785$	252.000			0.321019
$786$	−157.500	−	272.798i	−0.200382	−	0.347071i
$787$	−354.000	−	204.382i	−0.449809	−	0.259698i	0.257940	−	0.966161i	$-0.416956\pi$
$787$	−354.000	−	204.382i	−0.449809	−	0.259698i	−0.707750	+	0.706463i	$0.750290\pi$
$788$	−39.0000	+	67.5500i	−0.0494924	+	0.0857233i
$789$	159.000	−	91.7987i	0.201521	−	0.116348i
$790$			88.3346i			0.111816i
$791$		0			0
$792$	−231.000			−0.291667
$793$	−48.0000	−	83.1384i	−0.0605296	−	0.104840i
$794$	−498.000	−	287.520i	−0.627204	−	0.362116i
$795$	139.500	−	241.621i	0.175472	−	0.303926i
$796$	630.000	−	363.731i	0.791457	−	0.456948i
$797$		−	625.270i		−	0.784530i	−0.919852	−	0.392265i	$-0.871692\pi$
$797$		−	625.270i		−	0.784530i	0.919852	−	0.392265i	$-0.128308\pi$
$798$		0			0
$799$	−1848.00			−2.31289
$800$	33.0000	+	57.1577i	0.0412500	+	0.0714471i
$801$	207.000	+	119.512i	0.258427	+	0.149203i
$802$	142.000	−	245.951i	0.177057	−	0.306672i
$803$	−66.0000	+	38.1051i	−0.0821918	+	0.0474534i
$804$			270.200i			0.336070i
$805$		0			0
$806$	228.000			0.282878
$807$	376.500	+	652.117i	0.466543	+	0.808076i
$808$	−126.000	−	72.7461i	−0.155941	−	0.0900323i
$809$	376.000	−	651.251i	0.464771	−	0.805008i	−0.534420	−	0.845219i	$-0.679470\pi$
$809$	376.000	−	651.251i	0.464771	−	0.805008i	0.999191	+	0.0402116i	$0.0128032\pi$
$810$	40.5000	−	23.3827i	0.0500000	−	0.0288675i
$811$			270.200i			0.333169i	0.986027	+	0.166584i	$0.0532738\pi$
$811$			270.200i			0.333169i	−0.986027	+	0.166584i	$0.946726\pi$
$812$		0			0
$813$	219.000			0.269373
$814$	−319.000	−	552.524i	−0.391892	−	0.678777i
$815$	−954.000	−	550.792i	−1.17055	−	0.675819i
$816$	105.000	−	181.865i	0.128676	−	0.222874i
$817$	78.0000	−	45.0333i	0.0954712	−	0.0551203i
$818$		−	209.578i		−	0.256208i
$819$		0			0
$820$	54.0000			0.0658537
$821$	−441.500	−	764.700i	−0.537759	−	0.931426i	−0.999024	−	0.0441635i	$-0.985938\pi$
$821$	−441.500	−	764.700i	−0.537759	−	0.931426i	0.461265	−	0.887262i	$-0.347396\pi$
$822$	−132.000	−	76.2102i	−0.160584	−	0.0927132i
$823$	245.000	−	424.352i	0.297691	−	0.515617i	−0.677916	−	0.735139i	$-0.737117\pi$
$823$	245.000	−	424.352i	0.297691	−	0.515617i	0.975607	+	0.219523i	$0.0704500\pi$
$824$		0			0
$825$			38.1051i			0.0461880i
$826$		0			0
$827$	1279.00			1.54655			0.773277	−	0.634068i	$-0.218616\pi$
$827$	1279.00			1.54655			0.773277	+	0.634068i	$0.218616\pi$
$828$	−126.000	−	218.238i	−0.152174	−	0.263573i
$829$	−1311.00	−	756.906i	−1.58142	−	0.913035i	−0.994652	−	0.103283i	$-0.967065\pi$
$829$	−1311.00	−	756.906i	−1.58142	−	0.913035i	−0.586771	−	0.809753i	$-0.699601\pi$
$830$	139.500	−	241.621i	0.168072	−	0.291110i
$831$	354.000	−	204.382i	0.425993	−	0.245947i
$832$			90.0666i			0.108253i
$833$		0			0
$834$	330.000			0.395683
$835$	252.000	+	436.477i	0.301796	+	0.522727i
$836$	−99.0000	−	57.1577i	−0.118421	−	0.0683704i
$837$	85.5000	−	148.090i	0.102151	−	0.176930i
$838$	−114.000	+	65.8179i	−0.136038	+	0.0785417i
$839$		−	523.079i		−	0.623456i	−0.950171	−	0.311728i	$-0.899092\pi$
$839$		−	523.079i		−	0.623456i	0.950171	−	0.311728i	$-0.100908\pi$
$840$		0			0
$841$	−216.000			−0.256837
$842$	14.0000	+	24.2487i	0.0166271	+	0.0287989i
$843$	174.000	+	100.459i	0.206406	+	0.119168i
$844$	−78.0000	+	135.100i	−0.0924171	+	0.160071i
$845$	544.500	−	314.367i	0.644379	−	0.372032i
$846$		−	228.631i		−	0.270249i
$847$		0			0
$848$	155.000			0.182783
$849$	−321.000	−	555.988i	−0.378092	−	0.654874i
$850$	42.0000	+	24.2487i	0.0494118	+	0.0285279i
$851$	812.000	−	1406.43i	0.954172	−	1.65267i
$852$	−288.000	+	166.277i	−0.338028	+	0.195161i
$853$			387.979i			0.454841i	0.973797	+	0.227421i	$0.0730292\pi$
$853$			387.979i			0.454841i	−0.973797	+	0.227421i	$0.926971\pi$
$854$		0			0
$855$	54.0000			0.0631579
$856$	108.500	+	187.928i	0.126752	+	0.219541i
$857$	720.000	+	415.692i	0.840140	+	0.485055i	0.857312	−	0.514797i	$-0.172133\pi$
$857$	720.000	+	415.692i	0.840140	+	0.485055i	−0.0171718	+	0.999853i	$0.505466\pi$
$858$	−66.0000	+	114.315i	−0.0769231	+	0.133235i
$859$	−981.000	+	566.381i	−1.14203	+	0.659349i	−0.946931	−	0.321436i	$-0.895835\pi$
$859$	−981.000	+	566.381i	−1.14203	+	0.659349i	−0.195094	+	0.980785i	$0.562501\pi$
$860$		−	405.300i		−	0.471279i
$861$		0			0
$862$	118.000			0.136891
$863$	−11.0000	−	19.0526i	−0.0127462	−	0.0220771i	0.859582	−	0.510998i	$-0.170724\pi$
$863$	−11.0000	−	19.0526i	−0.0127462	−	0.0220771i	−0.872328	+	0.488921i	$0.837391\pi$
$864$	148.500	+	85.7365i	0.171875	+	0.0992321i
$865$	−558.000	+	966.484i	−0.645087	+	1.11732i
$866$	−486.000	+	280.592i	−0.561201	+	0.324010i
$867$		−	517.883i		−	0.597328i
$868$		0			0
$869$	−187.000			−0.215190
$870$	112.500	+	194.856i	0.129310	+	0.223972i
$871$	312.000	+	180.133i	0.358209	+	0.206812i
$872$	−476.000	+	824.456i	−0.545872	+	0.945477i
$873$	−238.500	+	137.698i	−0.273196	+	0.157730i
$874$			96.9948i			0.110978i
$875$		0			0
$876$	36.0000			0.0410959
$877$	20.0000	+	34.6410i	0.0228050	+	0.0394994i	0.877203	−	0.480120i	$-0.159407\pi$
$877$	20.0000	+	34.6410i	0.0228050	+	0.0394994i	−0.854398	+	0.519620i	$0.826074\pi$
$878$	−640.500	−	369.793i	−0.729499	−	0.421176i
$879$	16.5000	−	28.5788i	0.0187713	−	0.0325129i
$880$	−247.500	+	142.894i	−0.281250	+	0.162380i
$881$			20.7846i			0.0235921i	0.999930	+	0.0117960i	$0.00375488\pi$
$881$			20.7846i			0.0235921i	−0.999930	+	0.0117960i	$0.996245\pi$
$882$		0			0
$883$	386.000			0.437146			0.218573	−	0.975821i	$-0.429860\pi$
$883$	386.000			0.437146			0.218573	+	0.975821i	$0.429860\pi$
$884$	−252.000	−	436.477i	−0.285068	−	0.493752i
$885$	−67.5000	−	38.9711i	−0.0762712	−	0.0440352i
$886$	77.5000	−	134.234i	0.0874718	−	0.151506i
$887$	1494.00	−	862.561i	1.68433	−	0.972448i	0.725604	−	0.688112i	$-0.241560\pi$
$887$	1494.00	−	862.561i	1.68433	−	0.972448i	0.958725	−	0.284336i	$-0.0917731\pi$
$888$			703.213i			0.791906i
$889$		0			0
$890$	−414.000			−0.465169
$891$	49.5000	+	85.7365i	0.0555556	+	0.0962250i
$892$	−58.5000	−	33.7750i	−0.0655830	−	0.0378643i
$893$	132.000	−	228.631i	0.147816	−	0.256025i
$894$	−345.000	+	199.186i	−0.385906	+	0.222803i
$895$			239.023i			0.267065i
$896$		0			0
$897$	−336.000			−0.374582
$898$	184.000	+	318.697i	0.204900	+	0.354897i
$899$	712.500	+	411.362i	0.792547	+	0.457577i
$900$	9.00000	−	15.5885i	0.0100000	−	0.0173205i
$901$	651.000	−	375.855i	0.722531	−	0.417153i
$902$		−	38.1051i		−	0.0422451i
$903$		0			0
$904$	518.000			0.573009
$905$	−81.0000	−	140.296i	−0.0895028	−	0.155023i
$906$	−340.500	−	196.588i	−0.375828	−	0.216984i
$907$	296.000	−	512.687i	0.326351	−	0.565256i	−0.655434	−	0.755252i	$-0.727514\pi$
$907$	296.000	−	512.687i	0.326351	−	0.565256i	0.981785	+	0.189996i	$0.0608477\pi$
$908$	−175.500	+	101.325i	−0.193282	+	0.111591i
$909$			62.3538i			0.0685961i
$910$		0			0
$911$	−416.000			−0.456641			−0.228321	−	0.973586i	$-0.573323\pi$
$911$	−416.000			−0.456641			−0.228321	+	0.973586i	$0.573323\pi$
$912$	15.0000	+	25.9808i	0.0164474	+	0.0284877i
$913$	511.500	+	295.315i	0.560241	+	0.323455i
$914$	−170.500	+	295.315i	−0.186543	+	0.323101i
$915$	108.000	−	62.3538i	0.118033	−	0.0681463i
$916$		−	93.5307i		−	0.102108i
$917$		0			0
$918$	126.000			0.137255
$919$	−25.0000	−	43.3013i	−0.0272035	−	0.0471178i	0.852103	−	0.523374i	$-0.175327\pi$
$919$	−25.0000	−	43.3013i	−0.0272035	−	0.0471178i	−0.879307	+	0.476256i	$0.841994\pi$
$920$	882.000	+	509.223i	0.958696	+	0.553503i
$921$	−396.000	+	685.892i	−0.429967	+	0.744725i
$922$	−48.0000	+	27.7128i	−0.0520607	+	0.0300573i
$923$			443.405i			0.480395i
$924$		0			0
$925$	116.000			0.125405
$926$	89.0000	+	154.153i	0.0961123	+	0.166471i
$927$		0			0
$928$	−412.500	+	714.471i	−0.444504	+	0.769904i
$929$	−357.000	+	206.114i	−0.384284	+	0.221867i	−0.679681	−	0.733508i	$-0.737882\pi$
$929$	−357.000	+	206.114i	−0.384284	+	0.221867i	0.295396	+	0.955375i	$0.404548\pi$
$930$			296.181i			0.318474i
$931$		0			0
$932$	−786.000			−0.843348
$933$	285.000	+	493.634i	0.305466	+	0.529083i
$934$	570.000	+	329.090i	0.610278	+	0.352344i
$935$	−693.000	+	1200.31i	−0.741176	+	1.28376i
$936$	126.000	−	72.7461i	0.134615	−	0.0777202i
$937$		−	1605.61i		−	1.71357i	−0.515677	−	0.856783i	$-0.672460\pi$
$937$		−	1605.61i		−	1.71357i	0.515677	−	0.856783i	$-0.327540\pi$
$938$		0			0
$939$	951.000			1.01278
$940$	−594.000	−	1028.84i	−0.631915	−	1.09451i
$941$	1150.50	+	664.241i	1.22264	+	0.705889i	0.965479	−	0.260481i	$-0.0838811\pi$
$941$	1150.50	+	664.241i	1.22264	+	0.705889i	0.257156	+	0.966370i	$0.417214\pi$
$942$	−42.0000	+	72.7461i	−0.0445860	+	0.0772252i
$943$	84.0000	−	48.4974i	0.0890774	−	0.0514289i
$944$		−	43.3013i		−	0.0458700i
$945$		0			0
$946$	−286.000			−0.302326
$947$	685.000	+	1186.45i	0.723337	+	1.25286i	0.959655	+	0.281180i	$0.0907259\pi$
$947$	685.000	+	1186.45i	0.723337	+	1.25286i	−0.236318	+	0.971676i	$0.575941\pi$
$948$	76.5000	+	44.1673i	0.0806962	+	0.0465900i
$949$	24.0000	−	41.5692i	0.0252898	−	0.0438032i
$950$	−6.00000	+	3.46410i	−0.00631579	+	0.00364642i
$951$			323.894i			0.340582i
$952$		0			0
$953$	1150.00			1.20672			0.603358	−	0.797471i	$-0.293829\pi$
$953$	1150.00			1.20672			0.603358	+	0.797471i	$0.293829\pi$
$954$	46.5000	+	80.5404i	0.0487421	+	0.0844239i
$955$	−936.000	−	540.400i	−0.980105	−	0.565864i
$956$	240.000	−	415.692i	0.251046	−	0.434824i
$957$	−412.500	+	238.157i	−0.431034	+	0.248858i
$958$			509.223i			0.531548i
$959$		0			0
$960$	−117.000			−0.121875
$961$	61.0000	+	105.655i	0.0634755	+	0.109943i
$962$	348.000	+	200.918i	0.361746	+	0.208854i
$963$	46.5000	−	80.5404i	0.0482866	−	0.0836349i
$964$	−1228.50	+	709.275i	−1.27438	+	0.735762i
$965$			1241.88i			1.28692i
$966$		0			0
$967$	5.00000			0.00517063			0.00258532	−	0.999997i	$-0.499177\pi$
$967$	5.00000			0.00517063			0.00258532	+	0.999997i	$0.499177\pi$
$968$		0			0
$969$	126.000	+	72.7461i	0.130031	+	0.0750734i
$970$	238.500	−	413.094i	0.245876	−	0.425870i
$971$	−385.500	+	222.569i	−0.397013	+	0.229216i	−0.685195	−	0.728360i	$-0.740283\pi$
$971$	−385.500	+	222.569i	−0.397013	+	0.229216i	0.288181	+	0.957576i	$0.406949\pi$
$972$		−	46.7654i		−	0.0481125i
$973$		0			0
$974$	−841.000			−0.863450
$975$	−12.0000	−	20.7846i	−0.0123077	−	0.0213175i
$976$	60.0000	+	34.6410i	0.0614754	+	0.0354928i
$977$	−479.000	+	829.652i	−0.490276	+	0.849184i	−0.999937	−	0.0111917i	$-0.996437\pi$
$977$	−479.000	+	829.652i	−0.490276	+	0.849184i	0.509661	+	0.860375i	$0.329771\pi$
$978$	318.000	−	183.597i	0.325153	−	0.187727i
$979$		−	876.418i		−	0.895217i
$980$		0			0
$981$	408.000			0.415902
$982$	479.500	+	830.518i	0.488289	+	0.845742i
$983$	−243.000	−	140.296i	−0.247202	−	0.142722i	0.371280	−	0.928521i	$-0.378919\pi$
$983$	−243.000	−	140.296i	−0.247202	−	0.142722i	−0.618483	+	0.785798i	$0.712252\pi$
$984$	−21.0000	+	36.3731i	−0.0213415	+	0.0369645i
$985$	−117.000	+	67.5500i	−0.118782	+	0.0685787i
$986$			606.218i			0.614825i
$987$		0			0
$988$	72.0000			0.0728745
$989$	−364.000	−	630.466i	−0.368049	−	0.637479i
$990$	−148.500	−	85.7365i	−0.150000	−	0.0866025i
$991$	−461.500	+	799.341i	−0.465691	+	0.806601i	−0.999232	−	0.0391732i	$-0.987528\pi$
$991$	−461.500	+	799.341i	−0.465691	+	0.806601i	0.533541	+	0.845774i	$0.320861\pi$
$992$	−940.500	+	542.998i	−0.948085	+	0.547377i
$993$		−	27.7128i		−	0.0279082i
$994$		0			0
$995$	1260.00			1.26633
$996$	−139.500	−	241.621i	−0.140060	−	0.242591i
$997$	−18.0000	−	10.3923i	−0.0180542	−	0.0104236i	0.490946	−	0.871190i	$-0.336651\pi$
$997$	−18.0000	−	10.3923i	−0.0180542	−	0.0104236i	−0.509000	+	0.860767i	$0.669985\pi$
$998$	59.0000	−	102.191i	0.0591182	−	0.102396i
$999$	261.000	−	150.688i	0.261261	−	0.150839i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.3.f.c.31.1		2
3.2	odd	2		441.3.m.e.325.1		2
7.2	even	3		21.3.f.b.19.1	yes	2
7.3	odd	6		147.3.d.b.97.1		2
7.4	even	3		147.3.d.b.97.2		2
7.5	odd	6	inner	147.3.f.c.19.1		2
7.6	odd	2		21.3.f.b.10.1	✓	2
21.2	odd	6		63.3.m.c.19.1		2
21.5	even	6		441.3.m.e.19.1		2
21.11	odd	6		441.3.d.b.244.1		2
21.17	even	6		441.3.d.b.244.2		2
21.20	even	2		63.3.m.c.10.1		2
28.3	even	6		2352.3.f.d.97.2		2
28.11	odd	6		2352.3.f.d.97.1		2
28.23	odd	6		336.3.bh.a.145.1		2
28.27	even	2		336.3.bh.a.241.1		2
35.2	odd	12		525.3.s.c.124.1		4
35.9	even	6		525.3.o.g.376.1		2
35.13	even	4		525.3.s.c.199.1		4
35.23	odd	12		525.3.s.c.124.2		4
35.27	even	4		525.3.s.c.199.2		4
35.34	odd	2		525.3.o.g.451.1		2
84.23	even	6		1008.3.cg.g.145.1		2
84.83	odd	2		1008.3.cg.g.577.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.3.f.b.10.1	✓	2	7.6	odd	2
21.3.f.b.19.1	yes	2	7.2	even	3
63.3.m.c.10.1		2	21.20	even	2
63.3.m.c.19.1		2	21.2	odd	6
147.3.d.b.97.1		2	7.3	odd	6
147.3.d.b.97.2		2	7.4	even	3
147.3.f.c.19.1		2	7.5	odd	6	inner
147.3.f.c.31.1		2	1.1	even	1	trivial
336.3.bh.a.145.1		2	28.23	odd	6
336.3.bh.a.241.1		2	28.27	even	2
441.3.d.b.244.1		2	21.11	odd	6
441.3.d.b.244.2		2	21.17	even	6
441.3.m.e.19.1		2	21.5	even	6
441.3.m.e.325.1		2	3.2	odd	2
525.3.o.g.376.1		2	35.9	even	6
525.3.o.g.451.1		2	35.34	odd	2
525.3.s.c.124.1		4	35.2	odd	12
525.3.s.c.124.2		4	35.23	odd	12
525.3.s.c.199.1		4	35.13	even	4
525.3.s.c.199.2		4	35.27	even	4
1008.3.cg.g.145.1		2	84.23	even	6
1008.3.cg.g.577.1		2	84.83	odd	2
2352.3.f.d.97.1		2	28.11	odd	6
2352.3.f.d.97.2		2	28.3	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(1.50000 - 2.59808i) q^{4} +(4.50000 - 2.59808i) q^{5} +1.73205i q^{6} -7.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(1.50000 - 2.59808i) q^{4} +(4.50000 - 2.59808i) q^{5} +1.73205i q^{6} -7.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(-4.50000 - 2.59808i) q^{10} +(5.50000 - 9.52628i) q^{11} +(-4.50000 + 2.59808i) q^{12} +6.92820i q^{13} -9.00000 q^{15} +(-2.50000 - 4.33013i) q^{16} +(-21.0000 - 12.1244i) q^{17} +(1.50000 - 2.59808i) q^{18} +(3.00000 - 1.73205i) q^{19} -15.5885i q^{20} -11.0000 q^{22} +(-14.0000 - 24.2487i) q^{23} +(10.5000 + 6.06218i) q^{24} +(1.00000 - 1.73205i) q^{25} +(6.00000 - 3.46410i) q^{26} -5.19615i q^{27} +25.0000 q^{29} +(4.50000 + 7.79423i) q^{30} +(28.5000 + 16.4545i) q^{31} +(-16.5000 + 28.5788i) q^{32} +(-16.5000 + 9.52628i) q^{33} +24.2487i q^{34} +9.00000 q^{36} +(29.0000 + 50.2295i) q^{37} +(-3.00000 - 1.73205i) q^{38} +(6.00000 - 10.3923i) q^{39} +(-31.5000 + 18.1865i) q^{40} +3.46410i q^{41} +26.0000 q^{43} +(-16.5000 - 28.5788i) q^{44} +(13.5000 + 7.79423i) q^{45} +(-14.0000 + 24.2487i) q^{46} +(66.0000 - 38.1051i) q^{47} +8.66025i q^{48} -2.00000 q^{50} +(21.0000 + 36.3731i) q^{51} +(18.0000 + 10.3923i) q^{52} +(-15.5000 + 26.8468i) q^{53} +(-4.50000 + 2.59808i) q^{54} -57.1577i q^{55} -6.00000 q^{57} +(-12.5000 - 21.6506i) q^{58} +(7.50000 + 4.33013i) q^{59} +(-13.5000 + 23.3827i) q^{60} +(-12.0000 + 6.92820i) q^{61} -32.9090i q^{62} +13.0000 q^{64} +(18.0000 + 31.1769i) q^{65} +(16.5000 + 9.52628i) q^{66} +(26.0000 - 45.0333i) q^{67} +(-63.0000 + 36.3731i) q^{68} +48.4974i q^{69} +64.0000 q^{71} +(-10.5000 - 18.1865i) q^{72} +(-6.00000 - 3.46410i) q^{73} +(29.0000 - 50.2295i) q^{74} +(-3.00000 + 1.73205i) q^{75} -10.3923i q^{76} -12.0000 q^{78} +(-8.50000 - 14.7224i) q^{79} +(-22.5000 - 12.9904i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(3.00000 - 1.73205i) q^{82} +53.6936i q^{83} -126.000 q^{85} +(-13.0000 - 22.5167i) q^{86} +(-37.5000 - 21.6506i) q^{87} +(-38.5000 + 66.6840i) q^{88} +(69.0000 - 39.8372i) q^{89} -15.5885i q^{90} -84.0000 q^{92} +(-28.5000 - 49.3634i) q^{93} +(-66.0000 - 38.1051i) q^{94} +(9.00000 - 15.5885i) q^{95} +(49.5000 - 28.5788i) q^{96} +91.7987i q^{97} +33.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - 3 q^{3} + 3 q^{4} + 9 q^{5} - 14 q^{8} + 3 q^{9}+O(q^{10}) \) 2 * q - q^2 - 3 * q^3 + 3 * q^4 + 9 * q^5 - 14 * q^8 + 3 * q^9	\( 2 q - q^{2} - 3 q^{3} + 3 q^{4} + 9 q^{5} - 14 q^{8} + 3 q^{9} - 9 q^{10} + 11 q^{11} - 9 q^{12} - 18 q^{15} - 5 q^{16} - 42 q^{17} + 3 q^{18} + 6 q^{19} - 22 q^{22} - 28 q^{23} + 21 q^{24} + 2 q^{25} + 12 q^{26} + 50 q^{29} + 9 q^{30} + 57 q^{31} - 33 q^{32} - 33 q^{33} + 18 q^{36} + 58 q^{37} - 6 q^{38} + 12 q^{39} - 63 q^{40} + 52 q^{43} - 33 q^{44} + 27 q^{45} - 28 q^{46} + 132 q^{47} - 4 q^{50} + 42 q^{51} + 36 q^{52} - 31 q^{53} - 9 q^{54} - 12 q^{57} - 25 q^{58} + 15 q^{59} - 27 q^{60} - 24 q^{61} + 26 q^{64} + 36 q^{65} + 33 q^{66} + 52 q^{67} - 126 q^{68} + 128 q^{71} - 21 q^{72} - 12 q^{73} + 58 q^{74} - 6 q^{75} - 24 q^{78} - 17 q^{79} - 45 q^{80} - 9 q^{81} + 6 q^{82} - 252 q^{85} - 26 q^{86} - 75 q^{87} - 77 q^{88} + 138 q^{89} - 168 q^{92} - 57 q^{93} - 132 q^{94} + 18 q^{95} + 99 q^{96} + 66 q^{99}+O(q^{100}) \) 2 * q - q^2 - 3 * q^3 + 3 * q^4 + 9 * q^5 - 14 * q^8 + 3 * q^9 - 9 * q^10 + 11 * q^11 - 9 * q^12 - 18 * q^15 - 5 * q^16 - 42 * q^17 + 3 * q^18 + 6 * q^19 - 22 * q^22 - 28 * q^23 + 21 * q^24 + 2 * q^25 + 12 * q^26 + 50 * q^29 + 9 * q^30 + 57 * q^31 - 33 * q^32 - 33 * q^33 + 18 * q^36 + 58 * q^37 - 6 * q^38 + 12 * q^39 - 63 * q^40 + 52 * q^43 - 33 * q^44 + 27 * q^45 - 28 * q^46 + 132 * q^47 - 4 * q^50 + 42 * q^51 + 36 * q^52 - 31 * q^53 - 9 * q^54 - 12 * q^57 - 25 * q^58 + 15 * q^59 - 27 * q^60 - 24 * q^61 + 26 * q^64 + 36 * q^65 + 33 * q^66 + 52 * q^67 - 126 * q^68 + 128 * q^71 - 21 * q^72 - 12 * q^73 + 58 * q^74 - 6 * q^75 - 24 * q^78 - 17 * q^79 - 45 * q^80 - 9 * q^81 + 6 * q^82 - 252 * q^85 - 26 * q^86 - 75 * q^87 - 77 * q^88 + 138 * q^89 - 168 * q^92 - 57 * q^93 - 132 * q^94 + 18 * q^95 + 99 * q^96 + 66 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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