LMFDB - Embedded newform 9.3.d.a.5.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9,3,Mod(2,9)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("9.2");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 9 = 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	9.d (of order $6$, degree $2$, 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:	$0.245232237924$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			5.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	9.5
Dual form			9.3.d.a.2.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50000 + 0.866025i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(3.00000 + 1.73205i) q^{5} +(4.50000 + 2.59808i) q^{6} +(-1.00000 - 1.73205i) q^{7} -8.66025i q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})$	\(q+(-1.50000 + 0.866025i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(3.00000 + 1.73205i) q^{5} +(4.50000 + 2.59808i) q^{6} +(-1.00000 - 1.73205i) q^{7} -8.66025i q^{8} +(-4.50000 + 7.79423i) q^{9} -6.00000 q^{10} +(-1.50000 + 0.866025i) q^{11} +3.00000 q^{12} +(2.00000 - 3.46410i) q^{13} +(3.00000 + 1.73205i) q^{14} -10.3923i q^{15} +(5.50000 + 9.52628i) q^{16} +15.5885i q^{17} -15.5885i q^{18} +11.0000 q^{19} +(-3.00000 + 1.73205i) q^{20} +(-3.00000 + 5.19615i) q^{21} +(1.50000 - 2.59808i) q^{22} +(-24.0000 - 13.8564i) q^{23} +(-22.5000 + 12.9904i) q^{24} +(-6.50000 - 11.2583i) q^{25} +6.92820i q^{26} +27.0000 q^{27} +2.00000 q^{28} +(39.0000 - 22.5167i) q^{29} +(9.00000 + 15.5885i) q^{30} +(-16.0000 + 27.7128i) q^{31} +(13.5000 + 7.79423i) q^{32} +(4.50000 + 2.59808i) q^{33} +(-13.5000 - 23.3827i) q^{34} -6.92820i q^{35} +(-4.50000 - 7.79423i) q^{36} -34.0000 q^{37} +(-16.5000 + 9.52628i) q^{38} -12.0000 q^{39} +(15.0000 - 25.9808i) q^{40} +(-10.5000 - 6.06218i) q^{41} -10.3923i q^{42} +(30.5000 + 52.8275i) q^{43} -1.73205i q^{44} +(-27.0000 + 15.5885i) q^{45} +48.0000 q^{46} +(-42.0000 + 24.2487i) q^{47} +(16.5000 - 28.5788i) q^{48} +(22.5000 - 38.9711i) q^{49} +(19.5000 + 11.2583i) q^{50} +(40.5000 - 23.3827i) q^{51} +(2.00000 + 3.46410i) q^{52} +(-40.5000 + 23.3827i) q^{54} -6.00000 q^{55} +(-15.0000 + 8.66025i) q^{56} +(-16.5000 - 28.5788i) q^{57} +(-39.0000 + 67.5500i) q^{58} +(43.5000 + 25.1147i) q^{59} +(9.00000 + 5.19615i) q^{60} +(-28.0000 - 48.4974i) q^{61} -55.4256i q^{62} +18.0000 q^{63} -71.0000 q^{64} +(12.0000 - 6.92820i) q^{65} -9.00000 q^{66} +(15.5000 - 26.8468i) q^{67} +(-13.5000 - 7.79423i) q^{68} +83.1384i q^{69} +(6.00000 + 10.3923i) q^{70} -31.1769i q^{71} +(67.5000 + 38.9711i) q^{72} +65.0000 q^{73} +(51.0000 - 29.4449i) q^{74} +(-19.5000 + 33.7750i) q^{75} +(-5.50000 + 9.52628i) q^{76} +(3.00000 + 1.73205i) q^{77} +(18.0000 - 10.3923i) q^{78} +(-19.0000 - 32.9090i) q^{79} +38.1051i q^{80} +(-40.5000 - 70.1481i) q^{81} +21.0000 q^{82} +(-42.0000 + 24.2487i) q^{83} +(-3.00000 - 5.19615i) q^{84} +(-27.0000 + 46.7654i) q^{85} +(-91.5000 - 52.8275i) q^{86} +(-117.000 - 67.5500i) q^{87} +(7.50000 + 12.9904i) q^{88} +124.708i q^{89} +(27.0000 - 46.7654i) q^{90} -8.00000 q^{91} +(24.0000 - 13.8564i) q^{92} +96.0000 q^{93} +(42.0000 - 72.7461i) q^{94} +(33.0000 + 19.0526i) q^{95} -46.7654i q^{96} +(57.5000 + 99.5929i) q^{97} +77.9423i q^{98} -15.5885i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 3 q^{2} - 3 q^{3} - q^{4} + 6 q^{5} + 9 q^{6} - 2 q^{7} - 9 q^{9}+O(q^{10}) $ 2 * q - 3 * q^2 - 3 * q^3 - q^4 + 6 * q^5 + 9 * q^6 - 2 * q^7 - 9 * q^9	$ 2 q - 3 q^{2} - 3 q^{3} - q^{4} + 6 q^{5} + 9 q^{6} - 2 q^{7} - 9 q^{9} - 12 q^{10} - 3 q^{11} + 6 q^{12} + 4 q^{13} + 6 q^{14} + 11 q^{16} + 22 q^{19} - 6 q^{20} - 6 q^{21} + 3 q^{22} - 48 q^{23} - 45 q^{24} - 13 q^{25} + 54 q^{27} + 4 q^{28} + 78 q^{29} + 18 q^{30} - 32 q^{31} + 27 q^{32} + 9 q^{33} - 27 q^{34} - 9 q^{36} - 68 q^{37} - 33 q^{38} - 24 q^{39} + 30 q^{40} - 21 q^{41} + 61 q^{43} - 54 q^{45} + 96 q^{46} - 84 q^{47} + 33 q^{48} + 45 q^{49} + 39 q^{50} + 81 q^{51} + 4 q^{52} - 81 q^{54} - 12 q^{55} - 30 q^{56} - 33 q^{57} - 78 q^{58} + 87 q^{59} + 18 q^{60} - 56 q^{61} + 36 q^{63} - 142 q^{64} + 24 q^{65} - 18 q^{66} + 31 q^{67} - 27 q^{68} + 12 q^{70} + 135 q^{72} + 130 q^{73} + 102 q^{74} - 39 q^{75} - 11 q^{76} + 6 q^{77} + 36 q^{78} - 38 q^{79} - 81 q^{81} + 42 q^{82} - 84 q^{83} - 6 q^{84} - 54 q^{85} - 183 q^{86} - 234 q^{87} + 15 q^{88} + 54 q^{90} - 16 q^{91} + 48 q^{92} + 192 q^{93} + 84 q^{94} + 66 q^{95} + 115 q^{97}+O(q^{100}) $ 2 * q - 3 * q^2 - 3 * q^3 - q^4 + 6 * q^5 + 9 * q^6 - 2 * q^7 - 9 * q^9 - 12 * q^10 - 3 * q^11 + 6 * q^12 + 4 * q^13 + 6 * q^14 + 11 * q^16 + 22 * q^19 - 6 * q^20 - 6 * q^21 + 3 * q^22 - 48 * q^23 - 45 * q^24 - 13 * q^25 + 54 * q^27 + 4 * q^28 + 78 * q^29 + 18 * q^30 - 32 * q^31 + 27 * q^32 + 9 * q^33 - 27 * q^34 - 9 * q^36 - 68 * q^37 - 33 * q^38 - 24 * q^39 + 30 * q^40 - 21 * q^41 + 61 * q^43 - 54 * q^45 + 96 * q^46 - 84 * q^47 + 33 * q^48 + 45 * q^49 + 39 * q^50 + 81 * q^51 + 4 * q^52 - 81 * q^54 - 12 * q^55 - 30 * q^56 - 33 * q^57 - 78 * q^58 + 87 * q^59 + 18 * q^60 - 56 * q^61 + 36 * q^63 - 142 * q^64 + 24 * q^65 - 18 * q^66 + 31 * q^67 - 27 * q^68 + 12 * q^70 + 135 * q^72 + 130 * q^73 + 102 * q^74 - 39 * q^75 - 11 * q^76 + 6 * q^77 + 36 * q^78 - 38 * q^79 - 81 * q^81 + 42 * q^82 - 84 * q^83 - 6 * q^84 - 54 * q^85 - 183 * q^86 - 234 * q^87 + 15 * q^88 + 54 * q^90 - 16 * q^91 + 48 * q^92 + 192 * q^93 + 84 * q^94 + 66 * q^95 + 115 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/9\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.50000	+	0.866025i	−0.750000	+	0.433013i	−0.825694	−	0.564118i	$-0.809216\pi$
$2$	−1.50000	+	0.866025i	−0.750000	+	0.433013i	0.0756939	+	0.997131i	$0.475883\pi$
$3$	−1.50000	−	2.59808i	−0.500000	−	0.866025i
$3$	−1.50000	−	2.59808i	−0.500000	−	0.866025i
$4$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$5$	3.00000	+	1.73205i	0.600000	+	0.346410i	0.769042	−	0.639199i	$-0.220734\pi$
$5$	3.00000	+	1.73205i	0.600000	+	0.346410i	−0.169042	+	0.985609i	$0.554067\pi$
$6$	4.50000	+	2.59808i	0.750000	+	0.433013i
$7$	−1.00000	−	1.73205i	−0.142857	−	0.247436i	0.785714	−	0.618590i	$-0.212296\pi$
$7$	−1.00000	−	1.73205i	−0.142857	−	0.247436i	−0.928571	+	0.371154i	$0.878962\pi$
$8$		−	8.66025i		−	1.08253i
$9$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$10$	−6.00000			−0.600000
$11$	−1.50000	+	0.866025i	−0.136364	+	0.0787296i	−0.566630	−	0.823972i	$-0.691753\pi$
$11$	−1.50000	+	0.866025i	−0.136364	+	0.0787296i	0.430266	+	0.902702i	$0.358420\pi$
$12$	3.00000			0.250000
$13$	2.00000	−	3.46410i	0.153846	−	0.266469i	−0.778792	−	0.627282i	$-0.784167\pi$
$13$	2.00000	−	3.46410i	0.153846	−	0.266469i	0.932638	+	0.360813i	$0.117501\pi$
$14$	3.00000	+	1.73205i	0.214286	+	0.123718i
$15$		−	10.3923i		−	0.692820i
$16$	5.50000	+	9.52628i	0.343750	+	0.595392i
$17$			15.5885i			0.916968i	0.888703	+	0.458484i	$0.151607\pi$
$17$			15.5885i			0.916968i	−0.888703	+	0.458484i	$0.848393\pi$
$18$		−	15.5885i		−	0.866025i
$19$	11.0000			0.578947			0.289474	−	0.957186i	$-0.406520\pi$
$19$	11.0000			0.578947			0.289474	+	0.957186i	$0.406520\pi$
$20$	−3.00000	+	1.73205i	−0.150000	+	0.0866025i
$21$	−3.00000	+	5.19615i	−0.142857	+	0.247436i
$22$	1.50000	−	2.59808i	0.0681818	−	0.118094i
$23$	−24.0000	−	13.8564i	−1.04348	−	0.602452i	−0.122662	−	0.992449i	$-0.539143\pi$
$23$	−24.0000	−	13.8564i	−1.04348	−	0.602452i	−0.920817	+	0.389996i	$0.872476\pi$
$24$	−22.5000	+	12.9904i	−0.937500	+	0.541266i
$25$	−6.50000	−	11.2583i	−0.260000	−	0.450333i
$26$			6.92820i			0.266469i
$27$	27.0000			1.00000
$28$	2.00000			0.0714286
$29$	39.0000	−	22.5167i	1.34483	−	0.776437i	0.357316	−	0.933984i	$-0.383692\pi$
$29$	39.0000	−	22.5167i	1.34483	−	0.776437i	0.987511	+	0.157547i	$0.0503586\pi$
$30$	9.00000	+	15.5885i	0.300000	+	0.519615i
$31$	−16.0000	+	27.7128i	−0.516129	+	0.893962i	0.483696	+	0.875236i	$0.339294\pi$
$31$	−16.0000	+	27.7128i	−0.516129	+	0.893962i	−0.999825	+	0.0187254i	$0.994039\pi$
$32$	13.5000	+	7.79423i	0.421875	+	0.243570i
$33$	4.50000	+	2.59808i	0.136364	+	0.0787296i
$34$	−13.5000	−	23.3827i	−0.397059	−	0.687726i
$35$		−	6.92820i		−	0.197949i
$36$	−4.50000	−	7.79423i	−0.125000	−	0.216506i
$37$	−34.0000			−0.918919			−0.459459	−	0.888199i	$-0.651957\pi$
$37$	−34.0000			−0.918919			−0.459459	+	0.888199i	$0.651957\pi$
$38$	−16.5000	+	9.52628i	−0.434211	+	0.250692i
$39$	−12.0000			−0.307692
$40$	15.0000	−	25.9808i	0.375000	−	0.649519i
$41$	−10.5000	−	6.06218i	−0.256098	−	0.147858i	0.366456	−	0.930436i	$-0.380571\pi$
$41$	−10.5000	−	6.06218i	−0.256098	−	0.147858i	−0.622553	+	0.782578i	$0.713905\pi$
$42$		−	10.3923i		−	0.247436i
$43$	30.5000	+	52.8275i	0.709302	+	1.22855i	0.965116	+	0.261822i	$0.0843232\pi$
$43$	30.5000	+	52.8275i	0.709302	+	1.22855i	−0.255814	+	0.966726i	$0.582343\pi$
$44$		−	1.73205i		−	0.0393648i
$45$	−27.0000	+	15.5885i	−0.600000	+	0.346410i
$46$	48.0000			1.04348
$47$	−42.0000	+	24.2487i	−0.893617	+	0.515930i	−0.875124	−	0.483899i	$-0.839220\pi$
$47$	−42.0000	+	24.2487i	−0.893617	+	0.515930i	−0.0184931	+	0.999829i	$0.505887\pi$
$48$	16.5000	−	28.5788i	0.343750	−	0.595392i
$49$	22.5000	−	38.9711i	0.459184	−	0.795329i
$50$	19.5000	+	11.2583i	0.390000	+	0.225167i
$51$	40.5000	−	23.3827i	0.794118	−	0.458484i
$52$	2.00000	+	3.46410i	0.0384615	+	0.0666173i
$53$		0			0		1.00000			$0$
$53$		0			0		−1.00000			$\pi$
$54$	−40.5000	+	23.3827i	−0.750000	+	0.433013i
$55$	−6.00000			−0.109091
$56$	−15.0000	+	8.66025i	−0.267857	+	0.154647i
$57$	−16.5000	−	28.5788i	−0.289474	−	0.501383i
$58$	−39.0000	+	67.5500i	−0.672414	+	1.16465i
$59$	43.5000	+	25.1147i	0.737288	+	0.425674i	0.821082	−	0.570810i	$-0.193371\pi$
$59$	43.5000	+	25.1147i	0.737288	+	0.425674i	−0.0837943	+	0.996483i	$0.526704\pi$
$60$	9.00000	+	5.19615i	0.150000	+	0.0866025i
$61$	−28.0000	−	48.4974i	−0.459016	−	0.795040i	0.539893	−	0.841734i	$-0.318465\pi$
$61$	−28.0000	−	48.4974i	−0.459016	−	0.795040i	−0.998909	+	0.0466940i	$0.985131\pi$
$62$		−	55.4256i		−	0.893962i
$63$	18.0000			0.285714
$64$	−71.0000			−1.10938
$65$	12.0000	−	6.92820i	0.184615	−	0.106588i
$66$	−9.00000			−0.136364
$67$	15.5000	−	26.8468i	0.231343	−	0.400698i	−0.726860	−	0.686785i	$-0.759021\pi$
$67$	15.5000	−	26.8468i	0.231343	−	0.400698i	0.958204	+	0.286087i	$0.0923546\pi$
$68$	−13.5000	−	7.79423i	−0.198529	−	0.114621i
$69$			83.1384i			1.20490i
$70$	6.00000	+	10.3923i	0.0857143	+	0.148461i
$71$		−	31.1769i		−	0.439111i	−0.975600	−	0.219556i	$-0.929539\pi$
$71$		−	31.1769i		−	0.439111i	0.975600	−	0.219556i	$-0.0704608\pi$
$72$	67.5000	+	38.9711i	0.937500	+	0.541266i
$73$	65.0000			0.890411			0.445205	−	0.895428i	$-0.353131\pi$
$73$	65.0000			0.890411			0.445205	+	0.895428i	$0.353131\pi$
$74$	51.0000	−	29.4449i	0.689189	−	0.397904i
$75$	−19.5000	+	33.7750i	−0.260000	+	0.450333i
$76$	−5.50000	+	9.52628i	−0.0723684	+	0.125346i
$77$	3.00000	+	1.73205i	0.0389610	+	0.0224942i
$78$	18.0000	−	10.3923i	0.230769	−	0.133235i
$79$	−19.0000	−	32.9090i	−0.240506	−	0.416569i	0.720352	−	0.693608i	$-0.243980\pi$
$79$	−19.0000	−	32.9090i	−0.240506	−	0.416569i	−0.960859	+	0.277039i	$0.910647\pi$
$80$			38.1051i			0.476314i
$81$	−40.5000	−	70.1481i	−0.500000	−	0.866025i
$82$	21.0000			0.256098
$83$	−42.0000	+	24.2487i	−0.506024	+	0.292153i	−0.731198	−	0.682165i	$-0.761038\pi$
$83$	−42.0000	+	24.2487i	−0.506024	+	0.292153i	0.225174	+	0.974319i	$0.427705\pi$
$84$	−3.00000	−	5.19615i	−0.0357143	−	0.0618590i
$85$	−27.0000	+	46.7654i	−0.317647	+	0.550181i
$86$	−91.5000	−	52.8275i	−1.06395	−	0.614274i
$87$	−117.000	−	67.5500i	−1.34483	−	0.776437i
$88$	7.50000	+	12.9904i	0.0852273	+	0.147618i
$89$			124.708i			1.40121i	0.713549	+	0.700605i	$0.247086\pi$
$89$			124.708i			1.40121i	−0.713549	+	0.700605i	$0.752914\pi$
$90$	27.0000	−	46.7654i	0.300000	−	0.519615i
$91$	−8.00000			−0.0879121
$92$	24.0000	−	13.8564i	0.260870	−	0.150613i
$93$	96.0000			1.03226
$94$	42.0000	−	72.7461i	0.446809	−	0.773895i
$95$	33.0000	+	19.0526i	0.347368	+	0.200553i
$96$		−	46.7654i		−	0.487139i
$97$	57.5000	+	99.5929i	0.592784	+	1.02673i	0.993856	+	0.110685i	$0.0353044\pi$
$97$	57.5000	+	99.5929i	0.592784	+	1.02673i	−0.401072	+	0.916047i	$0.631362\pi$
$98$			77.9423i			0.795329i
$99$		−	15.5885i		−	0.157459i
$100$	13.0000			0.130000
$101$	39.0000	−	22.5167i	0.386139	−	0.222937i	−0.294347	−	0.955699i	$-0.595102\pi$
$101$	39.0000	−	22.5167i	0.386139	−	0.222937i	0.680486	+	0.732761i	$0.261769\pi$
$102$	−40.5000	+	70.1481i	−0.397059	+	0.687726i
$103$	20.0000	−	34.6410i	0.194175	−	0.336321i	−0.752455	−	0.658644i	$-0.771130\pi$
$103$	20.0000	−	34.6410i	0.194175	−	0.336321i	0.946630	+	0.322323i	$0.104464\pi$
$104$	−30.0000	−	17.3205i	−0.288462	−	0.166543i
$105$	−18.0000	+	10.3923i	−0.171429	+	0.0989743i
$106$		0			0
$107$		−	140.296i		−	1.31118i	−0.755118	−	0.655589i	$-0.772420\pi$
$107$		−	140.296i		−	1.31118i	0.755118	−	0.655589i	$-0.227580\pi$
$108$	−13.5000	+	23.3827i	−0.125000	+	0.216506i
$109$	−52.0000			−0.477064			−0.238532	−	0.971135i	$-0.576666\pi$
$109$	−52.0000			−0.477064			−0.238532	+	0.971135i	$0.576666\pi$
$110$	9.00000	−	5.19615i	0.0818182	−	0.0472377i
$111$	51.0000	+	88.3346i	0.459459	+	0.795807i
$112$	11.0000	−	19.0526i	0.0982143	−	0.170112i
$113$	−78.0000	−	45.0333i	−0.690265	−	0.398525i	0.113446	−	0.993544i	$-0.463811\pi$
$113$	−78.0000	−	45.0333i	−0.690265	−	0.398525i	−0.803711	+	0.595019i	$0.797144\pi$
$114$	49.5000	+	28.5788i	0.434211	+	0.250692i
$115$	−48.0000	−	83.1384i	−0.417391	−	0.722943i
$116$			45.0333i			0.388218i
$117$	18.0000	+	31.1769i	0.153846	+	0.266469i
$118$	−87.0000			−0.737288
$119$	27.0000	−	15.5885i	0.226891	−	0.130995i
$120$	−90.0000			−0.750000
$121$	−59.0000	+	102.191i	−0.487603	+	0.844554i
$122$	84.0000	+	48.4974i	0.688525	+	0.397520i
$123$			36.3731i			0.295716i
$124$	−16.0000	−	27.7128i	−0.129032	−	0.223490i
$125$		−	131.636i		−	1.05309i
$126$	−27.0000	+	15.5885i	−0.214286	+	0.123718i
$127$	−16.0000			−0.125984			−0.0629921	−	0.998014i	$-0.520064\pi$
$127$	−16.0000			−0.125984			−0.0629921	+	0.998014i	$0.520064\pi$
$128$	52.5000	−	30.3109i	0.410156	−	0.236804i
$129$	91.5000	−	158.483i	0.709302	−	1.22855i
$130$	−12.0000	+	20.7846i	−0.0923077	+	0.159882i
$131$	138.000	+	79.6743i	1.05344	+	0.608201i	0.923609	−	0.383336i	$-0.125225\pi$
$131$	138.000	+	79.6743i	1.05344	+	0.608201i	0.129826	+	0.991537i	$0.458558\pi$
$132$	−4.50000	+	2.59808i	−0.0340909	+	0.0196824i
$133$	−11.0000	−	19.0526i	−0.0827068	−	0.143252i
$134$			53.6936i			0.400698i
$135$	81.0000	+	46.7654i	0.600000	+	0.346410i
$136$	135.000			0.992647
$137$	−163.500	+	94.3968i	−1.19343	+	0.689028i	−0.959083	−	0.283125i	$-0.908629\pi$
$137$	−163.500	+	94.3968i	−1.19343	+	0.689028i	−0.234348	+	0.972153i	$0.575295\pi$
$138$	−72.0000	−	124.708i	−0.521739	−	0.903679i
$139$	−2.50000	+	4.33013i	−0.0179856	+	0.0311520i	−0.874878	−	0.484343i	$-0.839059\pi$
$139$	−2.50000	+	4.33013i	−0.0179856	+	0.0311520i	0.856893	+	0.515495i	$0.172392\pi$
$140$	6.00000	+	3.46410i	0.0428571	+	0.0247436i
$141$	126.000	+	72.7461i	0.893617	+	0.515930i
$142$	27.0000	+	46.7654i	0.190141	+	0.329334i
$143$			6.92820i			0.0484490i
$144$	−99.0000			−0.687500
$145$	156.000			1.07586
$146$	−97.5000	+	56.2917i	−0.667808	+	0.385559i
$147$	−135.000			−0.918367
$148$	17.0000	−	29.4449i	0.114865	−	0.198952i
$149$	−132.000	−	76.2102i	−0.885906	−	0.511478i	−0.0133049	−	0.999911i	$-0.504235\pi$
$149$	−132.000	−	76.2102i	−0.885906	−	0.511478i	−0.872601	+	0.488433i	$0.837569\pi$
$150$		−	67.5500i		−	0.450333i
$151$	−10.0000	−	17.3205i	−0.0662252	−	0.114705i	0.831012	−	0.556255i	$-0.187762\pi$
$151$	−10.0000	−	17.3205i	−0.0662252	−	0.114705i	−0.897237	+	0.441550i	$0.854429\pi$
$152$		−	95.2628i		−	0.626729i
$153$	−121.500	−	70.1481i	−0.794118	−	0.458484i
$154$	−6.00000			−0.0389610
$155$	−96.0000	+	55.4256i	−0.619355	+	0.357585i
$156$	6.00000	−	10.3923i	0.0384615	−	0.0666173i
$157$	20.0000	−	34.6410i	0.127389	−	0.220643i	−0.795276	−	0.606248i	$-0.792674\pi$
$157$	20.0000	−	34.6410i	0.127389	−	0.220643i	0.922664	+	0.385605i	$0.126007\pi$
$158$	57.0000	+	32.9090i	0.360759	+	0.208285i
$159$		0			0
$160$	27.0000	+	46.7654i	0.168750	+	0.292284i
$161$			55.4256i			0.344259i
$162$	121.500	+	70.1481i	0.750000	+	0.433013i
$163$	−106.000			−0.650307			−0.325153	−	0.945661i	$-0.605416\pi$
$163$	−106.000			−0.650307			−0.325153	+	0.945661i	$0.605416\pi$
$164$	10.5000	−	6.06218i	0.0640244	−	0.0369645i
$165$	9.00000	+	15.5885i	0.0545455	+	0.0944755i
$166$	42.0000	−	72.7461i	0.253012	−	0.438230i
$167$	165.000	+	95.2628i	0.988024	+	0.570436i	0.904683	−	0.426085i	$-0.140108\pi$
$167$	165.000	+	95.2628i	0.988024	+	0.570436i	0.0833409	+	0.996521i	$0.473441\pi$
$168$	45.0000	+	25.9808i	0.267857	+	0.154647i
$169$	76.5000	+	132.502i	0.452663	+	0.784035i
$170$		−	93.5307i		−	0.550181i
$171$	−49.5000	+	85.7365i	−0.289474	+	0.501383i
$172$	−61.0000			−0.354651
$173$	201.000	−	116.047i	1.16185	−	0.670794i	0.210103	−	0.977679i	$-0.432620\pi$
$173$	201.000	−	116.047i	1.16185	−	0.670794i	0.951747	+	0.306885i	$0.0992867\pi$
$174$	234.000			1.34483
$175$	−13.0000	+	22.5167i	−0.0742857	+	0.128667i
$176$	−16.5000	−	9.52628i	−0.0937500	−	0.0541266i
$177$		−	150.688i		−	0.851347i
$178$	−108.000	−	187.061i	−0.606742	−	1.05091i
$179$			62.3538i			0.348345i	0.984715	+	0.174173i	$0.0557251\pi$
$179$			62.3538i			0.348345i	−0.984715	+	0.174173i	$0.944275\pi$
$180$		−	31.1769i		−	0.173205i
$181$	−232.000			−1.28177			−0.640884	−	0.767638i	$-0.721432\pi$
$181$	−232.000			−1.28177			−0.640884	+	0.767638i	$0.721432\pi$
$182$	12.0000	−	6.92820i	0.0659341	−	0.0380671i
$183$	−84.0000	+	145.492i	−0.459016	+	0.795040i
$184$	−120.000	+	207.846i	−0.652174	+	1.12960i
$185$	−102.000	−	58.8897i	−0.551351	−	0.318323i
$186$	−144.000	+	83.1384i	−0.774194	+	0.446981i
$187$	−13.5000	−	23.3827i	−0.0721925	−	0.125041i
$188$		−	48.4974i		−	0.257965i
$189$	−27.0000	−	46.7654i	−0.142857	−	0.247436i
$190$	−66.0000			−0.347368
$191$	201.000	−	116.047i	1.05236	−	0.607578i	0.129048	−	0.991638i	$-0.458808\pi$
$191$	201.000	−	116.047i	1.05236	−	0.607578i	0.923308	+	0.384060i	$0.125475\pi$
$192$	106.500	+	184.463i	0.554688	+	0.960747i
$193$	132.500	−	229.497i	0.686528	−	1.18910i	−0.286425	−	0.958103i	$-0.592467\pi$
$193$	132.500	−	229.497i	0.686528	−	1.18910i	0.972954	−	0.231000i	$-0.0741996\pi$
$194$	−172.500	−	99.5929i	−0.889175	−	0.513366i
$195$	−36.0000	−	20.7846i	−0.184615	−	0.106588i
$196$	22.5000	+	38.9711i	0.114796	+	0.198832i
$197$			124.708i			0.633034i	0.948587	+	0.316517i	$0.102513\pi$
$197$			124.708i			0.633034i	−0.948587	+	0.316517i	$0.897487\pi$
$198$	13.5000	+	23.3827i	0.0681818	+	0.118094i
$199$	290.000			1.45729			0.728643	−	0.684893i	$-0.240151\pi$
$199$	290.000			1.45729			0.728643	+	0.684893i	$0.240151\pi$
$200$	−97.5000	+	56.2917i	−0.487500	+	0.281458i
$201$	−93.0000			−0.462687
$202$	−39.0000	+	67.5500i	−0.193069	+	0.334406i
$203$	−78.0000	−	45.0333i	−0.384236	−	0.221839i
$204$			46.7654i			0.229242i
$205$	−21.0000	−	36.3731i	−0.102439	−	0.177430i
$206$			69.2820i			0.336321i
$207$	216.000	−	124.708i	1.04348	−	0.602452i
$208$	44.0000			0.211538
$209$	−16.5000	+	9.52628i	−0.0789474	+	0.0455803i
$210$	18.0000	−	31.1769i	0.0857143	−	0.148461i
$211$	47.0000	−	81.4064i	0.222749	−	0.385812i	−0.732893	−	0.680344i	$-0.761830\pi$
$211$	47.0000	−	81.4064i	0.222749	−	0.385812i	0.955642	+	0.294532i	$0.0951637\pi$
$212$		0			0
$213$	−81.0000	+	46.7654i	−0.380282	+	0.219556i
$214$	121.500	+	210.444i	0.567757	+	0.983384i
$215$			211.310i			0.982838i
$216$		−	233.827i		−	1.08253i
$217$	64.0000			0.294931
$218$	78.0000	−	45.0333i	0.357798	−	0.206575i
$219$	−97.5000	−	168.875i	−0.445205	−	0.771119i
$220$	3.00000	−	5.19615i	0.0136364	−	0.0236189i
$221$	54.0000	+	31.1769i	0.244344	+	0.141072i
$222$	−153.000	−	88.3346i	−0.689189	−	0.397904i
$223$	26.0000	+	45.0333i	0.116592	+	0.201943i	0.918415	−	0.395618i	$-0.129470\pi$
$223$	26.0000	+	45.0333i	0.116592	+	0.201943i	−0.801823	+	0.597562i	$0.796136\pi$
$224$		−	31.1769i		−	0.139183i
$225$	117.000			0.520000
$226$	156.000			0.690265
$227$	−163.500	+	94.3968i	−0.720264	+	0.415845i	−0.814850	−	0.579672i	$-0.803181\pi$
$227$	−163.500	+	94.3968i	−0.720264	+	0.415845i	0.0945856	+	0.995517i	$0.469847\pi$
$228$	33.0000			0.144737
$229$	−133.000	+	230.363i	−0.580786	+	1.00595i	0.414600	+	0.910004i	$0.363921\pi$
$229$	−133.000	+	230.363i	−0.580786	+	1.00595i	−0.995386	+	0.0959473i	$0.969412\pi$
$230$	144.000	+	83.1384i	0.626087	+	0.361471i
$231$		−	10.3923i		−	0.0449883i
$232$	−195.000	−	337.750i	−0.840517	−	1.45582i
$233$			202.650i			0.869742i	0.900493	+	0.434871i	$0.143206\pi$
$233$			202.650i			0.869742i	−0.900493	+	0.434871i	$0.856794\pi$
$234$	−54.0000	−	31.1769i	−0.230769	−	0.133235i
$235$	−168.000			−0.714894
$236$	−43.5000	+	25.1147i	−0.184322	+	0.106418i
$237$	−57.0000	+	98.7269i	−0.240506	+	0.416569i
$238$	−27.0000	+	46.7654i	−0.113445	+	0.196493i
$239$	−348.000	−	200.918i	−1.45607	−	0.840661i	−0.457252	−	0.889337i	$-0.651166\pi$
$239$	−348.000	−	200.918i	−1.45607	−	0.840661i	−0.998815	+	0.0486764i	$0.984500\pi$
$240$	99.0000	−	57.1577i	0.412500	−	0.238157i
$241$	−59.5000	−	103.057i	−0.246888	−	0.427623i	0.715773	−	0.698333i	$-0.246075\pi$
$241$	−59.5000	−	103.057i	−0.246888	−	0.427623i	−0.962661	+	0.270711i	$0.912741\pi$
$242$		−	204.382i		−	0.844554i
$243$	−121.500	+	210.444i	−0.500000	+	0.866025i
$244$	56.0000			0.229508
$245$	135.000	−	77.9423i	0.551020	−	0.318132i
$246$	−31.5000	−	54.5596i	−0.128049	−	0.221787i
$247$	22.0000	−	38.1051i	0.0890688	−	0.154272i
$248$	240.000	+	138.564i	0.967742	+	0.558726i
$249$	126.000	+	72.7461i	0.506024	+	0.292153i
$250$	114.000	+	197.454i	0.456000	+	0.789815i
$251$		−	389.711i		−	1.55264i	−0.630342	−	0.776318i	$-0.717085\pi$
$251$		−	389.711i		−	1.55264i	0.630342	−	0.776318i	$-0.282915\pi$
$252$	−9.00000	+	15.5885i	−0.0357143	+	0.0618590i
$253$	48.0000			0.189723
$254$	24.0000	−	13.8564i	0.0944882	−	0.0545528i
$255$	162.000			0.635294
$256$	89.5000	−	155.019i	0.349609	−	0.605541i
$257$	151.500	+	87.4686i	0.589494	+	0.340345i	0.764897	−	0.644152i	$-0.222790\pi$
$257$	151.500	+	87.4686i	0.589494	+	0.340345i	−0.175403	+	0.984497i	$0.556123\pi$
$258$			316.965i			1.22855i
$259$	34.0000	+	58.8897i	0.131274	+	0.227373i
$260$			13.8564i			0.0532939i
$261$			405.300i			1.55287i
$262$	−276.000			−1.05344
$263$	39.0000	−	22.5167i	0.148289	−	0.0856147i	−0.424020	−	0.905653i	$-0.639381\pi$
$263$	39.0000	−	22.5167i	0.148289	−	0.0856147i	0.572309	+	0.820038i	$0.306048\pi$
$264$	22.5000	−	38.9711i	0.0852273	−	0.147618i
$265$		0			0
$266$	33.0000	+	19.0526i	0.124060	+	0.0716262i
$267$	324.000	−	187.061i	1.21348	−	0.700605i
$268$	15.5000	+	26.8468i	0.0578358	+	0.100175i
$269$		−	187.061i		−	0.695396i	−0.937607	−	0.347698i	$-0.886963\pi$
$269$		−	187.061i		−	0.695396i	0.937607	−	0.347698i	$-0.113037\pi$
$270$	−162.000			−0.600000
$271$	−268.000			−0.988930			−0.494465	−	0.869198i	$-0.664636\pi$
$271$	−268.000			−0.988930			−0.494465	+	0.869198i	$0.664636\pi$
$272$	−148.500	+	85.7365i	−0.545956	+	0.315208i
$273$	12.0000	+	20.7846i	0.0439560	+	0.0761341i
$274$	163.500	−	283.190i	0.596715	−	1.03354i
$275$	19.5000	+	11.2583i	0.0709091	+	0.0409394i
$276$	−72.0000	−	41.5692i	−0.260870	−	0.150613i
$277$	−28.0000	−	48.4974i	−0.101083	−	0.175081i	0.811048	−	0.584979i	$-0.198897\pi$
$277$	−28.0000	−	48.4974i	−0.101083	−	0.175081i	−0.912131	+	0.409899i	$0.865564\pi$
$278$		−	8.66025i		−	0.0311520i
$279$	−144.000	−	249.415i	−0.516129	−	0.893962i
$280$	−60.0000			−0.214286
$281$	−42.0000	+	24.2487i	−0.149466	+	0.0862943i	−0.572868	−	0.819648i	$-0.694169\pi$
$281$	−42.0000	+	24.2487i	−0.149466	+	0.0862943i	0.423402	+	0.905942i	$0.360836\pi$
$282$	−252.000			−0.893617
$283$	−187.000	+	323.894i	−0.660777	+	1.14450i	0.319634	+	0.947541i	$0.396440\pi$
$283$	−187.000	+	323.894i	−0.660777	+	1.14450i	−0.980412	+	0.196959i	$0.936893\pi$
$284$	27.0000	+	15.5885i	0.0950704	+	0.0548889i
$285$		−	114.315i		−	0.401107i
$286$	−6.00000	−	10.3923i	−0.0209790	−	0.0363367i
$287$			24.2487i			0.0844903i
$288$	−121.500	+	70.1481i	−0.421875	+	0.243570i
$289$	46.0000			0.159170
$290$	−234.000	+	135.100i	−0.806897	+	0.465862i
$291$	172.500	−	298.779i	0.592784	−	1.02673i
$292$	−32.5000	+	56.2917i	−0.111301	+	0.192780i
$293$	219.000	+	126.440i	0.747440	+	0.431535i	0.824768	−	0.565471i	$-0.191306\pi$
$293$	219.000	+	126.440i	0.747440	+	0.431535i	−0.0773280	+	0.997006i	$0.524639\pi$
$294$	202.500	−	116.913i	0.688776	−	0.397665i
$295$	87.0000	+	150.688i	0.294915	+	0.510808i
$296$			294.449i			0.994759i
$297$	−40.5000	+	23.3827i	−0.136364	+	0.0787296i
$298$	264.000			0.885906
$299$	−96.0000	+	55.4256i	−0.321070	+	0.185370i
$300$	−19.5000	−	33.7750i	−0.0650000	−	0.112583i
$301$	61.0000	−	105.655i	0.202658	−	0.351014i
$302$	30.0000	+	17.3205i	0.0993377	+	0.0573527i
$303$	−117.000	−	67.5500i	−0.386139	−	0.222937i
$304$	60.5000	+	104.789i	0.199013	+	0.344701i
$305$		−	193.990i		−	0.636032i
$306$	243.000			0.794118
$307$	533.000			1.73616			0.868078	−	0.496428i	$-0.165355\pi$
$307$	533.000			1.73616			0.868078	+	0.496428i	$0.165355\pi$
$308$	−3.00000	+	1.73205i	−0.00974026	+	0.00562354i
$309$	−120.000			−0.388350
$310$	96.0000	−	166.277i	0.309677	−	0.536377i
$311$	−213.000	−	122.976i	−0.684887	−	0.395420i	0.116806	−	0.993155i	$-0.462734\pi$
$311$	−213.000	−	122.976i	−0.684887	−	0.395420i	−0.801694	+	0.597735i	$0.796068\pi$
$312$			103.923i			0.333087i
$313$	−77.5000	−	134.234i	−0.247604	−	0.428862i	0.715257	−	0.698862i	$-0.246310\pi$
$313$	−77.5000	−	134.234i	−0.247604	−	0.428862i	−0.962860	+	0.269999i	$0.912976\pi$
$314$			69.2820i			0.220643i
$315$	54.0000	+	31.1769i	0.171429	+	0.0989743i
$316$	38.0000			0.120253
$317$	−42.0000	+	24.2487i	−0.132492	+	0.0764944i	−0.564781	−	0.825241i	$-0.691039\pi$
$317$	−42.0000	+	24.2487i	−0.132492	+	0.0764944i	0.432289	+	0.901735i	$0.357706\pi$
$318$		0			0
$319$	−39.0000	+	67.5500i	−0.122257	+	0.211755i
$320$	−213.000	−	122.976i	−0.665625	−	0.384299i
$321$	−364.500	+	210.444i	−1.13551	+	0.655589i
$322$	−48.0000	−	83.1384i	−0.149068	−	0.258194i
$323$			171.473i			0.530876i
$324$	81.0000			0.250000
$325$	−52.0000			−0.160000
$326$	159.000	−	91.7987i	0.487730	−	0.281591i
$327$	78.0000	+	135.100i	0.238532	+	0.413150i
$328$	−52.5000	+	90.9327i	−0.160061	+	0.277234i
$329$	84.0000	+	48.4974i	0.255319	+	0.147409i
$330$	−27.0000	−	15.5885i	−0.0818182	−	0.0472377i
$331$	−1.00000	−	1.73205i	−0.00302115	−	0.00523278i	0.864511	−	0.502614i	$-0.167628\pi$
$331$	−1.00000	−	1.73205i	−0.00302115	−	0.00523278i	−0.867532	+	0.497381i	$0.834295\pi$
$332$		−	48.4974i		−	0.146077i
$333$	153.000	−	265.004i	0.459459	−	0.795807i
$334$	−330.000			−0.988024
$335$	93.0000	−	53.6936i	0.277612	−	0.160279i
$336$	−66.0000			−0.196429
$337$	−38.5000	+	66.6840i	−0.114243	+	0.197875i	−0.917477	−	0.397789i	$-0.869778\pi$
$337$	−38.5000	+	66.6840i	−0.114243	+	0.197875i	0.803234	+	0.595664i	$0.203111\pi$
$338$	−229.500	−	132.502i	−0.678994	−	0.392017i
$339$			270.200i			0.797050i
$340$	−27.0000	−	46.7654i	−0.0794118	−	0.137545i
$341$		−	55.4256i		−	0.162538i
$342$		−	171.473i		−	0.501383i
$343$	−188.000			−0.548105
$344$	457.500	−	264.138i	1.32994	−	0.767842i
$345$	−144.000	+	249.415i	−0.417391	+	0.722943i
$346$	−201.000	+	348.142i	−0.580925	+	1.00619i
$347$	97.5000	+	56.2917i	0.280980	+	0.162224i	0.633867	−	0.773442i	$-0.281467\pi$
$347$	97.5000	+	56.2917i	0.280980	+	0.162224i	−0.352887	+	0.935666i	$0.614800\pi$
$348$	117.000	−	67.5500i	0.336207	−	0.194109i
$349$	−208.000	−	360.267i	−0.595989	−	1.03228i	−0.993407	−	0.114645i	$-0.963427\pi$
$349$	−208.000	−	360.267i	−0.595989	−	1.03228i	0.397418	−	0.917638i	$-0.369906\pi$
$350$		−	45.0333i		−	0.128667i
$351$	54.0000	−	93.5307i	0.153846	−	0.266469i
$352$	−27.0000			−0.0767045
$353$	−1.50000	+	0.866025i	−0.00424929	+	0.00245333i	−0.502123	−	0.864796i	$-0.667448\pi$
$353$	−1.50000	+	0.866025i	−0.00424929	+	0.00245333i	0.497874	+	0.867249i	$0.334114\pi$
$354$	130.500	+	226.033i	0.368644	+	0.638510i
$355$	54.0000	−	93.5307i	0.152113	−	0.263467i
$356$	−108.000	−	62.3538i	−0.303371	−	0.175151i
$357$	−81.0000	−	46.7654i	−0.226891	−	0.130995i
$358$	−54.0000	−	93.5307i	−0.150838	−	0.261259i
$359$			592.361i			1.65003i	0.565110	+	0.825016i	$0.308834\pi$
$359$			592.361i			1.65003i	−0.565110	+	0.825016i	$0.691166\pi$
$360$	135.000	+	233.827i	0.375000	+	0.649519i
$361$	−240.000			−0.664820
$362$	348.000	−	200.918i	0.961326	−	0.555022i
$363$	354.000			0.975207
$364$	4.00000	−	6.92820i	0.0109890	−	0.0190335i
$365$	195.000	+	112.583i	0.534247	+	0.308447i
$366$		−	290.985i		−	0.795040i
$367$	179.000	+	310.037i	0.487738	+	0.844788i	0.999901	−	0.0141011i	$-0.00448865\pi$
$367$	179.000	+	310.037i	0.487738	+	0.844788i	−0.512162	+	0.858889i	$0.671155\pi$
$368$		−	304.841i		−	0.828372i
$369$	94.5000	−	54.5596i	0.256098	−	0.147858i
$370$	204.000			0.551351
$371$		0			0
$372$	−48.0000	+	83.1384i	−0.129032	+	0.223490i
$373$	290.000	−	502.295i	0.777480	−	1.34663i	−0.155910	−	0.987771i	$-0.549831\pi$
$373$	290.000	−	502.295i	0.777480	−	1.34663i	0.933390	−	0.358863i	$-0.116836\pi$
$374$	40.5000	+	23.3827i	0.108289	+	0.0625206i
$375$	−342.000	+	197.454i	−0.912000	+	0.526543i
$376$	210.000	+	363.731i	0.558511	+	0.967369i
$377$		−	180.133i		−	0.477807i
$378$	81.0000	+	46.7654i	0.214286	+	0.123718i
$379$	83.0000			0.218997			0.109499	−	0.993987i	$-0.465075\pi$
$379$	83.0000			0.218997			0.109499	+	0.993987i	$0.465075\pi$
$380$	−33.0000	+	19.0526i	−0.0868421	+	0.0501383i
$381$	24.0000	+	41.5692i	0.0629921	+	0.109106i
$382$	−201.000	+	348.142i	−0.526178	+	0.911367i
$383$	−483.000	−	278.860i	−1.26110	−	0.728094i	−0.287810	−	0.957688i	$-0.592927\pi$
$383$	−483.000	−	278.860i	−1.26110	−	0.728094i	−0.973287	+	0.229593i	$0.926260\pi$
$384$	−157.500	−	90.9327i	−0.410156	−	0.236804i
$385$	6.00000	+	10.3923i	0.0155844	+	0.0269930i
$386$			458.993i			1.18910i
$387$	−549.000			−1.41860
$388$	−115.000			−0.296392
$389$	−447.000	+	258.076i	−1.14910	+	0.663433i	−0.948668	−	0.316274i	$-0.897568\pi$
$389$	−447.000	+	258.076i	−1.14910	+	0.663433i	−0.200432	+	0.979708i	$0.564235\pi$
$390$	72.0000			0.184615
$391$	216.000	−	374.123i	0.552430	−	0.956836i
$392$	−337.500	−	194.856i	−0.860969	−	0.497081i
$393$		−	478.046i		−	1.21640i
$394$	−108.000	−	187.061i	−0.274112	−	0.474775i
$395$		−	131.636i		−	0.333255i
$396$	13.5000	+	7.79423i	0.0340909	+	0.0196824i
$397$	362.000			0.911839			0.455919	−	0.890021i	$-0.349311\pi$
$397$	362.000			0.911839			0.455919	+	0.890021i	$0.349311\pi$
$398$	−435.000	+	251.147i	−1.09296	+	0.631024i
$399$	−33.0000	+	57.1577i	−0.0827068	+	0.143252i
$400$	71.5000	−	123.842i	0.178750	−	0.309604i
$401$	340.500	+	196.588i	0.849127	+	0.490244i	0.860356	−	0.509693i	$-0.170241\pi$
$401$	340.500	+	196.588i	0.849127	+	0.490244i	−0.0112291	+	0.999937i	$0.503574\pi$
$402$	139.500	−	80.5404i	0.347015	−	0.200349i
$403$	64.0000	+	110.851i	0.158809	+	0.275065i
$404$			45.0333i			0.111469i
$405$		−	280.592i		−	0.692820i
$406$	156.000			0.384236
$407$	51.0000	−	29.4449i	0.125307	−	0.0723461i
$408$	−202.500	−	350.740i	−0.496324	−	0.859658i
$409$	−110.500	+	191.392i	−0.270171	+	0.467950i	−0.968905	−	0.247431i	$-0.920414\pi$
$409$	−110.500	+	191.392i	−0.270171	+	0.467950i	0.698734	+	0.715381i	$0.253747\pi$
$410$	63.0000	+	36.3731i	0.153659	+	0.0887148i
$411$	490.500	+	283.190i	1.19343	+	0.689028i
$412$	20.0000	+	34.6410i	0.0485437	+	0.0840801i
$413$		−	100.459i		−	0.243242i
$414$	−216.000	+	374.123i	−0.521739	+	0.903679i
$415$	−168.000			−0.404819
$416$	54.0000	−	31.1769i	0.129808	−	0.0749445i
$417$	15.0000			0.0359712
$418$	16.5000	−	28.5788i	0.0394737	−	0.0683704i
$419$	678.000	+	391.443i	1.61814	+	0.934233i	0.987401	+	0.158236i	$0.0505807\pi$
$419$	678.000	+	391.443i	1.61814	+	0.934233i	0.630737	+	0.775997i	$0.282753\pi$
$420$		−	20.7846i		−	0.0494872i
$421$	341.000	+	590.629i	0.809976	+	1.40292i	0.912880	+	0.408229i	$0.133853\pi$
$421$	341.000	+	590.629i	0.809976	+	1.40292i	−0.102903	+	0.994691i	$0.532813\pi$
$422$			162.813i			0.385812i
$423$		−	436.477i		−	1.03186i
$424$		0			0
$425$	175.500	−	101.325i	0.412941	−	0.238412i
$426$	81.0000	−	140.296i	0.190141	−	0.329334i
$427$	−56.0000	+	96.9948i	−0.131148	+	0.227154i
$428$	121.500	+	70.1481i	0.283879	+	0.163897i
$429$	18.0000	−	10.3923i	0.0419580	−	0.0242245i
$430$	−183.000	−	316.965i	−0.425581	−	0.737129i
$431$		−	280.592i		−	0.651026i	−0.945538	−	0.325513i	$-0.894463\pi$
$431$		−	280.592i		−	0.651026i	0.945538	−	0.325513i	$-0.105537\pi$
$432$	148.500	+	257.210i	0.343750	+	0.595392i
$433$	−295.000			−0.681293			−0.340647	−	0.940191i	$-0.610646\pi$
$433$	−295.000			−0.681293			−0.340647	+	0.940191i	$0.610646\pi$
$434$	−96.0000	+	55.4256i	−0.221198	+	0.127709i
$435$	−234.000	−	405.300i	−0.537931	−	0.931724i
$436$	26.0000	−	45.0333i	0.0596330	−	0.103287i
$437$	−264.000	−	152.420i	−0.604119	−	0.348788i
$438$	292.500	+	168.875i	0.667808	+	0.385559i
$439$	−406.000	−	703.213i	−0.924829	−	1.60185i	−0.791836	−	0.610734i	$-0.790874\pi$
$439$	−406.000	−	703.213i	−0.924829	−	1.60185i	−0.132993	−	0.991117i	$-0.542459\pi$
$440$			51.9615i			0.118094i
$441$	202.500	+	350.740i	0.459184	+	0.795329i
$442$	−108.000			−0.244344
$443$	79.5000	−	45.8993i	0.179458	−	0.103610i	−0.407580	−	0.913170i	$-0.633627\pi$
$443$	79.5000	−	45.8993i	0.179458	−	0.103610i	0.587038	+	0.809559i	$0.300294\pi$
$444$	−102.000			−0.229730
$445$	−216.000	+	374.123i	−0.485393	+	0.840726i
$446$	−78.0000	−	45.0333i	−0.174888	−	0.100972i
$447$			457.261i			1.02296i
$448$	71.0000	+	122.976i	0.158482	+	0.274499i
$449$		−	639.127i		−	1.42344i	−0.702461	−	0.711722i	$-0.747915\pi$
$449$		−	639.127i		−	1.42344i	0.702461	−	0.711722i	$-0.252085\pi$
$450$	−175.500	+	101.325i	−0.390000	+	0.225167i
$451$	21.0000			0.0465632
$452$	78.0000	−	45.0333i	0.172566	−	0.0996312i
$453$	−30.0000	+	51.9615i	−0.0662252	+	0.114705i
$454$	163.500	−	283.190i	0.360132	−	0.623767i
$455$	−24.0000	−	13.8564i	−0.0527473	−	0.0304536i
$456$	−247.500	+	142.894i	−0.542763	+	0.313364i
$457$	−32.5000	−	56.2917i	−0.0711160	−	0.123176i	0.828275	−	0.560322i	$-0.189323\pi$
$457$	−32.5000	−	56.2917i	−0.0711160	−	0.123176i	−0.899391	+	0.437146i	$0.855989\pi$
$458$		−	460.726i		−	1.00595i
$459$			420.888i			0.916968i
$460$	96.0000			0.208696
$461$	−690.000	+	398.372i	−1.49675	+	0.864147i	−0.999993	−	0.00374501i	$-0.998808\pi$
$461$	−690.000	+	398.372i	−1.49675	+	0.864147i	−0.496753	+	0.867892i	$0.665475\pi$
$462$	9.00000	+	15.5885i	0.0194805	+	0.0337412i
$463$	−367.000	+	635.663i	−0.792657	+	1.37292i	0.131660	+	0.991295i	$0.457969\pi$
$463$	−367.000	+	635.663i	−0.792657	+	1.37292i	−0.924317	+	0.381627i	$0.875364\pi$
$464$	429.000	+	247.683i	0.924569	+	0.533800i
$465$	288.000	+	166.277i	0.619355	+	0.357585i
$466$	−175.500	−	303.975i	−0.376609	−	0.652307i
$467$		−	202.650i		−	0.433940i	−0.976178	−	0.216970i	$-0.930383\pi$
$467$		−	202.650i		−	0.433940i	0.976178	−	0.216970i	$-0.0696174\pi$
$468$	−36.0000			−0.0769231
$469$	−62.0000			−0.132196
$470$	252.000	−	145.492i	0.536170	−	0.309558i
$471$	−120.000			−0.254777
$472$	217.500	−	376.721i	0.460805	−	0.798138i
$473$	−91.5000	−	52.8275i	−0.193446	−	0.111686i
$474$		−	197.454i		−	0.416569i
$475$	−71.5000	−	123.842i	−0.150526	−	0.260719i
$476$			31.1769i			0.0654977i
$477$		0			0
$478$	696.000			1.45607
$479$	525.000	−	303.109i	1.09603	−	0.632795i	0.160857	−	0.986978i	$-0.448574\pi$
$479$	525.000	−	303.109i	1.09603	−	0.632795i	0.935176	+	0.354183i	$0.115241\pi$
$480$	81.0000	−	140.296i	0.168750	−	0.292284i
$481$	−68.0000	+	117.779i	−0.141372	+	0.244864i
$482$	178.500	+	103.057i	0.370332	+	0.213811i
$483$	144.000	−	83.1384i	0.298137	−	0.172129i
$484$	−59.0000	−	102.191i	−0.121901	−	0.211138i
$485$			398.372i			0.821385i
$486$		−	420.888i		−	0.866025i
$487$	−106.000			−0.217659			−0.108830	−	0.994060i	$-0.534710\pi$
$487$	−106.000			−0.217659			−0.108830	+	0.994060i	$0.534710\pi$
$488$	−420.000	+	242.487i	−0.860656	+	0.496900i
$489$	159.000	+	275.396i	0.325153	+	0.563182i
$490$	−135.000	+	233.827i	−0.275510	+	0.477198i
$491$	−199.500	−	115.181i	−0.406314	−	0.234585i	0.282891	−	0.959152i	$-0.408707\pi$
$491$	−199.500	−	115.181i	−0.406314	−	0.234585i	−0.689205	+	0.724567i	$0.742040\pi$
$492$	−31.5000	−	18.1865i	−0.0640244	−	0.0369645i
$493$	351.000	+	607.950i	0.711968	+	1.23316i
$494$			76.2102i			0.154272i
$495$	27.0000	−	46.7654i	0.0545455	−	0.0944755i
$496$	−352.000			−0.709677
$497$	−54.0000	+	31.1769i	−0.108652	+	0.0627302i
$498$	−252.000			−0.506024
$499$	393.500	−	681.562i	0.788577	−	1.36586i	−0.138261	−	0.990396i	$-0.544151\pi$
$499$	393.500	−	681.562i	0.788577	−	1.36586i	0.926839	−	0.375460i	$-0.122515\pi$
$500$	114.000	+	65.8179i	0.228000	+	0.131636i
$501$		−	571.577i		−	1.14087i
$502$	337.500	+	584.567i	0.672311	+	1.16448i
$503$			623.538i			1.23964i	0.784745	+	0.619819i	$0.212794\pi$
$503$			623.538i			1.23964i	−0.784745	+	0.619819i	$0.787206\pi$
$504$		−	155.885i		−	0.309295i
$505$	156.000			0.308911
$506$	−72.0000	+	41.5692i	−0.142292	+	0.0821526i
$507$	229.500	−	397.506i	0.452663	−	0.784035i
$508$	8.00000	−	13.8564i	0.0157480	−	0.0272764i
$509$	−186.000	−	107.387i	−0.365422	−	0.210977i	0.306034	−	0.952020i	$-0.400998\pi$
$509$	−186.000	−	107.387i	−0.365422	−	0.210977i	−0.671457	+	0.741044i	$0.734331\pi$
$510$	−243.000	+	140.296i	−0.476471	+	0.275090i
$511$	−65.0000	−	112.583i	−0.127202	−	0.220320i
$512$			552.524i			1.07915i
$513$	297.000			0.578947
$514$	−303.000			−0.589494
$515$	120.000	−	69.2820i	0.233010	−	0.134528i
$516$	91.5000	+	158.483i	0.177326	+	0.307137i
$517$	42.0000	−	72.7461i	0.0812379	−	0.140708i
$518$	−102.000	−	58.8897i	−0.196911	−	0.113687i
$519$	−603.000	−	348.142i	−1.16185	−	0.670794i
$520$	−60.0000	−	103.923i	−0.115385	−	0.199852i
$521$		−	202.650i		−	0.388963i	−0.980906	−	0.194482i	$-0.937698\pi$
$521$		−	202.650i		−	0.388963i	0.980906	−	0.194482i	$-0.0623025\pi$
$522$	−351.000	−	607.950i	−0.672414	−	1.16465i
$523$	−250.000			−0.478011			−0.239006	−	0.971018i	$-0.576821\pi$
$523$	−250.000			−0.478011			−0.239006	+	0.971018i	$0.576821\pi$
$524$	−138.000	+	79.6743i	−0.263359	+	0.152050i
$525$	78.0000			0.148571
$526$	−39.0000	+	67.5500i	−0.0741445	+	0.128422i
$527$	−432.000	−	249.415i	−0.819734	−	0.473274i
$528$			57.1577i			0.108253i
$529$	119.500	+	206.980i	0.225898	+	0.391267i
$530$		0			0
$531$	−391.500	+	226.033i	−0.737288	+	0.425674i
$532$	22.0000			0.0413534
$533$	−42.0000	+	24.2487i	−0.0787992	+	0.0454948i
$534$	−324.000	+	561.184i	−0.606742	+	1.05091i
$535$	243.000	−	420.888i	0.454206	−	0.786707i
$536$	−232.500	−	134.234i	−0.433769	−	0.250436i
$537$	162.000	−	93.5307i	0.301676	−	0.174173i
$538$	162.000	+	280.592i	0.301115	+	0.521547i
$539$			77.9423i			0.144605i
$540$	−81.0000	+	46.7654i	−0.150000	+	0.0866025i
$541$	650.000			1.20148			0.600739	−	0.799445i	$-0.294873\pi$
$541$	650.000			1.20148			0.600739	+	0.799445i	$0.294873\pi$
$542$	402.000	−	232.095i	0.741697	−	0.428219i
$543$	348.000	+	602.754i	0.640884	+	1.11004i
$544$	−121.500	+	210.444i	−0.223346	+	0.386846i
$545$	−156.000	−	90.0666i	−0.286239	−	0.165260i
$546$	−36.0000	−	20.7846i	−0.0659341	−	0.0380671i
$547$	−311.500	−	539.534i	−0.569470	−	0.986351i	−0.996618	−	0.0821692i	$-0.973815\pi$
$547$	−311.500	−	539.534i	−0.569470	−	0.986351i	0.427149	−	0.904181i	$-0.359518\pi$
$548$		−	188.794i		−	0.344514i
$549$	504.000			0.918033
$550$	−39.0000			−0.0709091
$551$	429.000	−	247.683i	0.778584	−	0.449516i
$552$	720.000			1.30435
$553$	−38.0000	+	65.8179i	−0.0687161	+	0.119020i
$554$	84.0000	+	48.4974i	0.151625	+	0.0875405i
$555$			353.338i			0.636646i
$556$	−2.50000	−	4.33013i	−0.00449640	−	0.00778800i
$557$			530.008i			0.951540i	0.879570	+	0.475770i	$0.157830\pi$
$557$			530.008i			0.951540i	−0.879570	+	0.475770i	$0.842170\pi$
$558$	432.000	+	249.415i	0.774194	+	0.446981i
$559$	244.000			0.436494
$560$	66.0000	−	38.1051i	0.117857	−	0.0680449i
$561$	−40.5000	+	70.1481i	−0.0721925	+	0.125041i
$562$	42.0000	−	72.7461i	0.0747331	−	0.129442i
$563$	97.5000	+	56.2917i	0.173179	+	0.0999852i	0.584084	−	0.811693i	$-0.301454\pi$
$563$	97.5000	+	56.2917i	0.173179	+	0.0999852i	−0.410905	+	0.911678i	$0.634787\pi$
$564$	−126.000	+	72.7461i	−0.223404	+	0.128983i
$565$	−156.000	−	270.200i	−0.276106	−	0.478230i
$566$		−	647.787i		−	1.14450i
$567$	−81.0000	+	140.296i	−0.142857	+	0.247436i
$568$	−270.000			−0.475352
$569$	565.500	−	326.492i	0.993849	−	0.573799i	0.0874263	−	0.996171i	$-0.472136\pi$
$569$	565.500	−	326.492i	0.993849	−	0.573799i	0.906423	+	0.422372i	$0.138802\pi$
$570$	99.0000	+	171.473i	0.173684	+	0.300830i
$571$	−272.500	+	471.984i	−0.477233	+	0.826592i	−0.999660	−	0.0260926i	$-0.991694\pi$
$571$	−272.500	+	471.984i	−0.477233	+	0.826592i	0.522427	+	0.852684i	$0.325027\pi$
$572$	−6.00000	−	3.46410i	−0.0104895	−	0.00605612i
$573$	−603.000	−	348.142i	−1.05236	−	0.607578i
$574$	−21.0000	−	36.3731i	−0.0365854	−	0.0633677i
$575$			360.267i			0.626551i
$576$	319.500	−	553.390i	0.554688	−	0.960747i
$577$	−871.000			−1.50953			−0.754766	−	0.655994i	$-0.772250\pi$
$577$	−871.000			−1.50953			−0.754766	+	0.655994i	$0.772250\pi$
$578$	−69.0000	+	39.8372i	−0.119377	+	0.0689224i
$579$	−795.000			−1.37306
$580$	−78.0000	+	135.100i	−0.134483	+	0.232931i
$581$	84.0000	+	48.4974i	0.144578	+	0.0834723i
$582$			597.558i			1.02673i
$583$		0			0
$584$		−	562.917i		−	0.963898i
$585$			124.708i			0.213175i
$586$	−438.000			−0.747440
$587$	−1.50000	+	0.866025i	−0.00255537	+	0.00147534i	−0.501277	−	0.865287i	$-0.667136\pi$
$587$	−1.50000	+	0.866025i	−0.00255537	+	0.00147534i	0.498722	+	0.866762i	$0.333803\pi$
$588$	67.5000	−	116.913i	0.114796	−	0.198832i
$589$	−176.000	+	304.841i	−0.298812	+	0.517557i
$590$	−261.000	−	150.688i	−0.442373	−	0.255404i
$591$	324.000	−	187.061i	0.548223	−	0.316517i
$592$	−187.000	−	323.894i	−0.315878	−	0.547117i
$593$			187.061i			0.315449i	0.987483	+	0.157725i	$0.0504159\pi$
$593$			187.061i			0.315449i	−0.987483	+	0.157725i	$0.949584\pi$
$594$	40.5000	−	70.1481i	0.0681818	−	0.118094i
$595$	108.000			0.181513
$596$	132.000	−	76.2102i	0.221477	−	0.127870i
$597$	−435.000	−	753.442i	−0.728643	−	1.26205i
$598$	96.0000	−	166.277i	0.160535	−	0.278055i
$599$	489.000	+	282.324i	0.816361	+	0.471326i	0.849160	−	0.528136i	$-0.177109\pi$
$599$	489.000	+	282.324i	0.816361	+	0.471326i	−0.0327992	+	0.999462i	$0.510442\pi$
$600$	292.500	+	168.875i	0.487500	+	0.281458i
$601$	−230.500	−	399.238i	−0.383527	−	0.664289i	0.608036	−	0.793909i	$-0.291958\pi$
$601$	−230.500	−	399.238i	−0.383527	−	0.664289i	−0.991564	+	0.129620i	$0.958624\pi$
$602$			211.310i			0.351014i
$603$	139.500	+	241.621i	0.231343	+	0.400698i
$604$	20.0000			0.0331126
$605$	−354.000	+	204.382i	−0.585124	+	0.337821i
$606$	234.000			0.386139
$607$	56.0000	−	96.9948i	0.0922570	−	0.159794i	−0.816204	−	0.577765i	$-0.803925\pi$
$607$	56.0000	−	96.9948i	0.0922570	−	0.159794i	0.908461	+	0.417971i	$0.137259\pi$
$608$	148.500	+	85.7365i	0.244243	+	0.141014i
$609$			270.200i			0.443678i
$610$	168.000	+	290.985i	0.275410	+	0.477024i
$611$			193.990i			0.317495i
$612$	121.500	−	70.1481i	0.198529	−	0.114621i
$613$	902.000			1.47145			0.735726	−	0.677279i	$-0.236841\pi$
$613$	902.000			1.47145			0.735726	+	0.677279i	$0.236841\pi$
$614$	−799.500	+	461.592i	−1.30212	+	0.751778i
$615$	−63.0000	+	109.119i	−0.102439	+	0.177430i
$616$	15.0000	−	25.9808i	0.0243506	−	0.0421766i
$617$	−307.500	−	177.535i	−0.498379	−	0.287739i	0.229665	−	0.973270i	$-0.426237\pi$
$617$	−307.500	−	177.535i	−0.498379	−	0.287739i	−0.728044	+	0.685530i	$0.759570\pi$
$618$	180.000	−	103.923i	0.291262	−	0.168160i
$619$	399.500	+	691.954i	0.645396	+	1.11786i	0.984210	+	0.177005i	$0.0566409\pi$
$619$	399.500	+	691.954i	0.645396	+	1.11786i	−0.338814	+	0.940853i	$0.610026\pi$
$620$		−	110.851i		−	0.178792i
$621$	−648.000	−	374.123i	−1.04348	−	0.602452i
$622$	426.000			0.684887
$623$	216.000	−	124.708i	0.346709	−	0.200173i
$624$	−66.0000	−	114.315i	−0.105769	−	0.183198i
$625$	65.5000	−	113.449i	0.104800	−	0.181519i
$626$	232.500	+	134.234i	0.371406	+	0.214431i
$627$	49.5000	+	28.5788i	0.0789474	+	0.0455803i
$628$	20.0000	+	34.6410i	0.0318471	+	0.0551609i
$629$		−	530.008i		−	0.842619i
$630$	−108.000			−0.171429
$631$	830.000			1.31537			0.657686	−	0.753292i	$-0.271535\pi$
$631$	830.000			1.31537			0.657686	+	0.753292i	$0.271535\pi$
$632$	−285.000	+	164.545i	−0.450949	+	0.260356i
$633$	−282.000			−0.445498
$634$	42.0000	−	72.7461i	0.0662461	−	0.114742i
$635$	−48.0000	−	27.7128i	−0.0755906	−	0.0436422i
$636$		0			0
$637$	−90.0000	−	155.885i	−0.141287	−	0.244717i
$638$		−	135.100i		−	0.211755i
$639$	243.000	+	140.296i	0.380282	+	0.219556i
$640$	210.000			0.328125
$641$	−325.500	+	187.928i	−0.507800	+	0.293179i	−0.731929	−	0.681381i	$-0.761380\pi$
$641$	−325.500	+	187.928i	−0.507800	+	0.293179i	0.224129	+	0.974560i	$0.428046\pi$
$642$	364.500	−	631.333i	0.567757	−	0.983384i
$643$	6.50000	−	11.2583i	0.0101089	−	0.0175091i	−0.860927	−	0.508729i	$-0.830116\pi$
$643$	6.50000	−	11.2583i	0.0101089	−	0.0175091i	0.871036	+	0.491220i	$0.163449\pi$
$644$	−48.0000	−	27.7128i	−0.0745342	−	0.0430323i
$645$	549.000	−	316.965i	0.851163	−	0.491419i
$646$	−148.500	−	257.210i	−0.229876	−	0.398157i
$647$			467.654i			0.722803i	0.932410	+	0.361402i	$0.117702\pi$
$647$			467.654i			0.722803i	−0.932410	+	0.361402i	$0.882298\pi$
$648$	−607.500	+	350.740i	−0.937500	+	0.541266i
$649$	−87.0000			−0.134052
$650$	78.0000	−	45.0333i	0.120000	−	0.0692820i
$651$	−96.0000	−	166.277i	−0.147465	−	0.255418i
$652$	53.0000	−	91.7987i	0.0812883	−	0.140796i
$653$	327.000	+	188.794i	0.500766	+	0.289117i	0.729030	−	0.684482i	$-0.239972\pi$
$653$	327.000	+	188.794i	0.500766	+	0.289117i	−0.228264	+	0.973599i	$0.573305\pi$
$654$	−234.000	−	135.100i	−0.357798	−	0.206575i
$655$	276.000	+	478.046i	0.421374	+	0.729841i
$656$		−	133.368i		−	0.203305i
$657$	−292.500	+	506.625i	−0.445205	+	0.771119i
$658$	−168.000			−0.255319
$659$	−852.000	+	491.902i	−1.29287	+	0.746438i	−0.979162	−	0.203082i	$-0.934904\pi$
$659$	−852.000	+	491.902i	−1.29287	+	0.746438i	−0.313706	+	0.949520i	$0.601571\pi$
$660$	−18.0000			−0.0272727
$661$	191.000	−	330.822i	0.288956	−	0.500487i	−0.684605	−	0.728915i	$-0.740025\pi$
$661$	191.000	−	330.822i	0.288956	−	0.500487i	0.973561	+	0.228428i	$0.0733585\pi$
$662$	3.00000	+	1.73205i	0.00453172	+	0.00261639i
$663$		−	187.061i		−	0.282144i
$664$	210.000	+	363.731i	0.316265	+	0.547787i
$665$		−	76.2102i		−	0.114602i
$666$			530.008i			0.795807i
$667$	−1248.00			−1.87106
$668$	−165.000	+	95.2628i	−0.247006	+	0.142609i
$669$	78.0000	−	135.100i	0.116592	−	0.201943i
$670$	−93.0000	+	161.081i	−0.138806	+	0.240419i
$671$	84.0000	+	48.4974i	0.125186	+	0.0722763i
$672$	−81.0000	+	46.7654i	−0.120536	+	0.0695913i
$673$	−289.000	−	500.563i	−0.429421	−	0.743778i	0.567401	−	0.823441i	$-0.307949\pi$
$673$	−289.000	−	500.563i	−0.429421	−	0.743778i	−0.996822	+	0.0796633i	$0.974615\pi$
$674$		−	133.368i		−	0.197875i
$675$	−175.500	−	303.975i	−0.260000	−	0.450333i
$676$	−153.000			−0.226331
$677$	606.000	−	349.874i	0.895126	−	0.516801i	0.0195100	−	0.999810i	$-0.493789\pi$
$677$	606.000	−	349.874i	0.895126	−	0.516801i	0.875616	+	0.483009i	$0.160456\pi$
$678$	−234.000	−	405.300i	−0.345133	−	0.597787i
$679$	115.000	−	199.186i	0.169367	−	0.293352i
$680$	405.000	+	233.827i	0.595588	+	0.343863i
$681$	490.500	+	283.190i	0.720264	+	0.415845i
$682$	48.0000	+	83.1384i	0.0703812	+	0.121904i
$683$		−	1044.43i		−	1.52918i	−0.644520	−	0.764588i	$-0.722943\pi$
$683$		−	1044.43i		−	1.52918i	0.644520	−	0.764588i	$-0.277057\pi$
$684$	−49.5000	−	85.7365i	−0.0723684	−	0.125346i
$685$	−654.000			−0.954745
$686$	282.000	−	162.813i	0.411079	−	0.237336i
$687$	798.000			1.16157
$688$	−335.500	+	581.103i	−0.487645	+	0.844627i
$689$		0			0
$690$		−	498.831i		−	0.722943i
$691$	−91.0000	−	157.617i	−0.131693	−	0.228099i	0.792636	−	0.609695i	$-0.208708\pi$
$691$	−91.0000	−	157.617i	−0.131693	−	0.228099i	−0.924329	+	0.381596i	$0.875375\pi$
$692$			232.095i			0.335397i
$693$	−27.0000	+	15.5885i	−0.0389610	+	0.0224942i
$694$	−195.000			−0.280980
$695$	−15.0000	+	8.66025i	−0.0215827	+	0.0124608i
$696$	−585.000	+	1013.25i	−0.840517	+	1.45582i
$697$	94.5000	−	163.679i	0.135581	−	0.234833i
$698$	624.000	+	360.267i	0.893983	+	0.516141i
$699$	526.500	−	303.975i	0.753219	−	0.434871i
$700$	−13.0000	−	22.5167i	−0.0185714	−	0.0321667i
$701$		0			0		1.00000			$0$
$701$		0			0		−1.00000			$\pi$
$702$			187.061i			0.266469i
$703$	−374.000			−0.532006
$704$	106.500	−	61.4878i	0.151278	−	0.0873406i
$705$	252.000	+	436.477i	0.357447	+	0.619116i
$706$	1.50000	−	2.59808i	0.00212465	−	0.00367999i
$707$	−78.0000	−	45.0333i	−0.110325	−	0.0636964i
$708$	130.500	+	75.3442i	0.184322	+	0.106418i
$709$	350.000	+	606.218i	0.493653	+	0.855032i	0.999973	−	0.00731341i	$-0.00232795\pi$
$709$	350.000	+	606.218i	0.493653	+	0.855032i	−0.506320	+	0.862346i	$0.668995\pi$
$710$			187.061i			0.263467i
$711$	342.000			0.481013
$712$	1080.00			1.51685
$713$	768.000	−	443.405i	1.07714	−	0.621886i
$714$	162.000			0.226891
$715$	−12.0000	+	20.7846i	−0.0167832	+	0.0290694i
$716$	−54.0000	−	31.1769i	−0.0754190	−	0.0435432i
$717$			1205.51i			1.68132i
$718$	−513.000	−	888.542i	−0.714485	−	1.23752i
$719$		−	592.361i		−	0.823868i	−0.911214	−	0.411934i	$-0.864853\pi$
$719$		−	592.361i		−	0.823868i	0.911214	−	0.411934i	$-0.135147\pi$
$720$	−297.000	−	171.473i	−0.412500	−	0.238157i
$721$	−80.0000			−0.110957
$722$	360.000	−	207.846i	0.498615	−	0.287875i
$723$	−178.500	+	309.171i	−0.246888	+	0.427623i
$724$	116.000	−	200.918i	0.160221	−	0.277511i
$725$	−507.000	−	292.717i	−0.699310	−	0.403747i
$726$	−531.000	+	306.573i	−0.731405	+	0.422277i
$727$	332.000	+	575.041i	0.456671	+	0.790978i	0.998783	−	0.0493289i	$-0.0157082\pi$
$727$	332.000	+	575.041i	0.456671	+	0.790978i	−0.542111	+	0.840307i	$0.682375\pi$
$728$			69.2820i			0.0951676i
$729$	729.000			1.00000
$730$	−390.000			−0.534247
$731$	−823.500	+	475.448i	−1.12654	+	0.650408i
$732$	−84.0000	−	145.492i	−0.114754	−	0.198760i
$733$	335.000	−	580.237i	0.457026	−	0.791592i	−0.541776	−	0.840523i	$-0.682248\pi$
$733$	335.000	−	580.237i	0.457026	−	0.791592i	0.998802	+	0.0489306i	$0.0155813\pi$
$734$	−537.000	−	310.037i	−0.731608	−	0.422394i
$735$	−405.000	−	233.827i	−0.551020	−	0.318132i
$736$	−216.000	−	374.123i	−0.293478	−	0.508319i
$737$			53.6936i			0.0728542i
$738$	−94.5000	+	163.679i	−0.128049	+	0.221787i
$739$	317.000			0.428958			0.214479	−	0.976729i	$-0.431195\pi$
$739$	317.000			0.428958			0.214479	+	0.976729i	$0.431195\pi$
$740$	102.000	−	58.8897i	0.137838	−	0.0795807i
$741$	−132.000			−0.178138
$742$		0			0
$743$	−537.000	−	310.037i	−0.722746	−	0.417277i	0.0930168	−	0.995665i	$-0.470349\pi$
$743$	−537.000	−	310.037i	−0.722746	−	0.417277i	−0.815762	+	0.578387i	$0.803682\pi$
$744$		−	831.384i		−	1.11745i
$745$	−264.000	−	457.261i	−0.354362	−	0.613774i
$746$			1004.59i			1.34663i
$747$		−	436.477i		−	0.584306i
$748$	27.0000			0.0360963
$749$	−243.000	+	140.296i	−0.324433	+	0.187311i
$750$	342.000	−	592.361i	0.456000	−	0.789815i
$751$	−655.000	+	1134.49i	−0.872170	+	1.51064i	−0.0124237	+	0.999923i	$0.503955\pi$
$751$	−655.000	+	1134.49i	−0.872170	+	1.51064i	−0.859747	+	0.510721i	$0.829379\pi$
$752$	−462.000	−	266.736i	−0.614362	−	0.354702i
$753$	−1012.50	+	584.567i	−1.34462	+	0.776318i
$754$	156.000	+	270.200i	0.206897	+	0.358355i
$755$		−	69.2820i		−	0.0917643i
$756$	54.0000			0.0714286
$757$	218.000			0.287979			0.143989	−	0.989579i	$-0.454007\pi$
$757$	218.000			0.287979			0.143989	+	0.989579i	$0.454007\pi$
$758$	−124.500	+	71.8801i	−0.164248	+	0.0948286i
$759$	−72.0000	−	124.708i	−0.0948617	−	0.164305i
$760$	165.000	−	285.788i	0.217105	−	0.376037i
$761$	570.000	+	329.090i	0.749014	+	0.432444i	0.825338	−	0.564639i	$-0.190985\pi$
$761$	570.000	+	329.090i	0.749014	+	0.432444i	−0.0763232	+	0.997083i	$0.524318\pi$
$762$	−72.0000	−	41.5692i	−0.0944882	−	0.0545528i
$763$	52.0000	+	90.0666i	0.0681520	+	0.118043i
$764$			232.095i			0.303789i
$765$	−243.000	−	420.888i	−0.317647	−	0.550181i
$766$	966.000			1.26110
$767$	174.000	−	100.459i	0.226858	−	0.130976i
$768$	−537.000			−0.699219
$769$	−511.000	+	885.078i	−0.664499	+	1.15095i	0.314921	+	0.949118i	$0.398022\pi$
$769$	−511.000	+	885.078i	−0.664499	+	1.15095i	−0.979421	+	0.201829i	$0.935312\pi$
$770$	−18.0000	−	10.3923i	−0.0233766	−	0.0134965i
$771$		−	524.811i		−	0.680689i
$772$	132.500	+	229.497i	0.171632	+	0.297276i
$773$			1184.72i			1.53263i	0.642465	+	0.766315i	$0.277912\pi$
$773$			1184.72i			1.53263i	−0.642465	+	0.766315i	$0.722088\pi$
$774$	823.500	−	475.448i	1.06395	−	0.614274i
$775$	416.000			0.536774
$776$	862.500	−	497.965i	1.11147	−	0.641707i
$777$	102.000	−	176.669i	0.131274	−	0.227373i
$778$	447.000	−	774.227i	0.574550	−	0.995150i
$779$	−115.500	−	66.6840i	−0.148267	−	0.0856020i
$780$	36.0000	−	20.7846i	0.0461538	−	0.0266469i
$781$	27.0000	+	46.7654i	0.0345711	+	0.0598788i
$782$			748.246i			0.956836i
$783$	1053.00	−	607.950i	1.34483	−	0.776437i
$784$	495.000			0.631378
$785$	120.000	−	69.2820i	0.152866	−	0.0882574i
$786$	414.000	+	717.069i	0.526718	+	0.912302i
$787$	65.0000	−	112.583i	0.0825921	−	0.143054i	−0.821771	−	0.569819i	$-0.807013\pi$
$787$	65.0000	−	112.583i	0.0825921	−	0.143054i	0.904363	+	0.426765i	$0.140347\pi$
$788$	−108.000	−	62.3538i	−0.137056	−	0.0791292i
$789$	−117.000	−	67.5500i	−0.148289	−	0.0856147i
$790$	114.000	+	197.454i	0.144304	+	0.249942i
$791$			180.133i			0.227729i
$792$	−135.000			−0.170455
$793$	−224.000			−0.282472
$794$	−543.000	+	313.501i	−0.683879	+	0.394838i
$795$		0			0
$796$	−145.000	+	251.147i	−0.182161	+	0.315512i
$797$	273.000	+	157.617i	0.342535	+	0.197762i	0.661392	−	0.750040i	$-0.269966\pi$
$797$	273.000	+	157.617i	0.342535	+	0.197762i	−0.318858	+	0.947803i	$0.603299\pi$
$798$		−	114.315i		−	0.143252i
$799$	−378.000	−	654.715i	−0.473091	−	0.819418i
$800$		−	202.650i		−	0.253312i
$801$	−972.000	−	561.184i	−1.21348	−	0.700605i
$802$	−681.000			−0.849127
$803$	−97.5000	+	56.2917i	−0.121420	+	0.0701017i
$804$	46.5000	−	80.5404i	0.0578358	−	0.100175i
$805$	−96.0000	+	166.277i	−0.119255	+	0.206555i
$806$	−192.000	−	110.851i	−0.238213	−	0.137533i
$807$	−486.000	+	280.592i	−0.602230	+	0.347698i
$808$	−195.000	−	337.750i	−0.241337	−	0.418007i
$809$		−	140.296i		−	0.173419i	−0.996234	−	0.0867096i	$-0.972365\pi$
$809$		−	140.296i		−	0.173419i	0.996234	−	0.0867096i	$-0.0276352\pi$
$810$	243.000	+	420.888i	0.300000	+	0.519615i
$811$	299.000			0.368681			0.184340	−	0.982862i	$-0.440985\pi$
$811$	299.000			0.368681			0.184340	+	0.982862i	$0.440985\pi$
$812$	78.0000	−	45.0333i	0.0960591	−	0.0554598i
$813$	402.000	+	696.284i	0.494465	+	0.856438i
$814$	−51.0000	+	88.3346i	−0.0626536	+	0.108519i
$815$	−318.000	−	183.597i	−0.390184	−	0.225273i
$816$	445.500	+	257.210i	0.545956	+	0.315208i
$817$	335.500	+	581.103i	0.410649	+	0.711264i
$818$		−	382.783i		−	0.467950i
$819$	36.0000	−	62.3538i	0.0439560	−	0.0761341i
$820$	42.0000			0.0512195
$821$	525.000	−	303.109i	0.639464	−	0.369195i	−0.144944	−	0.989440i	$-0.546300\pi$
$821$	525.000	−	303.109i	0.639464	−	0.369195i	0.784408	+	0.620245i	$0.212967\pi$
$822$	−981.000			−1.19343
$823$	407.000	−	704.945i	0.494532	−	0.856555i	−0.505448	−	0.862857i	$-0.668673\pi$
$823$	407.000	−	704.945i	0.494532	−	0.856555i	0.999980	+	0.00630221i	$0.00200607\pi$
$824$	−300.000	−	173.205i	−0.364078	−	0.210200i
$825$		−	67.5500i		−	0.0818788i
$826$	87.0000	+	150.688i	0.105327	+	0.182432i
$827$		−	1434.14i		−	1.73415i	−0.498182	−	0.867073i	$-0.665999\pi$
$827$		−	1434.14i		−	1.73415i	0.498182	−	0.867073i	$-0.334001\pi$
$828$			249.415i			0.301226i
$829$	−718.000			−0.866104			−0.433052	−	0.901369i	$-0.642563\pi$
$829$	−718.000			−0.866104			−0.433052	+	0.901369i	$0.642563\pi$
$830$	252.000	−	145.492i	0.303614	−	0.175292i
$831$	−84.0000	+	145.492i	−0.101083	+	0.175081i
$832$	−142.000	+	245.951i	−0.170673	+	0.295614i
$833$	607.500	+	350.740i	0.729292	+	0.421057i
$834$	−22.5000	+	12.9904i	−0.0269784	+	0.0155760i
$835$	330.000	+	571.577i	0.395210	+	0.684523i
$836$		−	19.0526i		−	0.0227901i
$837$	−432.000	+	748.246i	−0.516129	+	0.893962i
$838$	−1356.00			−1.61814
$839$	−690.000	+	398.372i	−0.822408	+	0.474817i	−0.851246	−	0.524767i	$-0.824153\pi$
$839$	−690.000	+	398.372i	−0.822408	+	0.474817i	0.0288384	+	0.999584i	$0.490819\pi$
$840$	90.0000	+	155.885i	0.107143	+	0.185577i
$841$	593.500	−	1027.97i	0.705707	−	1.22232i
$842$	−1023.00	−	590.629i	−1.21496	−	0.701460i
$843$	126.000	+	72.7461i	0.149466	+	0.0862943i
$844$	47.0000	+	81.4064i	0.0556872	+	0.0964531i
$845$			530.008i			0.627228i
$846$	378.000	+	654.715i	0.446809	+	0.773895i
$847$	236.000			0.278630
$848$		0			0
$849$	1122.00			1.32155
$850$	−175.500	+	303.975i	−0.206471	+	0.357618i
$851$	816.000	+	471.118i	0.958872	+	0.553605i
$852$		−	93.5307i		−	0.109778i
$853$	−712.000	−	1233.22i	−0.834701	−	1.44574i	−0.894274	−	0.447521i	$-0.852307\pi$
$853$	−712.000	−	1233.22i	−0.834701	−	1.44574i	0.0595725	−	0.998224i	$-0.481026\pi$
$854$		−	193.990i		−	0.227154i
$855$	−297.000	+	171.473i	−0.347368	+	0.200553i
$856$	−1215.00			−1.41939
$857$	606.000	−	349.874i	0.707118	−	0.408255i	−0.102875	−	0.994694i	$-0.532804\pi$
$857$	606.000	−	349.874i	0.707118	−	0.408255i	0.809993	+	0.586440i	$0.199471\pi$
$858$	−18.0000	+	31.1769i	−0.0209790	+	0.0363367i
$859$	−155.500	+	269.334i	−0.181024	+	0.313544i	−0.942230	−	0.334968i	$-0.891275\pi$
$859$	−155.500	+	269.334i	−0.181024	+	0.313544i	0.761205	+	0.648511i	$0.224608\pi$
$860$	−183.000	−	105.655i	−0.212791	−	0.122855i
$861$	63.0000	−	36.3731i	0.0731707	−	0.0422451i
$862$	243.000	+	420.888i	0.281903	+	0.488270i
$863$		−	1028.84i		−	1.19216i	−0.802923	−	0.596082i	$-0.796723\pi$
$863$		−	1028.84i		−	1.19216i	0.802923	−	0.596082i	$-0.203277\pi$
$864$	364.500	+	210.444i	0.421875	+	0.243570i
$865$	804.000			0.929480
$866$	442.500	−	255.477i	0.510970	−	0.295009i
$867$	−69.0000	−	119.512i	−0.0795848	−	0.137845i
$868$	−32.0000	+	55.4256i	−0.0368664	+	0.0638544i
$869$	57.0000	+	32.9090i	0.0655926	+	0.0378699i
$870$	702.000	+	405.300i	0.806897	+	0.465862i
$871$	−62.0000	−	107.387i	−0.0711825	−	0.123292i
$872$			450.333i			0.516437i
$873$	−1035.00			−1.18557
$874$	528.000			0.604119
$875$	−228.000	+	131.636i	−0.260571	+	0.150441i
$876$	195.000			0.222603
$877$	−52.0000	+	90.0666i	−0.0592930	+	0.102699i	−0.894148	−	0.447771i	$-0.852218\pi$
$877$	−52.0000	+	90.0666i	−0.0592930	+	0.102699i	0.834855	+	0.550470i	$0.185551\pi$
$878$	1218.00	+	703.213i	1.38724	+	0.800926i
$879$		−	758.638i		−	0.863070i
$880$	−33.0000	−	57.1577i	−0.0375000	−	0.0649519i
$881$			62.3538i			0.0707762i	0.999374	+	0.0353881i	$0.0112667\pi$
$881$			62.3538i			0.0707762i	−0.999374	+	0.0353881i	$0.988733\pi$
$882$	−607.500	−	350.740i	−0.688776	−	0.397665i
$883$	119.000			0.134768			0.0673839	−	0.997727i	$-0.478535\pi$
$883$	119.000			0.134768			0.0673839	+	0.997727i	$0.478535\pi$
$884$	−54.0000	+	31.1769i	−0.0610860	+	0.0352680i
$885$	261.000	−	452.065i	0.294915	−	0.510808i
$886$	−79.5000	+	137.698i	−0.0897291	+	0.155415i
$887$	1029.00	+	594.093i	1.16009	+	0.669778i	0.951326	−	0.308188i	$-0.0997224\pi$
$887$	1029.00	+	594.093i	1.16009	+	0.669778i	0.208765	+	0.977966i	$0.433056\pi$
$888$	765.000	−	441.673i	0.861486	−	0.497379i
$889$	16.0000	+	27.7128i	0.0179978	+	0.0311730i
$890$		−	748.246i		−	0.840726i
$891$	121.500	+	70.1481i	0.136364	+	0.0787296i
$892$	−52.0000			−0.0582960
$893$	−462.000	+	266.736i	−0.517357	+	0.298696i
$894$	−396.000	−	685.892i	−0.442953	−	0.767217i
$895$	−108.000	+	187.061i	−0.120670	+	0.209007i
$896$	−105.000	−	60.6218i	−0.117188	−	0.0676582i
$897$	288.000	+	166.277i	0.321070	+	0.185370i
$898$	553.500	+	958.690i	0.616370	+	1.06758i
$899$			1441.07i			1.60297i
$900$	−58.5000	+	101.325i	−0.0650000	+	0.112583i
$901$		0			0
$902$	−31.5000	+	18.1865i	−0.0349224	+	0.0201625i
$903$	−366.000			−0.405316
$904$	−390.000	+	675.500i	−0.431416	+	0.747234i
$905$	−696.000	−	401.836i	−0.769061	−	0.444017i
$906$		−	103.923i		−	0.114705i
$907$	−347.500	−	601.888i	−0.383131	−	0.663603i	0.608377	−	0.793648i	$-0.291821\pi$
$907$	−347.500	−	601.888i	−0.383131	−	0.663603i	−0.991508	+	0.130046i	$0.958488\pi$
$908$		−	188.794i		−	0.207922i
$909$			405.300i			0.445874i
$910$	48.0000			0.0527473
$911$	−1500.00	+	866.025i	−1.64654	+	0.950632i	−0.668110	+	0.744062i	$0.732897\pi$
$911$	−1500.00	+	866.025i	−1.64654	+	0.950632i	−0.978432	+	0.206569i	$0.933770\pi$
$912$	181.500	−	314.367i	0.199013	−	0.344701i
$913$	42.0000	−	72.7461i	0.0460022	−	0.0796781i
$914$	97.5000	+	56.2917i	0.106674	+	0.0615882i
$915$	−504.000	+	290.985i	−0.550820	+	0.318016i
$916$	−133.000	−	230.363i	−0.145197	−	0.251488i
$917$		−	318.697i		−	0.347543i
$918$	−364.500	−	631.333i	−0.397059	−	0.687726i
$919$	56.0000			0.0609358			0.0304679	−	0.999536i	$-0.490300\pi$
$919$	56.0000			0.0609358			0.0304679	+	0.999536i	$0.490300\pi$
$920$	−720.000	+	415.692i	−0.782609	+	0.451839i
$921$	−799.500	−	1384.77i	−0.868078	−	1.50356i
$922$	690.000	−	1195.12i	0.748373	−	1.29622i
$923$	−108.000	−	62.3538i	−0.117010	−	0.0675556i
$924$	9.00000	+	5.19615i	0.00974026	+	0.00562354i
$925$	221.000	+	382.783i	0.238919	+	0.413820i
$926$		−	1271.33i		−	1.37292i
$927$	180.000	+	311.769i	0.194175	+	0.336321i
$928$	702.000			0.756466
$929$	−690.000	+	398.372i	−0.742734	+	0.428818i	−0.823063	−	0.567951i	$-0.807736\pi$
$929$	−690.000	+	398.372i	−0.742734	+	0.428818i	0.0803285	+	0.996768i	$0.474403\pi$
$930$	−576.000			−0.619355
$931$	247.500	−	428.683i	0.265843	−	0.460454i
$932$	−175.500	−	101.325i	−0.188305	−	0.108718i
$933$			737.854i			0.790840i
$934$	175.500	+	303.975i	0.187901	+	0.325455i
$935$		−	93.5307i		−	0.100033i
$936$	270.000	−	155.885i	0.288462	−	0.166543i
$937$	470.000			0.501601			0.250800	−	0.968039i	$-0.419306\pi$
$937$	470.000			0.501601			0.250800	+	0.968039i	$0.419306\pi$
$938$	93.0000	−	53.6936i	0.0991471	−	0.0572426i
$939$	−232.500	+	402.702i	−0.247604	+	0.428862i
$940$	84.0000	−	145.492i	0.0893617	−	0.154779i
$941$	−348.000	−	200.918i	−0.369819	−	0.213515i	0.303560	−	0.952812i	$-0.401825\pi$
$941$	−348.000	−	200.918i	−0.369819	−	0.213515i	−0.673380	+	0.739297i	$0.735158\pi$
$942$	180.000	−	103.923i	0.191083	−	0.110322i
$943$	168.000	+	290.985i	0.178155	+	0.308573i
$944$			552.524i			0.585301i
$945$		−	187.061i		−	0.197949i
$946$	183.000			0.193446
$947$	−1.50000	+	0.866025i	−0.00158395	+	0.000914494i	−0.500792	−	0.865568i	$-0.666958\pi$
$947$	−1.50000	+	0.866025i	−0.00158395	+	0.000914494i	0.499208	+	0.866482i	$0.333624\pi$
$948$	−57.0000	−	98.7269i	−0.0601266	−	0.104142i
$949$	130.000	−	225.167i	0.136986	−	0.237267i
$950$	214.500	+	123.842i	0.225789	+	0.130360i
$951$	126.000	+	72.7461i	0.132492	+	0.0764944i
$952$	−135.000	−	233.827i	−0.141807	−	0.245616i
$953$			826.188i			0.866934i	0.901169	+	0.433467i	$0.142710\pi$
$953$			826.188i			0.866934i	−0.901169	+	0.433467i	$0.857290\pi$
$954$		0			0
$955$	804.000			0.841885
$956$	348.000	−	200.918i	0.364017	−	0.210165i
$957$	234.000			0.244514
$958$	−525.000	+	909.327i	−0.548017	+	0.949193i
$959$	327.000	+	188.794i	0.340980	+	0.196865i
$960$			737.854i			0.768598i
$961$	−31.5000	−	54.5596i	−0.0327784	−	0.0567738i
$962$		−	235.559i		−	0.244864i
$963$	1093.50	+	631.333i	1.13551	+	0.655589i
$964$	119.000			0.123444
$965$	795.000	−	458.993i	0.823834	−	0.475641i
$966$	−144.000	+	249.415i	−0.149068	+	0.258194i
$967$	−601.000	+	1040.96i	−0.621510	+	1.07649i	0.367695	+	0.929946i	$0.380147\pi$
$967$	−601.000	+	1040.96i	−0.621510	+	1.07649i	−0.989205	+	0.146540i	$0.953186\pi$
$968$	885.000	+	510.955i	0.914256	+	0.527846i
$969$	445.500	−	257.210i	0.459752	−	0.265438i
$970$	−345.000	−	597.558i	−0.355670	−	0.616039i
$971$		−	187.061i		−	0.192648i	−0.995350	−	0.0963241i	$-0.969291\pi$
$971$		−	187.061i		−	0.192648i	0.995350	−	0.0963241i	$-0.0307085\pi$
$972$	−121.500	−	210.444i	−0.125000	−	0.216506i
$973$	10.0000			0.0102775
$974$	159.000	−	91.7987i	0.163244	−	0.0942492i
$975$	78.0000	+	135.100i	0.0800000	+	0.138564i
$976$	308.000	−	533.472i	0.315574	−	0.546590i
$977$	−361.500	−	208.712i	−0.370010	−	0.213626i	0.303453	−	0.952847i	$-0.401861\pi$
$977$	−361.500	−	208.712i	−0.370010	−	0.213626i	−0.673463	+	0.739221i	$0.735194\pi$
$978$	−477.000	−	275.396i	−0.487730	−	0.281591i
$979$	−108.000	−	187.061i	−0.110317	−	0.191074i
$980$			155.885i			0.159066i
$981$	234.000	−	405.300i	0.238532	−	0.413150i
$982$	399.000			0.406314
$983$	1011.00	−	583.701i	1.02848	−	0.593796i	0.111934	−	0.993716i	$-0.464295\pi$
$983$	1011.00	−	583.701i	1.02848	−	0.593796i	0.916550	+	0.399920i	$0.130962\pi$
$984$	315.000			0.320122
$985$	−216.000	+	374.123i	−0.219289	+	0.379820i
$986$	−1053.00	−	607.950i	−1.06795	−	0.616582i
$987$		−	290.985i		−	0.294817i
$988$	22.0000	+	38.1051i	0.0222672	+	0.0385679i
$989$		−	1690.48i		−	1.70928i
$990$			93.5307i			0.0944755i
$991$	−1420.00			−1.43290			−0.716448	−	0.697640i	$-0.754233\pi$
$991$	−1420.00			−1.43290			−0.716448	+	0.697640i	$0.754233\pi$
$992$	−432.000	+	249.415i	−0.435484	+	0.251427i
$993$	−3.00000	+	5.19615i	−0.00302115	+	0.00523278i
$994$	54.0000	−	93.5307i	0.0543260	−	0.0940953i
$995$	870.000	+	502.295i	0.874372	+	0.504819i
$996$	−126.000	+	72.7461i	−0.126506	+	0.0730383i
$997$	−262.000	−	453.797i	−0.262788	−	0.455163i	0.704193	−	0.710008i	$-0.251309\pi$
$997$	−262.000	−	453.797i	−0.262788	−	0.455163i	−0.966982	+	0.254845i	$0.917975\pi$
$998$			1363.12i			1.36586i
$999$	−918.000			−0.918919

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.3.d.a.5.1	yes	2
3.2	odd	2		27.3.d.a.17.1		2
4.3	odd	2		144.3.q.a.113.1		2
5.2	odd	4		225.3.i.a.149.1		4
5.3	odd	4		225.3.i.a.149.2		4
5.4	even	2		225.3.j.a.176.1		2
7.2	even	3		441.3.n.b.410.1		2
7.3	odd	6		441.3.j.b.275.1		2
7.4	even	3		441.3.j.a.275.1		2
7.5	odd	6		441.3.n.a.410.1		2
7.6	odd	2		441.3.r.a.50.1		2
8.3	odd	2		576.3.q.a.257.1		2
8.5	even	2		576.3.q.b.257.1		2
9.2	odd	6	inner	9.3.d.a.2.1	✓	2
9.4	even	3		81.3.b.a.80.1		2
9.5	odd	6		81.3.b.a.80.2		2
9.7	even	3		27.3.d.a.8.1		2
12.11	even	2		432.3.q.a.17.1		2
15.2	even	4		675.3.i.a.449.2		4
15.8	even	4		675.3.i.a.449.1		4
15.14	odd	2		675.3.j.a.476.1		2
24.5	odd	2		1728.3.q.a.449.1		2
24.11	even	2		1728.3.q.b.449.1		2
36.7	odd	6		432.3.q.a.305.1		2
36.11	even	6		144.3.q.a.65.1		2
36.23	even	6		1296.3.e.a.161.2		2
36.31	odd	6		1296.3.e.a.161.1		2
45.2	even	12		225.3.i.a.74.2		4
45.7	odd	12		675.3.i.a.224.1		4
45.29	odd	6		225.3.j.a.101.1		2
45.34	even	6		675.3.j.a.251.1		2
45.38	even	12		225.3.i.a.74.1		4
45.43	odd	12		675.3.i.a.224.2		4
63.2	odd	6		441.3.j.a.263.1		2
63.11	odd	6		441.3.n.b.128.1		2
63.20	even	6		441.3.r.a.344.1		2
63.38	even	6		441.3.n.a.128.1		2
63.47	even	6		441.3.j.b.263.1		2
72.11	even	6		576.3.q.a.65.1		2
72.29	odd	6		576.3.q.b.65.1		2
72.43	odd	6		1728.3.q.b.1601.1		2
72.61	even	6		1728.3.q.a.1601.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.3.d.a.2.1	✓	2	9.2	odd	6	inner
9.3.d.a.5.1	yes	2	1.1	even	1	trivial
27.3.d.a.8.1		2	9.7	even	3
27.3.d.a.17.1		2	3.2	odd	2
81.3.b.a.80.1		2	9.4	even	3
81.3.b.a.80.2		2	9.5	odd	6
144.3.q.a.65.1		2	36.11	even	6
144.3.q.a.113.1		2	4.3	odd	2
225.3.i.a.74.1		4	45.38	even	12
225.3.i.a.74.2		4	45.2	even	12
225.3.i.a.149.1		4	5.2	odd	4
225.3.i.a.149.2		4	5.3	odd	4
225.3.j.a.101.1		2	45.29	odd	6
225.3.j.a.176.1		2	5.4	even	2
432.3.q.a.17.1		2	12.11	even	2
432.3.q.a.305.1		2	36.7	odd	6
441.3.j.a.263.1		2	63.2	odd	6
441.3.j.a.275.1		2	7.4	even	3
441.3.j.b.263.1		2	63.47	even	6
441.3.j.b.275.1		2	7.3	odd	6
441.3.n.a.128.1		2	63.38	even	6
441.3.n.a.410.1		2	7.5	odd	6
441.3.n.b.128.1		2	63.11	odd	6
441.3.n.b.410.1		2	7.2	even	3
441.3.r.a.50.1		2	7.6	odd	2
441.3.r.a.344.1		2	63.20	even	6
576.3.q.a.65.1		2	72.11	even	6
576.3.q.a.257.1		2	8.3	odd	2
576.3.q.b.65.1		2	72.29	odd	6
576.3.q.b.257.1		2	8.5	even	2
675.3.i.a.224.1		4	45.7	odd	12
675.3.i.a.224.2		4	45.43	odd	12
675.3.i.a.449.1		4	15.8	even	4
675.3.i.a.449.2		4	15.2	even	4
675.3.j.a.251.1		2	45.34	even	6
675.3.j.a.476.1		2	15.14	odd	2
1296.3.e.a.161.1		2	36.31	odd	6
1296.3.e.a.161.2		2	36.23	even	6
1728.3.q.a.449.1		2	24.5	odd	2
1728.3.q.a.1601.1		2	72.61	even	6
1728.3.q.b.449.1		2	24.11	even	2
1728.3.q.b.1601.1		2	72.43	odd	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:	\( N \)	\(=\)	\( 9 = 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	9.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 + 0.866025i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(3.00000 + 1.73205i) q^{5} +(4.50000 + 2.59808i) q^{6} +(-1.00000 - 1.73205i) q^{7} -8.66025i q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\)	\(q+(-1.50000 + 0.866025i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(3.00000 + 1.73205i) q^{5} +(4.50000 + 2.59808i) q^{6} +(-1.00000 - 1.73205i) q^{7} -8.66025i q^{8} +(-4.50000 + 7.79423i) q^{9} -6.00000 q^{10} +(-1.50000 + 0.866025i) q^{11} +3.00000 q^{12} +(2.00000 - 3.46410i) q^{13} +(3.00000 + 1.73205i) q^{14} -10.3923i q^{15} +(5.50000 + 9.52628i) q^{16} +15.5885i q^{17} -15.5885i q^{18} +11.0000 q^{19} +(-3.00000 + 1.73205i) q^{20} +(-3.00000 + 5.19615i) q^{21} +(1.50000 - 2.59808i) q^{22} +(-24.0000 - 13.8564i) q^{23} +(-22.5000 + 12.9904i) q^{24} +(-6.50000 - 11.2583i) q^{25} +6.92820i q^{26} +27.0000 q^{27} +2.00000 q^{28} +(39.0000 - 22.5167i) q^{29} +(9.00000 + 15.5885i) q^{30} +(-16.0000 + 27.7128i) q^{31} +(13.5000 + 7.79423i) q^{32} +(4.50000 + 2.59808i) q^{33} +(-13.5000 - 23.3827i) q^{34} -6.92820i q^{35} +(-4.50000 - 7.79423i) q^{36} -34.0000 q^{37} +(-16.5000 + 9.52628i) q^{38} -12.0000 q^{39} +(15.0000 - 25.9808i) q^{40} +(-10.5000 - 6.06218i) q^{41} -10.3923i q^{42} +(30.5000 + 52.8275i) q^{43} -1.73205i q^{44} +(-27.0000 + 15.5885i) q^{45} +48.0000 q^{46} +(-42.0000 + 24.2487i) q^{47} +(16.5000 - 28.5788i) q^{48} +(22.5000 - 38.9711i) q^{49} +(19.5000 + 11.2583i) q^{50} +(40.5000 - 23.3827i) q^{51} +(2.00000 + 3.46410i) q^{52} +(-40.5000 + 23.3827i) q^{54} -6.00000 q^{55} +(-15.0000 + 8.66025i) q^{56} +(-16.5000 - 28.5788i) q^{57} +(-39.0000 + 67.5500i) q^{58} +(43.5000 + 25.1147i) q^{59} +(9.00000 + 5.19615i) q^{60} +(-28.0000 - 48.4974i) q^{61} -55.4256i q^{62} +18.0000 q^{63} -71.0000 q^{64} +(12.0000 - 6.92820i) q^{65} -9.00000 q^{66} +(15.5000 - 26.8468i) q^{67} +(-13.5000 - 7.79423i) q^{68} +83.1384i q^{69} +(6.00000 + 10.3923i) q^{70} -31.1769i q^{71} +(67.5000 + 38.9711i) q^{72} +65.0000 q^{73} +(51.0000 - 29.4449i) q^{74} +(-19.5000 + 33.7750i) q^{75} +(-5.50000 + 9.52628i) q^{76} +(3.00000 + 1.73205i) q^{77} +(18.0000 - 10.3923i) q^{78} +(-19.0000 - 32.9090i) q^{79} +38.1051i q^{80} +(-40.5000 - 70.1481i) q^{81} +21.0000 q^{82} +(-42.0000 + 24.2487i) q^{83} +(-3.00000 - 5.19615i) q^{84} +(-27.0000 + 46.7654i) q^{85} +(-91.5000 - 52.8275i) q^{86} +(-117.000 - 67.5500i) q^{87} +(7.50000 + 12.9904i) q^{88} +124.708i q^{89} +(27.0000 - 46.7654i) q^{90} -8.00000 q^{91} +(24.0000 - 13.8564i) q^{92} +96.0000 q^{93} +(42.0000 - 72.7461i) q^{94} +(33.0000 + 19.0526i) q^{95} -46.7654i q^{96} +(57.5000 + 99.5929i) q^{97} +77.9423i q^{98} -15.5885i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 3 q^{2} - 3 q^{3} - q^{4} + 6 q^{5} + 9 q^{6} - 2 q^{7} - 9 q^{9}+O(q^{10}) \) 2 * q - 3 * q^2 - 3 * q^3 - q^4 + 6 * q^5 + 9 * q^6 - 2 * q^7 - 9 * q^9	\( 2 q - 3 q^{2} - 3 q^{3} - q^{4} + 6 q^{5} + 9 q^{6} - 2 q^{7} - 9 q^{9} - 12 q^{10} - 3 q^{11} + 6 q^{12} + 4 q^{13} + 6 q^{14} + 11 q^{16} + 22 q^{19} - 6 q^{20} - 6 q^{21} + 3 q^{22} - 48 q^{23} - 45 q^{24} - 13 q^{25} + 54 q^{27} + 4 q^{28} + 78 q^{29} + 18 q^{30} - 32 q^{31} + 27 q^{32} + 9 q^{33} - 27 q^{34} - 9 q^{36} - 68 q^{37} - 33 q^{38} - 24 q^{39} + 30 q^{40} - 21 q^{41} + 61 q^{43} - 54 q^{45} + 96 q^{46} - 84 q^{47} + 33 q^{48} + 45 q^{49} + 39 q^{50} + 81 q^{51} + 4 q^{52} - 81 q^{54} - 12 q^{55} - 30 q^{56} - 33 q^{57} - 78 q^{58} + 87 q^{59} + 18 q^{60} - 56 q^{61} + 36 q^{63} - 142 q^{64} + 24 q^{65} - 18 q^{66} + 31 q^{67} - 27 q^{68} + 12 q^{70} + 135 q^{72} + 130 q^{73} + 102 q^{74} - 39 q^{75} - 11 q^{76} + 6 q^{77} + 36 q^{78} - 38 q^{79} - 81 q^{81} + 42 q^{82} - 84 q^{83} - 6 q^{84} - 54 q^{85} - 183 q^{86} - 234 q^{87} + 15 q^{88} + 54 q^{90} - 16 q^{91} + 48 q^{92} + 192 q^{93} + 84 q^{94} + 66 q^{95} + 115 q^{97}+O(q^{100}) \) 2 * q - 3 * q^2 - 3 * q^3 - q^4 + 6 * q^5 + 9 * q^6 - 2 * q^7 - 9 * q^9 - 12 * q^10 - 3 * q^11 + 6 * q^12 + 4 * q^13 + 6 * q^14 + 11 * q^16 + 22 * q^19 - 6 * q^20 - 6 * q^21 + 3 * q^22 - 48 * q^23 - 45 * q^24 - 13 * q^25 + 54 * q^27 + 4 * q^28 + 78 * q^29 + 18 * q^30 - 32 * q^31 + 27 * q^32 + 9 * q^33 - 27 * q^34 - 9 * q^36 - 68 * q^37 - 33 * q^38 - 24 * q^39 + 30 * q^40 - 21 * q^41 + 61 * q^43 - 54 * q^45 + 96 * q^46 - 84 * q^47 + 33 * q^48 + 45 * q^49 + 39 * q^50 + 81 * q^51 + 4 * q^52 - 81 * q^54 - 12 * q^55 - 30 * q^56 - 33 * q^57 - 78 * q^58 + 87 * q^59 + 18 * q^60 - 56 * q^61 + 36 * q^63 - 142 * q^64 + 24 * q^65 - 18 * q^66 + 31 * q^67 - 27 * q^68 + 12 * q^70 + 135 * q^72 + 130 * q^73 + 102 * q^74 - 39 * q^75 - 11 * q^76 + 6 * q^77 + 36 * q^78 - 38 * q^79 - 81 * q^81 + 42 * q^82 - 84 * q^83 - 6 * q^84 - 54 * q^85 - 183 * q^86 - 234 * q^87 + 15 * q^88 + 54 * q^90 - 16 * q^91 + 48 * q^92 + 192 * q^93 + 84 * q^94 + 66 * q^95 + 115 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more