LMFDB - Embedded newform 798.2.k.i.505.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [798,2,Mod(463,798)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(798, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("798.463");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 798 = 2 \cdot 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	798.k (of order $3$, 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:	$6.37206208130$
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:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			505.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	798.505
Dual form			798.2.k.i.463.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.50000 - 2.59808i) q^{5} +(-0.500000 - 0.866025i) q^{6} -1.00000 q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.50000 - 2.59808i) q^{5} +(-0.500000 - 0.866025i) q^{6} -1.00000 q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.50000 - 2.59808i) q^{10} +4.00000 q^{11} -1.00000 q^{12} +(-1.50000 - 2.59808i) q^{13} +(-0.500000 + 0.866025i) q^{14} +(-1.50000 - 2.59808i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.00000 - 1.73205i) q^{17} -1.00000 q^{18} +(-0.500000 + 4.33013i) q^{19} -3.00000 q^{20} +(-0.500000 + 0.866025i) q^{21} +(2.00000 - 3.46410i) q^{22} +(-0.500000 - 0.866025i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-2.00000 - 3.46410i) q^{25} -3.00000 q^{26} -1.00000 q^{27} +(0.500000 + 0.866025i) q^{28} -3.00000 q^{30} -6.00000 q^{31} +(0.500000 + 0.866025i) q^{32} +(2.00000 - 3.46410i) q^{33} +(-1.00000 - 1.73205i) q^{34} +(-1.50000 + 2.59808i) q^{35} +(-0.500000 + 0.866025i) q^{36} +4.00000 q^{37} +(3.50000 + 2.59808i) q^{38} -3.00000 q^{39} +(-1.50000 + 2.59808i) q^{40} +(-2.00000 + 3.46410i) q^{41} +(0.500000 + 0.866025i) q^{42} +(3.00000 - 5.19615i) q^{43} +(-2.00000 - 3.46410i) q^{44} -3.00000 q^{45} -1.00000 q^{46} +(1.00000 + 1.73205i) q^{47} +(0.500000 + 0.866025i) q^{48} +1.00000 q^{49} -4.00000 q^{50} +(-1.00000 - 1.73205i) q^{51} +(-1.50000 + 2.59808i) q^{52} +(2.00000 + 3.46410i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(6.00000 - 10.3923i) q^{55} +1.00000 q^{56} +(3.50000 + 2.59808i) q^{57} +(-6.50000 + 11.2583i) q^{59} +(-1.50000 + 2.59808i) q^{60} +(-2.50000 - 4.33013i) q^{61} +(-3.00000 + 5.19615i) q^{62} +(0.500000 + 0.866025i) q^{63} +1.00000 q^{64} -9.00000 q^{65} +(-2.00000 - 3.46410i) q^{66} +(6.00000 + 10.3923i) q^{67} -2.00000 q^{68} -1.00000 q^{69} +(1.50000 + 2.59808i) q^{70} +(3.50000 - 6.06218i) q^{71} +(0.500000 + 0.866025i) q^{72} +(1.00000 - 1.73205i) q^{73} +(2.00000 - 3.46410i) q^{74} -4.00000 q^{75} +(4.00000 - 1.73205i) q^{76} -4.00000 q^{77} +(-1.50000 + 2.59808i) q^{78} +(4.00000 - 6.92820i) q^{79} +(1.50000 + 2.59808i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(2.00000 + 3.46410i) q^{82} +17.0000 q^{83} +1.00000 q^{84} +(-3.00000 - 5.19615i) q^{85} +(-3.00000 - 5.19615i) q^{86} -4.00000 q^{88} +(-2.00000 - 3.46410i) q^{89} +(-1.50000 + 2.59808i) q^{90} +(1.50000 + 2.59808i) q^{91} +(-0.500000 + 0.866025i) q^{92} +(-3.00000 + 5.19615i) q^{93} +2.00000 q^{94} +(10.5000 + 7.79423i) q^{95} +1.00000 q^{96} +(5.00000 - 8.66025i) q^{97} +(0.500000 - 0.866025i) q^{98} +(-2.00000 - 3.46410i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + q^{3} - q^{4} + 3 q^{5} - q^{6} - 2 q^{7} - 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q + q^2 + q^3 - q^4 + 3 * q^5 - q^6 - 2 * q^7 - 2 * q^8 - q^9	$ 2 q + q^{2} + q^{3} - q^{4} + 3 q^{5} - q^{6} - 2 q^{7} - 2 q^{8} - q^{9} - 3 q^{10} + 8 q^{11} - 2 q^{12} - 3 q^{13} - q^{14} - 3 q^{15} - q^{16} + 2 q^{17} - 2 q^{18} - q^{19} - 6 q^{20} - q^{21} + 4 q^{22} - q^{23} - q^{24} - 4 q^{25} - 6 q^{26} - 2 q^{27} + q^{28} - 6 q^{30} - 12 q^{31} + q^{32} + 4 q^{33} - 2 q^{34} - 3 q^{35} - q^{36} + 8 q^{37} + 7 q^{38} - 6 q^{39} - 3 q^{40} - 4 q^{41} + q^{42} + 6 q^{43} - 4 q^{44} - 6 q^{45} - 2 q^{46} + 2 q^{47} + q^{48} + 2 q^{49} - 8 q^{50} - 2 q^{51} - 3 q^{52} + 4 q^{53} - q^{54} + 12 q^{55} + 2 q^{56} + 7 q^{57} - 13 q^{59} - 3 q^{60} - 5 q^{61} - 6 q^{62} + q^{63} + 2 q^{64} - 18 q^{65} - 4 q^{66} + 12 q^{67} - 4 q^{68} - 2 q^{69} + 3 q^{70} + 7 q^{71} + q^{72} + 2 q^{73} + 4 q^{74} - 8 q^{75} + 8 q^{76} - 8 q^{77} - 3 q^{78} + 8 q^{79} + 3 q^{80} - q^{81} + 4 q^{82} + 34 q^{83} + 2 q^{84} - 6 q^{85} - 6 q^{86} - 8 q^{88} - 4 q^{89} - 3 q^{90} + 3 q^{91} - q^{92} - 6 q^{93} + 4 q^{94} + 21 q^{95} + 2 q^{96} + 10 q^{97} + q^{98} - 4 q^{99}+O(q^{100}) $ 2 * q + q^2 + q^3 - q^4 + 3 * q^5 - q^6 - 2 * q^7 - 2 * q^8 - q^9 - 3 * q^10 + 8 * q^11 - 2 * q^12 - 3 * q^13 - q^14 - 3 * q^15 - q^16 + 2 * q^17 - 2 * q^18 - q^19 - 6 * q^20 - q^21 + 4 * q^22 - q^23 - q^24 - 4 * q^25 - 6 * q^26 - 2 * q^27 + q^28 - 6 * q^30 - 12 * q^31 + q^32 + 4 * q^33 - 2 * q^34 - 3 * q^35 - q^36 + 8 * q^37 + 7 * q^38 - 6 * q^39 - 3 * q^40 - 4 * q^41 + q^42 + 6 * q^43 - 4 * q^44 - 6 * q^45 - 2 * q^46 + 2 * q^47 + q^48 + 2 * q^49 - 8 * q^50 - 2 * q^51 - 3 * q^52 + 4 * q^53 - q^54 + 12 * q^55 + 2 * q^56 + 7 * q^57 - 13 * q^59 - 3 * q^60 - 5 * q^61 - 6 * q^62 + q^63 + 2 * q^64 - 18 * q^65 - 4 * q^66 + 12 * q^67 - 4 * q^68 - 2 * q^69 + 3 * q^70 + 7 * q^71 + q^72 + 2 * q^73 + 4 * q^74 - 8 * q^75 + 8 * q^76 - 8 * q^77 - 3 * q^78 + 8 * q^79 + 3 * q^80 - q^81 + 4 * q^82 + 34 * q^83 + 2 * q^84 - 6 * q^85 - 6 * q^86 - 8 * q^88 - 4 * q^89 - 3 * q^90 + 3 * q^91 - q^92 - 6 * q^93 + 4 * q^94 + 21 * q^95 + 2 * q^96 + 10 * q^97 + q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/798\mathbb{Z}\right)^\times$.

$n$	$115$	$211$	$533$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	1.50000	−	2.59808i	0.670820	−	1.16190i	−0.306851	−	0.951757i	$-0.599275\pi$
$5$	1.50000	−	2.59808i	0.670820	−	1.16190i	0.977672	−	0.210138i	$-0.0673912\pi$
$6$	−0.500000	−	0.866025i	−0.204124	−	0.353553i
$7$	−1.00000			−0.377964
$7$	−1.00000			−0.377964
$8$	−1.00000			−0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−1.50000	−	2.59808i	−0.474342	−	0.821584i
$11$	4.00000			1.20605			0.603023	−	0.797724i	$-0.293963\pi$
$11$	4.00000			1.20605			0.603023	+	0.797724i	$0.293963\pi$
$12$	−1.00000			−0.288675
$13$	−1.50000	−	2.59808i	−0.416025	−	0.720577i	0.579510	−	0.814965i	$-0.303244\pi$
$13$	−1.50000	−	2.59808i	−0.416025	−	0.720577i	−0.995535	+	0.0943882i	$0.969911\pi$
$14$	−0.500000	+	0.866025i	−0.133631	+	0.231455i
$15$	−1.50000	−	2.59808i	−0.387298	−	0.670820i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.00000	−	1.73205i	0.242536	−	0.420084i	−0.718900	−	0.695113i	$-0.755354\pi$
$17$	1.00000	−	1.73205i	0.242536	−	0.420084i	0.961436	+	0.275029i	$0.0886875\pi$
$18$	−1.00000			−0.235702
$19$	−0.500000	+	4.33013i	−0.114708	+	0.993399i
$19$	−0.500000	+	4.33013i	−0.114708	+	0.993399i
$20$	−3.00000			−0.670820
$21$	−0.500000	+	0.866025i	−0.109109	+	0.188982i
$22$	2.00000	−	3.46410i	0.426401	−	0.738549i
$23$	−0.500000	−	0.866025i	−0.104257	−	0.180579i	0.809177	−	0.587565i	$-0.199913\pi$
$23$	−0.500000	−	0.866025i	−0.104257	−	0.180579i	−0.913434	+	0.406986i	$0.866580\pi$
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	−2.00000	−	3.46410i	−0.400000	−	0.692820i
$26$	−3.00000			−0.588348
$27$	−1.00000			−0.192450
$28$	0.500000	+	0.866025i	0.0944911	+	0.163663i
$29$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$29$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$30$	−3.00000			−0.547723
$31$	−6.00000			−1.07763			−0.538816	−	0.842424i	$-0.681128\pi$
$31$	−6.00000			−1.07763			−0.538816	+	0.842424i	$0.681128\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	2.00000	−	3.46410i	0.348155	−	0.603023i
$34$	−1.00000	−	1.73205i	−0.171499	−	0.297044i
$35$	−1.50000	+	2.59808i	−0.253546	+	0.439155i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	4.00000			0.657596			0.328798	−	0.944400i	$-0.393356\pi$
$37$	4.00000			0.657596			0.328798	+	0.944400i	$0.393356\pi$
$38$	3.50000	+	2.59808i	0.567775	+	0.421464i
$39$	−3.00000			−0.480384
$40$	−1.50000	+	2.59808i	−0.237171	+	0.410792i
$41$	−2.00000	+	3.46410i	−0.312348	+	0.541002i	−0.978870	−	0.204483i	$-0.934449\pi$
$41$	−2.00000	+	3.46410i	−0.312348	+	0.541002i	0.666523	+	0.745485i	$0.267782\pi$
$42$	0.500000	+	0.866025i	0.0771517	+	0.133631i
$43$	3.00000	−	5.19615i	0.457496	−	0.792406i	−0.541332	−	0.840809i	$-0.682080\pi$
$43$	3.00000	−	5.19615i	0.457496	−	0.792406i	0.998828	+	0.0484030i	$0.0154132\pi$
$44$	−2.00000	−	3.46410i	−0.301511	−	0.522233i
$45$	−3.00000			−0.447214
$46$	−1.00000			−0.147442
$47$	1.00000	+	1.73205i	0.145865	+	0.252646i	0.929695	−	0.368329i	$-0.120070\pi$
$47$	1.00000	+	1.73205i	0.145865	+	0.252646i	−0.783830	+	0.620975i	$0.786737\pi$
$48$	0.500000	+	0.866025i	0.0721688	+	0.125000i
$49$	1.00000			0.142857
$50$	−4.00000			−0.565685
$51$	−1.00000	−	1.73205i	−0.140028	−	0.242536i
$52$	−1.50000	+	2.59808i	−0.208013	+	0.360288i
$53$	2.00000	+	3.46410i	0.274721	+	0.475831i	0.970065	−	0.242846i	$-0.0780811\pi$
$53$	2.00000	+	3.46410i	0.274721	+	0.475831i	−0.695344	+	0.718677i	$0.744748\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$	6.00000	−	10.3923i	0.809040	−	1.40130i
$56$	1.00000			0.133631
$57$	3.50000	+	2.59808i	0.463586	+	0.344124i
$58$		0			0
$59$	−6.50000	+	11.2583i	−0.846228	+	1.46571i	0.0383226	+	0.999265i	$0.487799\pi$
$59$	−6.50000	+	11.2583i	−0.846228	+	1.46571i	−0.884551	+	0.466444i	$0.845535\pi$
$60$	−1.50000	+	2.59808i	−0.193649	+	0.335410i
$61$	−2.50000	−	4.33013i	−0.320092	−	0.554416i	0.660415	−	0.750901i	$-0.270381\pi$
$61$	−2.50000	−	4.33013i	−0.320092	−	0.554416i	−0.980507	+	0.196485i	$0.937047\pi$
$62$	−3.00000	+	5.19615i	−0.381000	+	0.659912i
$63$	0.500000	+	0.866025i	0.0629941	+	0.109109i
$64$	1.00000			0.125000
$65$	−9.00000			−1.11631
$66$	−2.00000	−	3.46410i	−0.246183	−	0.426401i
$67$	6.00000	+	10.3923i	0.733017	+	1.26962i	0.955588	+	0.294706i	$0.0952216\pi$
$67$	6.00000	+	10.3923i	0.733017	+	1.26962i	−0.222571	+	0.974916i	$0.571445\pi$
$68$	−2.00000			−0.242536
$69$	−1.00000			−0.120386
$70$	1.50000	+	2.59808i	0.179284	+	0.310530i
$71$	3.50000	−	6.06218i	0.415374	−	0.719448i	−0.580094	−	0.814550i	$-0.696984\pi$
$71$	3.50000	−	6.06218i	0.415374	−	0.719448i	0.995468	+	0.0951014i	$0.0303175\pi$
$72$	0.500000	+	0.866025i	0.0589256	+	0.102062i
$73$	1.00000	−	1.73205i	0.117041	−	0.202721i	−0.801553	−	0.597924i	$-0.795992\pi$
$73$	1.00000	−	1.73205i	0.117041	−	0.202721i	0.918594	+	0.395203i	$0.129326\pi$
$74$	2.00000	−	3.46410i	0.232495	−	0.402694i
$75$	−4.00000			−0.461880
$76$	4.00000	−	1.73205i	0.458831	−	0.198680i
$77$	−4.00000			−0.455842
$78$	−1.50000	+	2.59808i	−0.169842	+	0.294174i
$79$	4.00000	−	6.92820i	0.450035	−	0.779484i	−0.548352	−	0.836247i	$-0.684745\pi$
$79$	4.00000	−	6.92820i	0.450035	−	0.779484i	0.998388	+	0.0567635i	$0.0180781\pi$
$80$	1.50000	+	2.59808i	0.167705	+	0.290474i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	2.00000	+	3.46410i	0.220863	+	0.382546i
$83$	17.0000			1.86599			0.932996	−	0.359886i	$-0.117184\pi$
$83$	17.0000			1.86599			0.932996	+	0.359886i	$0.117184\pi$
$84$	1.00000			0.109109
$85$	−3.00000	−	5.19615i	−0.325396	−	0.563602i
$86$	−3.00000	−	5.19615i	−0.323498	−	0.560316i
$87$		0			0
$88$	−4.00000			−0.426401
$89$	−2.00000	−	3.46410i	−0.212000	−	0.367194i	0.740341	−	0.672232i	$-0.234664\pi$
$89$	−2.00000	−	3.46410i	−0.212000	−	0.367194i	−0.952340	+	0.305038i	$0.901331\pi$
$90$	−1.50000	+	2.59808i	−0.158114	+	0.273861i
$91$	1.50000	+	2.59808i	0.157243	+	0.272352i
$92$	−0.500000	+	0.866025i	−0.0521286	+	0.0902894i
$93$	−3.00000	+	5.19615i	−0.311086	+	0.538816i
$94$	2.00000			0.206284
$95$	10.5000	+	7.79423i	1.07728	+	0.799671i
$96$	1.00000			0.102062
$97$	5.00000	−	8.66025i	0.507673	−	0.879316i	−0.492287	−	0.870433i	$-0.663839\pi$
$97$	5.00000	−	8.66025i	0.507673	−	0.879316i	0.999961	−	0.00888289i	$-0.00282755\pi$
$98$	0.500000	−	0.866025i	0.0505076	−	0.0874818i
$99$	−2.00000	−	3.46410i	−0.201008	−	0.348155i
$100$	−2.00000	+	3.46410i	−0.200000	+	0.346410i
$101$	−7.00000	−	12.1244i	−0.696526	−	1.20642i	−0.969664	−	0.244443i	$-0.921395\pi$
$101$	−7.00000	−	12.1244i	−0.696526	−	1.20642i	0.273138	−	0.961975i	$-0.411939\pi$
$102$	−2.00000			−0.198030
$103$		0			0			−	1.00000i	$-0.5\pi$
$103$		0			0				1.00000i	$0.5\pi$
$104$	1.50000	+	2.59808i	0.147087	+	0.254762i
$105$	1.50000	+	2.59808i	0.146385	+	0.253546i
$106$	4.00000			0.388514
$107$	−10.0000			−0.966736			−0.483368	−	0.875417i	$-0.660587\pi$
$107$	−10.0000			−0.966736			−0.483368	+	0.875417i	$0.660587\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$	2.00000	−	3.46410i	0.191565	−	0.331801i	−0.754204	−	0.656640i	$-0.771977\pi$
$109$	2.00000	−	3.46410i	0.191565	−	0.331801i	0.945769	+	0.324840i	$0.105310\pi$
$110$	−6.00000	−	10.3923i	−0.572078	−	0.990867i
$111$	2.00000	−	3.46410i	0.189832	−	0.328798i
$112$	0.500000	−	0.866025i	0.0472456	−	0.0818317i
$113$	−5.00000			−0.470360			−0.235180	−	0.971952i	$-0.575568\pi$
$113$	−5.00000			−0.470360			−0.235180	+	0.971952i	$0.575568\pi$
$114$	4.00000	−	1.73205i	0.374634	−	0.162221i
$115$	−3.00000			−0.279751
$116$		0			0
$117$	−1.50000	+	2.59808i	−0.138675	+	0.240192i
$118$	6.50000	+	11.2583i	0.598374	+	1.03641i
$119$	−1.00000	+	1.73205i	−0.0916698	+	0.158777i
$120$	1.50000	+	2.59808i	0.136931	+	0.237171i
$121$	5.00000			0.454545
$122$	−5.00000			−0.452679
$123$	2.00000	+	3.46410i	0.180334	+	0.312348i
$124$	3.00000	+	5.19615i	0.269408	+	0.466628i
$125$	3.00000			0.268328
$126$	1.00000			0.0890871
$127$	5.50000	+	9.52628i	0.488046	+	0.845321i	0.999905	−	0.0137486i	$-0.00437646\pi$
$127$	5.50000	+	9.52628i	0.488046	+	0.845321i	−0.511859	+	0.859069i	$0.671043\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−3.00000	−	5.19615i	−0.264135	−	0.457496i
$130$	−4.50000	+	7.79423i	−0.394676	+	0.683599i
$131$	4.50000	−	7.79423i	0.393167	−	0.680985i	−0.599699	−	0.800226i	$-0.704713\pi$
$131$	4.50000	−	7.79423i	0.393167	−	0.680985i	0.992865	+	0.119241i	$0.0380462\pi$
$132$	−4.00000			−0.348155
$133$	0.500000	−	4.33013i	0.0433555	−	0.375470i
$134$	12.0000			1.03664
$135$	−1.50000	+	2.59808i	−0.129099	+	0.223607i
$136$	−1.00000	+	1.73205i	−0.0857493	+	0.148522i
$137$	10.5000	+	18.1865i	0.897076	+	1.55378i	0.831215	+	0.555952i	$0.187646\pi$
$137$	10.5000	+	18.1865i	0.897076	+	1.55378i	0.0658609	+	0.997829i	$0.479021\pi$
$138$	−0.500000	+	0.866025i	−0.0425628	+	0.0737210i
$139$	8.00000	+	13.8564i	0.678551	+	1.17529i	0.975417	+	0.220366i	$0.0707252\pi$
$139$	8.00000	+	13.8564i	0.678551	+	1.17529i	−0.296866	+	0.954919i	$0.595942\pi$
$140$	3.00000			0.253546
$141$	2.00000			0.168430
$142$	−3.50000	−	6.06218i	−0.293713	−	0.508727i
$143$	−6.00000	−	10.3923i	−0.501745	−	0.869048i
$144$	1.00000			0.0833333
$145$		0			0
$146$	−1.00000	−	1.73205i	−0.0827606	−	0.143346i
$147$	0.500000	−	0.866025i	0.0412393	−	0.0714286i
$148$	−2.00000	−	3.46410i	−0.164399	−	0.284747i
$149$	−10.0000	+	17.3205i	−0.819232	+	1.41895i	0.0870170	+	0.996207i	$0.472267\pi$
$149$	−10.0000	+	17.3205i	−0.819232	+	1.41895i	−0.906249	+	0.422744i	$0.861067\pi$
$150$	−2.00000	+	3.46410i	−0.163299	+	0.282843i
$151$	19.0000			1.54620			0.773099	−	0.634285i	$-0.218706\pi$
$151$	19.0000			1.54620			0.773099	+	0.634285i	$0.218706\pi$
$152$	0.500000	−	4.33013i	0.0405554	−	0.351220i
$153$	−2.00000			−0.161690
$154$	−2.00000	+	3.46410i	−0.161165	+	0.279145i
$155$	−9.00000	+	15.5885i	−0.722897	+	1.25210i
$156$	1.50000	+	2.59808i	0.120096	+	0.208013i
$157$	4.50000	−	7.79423i	0.359139	−	0.622047i	−0.628678	−	0.777666i	$-0.716404\pi$
$157$	4.50000	−	7.79423i	0.359139	−	0.622047i	0.987817	+	0.155618i	$0.0497370\pi$
$158$	−4.00000	−	6.92820i	−0.318223	−	0.551178i
$159$	4.00000			0.317221
$160$	3.00000			0.237171
$161$	0.500000	+	0.866025i	0.0394055	+	0.0682524i
$162$	0.500000	+	0.866025i	0.0392837	+	0.0680414i
$163$	14.0000			1.09656			0.548282	−	0.836293i	$-0.315282\pi$
$163$	14.0000			1.09656			0.548282	+	0.836293i	$0.315282\pi$
$164$	4.00000			0.312348
$165$	−6.00000	−	10.3923i	−0.467099	−	0.809040i
$166$	8.50000	−	14.7224i	0.659728	−	1.14268i
$167$	9.00000	+	15.5885i	0.696441	+	1.20627i	0.969693	+	0.244328i	$0.0785675\pi$
$167$	9.00000	+	15.5885i	0.696441	+	1.20627i	−0.273252	+	0.961943i	$0.588099\pi$
$168$	0.500000	−	0.866025i	0.0385758	−	0.0668153i
$169$	2.00000	−	3.46410i	0.153846	−	0.266469i
$170$	−6.00000			−0.460179
$171$	4.00000	−	1.73205i	0.305888	−	0.132453i
$172$	−6.00000			−0.457496
$173$	−7.50000	+	12.9904i	−0.570214	+	0.987640i	0.426329	+	0.904568i	$0.359807\pi$
$173$	−7.50000	+	12.9904i	−0.570214	+	0.987640i	−0.996544	+	0.0830722i	$0.973527\pi$
$174$		0			0
$175$	2.00000	+	3.46410i	0.151186	+	0.261861i
$176$	−2.00000	+	3.46410i	−0.150756	+	0.261116i
$177$	6.50000	+	11.2583i	0.488570	+	0.846228i
$178$	−4.00000			−0.299813
$179$	10.0000			0.747435			0.373718	−	0.927543i	$-0.378083\pi$
$179$	10.0000			0.747435			0.373718	+	0.927543i	$0.378083\pi$
$180$	1.50000	+	2.59808i	0.111803	+	0.193649i
$181$	−1.50000	−	2.59808i	−0.111494	−	0.193113i	0.804879	−	0.593439i	$-0.202230\pi$
$181$	−1.50000	−	2.59808i	−0.111494	−	0.193113i	−0.916373	+	0.400326i	$0.868897\pi$
$182$	3.00000			0.222375
$183$	−5.00000			−0.369611
$184$	0.500000	+	0.866025i	0.0368605	+	0.0638442i
$185$	6.00000	−	10.3923i	0.441129	−	0.764057i
$186$	3.00000	+	5.19615i	0.219971	+	0.381000i
$187$	4.00000	−	6.92820i	0.292509	−	0.506640i
$188$	1.00000	−	1.73205i	0.0729325	−	0.126323i
$189$	1.00000			0.0727393
$190$	12.0000	−	5.19615i	0.870572	−	0.376969i
$191$	−11.0000			−0.795932			−0.397966	−	0.917400i	$-0.630284\pi$
$191$	−11.0000			−0.795932			−0.397966	+	0.917400i	$0.630284\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	−2.50000	+	4.33013i	−0.179954	+	0.311689i	−0.941865	−	0.335993i	$-0.890928\pi$
$193$	−2.50000	+	4.33013i	−0.179954	+	0.311689i	0.761911	+	0.647682i	$0.224262\pi$
$194$	−5.00000	−	8.66025i	−0.358979	−	0.621770i
$195$	−4.50000	+	7.79423i	−0.322252	+	0.558156i
$196$	−0.500000	−	0.866025i	−0.0357143	−	0.0618590i
$197$	4.00000			0.284988			0.142494	−	0.989796i	$-0.454488\pi$
$197$	4.00000			0.284988			0.142494	+	0.989796i	$0.454488\pi$
$198$	−4.00000			−0.284268
$199$	−7.00000	−	12.1244i	−0.496217	−	0.859473i	0.503774	−	0.863836i	$-0.331945\pi$
$199$	−7.00000	−	12.1244i	−0.496217	−	0.859473i	−0.999990	+	0.00436292i	$0.998611\pi$
$200$	2.00000	+	3.46410i	0.141421	+	0.244949i
$201$	12.0000			0.846415
$202$	−14.0000			−0.985037
$203$		0			0
$204$	−1.00000	+	1.73205i	−0.0700140	+	0.121268i
$205$	6.00000	+	10.3923i	0.419058	+	0.725830i
$206$		0			0
$207$	−0.500000	+	0.866025i	−0.0347524	+	0.0601929i
$208$	3.00000			0.208013
$209$	−2.00000	+	17.3205i	−0.138343	+	1.19808i
$210$	3.00000			0.207020
$211$	4.00000	−	6.92820i	0.275371	−	0.476957i	−0.694857	−	0.719148i	$-0.744533\pi$
$211$	4.00000	−	6.92820i	0.275371	−	0.476957i	0.970229	+	0.242190i	$0.0778659\pi$
$212$	2.00000	−	3.46410i	0.137361	−	0.237915i
$213$	−3.50000	−	6.06218i	−0.239816	−	0.415374i
$214$	−5.00000	+	8.66025i	−0.341793	+	0.592003i
$215$	−9.00000	−	15.5885i	−0.613795	−	1.06312i
$216$	1.00000			0.0680414
$217$	6.00000			0.407307
$218$	−2.00000	−	3.46410i	−0.135457	−	0.234619i
$219$	−1.00000	−	1.73205i	−0.0675737	−	0.117041i
$220$	−12.0000			−0.809040
$221$	−6.00000			−0.403604
$222$	−2.00000	−	3.46410i	−0.134231	−	0.232495i
$223$	9.00000	−	15.5885i	0.602685	−	1.04388i	−0.389728	−	0.920930i	$-0.627431\pi$
$223$	9.00000	−	15.5885i	0.602685	−	1.04388i	0.992413	−	0.122950i	$-0.0392356\pi$
$224$	−0.500000	−	0.866025i	−0.0334077	−	0.0578638i
$225$	−2.00000	+	3.46410i	−0.133333	+	0.230940i
$226$	−2.50000	+	4.33013i	−0.166298	+	0.288036i
$227$	5.00000			0.331862			0.165931	−	0.986137i	$-0.446937\pi$
$227$	5.00000			0.331862			0.165931	+	0.986137i	$0.446937\pi$
$228$	0.500000	−	4.33013i	0.0331133	−	0.286770i
$229$	−17.0000			−1.12339			−0.561696	−	0.827344i	$-0.689851\pi$
$229$	−17.0000			−1.12339			−0.561696	+	0.827344i	$0.689851\pi$
$230$	−1.50000	+	2.59808i	−0.0989071	+	0.171312i
$231$	−2.00000	+	3.46410i	−0.131590	+	0.227921i
$232$		0			0
$233$	−4.50000	+	7.79423i	−0.294805	+	0.510617i	−0.974939	−	0.222470i	$-0.928588\pi$
$233$	−4.50000	+	7.79423i	−0.294805	+	0.510617i	0.680135	+	0.733087i	$0.261921\pi$
$234$	1.50000	+	2.59808i	0.0980581	+	0.169842i
$235$	6.00000			0.391397
$236$	13.0000			0.846228
$237$	−4.00000	−	6.92820i	−0.259828	−	0.450035i
$238$	1.00000	+	1.73205i	0.0648204	+	0.112272i
$239$	27.0000			1.74648			0.873242	−	0.487286i	$-0.162013\pi$
$239$	27.0000			1.74648			0.873242	+	0.487286i	$0.162013\pi$
$240$	3.00000			0.193649
$241$	−11.0000	−	19.0526i	−0.708572	−	1.22728i	−0.965387	−	0.260822i	$-0.916006\pi$
$241$	−11.0000	−	19.0526i	−0.708572	−	1.22728i	0.256814	−	0.966461i	$-0.417327\pi$
$242$	2.50000	−	4.33013i	0.160706	−	0.278351i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−2.50000	+	4.33013i	−0.160046	+	0.277208i
$245$	1.50000	−	2.59808i	0.0958315	−	0.165985i
$246$	4.00000			0.255031
$247$	12.0000	−	5.19615i	0.763542	−	0.330623i
$248$	6.00000			0.381000
$249$	8.50000	−	14.7224i	0.538666	−	0.932996i
$250$	1.50000	−	2.59808i	0.0948683	−	0.164317i
$251$	−10.5000	−	18.1865i	−0.662754	−	1.14792i	−0.979889	−	0.199543i	$-0.936054\pi$
$251$	−10.5000	−	18.1865i	−0.662754	−	1.14792i	0.317135	−	0.948380i	$-0.397279\pi$
$252$	0.500000	−	0.866025i	0.0314970	−	0.0545545i
$253$	−2.00000	−	3.46410i	−0.125739	−	0.217786i
$254$	11.0000			0.690201
$255$	−6.00000			−0.375735
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−6.00000	−	10.3923i	−0.374270	−	0.648254i	0.615948	−	0.787787i	$-0.288773\pi$
$257$	−6.00000	−	10.3923i	−0.374270	−	0.648254i	−0.990217	+	0.139533i	$0.955440\pi$
$258$	−6.00000			−0.373544
$259$	−4.00000			−0.248548
$260$	4.50000	+	7.79423i	0.279078	+	0.483378i
$261$		0			0
$262$	−4.50000	−	7.79423i	−0.278011	−	0.481529i
$263$	1.50000	−	2.59808i	0.0924940	−	0.160204i	−0.816066	−	0.577959i	$-0.803849\pi$
$263$	1.50000	−	2.59808i	0.0924940	−	0.160204i	0.908560	+	0.417755i	$0.137183\pi$
$264$	−2.00000	+	3.46410i	−0.123091	+	0.213201i
$265$	12.0000			0.737154
$266$	−3.50000	−	2.59808i	−0.214599	−	0.159298i
$267$	−4.00000			−0.244796
$268$	6.00000	−	10.3923i	0.366508	−	0.634811i
$269$	−7.00000	+	12.1244i	−0.426798	+	0.739235i	−0.996586	−	0.0825561i	$-0.973692\pi$
$269$	−7.00000	+	12.1244i	−0.426798	+	0.739235i	0.569789	+	0.821791i	$0.307025\pi$
$270$	1.50000	+	2.59808i	0.0912871	+	0.158114i
$271$	−13.0000	+	22.5167i	−0.789694	+	1.36779i	0.136461	+	0.990645i	$0.456427\pi$
$271$	−13.0000	+	22.5167i	−0.789694	+	1.36779i	−0.926155	+	0.377144i	$0.876906\pi$
$272$	1.00000	+	1.73205i	0.0606339	+	0.105021i
$273$	3.00000			0.181568
$274$	21.0000			1.26866
$275$	−8.00000	−	13.8564i	−0.482418	−	0.835573i
$276$	0.500000	+	0.866025i	0.0300965	+	0.0521286i
$277$	−2.00000			−0.120168			−0.0600842	−	0.998193i	$-0.519137\pi$
$277$	−2.00000			−0.120168			−0.0600842	+	0.998193i	$0.519137\pi$
$278$	16.0000			0.959616
$279$	3.00000	+	5.19615i	0.179605	+	0.311086i
$280$	1.50000	−	2.59808i	0.0896421	−	0.155265i
$281$	13.0000	+	22.5167i	0.775515	+	1.34323i	0.934505	+	0.355951i	$0.115843\pi$
$281$	13.0000	+	22.5167i	0.775515	+	1.34323i	−0.158990	+	0.987280i	$0.550824\pi$
$282$	1.00000	−	1.73205i	0.0595491	−	0.103142i
$283$	−12.5000	+	21.6506i	−0.743048	+	1.28700i	0.208053	+	0.978117i	$0.433287\pi$
$283$	−12.5000	+	21.6506i	−0.743048	+	1.28700i	−0.951101	+	0.308879i	$0.900046\pi$
$284$	−7.00000			−0.415374
$285$	12.0000	−	5.19615i	0.710819	−	0.307794i
$286$	−12.0000			−0.709575
$287$	2.00000	−	3.46410i	0.118056	−	0.204479i
$288$	0.500000	−	0.866025i	0.0294628	−	0.0510310i
$289$	6.50000	+	11.2583i	0.382353	+	0.662255i
$290$		0			0
$291$	−5.00000	−	8.66025i	−0.293105	−	0.507673i
$292$	−2.00000			−0.117041
$293$	−19.0000			−1.10999			−0.554996	−	0.831853i	$-0.687280\pi$
$293$	−19.0000			−1.10999			−0.554996	+	0.831853i	$0.687280\pi$
$294$	−0.500000	−	0.866025i	−0.0291606	−	0.0505076i
$295$	19.5000	+	33.7750i	1.13533	+	1.96646i
$296$	−4.00000			−0.232495
$297$	−4.00000			−0.232104
$298$	10.0000	+	17.3205i	0.579284	+	1.00335i
$299$	−1.50000	+	2.59808i	−0.0867472	+	0.150251i
$300$	2.00000	+	3.46410i	0.115470	+	0.200000i
$301$	−3.00000	+	5.19615i	−0.172917	+	0.299501i
$302$	9.50000	−	16.4545i	0.546664	−	0.946849i
$303$	−14.0000			−0.804279
$304$	−3.50000	−	2.59808i	−0.200739	−	0.149010i
$305$	−15.0000			−0.858898
$306$	−1.00000	+	1.73205i	−0.0571662	+	0.0990148i
$307$	−7.50000	+	12.9904i	−0.428048	+	0.741400i	−0.996700	−	0.0811780i	$-0.974132\pi$
$307$	−7.50000	+	12.9904i	−0.428048	+	0.741400i	0.568652	+	0.822578i	$0.307465\pi$
$308$	2.00000	+	3.46410i	0.113961	+	0.197386i
$309$		0			0
$310$	9.00000	+	15.5885i	0.511166	+	0.885365i
$311$	−2.00000			−0.113410			−0.0567048	−	0.998391i	$-0.518059\pi$
$311$	−2.00000			−0.113410			−0.0567048	+	0.998391i	$0.518059\pi$
$312$	3.00000			0.169842
$313$	−12.0000	−	20.7846i	−0.678280	−	1.17482i	−0.975499	−	0.220006i	$-0.929392\pi$
$313$	−12.0000	−	20.7846i	−0.678280	−	1.17482i	0.297218	−	0.954810i	$-0.403941\pi$
$314$	−4.50000	−	7.79423i	−0.253950	−	0.439854i
$315$	3.00000			0.169031
$316$	−8.00000			−0.450035
$317$	−3.00000	−	5.19615i	−0.168497	−	0.291845i	0.769395	−	0.638774i	$-0.220558\pi$
$317$	−3.00000	−	5.19615i	−0.168497	−	0.291845i	−0.937892	+	0.346929i	$0.887225\pi$
$318$	2.00000	−	3.46410i	0.112154	−	0.194257i
$319$		0			0
$320$	1.50000	−	2.59808i	0.0838525	−	0.145237i
$321$	−5.00000	+	8.66025i	−0.279073	+	0.483368i
$322$	1.00000			0.0557278
$323$	7.00000	+	5.19615i	0.389490	+	0.289122i
$324$	1.00000			0.0555556
$325$	−6.00000	+	10.3923i	−0.332820	+	0.576461i
$326$	7.00000	−	12.1244i	0.387694	−	0.671506i
$327$	−2.00000	−	3.46410i	−0.110600	−	0.191565i
$328$	2.00000	−	3.46410i	0.110432	−	0.191273i
$329$	−1.00000	−	1.73205i	−0.0551318	−	0.0954911i
$330$	−12.0000			−0.660578
$331$	−24.0000			−1.31916			−0.659580	−	0.751635i	$-0.729266\pi$
$331$	−24.0000			−1.31916			−0.659580	+	0.751635i	$0.729266\pi$
$332$	−8.50000	−	14.7224i	−0.466498	−	0.807998i
$333$	−2.00000	−	3.46410i	−0.109599	−	0.189832i
$334$	18.0000			0.984916
$335$	36.0000			1.96689
$336$	−0.500000	−	0.866025i	−0.0272772	−	0.0472456i
$337$	−8.50000	+	14.7224i	−0.463025	+	0.801982i	−0.999110	−	0.0421818i	$-0.986569\pi$
$337$	−8.50000	+	14.7224i	−0.463025	+	0.801982i	0.536085	+	0.844164i	$0.319902\pi$
$338$	−2.00000	−	3.46410i	−0.108786	−	0.188422i
$339$	−2.50000	+	4.33013i	−0.135781	+	0.235180i
$340$	−3.00000	+	5.19615i	−0.162698	+	0.281801i
$341$	−24.0000			−1.29967
$342$	0.500000	−	4.33013i	0.0270369	−	0.234146i
$343$	−1.00000			−0.0539949
$344$	−3.00000	+	5.19615i	−0.161749	+	0.280158i
$345$	−1.50000	+	2.59808i	−0.0807573	+	0.139876i
$346$	7.50000	+	12.9904i	0.403202	+	0.698367i
$347$	−11.0000	+	19.0526i	−0.590511	+	1.02279i	0.403653	+	0.914912i	$0.367740\pi$
$347$	−11.0000	+	19.0526i	−0.590511	+	1.02279i	−0.994164	+	0.107883i	$0.965593\pi$
$348$		0			0
$349$	10.0000			0.535288			0.267644	−	0.963518i	$-0.413755\pi$
$349$	10.0000			0.535288			0.267644	+	0.963518i	$0.413755\pi$
$350$	4.00000			0.213809
$351$	1.50000	+	2.59808i	0.0800641	+	0.138675i
$352$	2.00000	+	3.46410i	0.106600	+	0.184637i
$353$	12.0000			0.638696			0.319348	−	0.947638i	$-0.396536\pi$
$353$	12.0000			0.638696			0.319348	+	0.947638i	$0.396536\pi$
$354$	13.0000			0.690942
$355$	−10.5000	−	18.1865i	−0.557282	−	0.965241i
$356$	−2.00000	+	3.46410i	−0.106000	+	0.183597i
$357$	1.00000	+	1.73205i	0.0529256	+	0.0916698i
$358$	5.00000	−	8.66025i	0.264258	−	0.457709i
$359$	−12.0000	+	20.7846i	−0.633336	+	1.09697i	0.353529	+	0.935423i	$0.384981\pi$
$359$	−12.0000	+	20.7846i	−0.633336	+	1.09697i	−0.986865	+	0.161546i	$0.948352\pi$
$360$	3.00000			0.158114
$361$	−18.5000	−	4.33013i	−0.973684	−	0.227901i
$362$	−3.00000			−0.157676
$363$	2.50000	−	4.33013i	0.131216	−	0.227273i
$364$	1.50000	−	2.59808i	0.0786214	−	0.136176i
$365$	−3.00000	−	5.19615i	−0.157027	−	0.271979i
$366$	−2.50000	+	4.33013i	−0.130677	+	0.226339i
$367$	−16.0000	−	27.7128i	−0.835193	−	1.44660i	−0.893873	−	0.448320i	$-0.852022\pi$
$367$	−16.0000	−	27.7128i	−0.835193	−	1.44660i	0.0586798	−	0.998277i	$-0.481311\pi$
$368$	1.00000			0.0521286
$369$	4.00000			0.208232
$370$	−6.00000	−	10.3923i	−0.311925	−	0.540270i
$371$	−2.00000	−	3.46410i	−0.103835	−	0.179847i
$372$	6.00000			0.311086
$373$	−10.0000			−0.517780			−0.258890	−	0.965907i	$-0.583357\pi$
$373$	−10.0000			−0.517780			−0.258890	+	0.965907i	$0.583357\pi$
$374$	−4.00000	−	6.92820i	−0.206835	−	0.358249i
$375$	1.50000	−	2.59808i	0.0774597	−	0.134164i
$376$	−1.00000	−	1.73205i	−0.0515711	−	0.0893237i
$377$		0			0
$378$	0.500000	−	0.866025i	0.0257172	−	0.0445435i
$379$	−34.0000			−1.74646			−0.873231	−	0.487306i	$-0.837980\pi$
$379$	−34.0000			−1.74646			−0.873231	+	0.487306i	$0.837980\pi$
$380$	1.50000	−	12.9904i	0.0769484	−	0.666392i
$381$	11.0000			0.563547
$382$	−5.50000	+	9.52628i	−0.281404	+	0.487407i
$383$	2.00000	−	3.46410i	0.102195	−	0.177007i	−0.810394	−	0.585886i	$-0.800747\pi$
$383$	2.00000	−	3.46410i	0.102195	−	0.177007i	0.912589	+	0.408879i	$0.134080\pi$
$384$	−0.500000	−	0.866025i	−0.0255155	−	0.0441942i
$385$	−6.00000	+	10.3923i	−0.305788	+	0.529641i
$386$	2.50000	+	4.33013i	0.127247	+	0.220398i
$387$	−6.00000			−0.304997
$388$	−10.0000			−0.507673
$389$	−4.00000	−	6.92820i	−0.202808	−	0.351274i	0.746624	−	0.665246i	$-0.231673\pi$
$389$	−4.00000	−	6.92820i	−0.202808	−	0.351274i	−0.949432	+	0.313972i	$0.898340\pi$
$390$	4.50000	+	7.79423i	0.227866	+	0.394676i
$391$	−2.00000			−0.101144
$392$	−1.00000			−0.0505076
$393$	−4.50000	−	7.79423i	−0.226995	−	0.393167i
$394$	2.00000	−	3.46410i	0.100759	−	0.174519i
$395$	−12.0000	−	20.7846i	−0.603786	−	1.04579i
$396$	−2.00000	+	3.46410i	−0.100504	+	0.174078i
$397$	−9.00000	+	15.5885i	−0.451697	+	0.782362i	−0.998492	−	0.0549046i	$-0.982515\pi$
$397$	−9.00000	+	15.5885i	−0.451697	+	0.782362i	0.546795	+	0.837267i	$0.315848\pi$
$398$	−14.0000			−0.701757
$399$	−3.50000	−	2.59808i	−0.175219	−	0.130066i
$400$	4.00000			0.200000
$401$	−1.50000	+	2.59808i	−0.0749064	+	0.129742i	−0.901046	−	0.433724i	$-0.857199\pi$
$401$	−1.50000	+	2.59808i	−0.0749064	+	0.129742i	0.826139	+	0.563466i	$0.190532\pi$
$402$	6.00000	−	10.3923i	0.299253	−	0.518321i
$403$	9.00000	+	15.5885i	0.448322	+	0.776516i
$404$	−7.00000	+	12.1244i	−0.348263	+	0.603209i
$405$	1.50000	+	2.59808i	0.0745356	+	0.129099i
$406$		0			0
$407$	16.0000			0.793091
$408$	1.00000	+	1.73205i	0.0495074	+	0.0857493i
$409$	−12.0000	−	20.7846i	−0.593362	−	1.02773i	−0.993776	−	0.111398i	$-0.964467\pi$
$409$	−12.0000	−	20.7846i	−0.593362	−	1.02773i	0.400414	−	0.916334i	$-0.368866\pi$
$410$	12.0000			0.592638
$411$	21.0000			1.03585
$412$		0			0
$413$	6.50000	−	11.2583i	0.319844	−	0.553986i
$414$	0.500000	+	0.866025i	0.0245737	+	0.0425628i
$415$	25.5000	−	44.1673i	1.25175	−	2.16809i
$416$	1.50000	−	2.59808i	0.0735436	−	0.127381i
$417$	16.0000			0.783523
$418$	14.0000	+	10.3923i	0.684762	+	0.508304i
$419$	−12.0000			−0.586238			−0.293119	−	0.956076i	$-0.594693\pi$
$419$	−12.0000			−0.586238			−0.293119	+	0.956076i	$0.594693\pi$
$420$	1.50000	−	2.59808i	0.0731925	−	0.126773i
$421$	4.00000	−	6.92820i	0.194948	−	0.337660i	−0.751935	−	0.659237i	$-0.770879\pi$
$421$	4.00000	−	6.92820i	0.194948	−	0.337660i	0.946883	+	0.321577i	$0.104213\pi$
$422$	−4.00000	−	6.92820i	−0.194717	−	0.337260i
$423$	1.00000	−	1.73205i	0.0486217	−	0.0842152i
$424$	−2.00000	−	3.46410i	−0.0971286	−	0.168232i
$425$	−8.00000			−0.388057
$426$	−7.00000			−0.339151
$427$	2.50000	+	4.33013i	0.120983	+	0.209550i
$428$	5.00000	+	8.66025i	0.241684	+	0.418609i
$429$	−12.0000			−0.579365
$430$	−18.0000			−0.868037
$431$	8.00000	+	13.8564i	0.385346	+	0.667440i	0.991817	−	0.127666i	$-0.0407486\pi$
$431$	8.00000	+	13.8564i	0.385346	+	0.667440i	−0.606471	+	0.795106i	$0.707415\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	12.0000	+	20.7846i	0.576683	+	0.998845i	0.995857	+	0.0909384i	$0.0289866\pi$
$433$	12.0000	+	20.7846i	0.576683	+	0.998845i	−0.419173	+	0.907906i	$0.637680\pi$
$434$	3.00000	−	5.19615i	0.144005	−	0.249423i
$435$		0			0
$436$	−4.00000			−0.191565
$437$	4.00000	−	1.73205i	0.191346	−	0.0828552i
$438$	−2.00000			−0.0955637
$439$	−5.00000	+	8.66025i	−0.238637	+	0.413331i	−0.960323	−	0.278889i	$-0.910034\pi$
$439$	−5.00000	+	8.66025i	−0.238637	+	0.413331i	0.721686	+	0.692220i	$0.243367\pi$
$440$	−6.00000	+	10.3923i	−0.286039	+	0.495434i
$441$	−0.500000	−	0.866025i	−0.0238095	−	0.0412393i
$442$	−3.00000	+	5.19615i	−0.142695	+	0.247156i
$443$	−9.00000	−	15.5885i	−0.427603	−	0.740630i	0.569057	−	0.822298i	$-0.307309\pi$
$443$	−9.00000	−	15.5885i	−0.427603	−	0.740630i	−0.996660	+	0.0816684i	$0.973975\pi$
$444$	−4.00000			−0.189832
$445$	−12.0000			−0.568855
$446$	−9.00000	−	15.5885i	−0.426162	−	0.738135i
$447$	10.0000	+	17.3205i	0.472984	+	0.819232i
$448$	−1.00000			−0.0472456
$449$	−39.0000			−1.84052			−0.920262	−	0.391303i	$-0.872024\pi$
$449$	−39.0000			−1.84052			−0.920262	+	0.391303i	$0.872024\pi$
$450$	2.00000	+	3.46410i	0.0942809	+	0.163299i
$451$	−8.00000	+	13.8564i	−0.376705	+	0.652473i
$452$	2.50000	+	4.33013i	0.117590	+	0.203672i
$453$	9.50000	−	16.4545i	0.446349	−	0.773099i
$454$	2.50000	−	4.33013i	0.117331	−	0.203223i
$455$	9.00000			0.421927
$456$	−3.50000	−	2.59808i	−0.163903	−	0.121666i
$457$	−7.00000			−0.327446			−0.163723	−	0.986506i	$-0.552350\pi$
$457$	−7.00000			−0.327446			−0.163723	+	0.986506i	$0.552350\pi$
$458$	−8.50000	+	14.7224i	−0.397179	+	0.687934i
$459$	−1.00000	+	1.73205i	−0.0466760	+	0.0808452i
$460$	1.50000	+	2.59808i	0.0699379	+	0.121136i
$461$	16.5000	−	28.5788i	0.768482	−	1.33105i	−0.169904	−	0.985461i	$-0.554346\pi$
$461$	16.5000	−	28.5788i	0.768482	−	1.33105i	0.938386	−	0.345589i	$-0.112321\pi$
$462$	2.00000	+	3.46410i	0.0930484	+	0.161165i
$463$	−9.00000			−0.418265			−0.209133	−	0.977887i	$-0.567064\pi$
$463$	−9.00000			−0.418265			−0.209133	+	0.977887i	$0.567064\pi$
$464$		0			0
$465$	9.00000	+	15.5885i	0.417365	+	0.722897i
$466$	4.50000	+	7.79423i	0.208458	+	0.361061i
$467$	−4.00000			−0.185098			−0.0925490	−	0.995708i	$-0.529501\pi$
$467$	−4.00000			−0.185098			−0.0925490	+	0.995708i	$0.529501\pi$
$468$	3.00000			0.138675
$469$	−6.00000	−	10.3923i	−0.277054	−	0.479872i
$470$	3.00000	−	5.19615i	0.138380	−	0.239681i
$471$	−4.50000	−	7.79423i	−0.207349	−	0.359139i
$472$	6.50000	−	11.2583i	0.299187	−	0.518207i
$473$	12.0000	−	20.7846i	0.551761	−	0.955677i
$474$	−8.00000			−0.367452
$475$	16.0000	−	6.92820i	0.734130	−	0.317888i
$476$	2.00000			0.0916698
$477$	2.00000	−	3.46410i	0.0915737	−	0.158610i
$478$	13.5000	−	23.3827i	0.617476	−	1.06950i
$479$	21.0000	+	36.3731i	0.959514	+	1.66193i	0.723681	+	0.690134i	$0.242449\pi$
$479$	21.0000	+	36.3731i	0.959514	+	1.66193i	0.235833	+	0.971794i	$0.424218\pi$
$480$	1.50000	−	2.59808i	0.0684653	−	0.118585i
$481$	−6.00000	−	10.3923i	−0.273576	−	0.473848i
$482$	−22.0000			−1.00207
$483$	1.00000			0.0455016
$484$	−2.50000	−	4.33013i	−0.113636	−	0.196824i
$485$	−15.0000	−	25.9808i	−0.681115	−	1.17973i
$486$	1.00000			0.0453609
$487$	−28.0000			−1.26880			−0.634401	−	0.773004i	$-0.718753\pi$
$487$	−28.0000			−1.26880			−0.634401	+	0.773004i	$0.718753\pi$
$488$	2.50000	+	4.33013i	0.113170	+	0.196016i
$489$	7.00000	−	12.1244i	0.316551	−	0.548282i
$490$	−1.50000	−	2.59808i	−0.0677631	−	0.117369i
$491$	−6.00000	+	10.3923i	−0.270776	+	0.468998i	−0.969061	−	0.246822i	$-0.920614\pi$
$491$	−6.00000	+	10.3923i	−0.270776	+	0.468998i	0.698285	+	0.715820i	$0.253947\pi$
$492$	2.00000	−	3.46410i	0.0901670	−	0.156174i
$493$		0			0
$494$	1.50000	−	12.9904i	0.0674882	−	0.584465i
$495$	−12.0000			−0.539360
$496$	3.00000	−	5.19615i	0.134704	−	0.233314i
$497$	−3.50000	+	6.06218i	−0.156996	+	0.271926i
$498$	−8.50000	−	14.7224i	−0.380894	−	0.659728i
$499$	5.00000	−	8.66025i	0.223831	−	0.387686i	−0.732137	−	0.681157i	$-0.761477\pi$
$499$	5.00000	−	8.66025i	0.223831	−	0.387686i	0.955968	+	0.293471i	$0.0948104\pi$
$500$	−1.50000	−	2.59808i	−0.0670820	−	0.116190i
$501$	18.0000			0.804181
$502$	−21.0000			−0.937276
$503$	−11.0000	−	19.0526i	−0.490466	−	0.849512i	0.509474	−	0.860486i	$-0.329840\pi$
$503$	−11.0000	−	19.0526i	−0.490466	−	0.849512i	−0.999940	+	0.0109744i	$0.996507\pi$
$504$	−0.500000	−	0.866025i	−0.0222718	−	0.0385758i
$505$	−42.0000			−1.86898
$506$	−4.00000			−0.177822
$507$	−2.00000	−	3.46410i	−0.0888231	−	0.153846i
$508$	5.50000	−	9.52628i	0.244023	−	0.422660i
$509$	6.50000	+	11.2583i	0.288107	+	0.499017i	0.973358	−	0.229291i	$-0.0736406\pi$
$509$	6.50000	+	11.2583i	0.288107	+	0.499017i	−0.685251	+	0.728307i	$0.740307\pi$
$510$	−3.00000	+	5.19615i	−0.132842	+	0.230089i
$511$	−1.00000	+	1.73205i	−0.0442374	+	0.0766214i
$512$	−1.00000			−0.0441942
$513$	0.500000	−	4.33013i	0.0220755	−	0.191180i
$514$	−12.0000			−0.529297
$515$		0			0
$516$	−3.00000	+	5.19615i	−0.132068	+	0.228748i
$517$	4.00000	+	6.92820i	0.175920	+	0.304702i
$518$	−2.00000	+	3.46410i	−0.0878750	+	0.152204i
$519$	7.50000	+	12.9904i	0.329213	+	0.570214i
$520$	9.00000			0.394676
$521$	−14.0000			−0.613351			−0.306676	−	0.951814i	$-0.599217\pi$
$521$	−14.0000			−0.613351			−0.306676	+	0.951814i	$0.599217\pi$
$522$		0			0
$523$	16.0000	+	27.7128i	0.699631	+	1.21180i	0.968594	+	0.248646i	$0.0799857\pi$
$523$	16.0000	+	27.7128i	0.699631	+	1.21180i	−0.268963	+	0.963150i	$0.586681\pi$
$524$	−9.00000			−0.393167
$525$	4.00000			0.174574
$526$	−1.50000	−	2.59808i	−0.0654031	−	0.113282i
$527$	−6.00000	+	10.3923i	−0.261364	+	0.452696i
$528$	2.00000	+	3.46410i	0.0870388	+	0.150756i
$529$	11.0000	−	19.0526i	0.478261	−	0.828372i
$530$	6.00000	−	10.3923i	0.260623	−	0.451413i
$531$	13.0000			0.564152
$532$	−4.00000	+	1.73205i	−0.173422	+	0.0750939i
$533$	12.0000			0.519778
$534$	−2.00000	+	3.46410i	−0.0865485	+	0.149906i
$535$	−15.0000	+	25.9808i	−0.648507	+	1.12325i
$536$	−6.00000	−	10.3923i	−0.259161	−	0.448879i
$537$	5.00000	−	8.66025i	0.215766	−	0.373718i
$538$	7.00000	+	12.1244i	0.301791	+	0.522718i
$539$	4.00000			0.172292
$540$	3.00000			0.129099
$541$	−16.0000	−	27.7128i	−0.687894	−	1.19147i	−0.972518	−	0.232828i	$-0.925202\pi$
$541$	−16.0000	−	27.7128i	−0.687894	−	1.19147i	0.284624	−	0.958639i	$-0.408131\pi$
$542$	13.0000	+	22.5167i	0.558398	+	0.967173i
$543$	−3.00000			−0.128742
$544$	2.00000			0.0857493
$545$	−6.00000	−	10.3923i	−0.257012	−	0.445157i
$546$	1.50000	−	2.59808i	0.0641941	−	0.111187i
$547$	23.0000	+	39.8372i	0.983409	+	1.70331i	0.648803	+	0.760956i	$0.275270\pi$
$547$	23.0000	+	39.8372i	0.983409	+	1.70331i	0.334606	+	0.942358i	$0.391397\pi$
$548$	10.5000	−	18.1865i	0.448538	−	0.776890i
$549$	−2.50000	+	4.33013i	−0.106697	+	0.184805i
$550$	−16.0000			−0.682242
$551$		0			0
$552$	1.00000			0.0425628
$553$	−4.00000	+	6.92820i	−0.170097	+	0.294617i
$554$	−1.00000	+	1.73205i	−0.0424859	+	0.0735878i
$555$	−6.00000	−	10.3923i	−0.254686	−	0.441129i
$556$	8.00000	−	13.8564i	0.339276	−	0.587643i
$557$	−11.0000	−	19.0526i	−0.466085	−	0.807283i	0.533165	−	0.846011i	$-0.321003\pi$
$557$	−11.0000	−	19.0526i	−0.466085	−	0.807283i	−0.999250	+	0.0387286i	$0.987669\pi$
$558$	6.00000			0.254000
$559$	−18.0000			−0.761319
$560$	−1.50000	−	2.59808i	−0.0633866	−	0.109789i
$561$	−4.00000	−	6.92820i	−0.168880	−	0.292509i
$562$	26.0000			1.09674
$563$	33.0000			1.39078			0.695392	−	0.718631i	$-0.255231\pi$
$563$	33.0000			1.39078			0.695392	+	0.718631i	$0.255231\pi$
$564$	−1.00000	−	1.73205i	−0.0421076	−	0.0729325i
$565$	−7.50000	+	12.9904i	−0.315527	+	0.546509i
$566$	12.5000	+	21.6506i	0.525414	+	0.910044i
$567$	0.500000	−	0.866025i	0.0209980	−	0.0363696i
$568$	−3.50000	+	6.06218i	−0.146857	+	0.254363i
$569$	−9.00000			−0.377300			−0.188650	−	0.982044i	$-0.560411\pi$
$569$	−9.00000			−0.377300			−0.188650	+	0.982044i	$0.560411\pi$
$570$	1.50000	−	12.9904i	0.0628281	−	0.544107i
$571$	2.00000			0.0836974			0.0418487	−	0.999124i	$-0.486675\pi$
$571$	2.00000			0.0836974			0.0418487	+	0.999124i	$0.486675\pi$
$572$	−6.00000	+	10.3923i	−0.250873	+	0.434524i
$573$	−5.50000	+	9.52628i	−0.229766	+	0.397966i
$574$	−2.00000	−	3.46410i	−0.0834784	−	0.144589i
$575$	−2.00000	+	3.46410i	−0.0834058	+	0.144463i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−8.00000			−0.333044			−0.166522	−	0.986038i	$-0.553254\pi$
$577$	−8.00000			−0.333044			−0.166522	+	0.986038i	$0.553254\pi$
$578$	13.0000			0.540729
$579$	2.50000	+	4.33013i	0.103896	+	0.179954i
$580$		0			0
$581$	−17.0000			−0.705279
$582$	−10.0000			−0.414513
$583$	8.00000	+	13.8564i	0.331326	+	0.573874i
$584$	−1.00000	+	1.73205i	−0.0413803	+	0.0716728i
$585$	4.50000	+	7.79423i	0.186052	+	0.322252i
$586$	−9.50000	+	16.4545i	−0.392441	+	0.679728i
$587$	10.0000	−	17.3205i	0.412744	−	0.714894i	−0.582445	−	0.812870i	$-0.697904\pi$
$587$	10.0000	−	17.3205i	0.412744	−	0.714894i	0.995189	+	0.0979766i	$0.0312370\pi$
$588$	−1.00000			−0.0412393
$589$	3.00000	−	25.9808i	0.123613	−	1.07052i
$590$	39.0000			1.60560
$591$	2.00000	−	3.46410i	0.0822690	−	0.142494i
$592$	−2.00000	+	3.46410i	−0.0821995	+	0.142374i
$593$	16.0000	+	27.7128i	0.657041	+	1.13803i	0.981378	+	0.192087i	$0.0615256\pi$
$593$	16.0000	+	27.7128i	0.657041	+	1.13803i	−0.324337	+	0.945942i	$0.605141\pi$
$594$	−2.00000	+	3.46410i	−0.0820610	+	0.142134i
$595$	3.00000	+	5.19615i	0.122988	+	0.213021i
$596$	20.0000			0.819232
$597$	−14.0000			−0.572982
$598$	1.50000	+	2.59808i	0.0613396	+	0.106243i
$599$	21.5000	+	37.2391i	0.878466	+	1.52155i	0.853024	+	0.521872i	$0.174766\pi$
$599$	21.5000	+	37.2391i	0.878466	+	1.52155i	0.0254422	+	0.999676i	$0.491901\pi$
$600$	4.00000			0.163299
$601$	−6.00000			−0.244745			−0.122373	−	0.992484i	$-0.539050\pi$
$601$	−6.00000			−0.244745			−0.122373	+	0.992484i	$0.539050\pi$
$602$	3.00000	+	5.19615i	0.122271	+	0.211779i
$603$	6.00000	−	10.3923i	0.244339	−	0.423207i
$604$	−9.50000	−	16.4545i	−0.386550	−	0.669523i
$605$	7.50000	−	12.9904i	0.304918	−	0.528134i
$606$	−7.00000	+	12.1244i	−0.284356	+	0.492518i
$607$	−16.0000			−0.649420			−0.324710	−	0.945814i	$-0.605267\pi$
$607$	−16.0000			−0.649420			−0.324710	+	0.945814i	$0.605267\pi$
$608$	−4.00000	+	1.73205i	−0.162221	+	0.0702439i
$609$		0			0
$610$	−7.50000	+	12.9904i	−0.303666	+	0.525965i
$611$	3.00000	−	5.19615i	0.121367	−	0.210214i
$612$	1.00000	+	1.73205i	0.0404226	+	0.0700140i
$613$	5.00000	−	8.66025i	0.201948	−	0.349784i	−0.747208	−	0.664590i	$-0.768606\pi$
$613$	5.00000	−	8.66025i	0.201948	−	0.349784i	0.949156	+	0.314806i	$0.101939\pi$
$614$	7.50000	+	12.9904i	0.302675	+	0.524249i
$615$	12.0000			0.483887
$616$	4.00000			0.161165
$617$	13.5000	+	23.3827i	0.543490	+	0.941351i	0.998700	+	0.0509678i	$0.0162306\pi$
$617$	13.5000	+	23.3827i	0.543490	+	0.941351i	−0.455211	+	0.890384i	$0.650436\pi$
$618$		0			0
$619$	−5.00000			−0.200967			−0.100483	−	0.994939i	$-0.532039\pi$
$619$	−5.00000			−0.200967			−0.100483	+	0.994939i	$0.532039\pi$
$620$	18.0000			0.722897
$621$	0.500000	+	0.866025i	0.0200643	+	0.0347524i
$622$	−1.00000	+	1.73205i	−0.0400963	+	0.0694489i
$623$	2.00000	+	3.46410i	0.0801283	+	0.138786i
$624$	1.50000	−	2.59808i	0.0600481	−	0.104006i
$625$	14.5000	−	25.1147i	0.580000	−	1.00459i
$626$	−24.0000			−0.959233
$627$	14.0000	+	10.3923i	0.559106	+	0.415029i
$628$	−9.00000			−0.359139
$629$	4.00000	−	6.92820i	0.159490	−	0.276246i
$630$	1.50000	−	2.59808i	0.0597614	−	0.103510i
$631$	−4.00000	−	6.92820i	−0.159237	−	0.275807i	0.775356	−	0.631524i	$-0.217570\pi$
$631$	−4.00000	−	6.92820i	−0.159237	−	0.275807i	−0.934594	+	0.355716i	$0.884237\pi$
$632$	−4.00000	+	6.92820i	−0.159111	+	0.275589i
$633$	−4.00000	−	6.92820i	−0.158986	−	0.275371i
$634$	−6.00000			−0.238290
$635$	33.0000			1.30957
$636$	−2.00000	−	3.46410i	−0.0793052	−	0.137361i
$637$	−1.50000	−	2.59808i	−0.0594322	−	0.102940i
$638$		0			0
$639$	−7.00000			−0.276916
$640$	−1.50000	−	2.59808i	−0.0592927	−	0.102698i
$641$	8.50000	−	14.7224i	0.335730	−	0.581501i	−0.647895	−	0.761730i	$-0.724350\pi$
$641$	8.50000	−	14.7224i	0.335730	−	0.581501i	0.983625	+	0.180229i	$0.0576838\pi$
$642$	5.00000	+	8.66025i	0.197334	+	0.341793i
$643$	20.5000	−	35.5070i	0.808441	−	1.40026i	−0.105502	−	0.994419i	$-0.533645\pi$
$643$	20.5000	−	35.5070i	0.808441	−	1.40026i	0.913943	−	0.405842i	$-0.133022\pi$
$644$	0.500000	−	0.866025i	0.0197028	−	0.0341262i
$645$	−18.0000			−0.708749
$646$	8.00000	−	3.46410i	0.314756	−	0.136293i
$647$	30.0000			1.17942			0.589711	−	0.807614i	$-0.299242\pi$
$647$	30.0000			1.17942			0.589711	+	0.807614i	$0.299242\pi$
$648$	0.500000	−	0.866025i	0.0196419	−	0.0340207i
$649$	−26.0000	+	45.0333i	−1.02059	+	1.76771i
$650$	6.00000	+	10.3923i	0.235339	+	0.407620i
$651$	3.00000	−	5.19615i	0.117579	−	0.203653i
$652$	−7.00000	−	12.1244i	−0.274141	−	0.474826i
$653$	6.00000			0.234798			0.117399	−	0.993085i	$-0.462544\pi$
$653$	6.00000			0.234798			0.117399	+	0.993085i	$0.462544\pi$
$654$	−4.00000			−0.156412
$655$	−13.5000	−	23.3827i	−0.527489	−	0.913637i
$656$	−2.00000	−	3.46410i	−0.0780869	−	0.135250i
$657$	−2.00000			−0.0780274
$658$	−2.00000			−0.0779681
$659$	13.0000	+	22.5167i	0.506408	+	0.877125i	0.999973	+	0.00741531i	$0.00236039\pi$
$659$	13.0000	+	22.5167i	0.506408	+	0.877125i	−0.493564	+	0.869709i	$0.664306\pi$
$660$	−6.00000	+	10.3923i	−0.233550	+	0.404520i
$661$	5.50000	+	9.52628i	0.213925	+	0.370529i	0.952940	−	0.303160i	$-0.0980418\pi$
$661$	5.50000	+	9.52628i	0.213925	+	0.370529i	−0.739014	+	0.673690i	$0.764708\pi$
$662$	−12.0000	+	20.7846i	−0.466393	+	0.807817i
$663$	−3.00000	+	5.19615i	−0.116510	+	0.201802i
$664$	−17.0000			−0.659728
$665$	−10.5000	−	7.79423i	−0.407173	−	0.302247i
$666$	−4.00000			−0.154997
$667$		0			0
$668$	9.00000	−	15.5885i	0.348220	−	0.603136i
$669$	−9.00000	−	15.5885i	−0.347960	−	0.602685i
$670$	18.0000	−	31.1769i	0.695401	−	1.20447i
$671$	−10.0000	−	17.3205i	−0.386046	−	0.668651i
$672$	−1.00000			−0.0385758
$673$	11.0000			0.424019			0.212009	−	0.977268i	$-0.431999\pi$
$673$	11.0000			0.424019			0.212009	+	0.977268i	$0.431999\pi$
$674$	8.50000	+	14.7224i	0.327408	+	0.567087i
$675$	2.00000	+	3.46410i	0.0769800	+	0.133333i
$676$	−4.00000			−0.153846
$677$	42.0000			1.61419			0.807096	−	0.590421i	$-0.201038\pi$
$677$	42.0000			1.61419			0.807096	+	0.590421i	$0.201038\pi$
$678$	2.50000	+	4.33013i	0.0960119	+	0.166298i
$679$	−5.00000	+	8.66025i	−0.191882	+	0.332350i
$680$	3.00000	+	5.19615i	0.115045	+	0.199263i
$681$	2.50000	−	4.33013i	0.0958002	−	0.165931i
$682$	−12.0000	+	20.7846i	−0.459504	+	0.795884i
$683$	−12.0000			−0.459167			−0.229584	−	0.973289i	$-0.573736\pi$
$683$	−12.0000			−0.459167			−0.229584	+	0.973289i	$0.573736\pi$
$684$	−3.50000	−	2.59808i	−0.133826	−	0.0993399i
$685$	63.0000			2.40711
$686$	−0.500000	+	0.866025i	−0.0190901	+	0.0330650i
$687$	−8.50000	+	14.7224i	−0.324295	+	0.561696i
$688$	3.00000	+	5.19615i	0.114374	+	0.198101i
$689$	6.00000	−	10.3923i	0.228582	−	0.395915i
$690$	1.50000	+	2.59808i	0.0571040	+	0.0989071i
$691$	−41.0000			−1.55971			−0.779857	−	0.625958i	$-0.784708\pi$
$691$	−41.0000			−1.55971			−0.779857	+	0.625958i	$0.784708\pi$
$692$	15.0000			0.570214
$693$	2.00000	+	3.46410i	0.0759737	+	0.131590i
$694$	11.0000	+	19.0526i	0.417554	+	0.723225i
$695$	48.0000			1.82074
$696$		0			0
$697$	4.00000	+	6.92820i	0.151511	+	0.262424i
$698$	5.00000	−	8.66025i	0.189253	−	0.327795i
$699$	4.50000	+	7.79423i	0.170206	+	0.294805i
$700$	2.00000	−	3.46410i	0.0755929	−	0.130931i
$701$	1.00000	−	1.73205i	0.0377695	−	0.0654187i	−0.846523	−	0.532353i	$-0.821308\pi$
$701$	1.00000	−	1.73205i	0.0377695	−	0.0654187i	0.884292	+	0.466934i	$0.154641\pi$
$702$	3.00000			0.113228
$703$	−2.00000	+	17.3205i	−0.0754314	+	0.653255i
$704$	4.00000			0.150756
$705$	3.00000	−	5.19615i	0.112987	−	0.195698i
$706$	6.00000	−	10.3923i	0.225813	−	0.391120i
$707$	7.00000	+	12.1244i	0.263262	+	0.455983i
$708$	6.50000	−	11.2583i	0.244285	−	0.423114i
$709$	2.00000	+	3.46410i	0.0751116	+	0.130097i	0.901135	−	0.433539i	$-0.142735\pi$
$709$	2.00000	+	3.46410i	0.0751116	+	0.130097i	−0.826023	+	0.563636i	$0.809402\pi$
$710$	−21.0000			−0.788116
$711$	−8.00000			−0.300023
$712$	2.00000	+	3.46410i	0.0749532	+	0.129823i
$713$	3.00000	+	5.19615i	0.112351	+	0.194597i
$714$	2.00000			0.0748481
$715$	−36.0000			−1.34632
$716$	−5.00000	−	8.66025i	−0.186859	−	0.323649i
$717$	13.5000	−	23.3827i	0.504167	−	0.873242i
$718$	12.0000	+	20.7846i	0.447836	+	0.775675i
$719$	−11.0000	+	19.0526i	−0.410231	+	0.710541i	−0.994915	−	0.100721i	$-0.967885\pi$
$719$	−11.0000	+	19.0526i	−0.410231	+	0.710541i	0.584684	+	0.811261i	$0.301219\pi$
$720$	1.50000	−	2.59808i	0.0559017	−	0.0968246i
$721$		0			0
$722$	−13.0000	+	13.8564i	−0.483810	+	0.515682i
$723$	−22.0000			−0.818189
$724$	−1.50000	+	2.59808i	−0.0557471	+	0.0965567i
$725$		0			0
$726$	−2.50000	−	4.33013i	−0.0927837	−	0.160706i
$727$	−22.0000	+	38.1051i	−0.815935	+	1.41324i	0.0927199	+	0.995692i	$0.470444\pi$
$727$	−22.0000	+	38.1051i	−0.815935	+	1.41324i	−0.908655	+	0.417548i	$0.862889\pi$
$728$	−1.50000	−	2.59808i	−0.0555937	−	0.0962911i
$729$	1.00000			0.0370370
$730$	−6.00000			−0.222070
$731$	−6.00000	−	10.3923i	−0.221918	−	0.384373i
$732$	2.50000	+	4.33013i	0.0924027	+	0.160046i
$733$	−11.0000			−0.406294			−0.203147	−	0.979148i	$-0.565117\pi$
$733$	−11.0000			−0.406294			−0.203147	+	0.979148i	$0.565117\pi$
$734$	−32.0000			−1.18114
$735$	−1.50000	−	2.59808i	−0.0553283	−	0.0958315i
$736$	0.500000	−	0.866025i	0.0184302	−	0.0319221i
$737$	24.0000	+	41.5692i	0.884051	+	1.53122i
$738$	2.00000	−	3.46410i	0.0736210	−	0.127515i
$739$	22.0000	−	38.1051i	0.809283	−	1.40172i	−0.104078	−	0.994569i	$-0.533189\pi$
$739$	22.0000	−	38.1051i	0.809283	−	1.40172i	0.913361	−	0.407150i	$-0.133477\pi$
$740$	−12.0000			−0.441129
$741$	1.50000	−	12.9904i	0.0551039	−	0.477214i
$742$	−4.00000			−0.146845
$743$	1.50000	−	2.59808i	0.0550297	−	0.0953142i	−0.837198	−	0.546899i	$-0.815808\pi$
$743$	1.50000	−	2.59808i	0.0550297	−	0.0953142i	0.892228	+	0.451585i	$0.149141\pi$
$744$	3.00000	−	5.19615i	0.109985	−	0.190500i
$745$	30.0000	+	51.9615i	1.09911	+	1.90372i
$746$	−5.00000	+	8.66025i	−0.183063	+	0.317074i
$747$	−8.50000	−	14.7224i	−0.310999	−	0.538666i
$748$	−8.00000			−0.292509
$749$	10.0000			0.365392
$750$	−1.50000	−	2.59808i	−0.0547723	−	0.0948683i
$751$	−20.0000	−	34.6410i	−0.729810	−	1.26407i	−0.956963	−	0.290209i	$-0.906275\pi$
$751$	−20.0000	−	34.6410i	−0.729810	−	1.26407i	0.227153	−	0.973859i	$-0.427058\pi$
$752$	−2.00000			−0.0729325
$753$	−21.0000			−0.765283
$754$		0			0
$755$	28.5000	−	49.3634i	1.03722	−	1.79652i
$756$	−0.500000	−	0.866025i	−0.0181848	−	0.0314970i
$757$	23.0000	−	39.8372i	0.835949	−	1.44791i	−0.0573060	−	0.998357i	$-0.518251\pi$
$757$	23.0000	−	39.8372i	0.835949	−	1.44791i	0.893255	−	0.449550i	$-0.148416\pi$
$758$	−17.0000	+	29.4449i	−0.617468	+	1.06949i
$759$	−4.00000			−0.145191
$760$	−10.5000	−	7.79423i	−0.380875	−	0.282726i
$761$	8.00000			0.290000			0.145000	−	0.989432i	$-0.453682\pi$
$761$	8.00000			0.290000			0.145000	+	0.989432i	$0.453682\pi$
$762$	5.50000	−	9.52628i	0.199244	−	0.345101i
$763$	−2.00000	+	3.46410i	−0.0724049	+	0.125409i
$764$	5.50000	+	9.52628i	0.198983	+	0.344649i
$765$	−3.00000	+	5.19615i	−0.108465	+	0.187867i
$766$	−2.00000	−	3.46410i	−0.0722629	−	0.125163i
$767$	39.0000			1.40821
$768$	−1.00000			−0.0360844
$769$	15.0000	+	25.9808i	0.540914	+	0.936890i	0.998852	+	0.0479061i	$0.0152548\pi$
$769$	15.0000	+	25.9808i	0.540914	+	0.936890i	−0.457938	+	0.888984i	$0.651412\pi$
$770$	6.00000	+	10.3923i	0.216225	+	0.374513i
$771$	−12.0000			−0.432169
$772$	5.00000			0.179954
$773$	−4.50000	−	7.79423i	−0.161854	−	0.280339i	0.773680	−	0.633577i	$-0.218414\pi$
$773$	−4.50000	−	7.79423i	−0.161854	−	0.280339i	−0.935534	+	0.353238i	$0.885081\pi$
$774$	−3.00000	+	5.19615i	−0.107833	+	0.186772i
$775$	12.0000	+	20.7846i	0.431053	+	0.746605i
$776$	−5.00000	+	8.66025i	−0.179490	+	0.310885i
$777$	−2.00000	+	3.46410i	−0.0717496	+	0.124274i
$778$	−8.00000			−0.286814
$779$	−14.0000	−	10.3923i	−0.501602	−	0.372343i
$780$	9.00000			0.322252
$781$	14.0000	−	24.2487i	0.500959	−	0.867687i
$782$	−1.00000	+	1.73205i	−0.0357599	+	0.0619380i
$783$		0			0
$784$	−0.500000	+	0.866025i	−0.0178571	+	0.0309295i
$785$	−13.5000	−	23.3827i	−0.481836	−	0.834564i
$786$	−9.00000			−0.321019
$787$	−47.0000			−1.67537			−0.837685	−	0.546154i	$-0.816091\pi$
$787$	−47.0000			−1.67537			−0.837685	+	0.546154i	$0.816091\pi$
$788$	−2.00000	−	3.46410i	−0.0712470	−	0.123404i
$789$	−1.50000	−	2.59808i	−0.0534014	−	0.0924940i
$790$	−24.0000			−0.853882
$791$	5.00000			0.177780
$792$	2.00000	+	3.46410i	0.0710669	+	0.123091i
$793$	−7.50000	+	12.9904i	−0.266333	+	0.461302i
$794$	9.00000	+	15.5885i	0.319398	+	0.553214i
$795$	6.00000	−	10.3923i	0.212798	−	0.368577i
$796$	−7.00000	+	12.1244i	−0.248108	+	0.429736i
$797$	−49.0000			−1.73567			−0.867835	−	0.496853i	$-0.834489\pi$
$797$	−49.0000			−1.73567			−0.867835	+	0.496853i	$0.834489\pi$
$798$	−4.00000	+	1.73205i	−0.141598	+	0.0613139i
$799$	4.00000			0.141510
$800$	2.00000	−	3.46410i	0.0707107	−	0.122474i
$801$	−2.00000	+	3.46410i	−0.0706665	+	0.122398i
$802$	1.50000	+	2.59808i	0.0529668	+	0.0917413i
$803$	4.00000	−	6.92820i	0.141157	−	0.244491i
$804$	−6.00000	−	10.3923i	−0.211604	−	0.366508i
$805$	3.00000			0.105736
$806$	18.0000			0.634023
$807$	7.00000	+	12.1244i	0.246412	+	0.426798i
$808$	7.00000	+	12.1244i	0.246259	+	0.426533i
$809$	9.00000			0.316423			0.158212	−	0.987405i	$-0.449427\pi$
$809$	9.00000			0.316423			0.158212	+	0.987405i	$0.449427\pi$
$810$	3.00000			0.105409
$811$	10.0000	+	17.3205i	0.351147	+	0.608205i	0.986451	−	0.164057i	$-0.0524582\pi$
$811$	10.0000	+	17.3205i	0.351147	+	0.608205i	−0.635303	+	0.772263i	$0.719125\pi$
$812$		0			0
$813$	13.0000	+	22.5167i	0.455930	+	0.789694i
$814$	8.00000	−	13.8564i	0.280400	−	0.485667i
$815$	21.0000	−	36.3731i	0.735598	−	1.27409i
$816$	2.00000			0.0700140
$817$	21.0000	+	15.5885i	0.734697	+	0.545371i
$818$	−24.0000			−0.839140
$819$	1.50000	−	2.59808i	0.0524142	−	0.0907841i
$820$	6.00000	−	10.3923i	0.209529	−	0.362915i
$821$	24.0000	+	41.5692i	0.837606	+	1.45078i	0.891891	+	0.452250i	$0.149379\pi$
$821$	24.0000	+	41.5692i	0.837606	+	1.45078i	−0.0542853	+	0.998525i	$0.517288\pi$
$822$	10.5000	−	18.1865i	0.366230	−	0.634328i
$823$	−18.5000	−	32.0429i	−0.644869	−	1.11695i	−0.984332	−	0.176327i	$-0.943578\pi$
$823$	−18.5000	−	32.0429i	−0.644869	−	1.11695i	0.339462	−	0.940620i	$-0.389755\pi$
$824$		0			0
$825$	−16.0000			−0.557048
$826$	−6.50000	−	11.2583i	−0.226164	−	0.391727i
$827$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$827$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$828$	1.00000			0.0347524
$829$	41.0000			1.42399			0.711994	−	0.702185i	$-0.247792\pi$
$829$	41.0000			1.42399			0.711994	+	0.702185i	$0.247792\pi$
$830$	−25.5000	−	44.1673i	−0.885118	−	1.53307i
$831$	−1.00000	+	1.73205i	−0.0346896	+	0.0600842i
$832$	−1.50000	−	2.59808i	−0.0520031	−	0.0900721i
$833$	1.00000	−	1.73205i	0.0346479	−	0.0600120i
$834$	8.00000	−	13.8564i	0.277017	−	0.479808i
$835$	54.0000			1.86875
$836$	16.0000	−	6.92820i	0.553372	−	0.239617i
$837$	6.00000			0.207390
$838$	−6.00000	+	10.3923i	−0.207267	+	0.358996i
$839$	−15.0000	+	25.9808i	−0.517858	+	0.896956i	0.481927	+	0.876211i	$0.339937\pi$
$839$	−15.0000	+	25.9808i	−0.517858	+	0.896956i	−0.999785	+	0.0207443i	$0.993396\pi$
$840$	−1.50000	−	2.59808i	−0.0517549	−	0.0896421i
$841$	14.5000	−	25.1147i	0.500000	−	0.866025i
$842$	−4.00000	−	6.92820i	−0.137849	−	0.238762i
$843$	26.0000			0.895488
$844$	−8.00000			−0.275371
$845$	−6.00000	−	10.3923i	−0.206406	−	0.357506i
$846$	−1.00000	−	1.73205i	−0.0343807	−	0.0595491i
$847$	−5.00000			−0.171802
$848$	−4.00000			−0.137361
$849$	12.5000	+	21.6506i	0.428999	+	0.743048i
$850$	−4.00000	+	6.92820i	−0.137199	+	0.237635i
$851$	−2.00000	−	3.46410i	−0.0685591	−	0.118748i
$852$	−3.50000	+	6.06218i	−0.119908	+	0.207687i
$853$	15.0000	−	25.9808i	0.513590	−	0.889564i	−0.486286	−	0.873800i	$-0.661649\pi$
$853$	15.0000	−	25.9808i	0.513590	−	0.889564i	0.999876	−	0.0157644i	$-0.00501816\pi$
$854$	5.00000			0.171096
$855$	1.50000	−	12.9904i	0.0512989	−	0.444262i
$856$	10.0000			0.341793
$857$	−21.0000	+	36.3731i	−0.717346	+	1.24248i	0.244701	+	0.969599i	$0.421310\pi$
$857$	−21.0000	+	36.3731i	−0.717346	+	1.24248i	−0.962048	+	0.272882i	$0.912023\pi$
$858$	−6.00000	+	10.3923i	−0.204837	+	0.354787i
$859$	10.0000	+	17.3205i	0.341196	+	0.590968i	0.984655	−	0.174512i	$-0.0558348\pi$
$859$	10.0000	+	17.3205i	0.341196	+	0.590968i	−0.643459	+	0.765480i	$0.722501\pi$
$860$	−9.00000	+	15.5885i	−0.306897	+	0.531562i
$861$	−2.00000	−	3.46410i	−0.0681598	−	0.118056i
$862$	16.0000			0.544962
$863$	−52.0000			−1.77010			−0.885050	−	0.465495i	$-0.845876\pi$
$863$	−52.0000			−1.77010			−0.885050	+	0.465495i	$0.845876\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$	22.5000	+	38.9711i	0.765023	+	1.32506i
$866$	24.0000			0.815553
$867$	13.0000			0.441503
$868$	−3.00000	−	5.19615i	−0.101827	−	0.176369i
$869$	16.0000	−	27.7128i	0.542763	−	0.940093i
$870$		0			0
$871$	18.0000	−	31.1769i	0.609907	−	1.05639i
$872$	−2.00000	+	3.46410i	−0.0677285	+	0.117309i
$873$	−10.0000			−0.338449
$874$	0.500000	−	4.33013i	0.0169128	−	0.146469i
$875$	−3.00000			−0.101419
$876$	−1.00000	+	1.73205i	−0.0337869	+	0.0585206i
$877$	−10.0000	+	17.3205i	−0.337676	+	0.584872i	−0.983995	−	0.178195i	$-0.942974\pi$
$877$	−10.0000	+	17.3205i	−0.337676	+	0.584872i	0.646319	+	0.763067i	$0.276307\pi$
$878$	5.00000	+	8.66025i	0.168742	+	0.292269i
$879$	−9.50000	+	16.4545i	−0.320427	+	0.554996i
$880$	6.00000	+	10.3923i	0.202260	+	0.350325i
$881$	−18.0000			−0.606435			−0.303218	−	0.952921i	$-0.598061\pi$
$881$	−18.0000			−0.606435			−0.303218	+	0.952921i	$0.598061\pi$
$882$	−1.00000			−0.0336718
$883$	15.0000	+	25.9808i	0.504790	+	0.874322i	0.999985	+	0.00554010i	$0.00176348\pi$
$883$	15.0000	+	25.9808i	0.504790	+	0.874322i	−0.495194	+	0.868782i	$0.664903\pi$
$884$	3.00000	+	5.19615i	0.100901	+	0.174766i
$885$	39.0000			1.31097
$886$	−18.0000			−0.604722
$887$	21.0000	+	36.3731i	0.705111	+	1.22129i	0.966651	+	0.256096i	$0.0824362\pi$
$887$	21.0000	+	36.3731i	0.705111	+	1.22129i	−0.261540	+	0.965193i	$0.584230\pi$
$888$	−2.00000	+	3.46410i	−0.0671156	+	0.116248i
$889$	−5.50000	−	9.52628i	−0.184464	−	0.319501i
$890$	−6.00000	+	10.3923i	−0.201120	+	0.348351i
$891$	−2.00000	+	3.46410i	−0.0670025	+	0.116052i
$892$	−18.0000			−0.602685
$893$	−8.00000	+	3.46410i	−0.267710	+	0.115922i
$894$	20.0000			0.668900
$895$	15.0000	−	25.9808i	0.501395	−	0.868441i
$896$	−0.500000	+	0.866025i	−0.0167038	+	0.0289319i
$897$	1.50000	+	2.59808i	0.0500835	+	0.0867472i
$898$	−19.5000	+	33.7750i	−0.650723	+	1.12709i
$899$		0			0
$900$	4.00000			0.133333
$901$	8.00000			0.266519
$902$	8.00000	+	13.8564i	0.266371	+	0.461368i
$903$	3.00000	+	5.19615i	0.0998337	+	0.172917i
$904$	5.00000			0.166298
$905$	−9.00000			−0.299170
$906$	−9.50000	−	16.4545i	−0.315616	−	0.546664i
$907$	−29.0000	+	50.2295i	−0.962929	+	1.66784i	−0.247851	+	0.968798i	$0.579724\pi$
$907$	−29.0000	+	50.2295i	−0.962929	+	1.66784i	−0.715079	+	0.699044i	$0.753609\pi$
$908$	−2.50000	−	4.33013i	−0.0829654	−	0.143700i
$909$	−7.00000	+	12.1244i	−0.232175	+	0.402139i
$910$	4.50000	−	7.79423i	0.149174	−	0.258376i
$911$	33.0000			1.09334			0.546669	−	0.837349i	$-0.315895\pi$
$911$	33.0000			1.09334			0.546669	+	0.837349i	$0.315895\pi$
$912$	−4.00000	+	1.73205i	−0.132453	+	0.0573539i
$913$	68.0000			2.25047
$914$	−3.50000	+	6.06218i	−0.115770	+	0.200519i
$915$	−7.50000	+	12.9904i	−0.247942	+	0.429449i
$916$	8.50000	+	14.7224i	0.280848	+	0.486443i
$917$	−4.50000	+	7.79423i	−0.148603	+	0.257388i
$918$	1.00000	+	1.73205i	0.0330049	+	0.0571662i
$919$	−17.0000			−0.560778			−0.280389	−	0.959886i	$-0.590464\pi$
$919$	−17.0000			−0.560778			−0.280389	+	0.959886i	$0.590464\pi$
$920$	3.00000			0.0989071
$921$	7.50000	+	12.9904i	0.247133	+	0.428048i
$922$	−16.5000	−	28.5788i	−0.543399	−	0.941194i
$923$	−21.0000			−0.691223
$924$	4.00000			0.131590
$925$	−8.00000	−	13.8564i	−0.263038	−	0.455596i
$926$	−4.50000	+	7.79423i	−0.147879	+	0.256134i
$927$		0			0
$928$		0			0
$929$	−24.0000	+	41.5692i	−0.787414	+	1.36384i	0.140132	+	0.990133i	$0.455247\pi$
$929$	−24.0000	+	41.5692i	−0.787414	+	1.36384i	−0.927546	+	0.373709i	$0.878086\pi$
$930$	18.0000			0.590243
$931$	−0.500000	+	4.33013i	−0.0163868	+	0.141914i
$932$	9.00000			0.294805
$933$	−1.00000	+	1.73205i	−0.0327385	+	0.0567048i
$934$	−2.00000	+	3.46410i	−0.0654420	+	0.113349i
$935$	−12.0000	−	20.7846i	−0.392442	−	0.679729i
$936$	1.50000	−	2.59808i	0.0490290	−	0.0849208i
$937$	23.0000	+	39.8372i	0.751377	+	1.30142i	0.947155	+	0.320775i	$0.103943\pi$
$937$	23.0000	+	39.8372i	0.751377	+	1.30142i	−0.195778	+	0.980648i	$0.562723\pi$
$938$	−12.0000			−0.391814
$939$	−24.0000			−0.783210
$940$	−3.00000	−	5.19615i	−0.0978492	−	0.169480i
$941$	−6.50000	−	11.2583i	−0.211894	−	0.367011i	0.740413	−	0.672152i	$-0.234630\pi$
$941$	−6.50000	−	11.2583i	−0.211894	−	0.367011i	−0.952307	+	0.305141i	$0.901296\pi$
$942$	−9.00000			−0.293236
$943$	4.00000			0.130258
$944$	−6.50000	−	11.2583i	−0.211557	−	0.366427i
$945$	1.50000	−	2.59808i	0.0487950	−	0.0845154i
$946$	−12.0000	−	20.7846i	−0.390154	−	0.675766i
$947$	−11.0000	+	19.0526i	−0.357452	+	0.619125i	−0.987534	−	0.157403i	$-0.949688\pi$
$947$	−11.0000	+	19.0526i	−0.357452	+	0.619125i	0.630082	+	0.776528i	$0.283021\pi$
$948$	−4.00000	+	6.92820i	−0.129914	+	0.225018i
$949$	−6.00000			−0.194768
$950$	2.00000	−	17.3205i	0.0648886	−	0.561951i
$951$	−6.00000			−0.194563
$952$	1.00000	−	1.73205i	0.0324102	−	0.0561361i
$953$	3.00000	−	5.19615i	0.0971795	−	0.168320i	−0.813337	−	0.581793i	$-0.802351\pi$
$953$	3.00000	−	5.19615i	0.0971795	−	0.168320i	0.910516	+	0.413473i	$0.135685\pi$
$954$	−2.00000	−	3.46410i	−0.0647524	−	0.112154i
$955$	−16.5000	+	28.5788i	−0.533927	+	0.924789i
$956$	−13.5000	−	23.3827i	−0.436621	−	0.756250i
$957$		0			0
$958$	42.0000			1.35696
$959$	−10.5000	−	18.1865i	−0.339063	−	0.587274i
$960$	−1.50000	−	2.59808i	−0.0484123	−	0.0838525i
$961$	5.00000			0.161290
$962$	−12.0000			−0.386896
$963$	5.00000	+	8.66025i	0.161123	+	0.279073i
$964$	−11.0000	+	19.0526i	−0.354286	+	0.613642i
$965$	7.50000	+	12.9904i	0.241434	+	0.418175i
$966$	0.500000	−	0.866025i	0.0160872	−	0.0278639i
$967$	22.5000	−	38.9711i	0.723551	−	1.25323i	−0.236016	−	0.971749i	$-0.575842\pi$
$967$	22.5000	−	38.9711i	0.723551	−	1.25323i	0.959568	−	0.281478i	$-0.0908248\pi$
$968$	−5.00000			−0.160706
$969$	8.00000	−	3.46410i	0.256997	−	0.111283i
$970$	−30.0000			−0.963242
$971$	16.5000	−	28.5788i	0.529510	−	0.917139i	−0.469897	−	0.882721i	$-0.655709\pi$
$971$	16.5000	−	28.5788i	0.529510	−	0.917139i	0.999408	−	0.0344175i	$-0.0109576\pi$
$972$	0.500000	−	0.866025i	0.0160375	−	0.0277778i
$973$	−8.00000	−	13.8564i	−0.256468	−	0.444216i
$974$	−14.0000	+	24.2487i	−0.448589	+	0.776979i
$975$	6.00000	+	10.3923i	0.192154	+	0.332820i
$976$	5.00000			0.160046
$977$	−9.00000			−0.287936			−0.143968	−	0.989582i	$-0.545986\pi$
$977$	−9.00000			−0.287936			−0.143968	+	0.989582i	$0.545986\pi$
$978$	−7.00000	−	12.1244i	−0.223835	−	0.387694i
$979$	−8.00000	−	13.8564i	−0.255681	−	0.442853i
$980$	−3.00000			−0.0958315
$981$	−4.00000			−0.127710
$982$	6.00000	+	10.3923i	0.191468	+	0.331632i
$983$	21.0000	−	36.3731i	0.669796	−	1.16012i	−0.308165	−	0.951333i	$-0.599715\pi$
$983$	21.0000	−	36.3731i	0.669796	−	1.16012i	0.977961	−	0.208788i	$-0.0669518\pi$
$984$	−2.00000	−	3.46410i	−0.0637577	−	0.110432i
$985$	6.00000	−	10.3923i	0.191176	−	0.331126i
$986$		0			0
$987$	−2.00000			−0.0636607
$988$	−10.5000	−	7.79423i	−0.334050	−	0.247967i
$989$	−6.00000			−0.190789
$990$	−6.00000	+	10.3923i	−0.190693	+	0.330289i
$991$	17.5000	−	30.3109i	0.555906	−	0.962857i	−0.441927	−	0.897051i	$-0.645705\pi$
$991$	17.5000	−	30.3109i	0.555906	−	0.962857i	0.997832	−	0.0658059i	$-0.0209618\pi$
$992$	−3.00000	−	5.19615i	−0.0952501	−	0.164978i
$993$	−12.0000	+	20.7846i	−0.380808	+	0.659580i
$994$	3.50000	+	6.06218i	0.111013	+	0.192281i
$995$	−42.0000			−1.33149
$996$	−17.0000			−0.538666
$997$	21.5000	+	37.2391i	0.680912	+	1.17937i	0.974703	+	0.223504i	$0.0717497\pi$
$997$	21.5000	+	37.2391i	0.680912	+	1.17937i	−0.293791	+	0.955870i	$0.594917\pi$
$998$	−5.00000	−	8.66025i	−0.158272	−	0.274136i
$999$	−4.00000			−0.126554

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.2.k.i.505.1	yes	2
3.2	odd	2		2394.2.o.a.505.1		2
19.7	even	3	inner	798.2.k.i.463.1	✓	2
57.26	odd	6		2394.2.o.a.1261.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.k.i.463.1	✓	2	19.7	even	3	inner
798.2.k.i.505.1	yes	2	1.1	even	1	trivial
2394.2.o.a.505.1		2	3.2	odd	2
2394.2.o.a.1261.1		2	57.26	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:	\( N \)	\(=\)	\( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	798.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.50000 - 2.59808i) q^{5} +(-0.500000 - 0.866025i) q^{6} -1.00000 q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.50000 - 2.59808i) q^{5} +(-0.500000 - 0.866025i) q^{6} -1.00000 q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.50000 - 2.59808i) q^{10} +4.00000 q^{11} -1.00000 q^{12} +(-1.50000 - 2.59808i) q^{13} +(-0.500000 + 0.866025i) q^{14} +(-1.50000 - 2.59808i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.00000 - 1.73205i) q^{17} -1.00000 q^{18} +(-0.500000 + 4.33013i) q^{19} -3.00000 q^{20} +(-0.500000 + 0.866025i) q^{21} +(2.00000 - 3.46410i) q^{22} +(-0.500000 - 0.866025i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-2.00000 - 3.46410i) q^{25} -3.00000 q^{26} -1.00000 q^{27} +(0.500000 + 0.866025i) q^{28} -3.00000 q^{30} -6.00000 q^{31} +(0.500000 + 0.866025i) q^{32} +(2.00000 - 3.46410i) q^{33} +(-1.00000 - 1.73205i) q^{34} +(-1.50000 + 2.59808i) q^{35} +(-0.500000 + 0.866025i) q^{36} +4.00000 q^{37} +(3.50000 + 2.59808i) q^{38} -3.00000 q^{39} +(-1.50000 + 2.59808i) q^{40} +(-2.00000 + 3.46410i) q^{41} +(0.500000 + 0.866025i) q^{42} +(3.00000 - 5.19615i) q^{43} +(-2.00000 - 3.46410i) q^{44} -3.00000 q^{45} -1.00000 q^{46} +(1.00000 + 1.73205i) q^{47} +(0.500000 + 0.866025i) q^{48} +1.00000 q^{49} -4.00000 q^{50} +(-1.00000 - 1.73205i) q^{51} +(-1.50000 + 2.59808i) q^{52} +(2.00000 + 3.46410i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(6.00000 - 10.3923i) q^{55} +1.00000 q^{56} +(3.50000 + 2.59808i) q^{57} +(-6.50000 + 11.2583i) q^{59} +(-1.50000 + 2.59808i) q^{60} +(-2.50000 - 4.33013i) q^{61} +(-3.00000 + 5.19615i) q^{62} +(0.500000 + 0.866025i) q^{63} +1.00000 q^{64} -9.00000 q^{65} +(-2.00000 - 3.46410i) q^{66} +(6.00000 + 10.3923i) q^{67} -2.00000 q^{68} -1.00000 q^{69} +(1.50000 + 2.59808i) q^{70} +(3.50000 - 6.06218i) q^{71} +(0.500000 + 0.866025i) q^{72} +(1.00000 - 1.73205i) q^{73} +(2.00000 - 3.46410i) q^{74} -4.00000 q^{75} +(4.00000 - 1.73205i) q^{76} -4.00000 q^{77} +(-1.50000 + 2.59808i) q^{78} +(4.00000 - 6.92820i) q^{79} +(1.50000 + 2.59808i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(2.00000 + 3.46410i) q^{82} +17.0000 q^{83} +1.00000 q^{84} +(-3.00000 - 5.19615i) q^{85} +(-3.00000 - 5.19615i) q^{86} -4.00000 q^{88} +(-2.00000 - 3.46410i) q^{89} +(-1.50000 + 2.59808i) q^{90} +(1.50000 + 2.59808i) q^{91} +(-0.500000 + 0.866025i) q^{92} +(-3.00000 + 5.19615i) q^{93} +2.00000 q^{94} +(10.5000 + 7.79423i) q^{95} +1.00000 q^{96} +(5.00000 - 8.66025i) q^{97} +(0.500000 - 0.866025i) q^{98} +(-2.00000 - 3.46410i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + q^{3} - q^{4} + 3 q^{5} - q^{6} - 2 q^{7} - 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q + q^2 + q^3 - q^4 + 3 * q^5 - q^6 - 2 * q^7 - 2 * q^8 - q^9	\( 2 q + q^{2} + q^{3} - q^{4} + 3 q^{5} - q^{6} - 2 q^{7} - 2 q^{8} - q^{9} - 3 q^{10} + 8 q^{11} - 2 q^{12} - 3 q^{13} - q^{14} - 3 q^{15} - q^{16} + 2 q^{17} - 2 q^{18} - q^{19} - 6 q^{20} - q^{21} + 4 q^{22} - q^{23} - q^{24} - 4 q^{25} - 6 q^{26} - 2 q^{27} + q^{28} - 6 q^{30} - 12 q^{31} + q^{32} + 4 q^{33} - 2 q^{34} - 3 q^{35} - q^{36} + 8 q^{37} + 7 q^{38} - 6 q^{39} - 3 q^{40} - 4 q^{41} + q^{42} + 6 q^{43} - 4 q^{44} - 6 q^{45} - 2 q^{46} + 2 q^{47} + q^{48} + 2 q^{49} - 8 q^{50} - 2 q^{51} - 3 q^{52} + 4 q^{53} - q^{54} + 12 q^{55} + 2 q^{56} + 7 q^{57} - 13 q^{59} - 3 q^{60} - 5 q^{61} - 6 q^{62} + q^{63} + 2 q^{64} - 18 q^{65} - 4 q^{66} + 12 q^{67} - 4 q^{68} - 2 q^{69} + 3 q^{70} + 7 q^{71} + q^{72} + 2 q^{73} + 4 q^{74} - 8 q^{75} + 8 q^{76} - 8 q^{77} - 3 q^{78} + 8 q^{79} + 3 q^{80} - q^{81} + 4 q^{82} + 34 q^{83} + 2 q^{84} - 6 q^{85} - 6 q^{86} - 8 q^{88} - 4 q^{89} - 3 q^{90} + 3 q^{91} - q^{92} - 6 q^{93} + 4 q^{94} + 21 q^{95} + 2 q^{96} + 10 q^{97} + q^{98} - 4 q^{99}+O(q^{100}) \) 2 * q + q^2 + q^3 - q^4 + 3 * q^5 - q^6 - 2 * q^7 - 2 * q^8 - q^9 - 3 * q^10 + 8 * q^11 - 2 * q^12 - 3 * q^13 - q^14 - 3 * q^15 - q^16 + 2 * q^17 - 2 * q^18 - q^19 - 6 * q^20 - q^21 + 4 * q^22 - q^23 - q^24 - 4 * q^25 - 6 * q^26 - 2 * q^27 + q^28 - 6 * q^30 - 12 * q^31 + q^32 + 4 * q^33 - 2 * q^34 - 3 * q^35 - q^36 + 8 * q^37 + 7 * q^38 - 6 * q^39 - 3 * q^40 - 4 * q^41 + q^42 + 6 * q^43 - 4 * q^44 - 6 * q^45 - 2 * q^46 + 2 * q^47 + q^48 + 2 * q^49 - 8 * q^50 - 2 * q^51 - 3 * q^52 + 4 * q^53 - q^54 + 12 * q^55 + 2 * q^56 + 7 * q^57 - 13 * q^59 - 3 * q^60 - 5 * q^61 - 6 * q^62 + q^63 + 2 * q^64 - 18 * q^65 - 4 * q^66 + 12 * q^67 - 4 * q^68 - 2 * q^69 + 3 * q^70 + 7 * q^71 + q^72 + 2 * q^73 + 4 * q^74 - 8 * q^75 + 8 * q^76 - 8 * q^77 - 3 * q^78 + 8 * q^79 + 3 * q^80 - q^81 + 4 * q^82 + 34 * q^83 + 2 * q^84 - 6 * q^85 - 6 * q^86 - 8 * q^88 - 4 * q^89 - 3 * q^90 + 3 * q^91 - q^92 - 6 * q^93 + 4 * q^94 + 21 * q^95 + 2 * q^96 + 10 * q^97 + q^98 - 4 * q^99

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