LMFDB - Embedded newform 770.2.i.i.331.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(221,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

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

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

chi := DirichletCharacter("770.221");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.i (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:	$6.14848095564$
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			331.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	770.331
Dual form			770.2.i.i.221.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +3.00000 q^{6} +(2.50000 + 0.866025i) q^{7} -1.00000 q^{8} +(-3.00000 + 5.19615i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +3.00000 q^{6} +(2.50000 + 0.866025i) q^{7} -1.00000 q^{8} +(-3.00000 + 5.19615i) q^{9} +(0.500000 + 0.866025i) q^{10} +(0.500000 + 0.866025i) q^{11} +(1.50000 - 2.59808i) q^{12} -6.00000 q^{13} +(2.00000 - 1.73205i) q^{14} -3.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(4.00000 + 6.92820i) q^{17} +(3.00000 + 5.19615i) q^{18} +(2.00000 - 3.46410i) q^{19} +1.00000 q^{20} +(1.50000 + 7.79423i) q^{21} +1.00000 q^{22} +(3.50000 - 6.06218i) q^{23} +(-1.50000 - 2.59808i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-3.00000 + 5.19615i) q^{26} -9.00000 q^{27} +(-0.500000 - 2.59808i) q^{28} -9.00000 q^{29} +(-1.50000 + 2.59808i) q^{30} +(3.00000 + 5.19615i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.50000 + 2.59808i) q^{33} +8.00000 q^{34} +(-2.00000 + 1.73205i) q^{35} +6.00000 q^{36} +(1.00000 - 1.73205i) q^{37} +(-2.00000 - 3.46410i) q^{38} +(-9.00000 - 15.5885i) q^{39} +(0.500000 - 0.866025i) q^{40} +3.00000 q^{41} +(7.50000 + 2.59808i) q^{42} -1.00000 q^{43} +(0.500000 - 0.866025i) q^{44} +(-3.00000 - 5.19615i) q^{45} +(-3.50000 - 6.06218i) q^{46} +(4.00000 - 6.92820i) q^{47} -3.00000 q^{48} +(5.50000 + 4.33013i) q^{49} -1.00000 q^{50} +(-12.0000 + 20.7846i) q^{51} +(3.00000 + 5.19615i) q^{52} +(1.00000 + 1.73205i) q^{53} +(-4.50000 + 7.79423i) q^{54} -1.00000 q^{55} +(-2.50000 - 0.866025i) q^{56} +12.0000 q^{57} +(-4.50000 + 7.79423i) q^{58} +(3.00000 + 5.19615i) q^{59} +(1.50000 + 2.59808i) q^{60} +(2.50000 - 4.33013i) q^{61} +6.00000 q^{62} +(-12.0000 + 10.3923i) q^{63} +1.00000 q^{64} +(3.00000 - 5.19615i) q^{65} +(1.50000 + 2.59808i) q^{66} +(-0.500000 - 0.866025i) q^{67} +(4.00000 - 6.92820i) q^{68} +21.0000 q^{69} +(0.500000 + 2.59808i) q^{70} +4.00000 q^{71} +(3.00000 - 5.19615i) q^{72} +(-4.00000 - 6.92820i) q^{73} +(-1.00000 - 1.73205i) q^{74} +(1.50000 - 2.59808i) q^{75} -4.00000 q^{76} +(0.500000 + 2.59808i) q^{77} -18.0000 q^{78} +(-5.00000 + 8.66025i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(1.50000 - 2.59808i) q^{82} +9.00000 q^{83} +(6.00000 - 5.19615i) q^{84} -8.00000 q^{85} +(-0.500000 + 0.866025i) q^{86} +(-13.5000 - 23.3827i) q^{87} +(-0.500000 - 0.866025i) q^{88} +(-0.500000 + 0.866025i) q^{89} -6.00000 q^{90} +(-15.0000 - 5.19615i) q^{91} -7.00000 q^{92} +(-9.00000 + 15.5885i) q^{93} +(-4.00000 - 6.92820i) q^{94} +(2.00000 + 3.46410i) q^{95} +(-1.50000 + 2.59808i) q^{96} +(6.50000 - 2.59808i) q^{98} -6.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + 3 q^{3} - q^{4} - q^{5} + 6 q^{6} + 5 q^{7} - 2 q^{8} - 6 q^{9}+O(q^{10}) $ 2 * q + q^2 + 3 * q^3 - q^4 - q^5 + 6 * q^6 + 5 * q^7 - 2 * q^8 - 6 * q^9	\( 2 q + q^{2} + 3 q^{3} - q^{4} - q^{5} + 6 q^{6} + 5 q^{7} - 2 q^{8} - 6 q^{9} + q^{10} + q^{11} + 3 q^{12} - 12 q^{13} + 4 q^{14} - 6 q^{15} - q^{16} + 8 q^{17} + 6 q^{18} + 4 q^{19} + 2 q^{20} + 3 q^{21} + 2 q^{22} + 7 q^{23} - 3 q^{24} - q^{25} - 6 q^{26} - 18 q^{27} - q^{28} - 18 q^{29} - 3 q^{30} + 6 q^{31} + q^{32} - 3 q^{33} + 16 q^{34} - 4 q^{35} + 12 q^{36} + 2 q^{37} - 4 q^{38} - 18 q^{39} + q^{40} + 6 q^{41} + 15 q^{42} - 2 q^{43} + q^{44} - 6 q^{45} - 7 q^{46} + 8 q^{47} - 6 q^{48} + 11 q^{49} - 2 q^{50} - 24 q^{51} + 6 q^{52} + 2 q^{53} - 9 q^{54} - 2 q^{55} - 5 q^{56} + 24 q^{57} - 9 q^{58} + 6 q^{59} + 3 q^{60} + 5 q^{61} + 12 q^{62} - 24 q^{63} + 2 q^{64} + 6 q^{65} + 3 q^{66} - q^{67} + 8 q^{68} + 42 q^{69} + q^{70} + 8 q^{71} + 6 q^{72} - 8 q^{73} - 2 q^{74} + 3 q^{75} - 8 q^{76} + q^{77} - 36 q^{78} - 10 q^{79} - q^{80} - 9 q^{81} + 3 q^{82} + 18 q^{83} + 12 q^{84} - 16 q^{85} - q^{86} - 27 q^{87} - q^{88} - q^{89} - 12 q^{90} - 30 q^{91} - 14 q^{92} - 18 q^{93} - 8 q^{94} + 4 q^{95} - 3 q^{96} + 13 q^{98} - 12 q^{99}+O(q^{100}) \) 2 * q + q^2 + 3 * q^3 - q^4 - q^5 + 6 * q^6 + 5 * q^7 - 2 * q^8 - 6 * q^9 + q^10 + q^11 + 3 * q^12 - 12 * q^13 + 4 * q^14 - 6 * q^15 - q^16 + 8 * q^17 + 6 * q^18 + 4 * q^19 + 2 * q^20 + 3 * q^21 + 2 * q^22 + 7 * q^23 - 3 * q^24 - q^25 - 6 * q^26 - 18 * q^27 - q^28 - 18 * q^29 - 3 * q^30 + 6 * q^31 + q^32 - 3 * q^33 + 16 * q^34 - 4 * q^35 + 12 * q^36 + 2 * q^37 - 4 * q^38 - 18 * q^39 + q^40 + 6 * q^41 + 15 * q^42 - 2 * q^43 + q^44 - 6 * q^45 - 7 * q^46 + 8 * q^47 - 6 * q^48 + 11 * q^49 - 2 * q^50 - 24 * q^51 + 6 * q^52 + 2 * q^53 - 9 * q^54 - 2 * q^55 - 5 * q^56 + 24 * q^57 - 9 * q^58 + 6 * q^59 + 3 * q^60 + 5 * q^61 + 12 * q^62 - 24 * q^63 + 2 * q^64 + 6 * q^65 + 3 * q^66 - q^67 + 8 * q^68 + 42 * q^69 + q^70 + 8 * q^71 + 6 * q^72 - 8 * q^73 - 2 * q^74 + 3 * q^75 - 8 * q^76 + q^77 - 36 * q^78 - 10 * q^79 - q^80 - 9 * q^81 + 3 * q^82 + 18 * q^83 + 12 * q^84 - 16 * q^85 - q^86 - 27 * q^87 - q^88 - q^89 - 12 * q^90 - 30 * q^91 - 14 * q^92 - 18 * q^93 - 8 * q^94 + 4 * q^95 - 3 * q^96 + 13 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	1.50000	+	2.59808i	0.866025	+	1.50000i	0.866025	+	0.500000i	$0.166667\pi$
$3$	1.50000	+	2.59808i	0.866025	+	1.50000i			1.00000i	$0.5\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	3.00000			1.22474
$7$	2.50000	+	0.866025i	0.944911	+	0.327327i
$7$	2.50000	+	0.866025i	0.944911	+	0.327327i
$8$	−1.00000			−0.353553
$9$	−3.00000	+	5.19615i	−1.00000	+	1.73205i
$10$	0.500000	+	0.866025i	0.158114	+	0.273861i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$12$	1.50000	−	2.59808i	0.433013	−	0.750000i
$13$	−6.00000			−1.66410			−0.832050	−	0.554700i	$-0.812833\pi$
$13$	−6.00000			−1.66410			−0.832050	+	0.554700i	$0.812833\pi$
$14$	2.00000	−	1.73205i	0.534522	−	0.462910i
$15$	−3.00000			−0.774597
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	4.00000	+	6.92820i	0.970143	+	1.68034i	0.695113	+	0.718900i	$0.255354\pi$
$17$	4.00000	+	6.92820i	0.970143	+	1.68034i	0.275029	+	0.961436i	$0.411312\pi$
$18$	3.00000	+	5.19615i	0.707107	+	1.22474i
$19$	2.00000	−	3.46410i	0.458831	−	0.794719i	−0.540068	−	0.841621i	$-0.681602\pi$
$19$	2.00000	−	3.46410i	0.458831	−	0.794719i	0.998899	+	0.0469020i	$0.0149348\pi$
$20$	1.00000			0.223607
$21$	1.50000	+	7.79423i	0.327327	+	1.70084i
$22$	1.00000			0.213201
$23$	3.50000	−	6.06218i	0.729800	−	1.26405i	−0.227167	−	0.973856i	$-0.572946\pi$
$23$	3.50000	−	6.06218i	0.729800	−	1.26405i	0.956967	−	0.290196i	$-0.0937204\pi$
$24$	−1.50000	−	2.59808i	−0.306186	−	0.530330i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−3.00000	+	5.19615i	−0.588348	+	1.01905i
$27$	−9.00000			−1.73205
$28$	−0.500000	−	2.59808i	−0.0944911	−	0.490990i
$29$	−9.00000			−1.67126			−0.835629	−	0.549294i	$-0.814897\pi$
$29$	−9.00000			−1.67126			−0.835629	+	0.549294i	$0.814897\pi$
$30$	−1.50000	+	2.59808i	−0.273861	+	0.474342i
$31$	3.00000	+	5.19615i	0.538816	+	0.933257i	0.998968	+	0.0454165i	$0.0144615\pi$
$31$	3.00000	+	5.19615i	0.538816	+	0.933257i	−0.460152	+	0.887840i	$0.652205\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−1.50000	+	2.59808i	−0.261116	+	0.452267i
$34$	8.00000			1.37199
$35$	−2.00000	+	1.73205i	−0.338062	+	0.292770i
$36$	6.00000			1.00000
$37$	1.00000	−	1.73205i	0.164399	−	0.284747i	−0.772043	−	0.635571i	$-0.780765\pi$
$37$	1.00000	−	1.73205i	0.164399	−	0.284747i	0.936442	+	0.350823i	$0.114098\pi$
$38$	−2.00000	−	3.46410i	−0.324443	−	0.561951i
$39$	−9.00000	−	15.5885i	−1.44115	−	2.49615i
$40$	0.500000	−	0.866025i	0.0790569	−	0.136931i
$41$	3.00000			0.468521			0.234261	−	0.972174i	$-0.424733\pi$
$41$	3.00000			0.468521			0.234261	+	0.972174i	$0.424733\pi$
$42$	7.50000	+	2.59808i	1.15728	+	0.400892i
$43$	−1.00000			−0.152499			−0.0762493	−	0.997089i	$-0.524294\pi$
$43$	−1.00000			−0.152499			−0.0762493	+	0.997089i	$0.524294\pi$
$44$	0.500000	−	0.866025i	0.0753778	−	0.130558i
$45$	−3.00000	−	5.19615i	−0.447214	−	0.774597i
$46$	−3.50000	−	6.06218i	−0.516047	−	0.893819i
$47$	4.00000	−	6.92820i	0.583460	−	1.01058i	−0.411606	−	0.911362i	$-0.635032\pi$
$47$	4.00000	−	6.92820i	0.583460	−	1.01058i	0.995066	−	0.0992202i	$-0.0316348\pi$
$48$	−3.00000			−0.433013
$49$	5.50000	+	4.33013i	0.785714	+	0.618590i
$50$	−1.00000			−0.141421
$51$	−12.0000	+	20.7846i	−1.68034	+	2.91043i
$52$	3.00000	+	5.19615i	0.416025	+	0.720577i
$53$	1.00000	+	1.73205i	0.137361	+	0.237915i	0.926497	−	0.376303i	$-0.122805\pi$
$53$	1.00000	+	1.73205i	0.137361	+	0.237915i	−0.789136	+	0.614218i	$0.789471\pi$
$54$	−4.50000	+	7.79423i	−0.612372	+	1.06066i
$55$	−1.00000			−0.134840
$56$	−2.50000	−	0.866025i	−0.334077	−	0.115728i
$57$	12.0000			1.58944
$58$	−4.50000	+	7.79423i	−0.590879	+	1.02343i
$59$	3.00000	+	5.19615i	0.390567	+	0.676481i	0.992524	−	0.122047i	$-0.0389457\pi$
$59$	3.00000	+	5.19615i	0.390567	+	0.676481i	−0.601958	+	0.798528i	$0.705612\pi$
$60$	1.50000	+	2.59808i	0.193649	+	0.335410i
$61$	2.50000	−	4.33013i	0.320092	−	0.554416i	−0.660415	−	0.750901i	$-0.729619\pi$
$61$	2.50000	−	4.33013i	0.320092	−	0.554416i	0.980507	+	0.196485i	$0.0629528\pi$
$62$	6.00000			0.762001
$63$	−12.0000	+	10.3923i	−1.51186	+	1.30931i
$64$	1.00000			0.125000
$65$	3.00000	−	5.19615i	0.372104	−	0.644503i
$66$	1.50000	+	2.59808i	0.184637	+	0.319801i
$67$	−0.500000	−	0.866025i	−0.0610847	−	0.105802i	0.833866	−	0.551967i	$-0.186123\pi$
$67$	−0.500000	−	0.866025i	−0.0610847	−	0.105802i	−0.894951	+	0.446165i	$0.852789\pi$
$68$	4.00000	−	6.92820i	0.485071	−	0.840168i
$69$	21.0000			2.52810
$70$	0.500000	+	2.59808i	0.0597614	+	0.310530i
$71$	4.00000			0.474713			0.237356	−	0.971423i	$-0.423719\pi$
$71$	4.00000			0.474713			0.237356	+	0.971423i	$0.423719\pi$
$72$	3.00000	−	5.19615i	0.353553	−	0.612372i
$73$	−4.00000	−	6.92820i	−0.468165	−	0.810885i	0.531174	−	0.847263i	$-0.321751\pi$
$73$	−4.00000	−	6.92820i	−0.468165	−	0.810885i	−0.999338	+	0.0363782i	$0.988418\pi$
$74$	−1.00000	−	1.73205i	−0.116248	−	0.201347i
$75$	1.50000	−	2.59808i	0.173205	−	0.300000i
$76$	−4.00000			−0.458831
$77$	0.500000	+	2.59808i	0.0569803	+	0.296078i
$78$	−18.0000			−2.03810
$79$	−5.00000	+	8.66025i	−0.562544	+	0.974355i	0.434730	+	0.900561i	$0.356844\pi$
$79$	−5.00000	+	8.66025i	−0.562544	+	0.974355i	−0.997274	+	0.0737937i	$0.976489\pi$
$80$	−0.500000	−	0.866025i	−0.0559017	−	0.0968246i
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$	1.50000	−	2.59808i	0.165647	−	0.286910i
$83$	9.00000			0.987878			0.493939	−	0.869496i	$-0.335557\pi$
$83$	9.00000			0.987878			0.493939	+	0.869496i	$0.335557\pi$
$84$	6.00000	−	5.19615i	0.654654	−	0.566947i
$85$	−8.00000			−0.867722
$86$	−0.500000	+	0.866025i	−0.0539164	+	0.0933859i
$87$	−13.5000	−	23.3827i	−1.44735	−	2.50689i
$88$	−0.500000	−	0.866025i	−0.0533002	−	0.0923186i
$89$	−0.500000	+	0.866025i	−0.0529999	+	0.0917985i	−0.891308	−	0.453398i	$-0.850212\pi$
$89$	−0.500000	+	0.866025i	−0.0529999	+	0.0917985i	0.838308	+	0.545197i	$0.183545\pi$
$90$	−6.00000			−0.632456
$91$	−15.0000	−	5.19615i	−1.57243	−	0.544705i
$92$	−7.00000			−0.729800
$93$	−9.00000	+	15.5885i	−0.933257	+	1.61645i
$94$	−4.00000	−	6.92820i	−0.412568	−	0.714590i
$95$	2.00000	+	3.46410i	0.205196	+	0.355409i
$96$	−1.50000	+	2.59808i	−0.153093	+	0.265165i
$97$		0			0			−	1.00000i	$-0.5\pi$
$97$		0			0				1.00000i	$0.5\pi$
$98$	6.50000	−	2.59808i	0.656599	−	0.262445i
$99$	−6.00000			−0.603023
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	−2.50000	−	4.33013i	−0.248759	−	0.430864i	0.714423	−	0.699715i	$-0.246689\pi$
$101$	−2.50000	−	4.33013i	−0.248759	−	0.430864i	−0.963182	+	0.268851i	$0.913356\pi$
$102$	12.0000	+	20.7846i	1.18818	+	2.05798i
$103$	6.50000	−	11.2583i	0.640464	−	1.10932i	−0.344865	−	0.938652i	$-0.612075\pi$
$103$	6.50000	−	11.2583i	0.640464	−	1.10932i	0.985329	−	0.170664i	$-0.0545913\pi$
$104$	6.00000			0.588348
$105$	−7.50000	−	2.59808i	−0.731925	−	0.253546i
$106$	2.00000			0.194257
$107$	8.50000	−	14.7224i	0.821726	−	1.42327i	−0.0826699	−	0.996577i	$-0.526345\pi$
$107$	8.50000	−	14.7224i	0.821726	−	1.42327i	0.904396	−	0.426694i	$-0.140322\pi$
$108$	4.50000	+	7.79423i	0.433013	+	0.750000i
$109$	−2.50000	−	4.33013i	−0.239457	−	0.414751i	0.721102	−	0.692829i	$-0.243636\pi$
$109$	−2.50000	−	4.33013i	−0.239457	−	0.414751i	−0.960558	+	0.278078i	$0.910303\pi$
$110$	−0.500000	+	0.866025i	−0.0476731	+	0.0825723i
$111$	6.00000			0.569495
$112$	−2.00000	+	1.73205i	−0.188982	+	0.163663i
$113$	12.0000			1.12887			0.564433	−	0.825479i	$-0.309095\pi$
$113$	12.0000			1.12887			0.564433	+	0.825479i	$0.309095\pi$
$114$	6.00000	−	10.3923i	0.561951	−	0.973329i
$115$	3.50000	+	6.06218i	0.326377	+	0.565301i
$116$	4.50000	+	7.79423i	0.417815	+	0.723676i
$117$	18.0000	−	31.1769i	1.66410	−	2.88231i
$118$	6.00000			0.552345
$119$	4.00000	+	20.7846i	0.366679	+	1.90532i
$120$	3.00000			0.273861
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	−2.50000	−	4.33013i	−0.226339	−	0.392031i
$123$	4.50000	+	7.79423i	0.405751	+	0.702782i
$124$	3.00000	−	5.19615i	0.269408	−	0.466628i
$125$	1.00000			0.0894427
$126$	3.00000	+	15.5885i	0.267261	+	1.38873i
$127$	−20.0000			−1.77471			−0.887357	−	0.461084i	$-0.847461\pi$
$127$	−20.0000			−1.77471			−0.887357	+	0.461084i	$0.847461\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−1.50000	−	2.59808i	−0.132068	−	0.228748i
$130$	−3.00000	−	5.19615i	−0.263117	−	0.455733i
$131$	9.00000	−	15.5885i	0.786334	−	1.36197i	−0.141865	−	0.989886i	$-0.545310\pi$
$131$	9.00000	−	15.5885i	0.786334	−	1.36197i	0.928199	−	0.372084i	$-0.121357\pi$
$132$	3.00000			0.261116
$133$	8.00000	−	6.92820i	0.693688	−	0.600751i
$134$	−1.00000			−0.0863868
$135$	4.50000	−	7.79423i	0.387298	−	0.670820i
$136$	−4.00000	−	6.92820i	−0.342997	−	0.594089i
$137$	−3.00000	−	5.19615i	−0.256307	−	0.443937i	0.708942	−	0.705266i	$-0.249173\pi$
$137$	−3.00000	−	5.19615i	−0.256307	−	0.443937i	−0.965250	+	0.261329i	$0.915839\pi$
$138$	10.5000	−	18.1865i	0.893819	−	1.54814i
$139$	−2.00000			−0.169638			−0.0848189	−	0.996396i	$-0.527031\pi$
$139$	−2.00000			−0.169638			−0.0848189	+	0.996396i	$0.527031\pi$
$140$	2.50000	+	0.866025i	0.211289	+	0.0731925i
$141$	24.0000			2.02116
$142$	2.00000	−	3.46410i	0.167836	−	0.290701i
$143$	−3.00000	−	5.19615i	−0.250873	−	0.434524i
$144$	−3.00000	−	5.19615i	−0.250000	−	0.433013i
$145$	4.50000	−	7.79423i	0.373705	−	0.647275i
$146$	−8.00000			−0.662085
$147$	−3.00000	+	20.7846i	−0.247436	+	1.71429i
$148$	−2.00000			−0.164399
$149$	7.50000	−	12.9904i	0.614424	−	1.06421i	−0.376061	−	0.926595i	$-0.622722\pi$
$149$	7.50000	−	12.9904i	0.614424	−	1.06421i	0.990485	−	0.137619i	$-0.0439449\pi$
$150$	−1.50000	−	2.59808i	−0.122474	−	0.212132i
$151$	8.00000	+	13.8564i	0.651031	+	1.12762i	0.982873	+	0.184284i	$0.0589965\pi$
$151$	8.00000	+	13.8564i	0.651031	+	1.12762i	−0.331842	+	0.943335i	$0.607670\pi$
$152$	−2.00000	+	3.46410i	−0.162221	+	0.280976i
$153$	−48.0000			−3.88057
$154$	2.50000	+	0.866025i	0.201456	+	0.0697863i
$155$	−6.00000			−0.481932
$156$	−9.00000	+	15.5885i	−0.720577	+	1.24808i
$157$	−2.00000	−	3.46410i	−0.159617	−	0.276465i	0.775113	−	0.631822i	$-0.217693\pi$
$157$	−2.00000	−	3.46410i	−0.159617	−	0.276465i	−0.934731	+	0.355357i	$0.884359\pi$
$158$	5.00000	+	8.66025i	0.397779	+	0.688973i
$159$	−3.00000	+	5.19615i	−0.237915	+	0.412082i
$160$	−1.00000			−0.0790569
$161$	14.0000	−	12.1244i	1.10335	−	0.955533i
$162$	−9.00000			−0.707107
$163$	−4.00000	+	6.92820i	−0.313304	+	0.542659i	−0.979076	−	0.203497i	$-0.934769\pi$
$163$	−4.00000	+	6.92820i	−0.313304	+	0.542659i	0.665771	+	0.746156i	$0.268103\pi$
$164$	−1.50000	−	2.59808i	−0.117130	−	0.202876i
$165$	−1.50000	−	2.59808i	−0.116775	−	0.202260i
$166$	4.50000	−	7.79423i	0.349268	−	0.604949i
$167$	3.00000			0.232147			0.116073	−	0.993241i	$-0.462969\pi$
$167$	3.00000			0.232147			0.116073	+	0.993241i	$0.462969\pi$
$168$	−1.50000	−	7.79423i	−0.115728	−	0.601338i
$169$	23.0000			1.76923
$170$	−4.00000	+	6.92820i	−0.306786	+	0.531369i
$171$	12.0000	+	20.7846i	0.917663	+	1.58944i
$172$	0.500000	+	0.866025i	0.0381246	+	0.0660338i
$173$	−5.00000	+	8.66025i	−0.380143	+	0.658427i	−0.991082	−	0.133250i	$-0.957459\pi$
$173$	−5.00000	+	8.66025i	−0.380143	+	0.658427i	0.610939	+	0.791677i	$0.290792\pi$
$174$	−27.0000			−2.04686
$175$	−0.500000	−	2.59808i	−0.0377964	−	0.196396i
$176$	−1.00000			−0.0753778
$177$	−9.00000	+	15.5885i	−0.676481	+	1.17170i
$178$	0.500000	+	0.866025i	0.0374766	+	0.0649113i
$179$	−4.00000	−	6.92820i	−0.298974	−	0.517838i	0.676927	−	0.736050i	$-0.263311\pi$
$179$	−4.00000	−	6.92820i	−0.298974	−	0.517838i	−0.975901	+	0.218212i	$0.929978\pi$
$180$	−3.00000	+	5.19615i	−0.223607	+	0.387298i
$181$	3.00000			0.222988			0.111494	−	0.993765i	$-0.464436\pi$
$181$	3.00000			0.222988			0.111494	+	0.993765i	$0.464436\pi$
$182$	−12.0000	+	10.3923i	−0.889499	+	0.770329i
$183$	15.0000			1.10883
$184$	−3.50000	+	6.06218i	−0.258023	+	0.446910i
$185$	1.00000	+	1.73205i	0.0735215	+	0.127343i
$186$	9.00000	+	15.5885i	0.659912	+	1.14300i
$187$	−4.00000	+	6.92820i	−0.292509	+	0.506640i
$188$	−8.00000			−0.583460
$189$	−22.5000	−	7.79423i	−1.63663	−	0.566947i
$190$	4.00000			0.290191
$191$	8.00000	−	13.8564i	0.578860	−	1.00261i	−0.416751	−	0.909021i	$-0.636831\pi$
$191$	8.00000	−	13.8564i	0.578860	−	1.00261i	0.995610	−	0.0935936i	$-0.0298354\pi$
$192$	1.50000	+	2.59808i	0.108253	+	0.187500i
$193$	−9.00000	−	15.5885i	−0.647834	−	1.12208i	−0.983639	−	0.180150i	$-0.942342\pi$
$193$	−9.00000	−	15.5885i	−0.647834	−	1.12208i	0.335805	−	0.941932i	$-0.390992\pi$
$194$		0			0
$195$	18.0000			1.28901
$196$	1.00000	−	6.92820i	0.0714286	−	0.494872i
$197$	−18.0000			−1.28245			−0.641223	−	0.767354i	$-0.721573\pi$
$197$	−18.0000			−1.28245			−0.641223	+	0.767354i	$0.721573\pi$
$198$	−3.00000	+	5.19615i	−0.213201	+	0.369274i
$199$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$199$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$200$	0.500000	+	0.866025i	0.0353553	+	0.0612372i
$201$	1.50000	−	2.59808i	0.105802	−	0.183254i
$202$	−5.00000			−0.351799
$203$	−22.5000	−	7.79423i	−1.57919	−	0.547048i
$204$	24.0000			1.68034
$205$	−1.50000	+	2.59808i	−0.104765	+	0.181458i
$206$	−6.50000	−	11.2583i	−0.452876	−	0.784405i
$207$	21.0000	+	36.3731i	1.45960	+	2.52810i
$208$	3.00000	−	5.19615i	0.208013	−	0.360288i
$209$	4.00000			0.276686
$210$	−6.00000	+	5.19615i	−0.414039	+	0.358569i
$211$	−14.0000			−0.963800			−0.481900	−	0.876226i	$-0.660053\pi$
$211$	−14.0000			−0.963800			−0.481900	+	0.876226i	$0.660053\pi$
$212$	1.00000	−	1.73205i	0.0686803	−	0.118958i
$213$	6.00000	+	10.3923i	0.411113	+	0.712069i
$214$	−8.50000	−	14.7224i	−0.581048	−	1.00640i
$215$	0.500000	−	0.866025i	0.0340997	−	0.0590624i
$216$	9.00000			0.612372
$217$	3.00000	+	15.5885i	0.203653	+	1.05821i
$218$	−5.00000			−0.338643
$219$	12.0000	−	20.7846i	0.810885	−	1.40449i
$220$	0.500000	+	0.866025i	0.0337100	+	0.0583874i
$221$	−24.0000	−	41.5692i	−1.61441	−	2.79625i
$222$	3.00000	−	5.19615i	0.201347	−	0.348743i
$223$	−16.0000			−1.07144			−0.535720	−	0.844396i	$-0.679960\pi$
$223$	−16.0000			−1.07144			−0.535720	+	0.844396i	$0.679960\pi$
$224$	0.500000	+	2.59808i	0.0334077	+	0.173591i
$225$	6.00000			0.400000
$226$	6.00000	−	10.3923i	0.399114	−	0.691286i
$227$	10.0000	+	17.3205i	0.663723	+	1.14960i	0.979630	+	0.200812i	$0.0643581\pi$
$227$	10.0000	+	17.3205i	0.663723	+	1.14960i	−0.315906	+	0.948790i	$0.602309\pi$
$228$	−6.00000	−	10.3923i	−0.397360	−	0.688247i
$229$	3.00000	−	5.19615i	0.198246	−	0.343371i	−0.749714	−	0.661762i	$-0.769809\pi$
$229$	3.00000	−	5.19615i	0.198246	−	0.343371i	0.947960	+	0.318390i	$0.103142\pi$
$230$	7.00000			0.461566
$231$	−6.00000	+	5.19615i	−0.394771	+	0.341882i
$232$	9.00000			0.590879
$233$	−13.0000	+	22.5167i	−0.851658	+	1.47512i	0.0280525	+	0.999606i	$0.491069\pi$
$233$	−13.0000	+	22.5167i	−0.851658	+	1.47512i	−0.879711	+	0.475509i	$0.842264\pi$
$234$	−18.0000	−	31.1769i	−1.17670	−	2.03810i
$235$	4.00000	+	6.92820i	0.260931	+	0.451946i
$236$	3.00000	−	5.19615i	0.195283	−	0.338241i
$237$	−30.0000			−1.94871
$238$	20.0000	+	6.92820i	1.29641	+	0.449089i
$239$	−6.00000			−0.388108			−0.194054	−	0.980991i	$-0.562164\pi$
$239$	−6.00000			−0.388108			−0.194054	+	0.980991i	$0.562164\pi$
$240$	1.50000	−	2.59808i	0.0968246	−	0.167705i
$241$	5.00000	+	8.66025i	0.322078	+	0.557856i	0.980917	−	0.194429i	$-0.0622852\pi$
$241$	5.00000	+	8.66025i	0.322078	+	0.557856i	−0.658838	+	0.752285i	$0.728952\pi$
$242$	0.500000	+	0.866025i	0.0321412	+	0.0556702i
$243$		0			0
$244$	−5.00000			−0.320092
$245$	−6.50000	+	2.59808i	−0.415270	+	0.165985i
$246$	9.00000			0.573819
$247$	−12.0000	+	20.7846i	−0.763542	+	1.32249i
$248$	−3.00000	−	5.19615i	−0.190500	−	0.329956i
$249$	13.5000	+	23.3827i	0.855528	+	1.48182i
$250$	0.500000	−	0.866025i	0.0316228	−	0.0547723i
$251$	2.00000			0.126239			0.0631194	−	0.998006i	$-0.479895\pi$
$251$	2.00000			0.126239			0.0631194	+	0.998006i	$0.479895\pi$
$252$	15.0000	+	5.19615i	0.944911	+	0.327327i
$253$	7.00000			0.440086
$254$	−10.0000	+	17.3205i	−0.627456	+	1.08679i
$255$	−12.0000	−	20.7846i	−0.751469	−	1.30158i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	3.00000	−	5.19615i	0.187135	−	0.324127i	−0.757159	−	0.653231i	$-0.773413\pi$
$257$	3.00000	−	5.19615i	0.187135	−	0.324127i	0.944294	+	0.329104i	$0.106747\pi$
$258$	−3.00000			−0.186772
$259$	4.00000	−	3.46410i	0.248548	−	0.215249i
$260$	−6.00000			−0.372104
$261$	27.0000	−	46.7654i	1.67126	−	2.89470i
$262$	−9.00000	−	15.5885i	−0.556022	−	0.963058i
$263$	−6.50000	−	11.2583i	−0.400807	−	0.694218i	0.593016	−	0.805190i	$-0.297937\pi$
$263$	−6.50000	−	11.2583i	−0.400807	−	0.694218i	−0.993824	+	0.110972i	$0.964604\pi$
$264$	1.50000	−	2.59808i	0.0923186	−	0.159901i
$265$	−2.00000			−0.122859
$266$	−2.00000	−	10.3923i	−0.122628	−	0.637193i
$267$	−3.00000			−0.183597
$268$	−0.500000	+	0.866025i	−0.0305424	+	0.0529009i
$269$	−3.50000	−	6.06218i	−0.213399	−	0.369618i	0.739377	−	0.673291i	$-0.235120\pi$
$269$	−3.50000	−	6.06218i	−0.213399	−	0.369618i	−0.952776	+	0.303674i	$0.901787\pi$
$270$	−4.50000	−	7.79423i	−0.273861	−	0.474342i
$271$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$271$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$272$	−8.00000			−0.485071
$273$	−9.00000	−	46.7654i	−0.544705	−	2.83037i
$274$	−6.00000			−0.362473
$275$	0.500000	−	0.866025i	0.0301511	−	0.0522233i
$276$	−10.5000	−	18.1865i	−0.632026	−	1.09470i
$277$	−1.00000	−	1.73205i	−0.0600842	−	0.104069i	0.834419	−	0.551131i	$-0.185804\pi$
$277$	−1.00000	−	1.73205i	−0.0600842	−	0.104069i	−0.894503	+	0.447062i	$0.852470\pi$
$278$	−1.00000	+	1.73205i	−0.0599760	+	0.103882i
$279$	−36.0000			−2.15526
$280$	2.00000	−	1.73205i	0.119523	−	0.103510i
$281$	30.0000			1.78965			0.894825	−	0.446417i	$-0.147300\pi$
$281$	30.0000			1.78965			0.894825	+	0.446417i	$0.147300\pi$
$282$	12.0000	−	20.7846i	0.714590	−	1.23771i
$283$	−2.00000	−	3.46410i	−0.118888	−	0.205919i	0.800439	−	0.599414i	$-0.204600\pi$
$283$	−2.00000	−	3.46410i	−0.118888	−	0.205919i	−0.919327	+	0.393494i	$0.871266\pi$
$284$	−2.00000	−	3.46410i	−0.118678	−	0.205557i
$285$	−6.00000	+	10.3923i	−0.355409	+	0.615587i
$286$	−6.00000			−0.354787
$287$	7.50000	+	2.59808i	0.442711	+	0.153360i
$288$	−6.00000			−0.353553
$289$	−23.5000	+	40.7032i	−1.38235	+	2.39431i
$290$	−4.50000	−	7.79423i	−0.264249	−	0.457693i
$291$		0			0
$292$	−4.00000	+	6.92820i	−0.234082	+	0.405442i
$293$	−26.0000			−1.51894			−0.759468	−	0.650545i	$-0.774541\pi$
$293$	−26.0000			−1.51894			−0.759468	+	0.650545i	$0.774541\pi$
$294$	16.5000	+	12.9904i	0.962300	+	0.757614i
$295$	−6.00000			−0.349334
$296$	−1.00000	+	1.73205i	−0.0581238	+	0.100673i
$297$	−4.50000	−	7.79423i	−0.261116	−	0.452267i
$298$	−7.50000	−	12.9904i	−0.434463	−	0.752513i
$299$	−21.0000	+	36.3731i	−1.21446	+	2.10351i
$300$	−3.00000			−0.173205
$301$	−2.50000	−	0.866025i	−0.144098	−	0.0499169i
$302$	16.0000			0.920697
$303$	7.50000	−	12.9904i	0.430864	−	0.746278i
$304$	2.00000	+	3.46410i	0.114708	+	0.198680i
$305$	2.50000	+	4.33013i	0.143150	+	0.247942i
$306$	−24.0000	+	41.5692i	−1.37199	+	2.37635i
$307$	7.00000			0.399511			0.199756	−	0.979846i	$-0.435985\pi$
$307$	7.00000			0.399511			0.199756	+	0.979846i	$0.435985\pi$
$308$	2.00000	−	1.73205i	0.113961	−	0.0986928i
$309$	39.0000			2.21863
$310$	−3.00000	+	5.19615i	−0.170389	+	0.295122i
$311$	9.00000	+	15.5885i	0.510343	+	0.883940i	0.999928	+	0.0119847i	$0.00381495\pi$
$311$	9.00000	+	15.5885i	0.510343	+	0.883940i	−0.489585	+	0.871956i	$0.662852\pi$
$312$	9.00000	+	15.5885i	0.509525	+	0.882523i
$313$	−8.00000	+	13.8564i	−0.452187	+	0.783210i	−0.998522	−	0.0543564i	$-0.982689\pi$
$313$	−8.00000	+	13.8564i	−0.452187	+	0.783210i	0.546335	+	0.837567i	$0.316023\pi$
$314$	−4.00000			−0.225733
$315$	−3.00000	−	15.5885i	−0.169031	−	0.878310i
$316$	10.0000			0.562544
$317$	−4.00000	+	6.92820i	−0.224662	+	0.389127i	−0.956218	−	0.292655i	$-0.905461\pi$
$317$	−4.00000	+	6.92820i	−0.224662	+	0.389127i	0.731556	+	0.681782i	$0.238795\pi$
$318$	3.00000	+	5.19615i	0.168232	+	0.291386i
$319$	−4.50000	−	7.79423i	−0.251952	−	0.436393i
$320$	−0.500000	+	0.866025i	−0.0279508	+	0.0484123i
$321$	51.0000			2.84654
$322$	−3.50000	−	18.1865i	−0.195047	−	1.01350i
$323$	32.0000			1.78053
$324$	−4.50000	+	7.79423i	−0.250000	+	0.433013i
$325$	3.00000	+	5.19615i	0.166410	+	0.288231i
$326$	4.00000	+	6.92820i	0.221540	+	0.383718i
$327$	7.50000	−	12.9904i	0.414751	−	0.718370i
$328$	−3.00000			−0.165647
$329$	16.0000	−	13.8564i	0.882109	−	0.763928i
$330$	−3.00000			−0.165145
$331$	−16.0000	+	27.7128i	−0.879440	+	1.52323i	−0.0274825	+	0.999622i	$0.508749\pi$
$331$	−16.0000	+	27.7128i	−0.879440	+	1.52323i	−0.851957	+	0.523612i	$0.824584\pi$
$332$	−4.50000	−	7.79423i	−0.246970	−	0.427764i
$333$	6.00000	+	10.3923i	0.328798	+	0.569495i
$334$	1.50000	−	2.59808i	0.0820763	−	0.142160i
$335$	1.00000			0.0546358
$336$	−7.50000	−	2.59808i	−0.409159	−	0.141737i
$337$	−20.0000			−1.08947			−0.544735	−	0.838608i	$-0.683370\pi$
$337$	−20.0000			−1.08947			−0.544735	+	0.838608i	$0.683370\pi$
$338$	11.5000	−	19.9186i	0.625518	−	1.08343i
$339$	18.0000	+	31.1769i	0.977626	+	1.69330i
$340$	4.00000	+	6.92820i	0.216930	+	0.375735i
$341$	−3.00000	+	5.19615i	−0.162459	+	0.281387i
$342$	24.0000			1.29777
$343$	10.0000	+	15.5885i	0.539949	+	0.841698i
$344$	1.00000			0.0539164
$345$	−10.5000	+	18.1865i	−0.565301	+	0.979130i
$346$	5.00000	+	8.66025i	0.268802	+	0.465578i
$347$	6.50000	+	11.2583i	0.348938	+	0.604379i	0.986061	−	0.166383i	$-0.0532089\pi$
$347$	6.50000	+	11.2583i	0.348938	+	0.604379i	−0.637123	+	0.770762i	$0.719876\pi$
$348$	−13.5000	+	23.3827i	−0.723676	+	1.25344i
$349$	−13.0000			−0.695874			−0.347937	−	0.937518i	$-0.613118\pi$
$349$	−13.0000			−0.695874			−0.347937	+	0.937518i	$0.613118\pi$
$350$	−2.50000	−	0.866025i	−0.133631	−	0.0462910i
$351$	54.0000			2.88231
$352$	−0.500000	+	0.866025i	−0.0266501	+	0.0461593i
$353$	4.00000	+	6.92820i	0.212899	+	0.368751i	0.952620	−	0.304162i	$-0.0983763\pi$
$353$	4.00000	+	6.92820i	0.212899	+	0.368751i	−0.739722	+	0.672913i	$0.765043\pi$
$354$	9.00000	+	15.5885i	0.478345	+	0.828517i
$355$	−2.00000	+	3.46410i	−0.106149	+	0.183855i
$356$	1.00000			0.0529999
$357$	−48.0000	+	41.5692i	−2.54043	+	2.20008i
$358$	−8.00000			−0.422813
$359$	8.00000	−	13.8564i	0.422224	−	0.731313i	−0.573933	−	0.818902i	$-0.694583\pi$
$359$	8.00000	−	13.8564i	0.422224	−	0.731313i	0.996157	+	0.0875892i	$0.0279163\pi$
$360$	3.00000	+	5.19615i	0.158114	+	0.273861i
$361$	1.50000	+	2.59808i	0.0789474	+	0.136741i
$362$	1.50000	−	2.59808i	0.0788382	−	0.136552i
$363$	−3.00000			−0.157459
$364$	3.00000	+	15.5885i	0.157243	+	0.817057i
$365$	8.00000			0.418739
$366$	7.50000	−	12.9904i	0.392031	−	0.679018i
$367$	−5.50000	−	9.52628i	−0.287098	−	0.497268i	0.686018	−	0.727585i	$-0.259357\pi$
$367$	−5.50000	−	9.52628i	−0.287098	−	0.497268i	−0.973116	+	0.230317i	$0.926024\pi$
$368$	3.50000	+	6.06218i	0.182450	+	0.316013i
$369$	−9.00000	+	15.5885i	−0.468521	+	0.811503i
$370$	2.00000			0.103975
$371$	1.00000	+	5.19615i	0.0519174	+	0.269771i
$372$	18.0000			0.933257
$373$	16.0000	−	27.7128i	0.828449	−	1.43492i	−0.0708063	−	0.997490i	$-0.522557\pi$
$373$	16.0000	−	27.7128i	0.828449	−	1.43492i	0.899255	−	0.437425i	$-0.144109\pi$
$374$	4.00000	+	6.92820i	0.206835	+	0.358249i
$375$	1.50000	+	2.59808i	0.0774597	+	0.134164i
$376$	−4.00000	+	6.92820i	−0.206284	+	0.357295i
$377$	54.0000			2.78114
$378$	−18.0000	+	15.5885i	−0.925820	+	0.801784i
$379$	−24.0000			−1.23280			−0.616399	−	0.787434i	$-0.711409\pi$
$379$	−24.0000			−1.23280			−0.616399	+	0.787434i	$0.711409\pi$
$380$	2.00000	−	3.46410i	0.102598	−	0.177705i
$381$	−30.0000	−	51.9615i	−1.53695	−	2.66207i
$382$	−8.00000	−	13.8564i	−0.409316	−	0.708955i
$383$	3.50000	−	6.06218i	0.178842	−	0.309763i	−0.762642	−	0.646820i	$-0.776098\pi$
$383$	3.50000	−	6.06218i	0.178842	−	0.309763i	0.941484	+	0.337058i	$0.109432\pi$
$384$	3.00000			0.153093
$385$	−2.50000	−	0.866025i	−0.127412	−	0.0441367i
$386$	−18.0000			−0.916176
$387$	3.00000	−	5.19615i	0.152499	−	0.264135i
$388$		0			0
$389$	15.0000	+	25.9808i	0.760530	+	1.31728i	0.942578	+	0.333987i	$0.108394\pi$
$389$	15.0000	+	25.9808i	0.760530	+	1.31728i	−0.182047	+	0.983290i	$0.558272\pi$
$390$	9.00000	−	15.5885i	0.455733	−	0.789352i
$391$	56.0000			2.83204
$392$	−5.50000	−	4.33013i	−0.277792	−	0.218704i
$393$	54.0000			2.72394
$394$	−9.00000	+	15.5885i	−0.453413	+	0.785335i
$395$	−5.00000	−	8.66025i	−0.251577	−	0.435745i
$396$	3.00000	+	5.19615i	0.150756	+	0.261116i
$397$	−10.0000	+	17.3205i	−0.501886	+	0.869291i	0.498112	+	0.867113i	$0.334027\pi$
$397$	−10.0000	+	17.3205i	−0.501886	+	0.869291i	−0.999998	+	0.00217869i	$0.999307\pi$
$398$		0			0
$399$	30.0000	+	10.3923i	1.50188	+	0.520266i
$400$	1.00000			0.0500000
$401$	2.50000	−	4.33013i	0.124844	−	0.216236i	−0.796828	−	0.604206i	$-0.793490\pi$
$401$	2.50000	−	4.33013i	0.124844	−	0.216236i	0.921672	+	0.387970i	$0.126824\pi$
$402$	−1.50000	−	2.59808i	−0.0748132	−	0.129580i
$403$	−18.0000	−	31.1769i	−0.896644	−	1.55303i
$404$	−2.50000	+	4.33013i	−0.124380	+	0.215432i
$405$	9.00000			0.447214
$406$	−18.0000	+	15.5885i	−0.893325	+	0.773642i
$407$	2.00000			0.0991363
$408$	12.0000	−	20.7846i	0.594089	−	1.02899i
$409$	−6.50000	−	11.2583i	−0.321404	−	0.556689i	0.659374	−	0.751815i	$-0.270822\pi$
$409$	−6.50000	−	11.2583i	−0.321404	−	0.556689i	−0.980778	+	0.195127i	$0.937488\pi$
$410$	1.50000	+	2.59808i	0.0740797	+	0.128310i
$411$	9.00000	−	15.5885i	0.443937	−	0.768922i
$412$	−13.0000			−0.640464
$413$	3.00000	+	15.5885i	0.147620	+	0.767058i
$414$	42.0000			2.06419
$415$	−4.50000	+	7.79423i	−0.220896	+	0.382604i
$416$	−3.00000	−	5.19615i	−0.147087	−	0.254762i
$417$	−3.00000	−	5.19615i	−0.146911	−	0.254457i
$418$	2.00000	−	3.46410i	0.0978232	−	0.169435i
$419$	30.0000			1.46560			0.732798	−	0.680446i	$-0.238214\pi$
$419$	30.0000			1.46560			0.732798	+	0.680446i	$0.238214\pi$
$420$	1.50000	+	7.79423i	0.0731925	+	0.380319i
$421$	25.0000			1.21843			0.609213	−	0.793007i	$-0.291486\pi$
$421$	25.0000			1.21843			0.609213	+	0.793007i	$0.291486\pi$
$422$	−7.00000	+	12.1244i	−0.340755	+	0.590204i
$423$	24.0000	+	41.5692i	1.16692	+	2.02116i
$424$	−1.00000	−	1.73205i	−0.0485643	−	0.0841158i
$425$	4.00000	−	6.92820i	0.194029	−	0.336067i
$426$	12.0000			0.581402
$427$	10.0000	−	8.66025i	0.483934	−	0.419099i
$428$	−17.0000			−0.821726
$429$	9.00000	−	15.5885i	0.434524	−	0.752618i
$430$	−0.500000	−	0.866025i	−0.0241121	−	0.0417635i
$431$	2.00000	+	3.46410i	0.0963366	+	0.166860i	0.910166	−	0.414244i	$-0.135954\pi$
$431$	2.00000	+	3.46410i	0.0963366	+	0.166860i	−0.813829	+	0.581104i	$0.802621\pi$
$432$	4.50000	−	7.79423i	0.216506	−	0.375000i
$433$	−30.0000			−1.44171			−0.720854	−	0.693087i	$-0.756250\pi$
$433$	−30.0000			−1.44171			−0.720854	+	0.693087i	$0.756250\pi$
$434$	15.0000	+	5.19615i	0.720023	+	0.249423i
$435$	27.0000			1.29455
$436$	−2.50000	+	4.33013i	−0.119728	+	0.207375i
$437$	−14.0000	−	24.2487i	−0.669711	−	1.15997i
$438$	−12.0000	−	20.7846i	−0.573382	−	0.993127i
$439$	−15.0000	+	25.9808i	−0.715911	+	1.23999i	0.246696	+	0.969093i	$0.420655\pi$
$439$	−15.0000	+	25.9808i	−0.715911	+	1.23999i	−0.962607	+	0.270901i	$0.912678\pi$
$440$	1.00000			0.0476731
$441$	−39.0000	+	15.5885i	−1.85714	+	0.742307i
$442$	−48.0000			−2.28313
$443$	−6.50000	+	11.2583i	−0.308824	+	0.534899i	−0.978105	−	0.208110i	$-0.933269\pi$
$443$	−6.50000	+	11.2583i	−0.308824	+	0.534899i	0.669281	+	0.743009i	$0.266602\pi$
$444$	−3.00000	−	5.19615i	−0.142374	−	0.246598i
$445$	−0.500000	−	0.866025i	−0.0237023	−	0.0410535i
$446$	−8.00000	+	13.8564i	−0.378811	+	0.656120i
$447$	45.0000			2.12843
$448$	2.50000	+	0.866025i	0.118114	+	0.0409159i
$449$	−25.0000			−1.17982			−0.589911	−	0.807468i	$-0.700837\pi$
$449$	−25.0000			−1.17982			−0.589911	+	0.807468i	$0.700837\pi$
$450$	3.00000	−	5.19615i	0.141421	−	0.244949i
$451$	1.50000	+	2.59808i	0.0706322	+	0.122339i
$452$	−6.00000	−	10.3923i	−0.282216	−	0.488813i
$453$	−24.0000	+	41.5692i	−1.12762	+	1.95309i
$454$	20.0000			0.938647
$455$	12.0000	−	10.3923i	0.562569	−	0.487199i
$456$	−12.0000			−0.561951
$457$	4.00000	−	6.92820i	0.187112	−	0.324088i	−0.757174	−	0.653213i	$-0.773421\pi$
$457$	4.00000	−	6.92820i	0.187112	−	0.324088i	0.944286	+	0.329125i	$0.106754\pi$
$458$	−3.00000	−	5.19615i	−0.140181	−	0.242800i
$459$	−36.0000	−	62.3538i	−1.68034	−	2.91043i
$460$	3.50000	−	6.06218i	0.163188	−	0.282650i
$461$	−18.0000			−0.838344			−0.419172	−	0.907907i	$-0.637680\pi$
$461$	−18.0000			−0.838344			−0.419172	+	0.907907i	$0.637680\pi$
$462$	1.50000	+	7.79423i	0.0697863	+	0.362620i
$463$	11.0000			0.511213			0.255607	−	0.966781i	$-0.417725\pi$
$463$	11.0000			0.511213			0.255607	+	0.966781i	$0.417725\pi$
$464$	4.50000	−	7.79423i	0.208907	−	0.361838i
$465$	−9.00000	−	15.5885i	−0.417365	−	0.722897i
$466$	13.0000	+	22.5167i	0.602213	+	1.04306i
$467$	13.5000	−	23.3827i	0.624705	−	1.08202i	−0.363892	−	0.931441i	$-0.618552\pi$
$467$	13.5000	−	23.3827i	0.624705	−	1.08202i	0.988598	−	0.150581i	$-0.0481143\pi$
$468$	−36.0000			−1.66410
$469$	−0.500000	−	2.59808i	−0.0230879	−	0.119968i
$470$	8.00000			0.369012
$471$	6.00000	−	10.3923i	0.276465	−	0.478852i
$472$	−3.00000	−	5.19615i	−0.138086	−	0.239172i
$473$	−0.500000	−	0.866025i	−0.0229900	−	0.0398199i
$474$	−15.0000	+	25.9808i	−0.688973	+	1.19334i
$475$	−4.00000			−0.183533
$476$	16.0000	−	13.8564i	0.733359	−	0.635107i
$477$	−12.0000			−0.549442
$478$	−3.00000	+	5.19615i	−0.137217	+	0.237666i
$479$	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
$482$	10.0000			0.455488
$483$	52.5000	+	18.1865i	2.38883	+	0.827516i
$484$	1.00000			0.0454545
$485$		0			0
$486$		0			0
$487$	2.00000	+	3.46410i	0.0906287	+	0.156973i	0.907776	−	0.419456i	$-0.137779\pi$
$487$	2.00000	+	3.46410i	0.0906287	+	0.156973i	−0.817147	+	0.576429i	$0.804446\pi$
$488$	−2.50000	+	4.33013i	−0.113170	+	0.196016i
$489$	−24.0000			−1.08532
$490$	−1.00000	+	6.92820i	−0.0451754	+	0.312984i
$491$	−22.0000			−0.992846			−0.496423	−	0.868081i	$-0.665354\pi$
$491$	−22.0000			−0.992846			−0.496423	+	0.868081i	$0.665354\pi$
$492$	4.50000	−	7.79423i	0.202876	−	0.351391i
$493$	−36.0000	−	62.3538i	−1.62136	−	2.80828i
$494$	12.0000	+	20.7846i	0.539906	+	0.935144i
$495$	3.00000	−	5.19615i	0.134840	−	0.233550i
$496$	−6.00000			−0.269408
$497$	10.0000	+	3.46410i	0.448561	+	0.155386i
$498$	27.0000			1.20990
$499$	−2.00000	+	3.46410i	−0.0895323	+	0.155074i	−0.907314	−	0.420455i	$-0.861871\pi$
$499$	−2.00000	+	3.46410i	−0.0895323	+	0.155074i	0.817781	+	0.575529i	$0.195204\pi$
$500$	−0.500000	−	0.866025i	−0.0223607	−	0.0387298i
$501$	4.50000	+	7.79423i	0.201045	+	0.348220i
$502$	1.00000	−	1.73205i	0.0446322	−	0.0773052i
$503$	19.0000			0.847168			0.423584	−	0.905857i	$-0.360772\pi$
$503$	19.0000			0.847168			0.423584	+	0.905857i	$0.360772\pi$
$504$	12.0000	−	10.3923i	0.534522	−	0.462910i
$505$	5.00000			0.222497
$506$	3.50000	−	6.06218i	0.155594	−	0.269497i
$507$	34.5000	+	59.7558i	1.53220	+	2.65385i
$508$	10.0000	+	17.3205i	0.443678	+	0.768473i
$509$	11.5000	−	19.9186i	0.509729	−	0.882876i	−0.490208	−	0.871606i	$-0.663079\pi$
$509$	11.5000	−	19.9186i	0.509729	−	0.882876i	0.999936	−	0.0112702i	$-0.00358750\pi$
$510$	−24.0000			−1.06274
$511$	−4.00000	−	20.7846i	−0.176950	−	0.919457i
$512$	−1.00000			−0.0441942
$513$	−18.0000	+	31.1769i	−0.794719	+	1.37649i
$514$	−3.00000	−	5.19615i	−0.132324	−	0.229192i
$515$	6.50000	+	11.2583i	0.286424	+	0.496101i
$516$	−1.50000	+	2.59808i	−0.0660338	+	0.114374i
$517$	8.00000			0.351840
$518$	−1.00000	−	5.19615i	−0.0439375	−	0.228306i
$519$	−30.0000			−1.31685
$520$	−3.00000	+	5.19615i	−0.131559	+	0.227866i
$521$	−7.00000	−	12.1244i	−0.306676	−	0.531178i	0.670957	−	0.741496i	$-0.265883\pi$
$521$	−7.00000	−	12.1244i	−0.306676	−	0.531178i	−0.977633	+	0.210318i	$0.932550\pi$
$522$	−27.0000	−	46.7654i	−1.18176	−	2.04686i
$523$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$523$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$524$	−18.0000			−0.786334
$525$	6.00000	−	5.19615i	0.261861	−	0.226779i
$526$	−13.0000			−0.566827
$527$	−24.0000	+	41.5692i	−1.04546	+	1.81078i
$528$	−1.50000	−	2.59808i	−0.0652791	−	0.113067i
$529$	−13.0000	−	22.5167i	−0.565217	−	0.978985i
$530$	−1.00000	+	1.73205i	−0.0434372	+	0.0752355i
$531$	−36.0000			−1.56227
$532$	−10.0000	−	3.46410i	−0.433555	−	0.150188i
$533$	−18.0000			−0.779667
$534$	−1.50000	+	2.59808i	−0.0649113	+	0.112430i
$535$	8.50000	+	14.7224i	0.367487	+	0.636506i
$536$	0.500000	+	0.866025i	0.0215967	+	0.0374066i
$537$	12.0000	−	20.7846i	0.517838	−	0.896922i
$538$	−7.00000			−0.301791
$539$	−1.00000	+	6.92820i	−0.0430730	+	0.298419i
$540$	−9.00000			−0.387298
$541$	7.50000	−	12.9904i	0.322450	−	0.558500i	−0.658543	−	0.752543i	$-0.728827\pi$
$541$	7.50000	−	12.9904i	0.322450	−	0.558500i	0.980993	+	0.194043i	$0.0621602\pi$
$542$		0			0
$543$	4.50000	+	7.79423i	0.193113	+	0.334482i
$544$	−4.00000	+	6.92820i	−0.171499	+	0.297044i
$545$	5.00000			0.214176
$546$	−45.0000	−	15.5885i	−1.92582	−	0.667124i
$547$	−45.0000			−1.92406			−0.962031	−	0.272942i	$-0.912003\pi$
$547$	−45.0000			−1.92406			−0.962031	+	0.272942i	$0.912003\pi$
$548$	−3.00000	+	5.19615i	−0.128154	+	0.221969i
$549$	15.0000	+	25.9808i	0.640184	+	1.10883i
$550$	−0.500000	−	0.866025i	−0.0213201	−	0.0369274i
$551$	−18.0000	+	31.1769i	−0.766826	+	1.32818i
$552$	−21.0000			−0.893819
$553$	−20.0000	+	17.3205i	−0.850487	+	0.736543i
$554$	−2.00000			−0.0849719
$555$	−3.00000	+	5.19615i	−0.127343	+	0.220564i
$556$	1.00000	+	1.73205i	0.0424094	+	0.0734553i
$557$	6.00000	+	10.3923i	0.254228	+	0.440336i	0.964686	−	0.263404i	$-0.0848453\pi$
$557$	6.00000	+	10.3923i	0.254228	+	0.440336i	−0.710457	+	0.703740i	$0.751512\pi$
$558$	−18.0000	+	31.1769i	−0.762001	+	1.31982i
$559$	6.00000			0.253773
$560$	−0.500000	−	2.59808i	−0.0211289	−	0.109789i
$561$	−24.0000			−1.01328
$562$	15.0000	−	25.9808i	0.632737	−	1.09593i
$563$	−20.5000	−	35.5070i	−0.863972	−	1.49644i	−0.868064	−	0.496452i	$-0.834636\pi$
$563$	−20.5000	−	35.5070i	−0.863972	−	1.49644i	0.00409232	−	0.999992i	$-0.498697\pi$
$564$	−12.0000	−	20.7846i	−0.505291	−	0.875190i
$565$	−6.00000	+	10.3923i	−0.252422	+	0.437208i
$566$	−4.00000			−0.168133
$567$	−4.50000	−	23.3827i	−0.188982	−	0.981981i
$568$	−4.00000			−0.167836
$569$	−3.00000	+	5.19615i	−0.125767	+	0.217834i	−0.922032	−	0.387113i	$-0.873472\pi$
$569$	−3.00000	+	5.19615i	−0.125767	+	0.217834i	0.796266	+	0.604947i	$0.206806\pi$
$570$	6.00000	+	10.3923i	0.251312	+	0.435286i
$571$	−5.00000	−	8.66025i	−0.209243	−	0.362420i	0.742233	−	0.670142i	$-0.233767\pi$
$571$	−5.00000	−	8.66025i	−0.209243	−	0.362420i	−0.951476	+	0.307722i	$0.900433\pi$
$572$	−3.00000	+	5.19615i	−0.125436	+	0.217262i
$573$	48.0000			2.00523
$574$	6.00000	−	5.19615i	0.250435	−	0.216883i
$575$	−7.00000			−0.291920
$576$	−3.00000	+	5.19615i	−0.125000	+	0.216506i
$577$	1.00000	+	1.73205i	0.0416305	+	0.0721062i	0.886090	−	0.463513i	$-0.153411\pi$
$577$	1.00000	+	1.73205i	0.0416305	+	0.0721062i	−0.844459	+	0.535620i	$0.820078\pi$
$578$	23.5000	+	40.7032i	0.977471	+	1.69303i
$579$	27.0000	−	46.7654i	1.12208	−	1.94350i
$580$	−9.00000			−0.373705
$581$	22.5000	+	7.79423i	0.933457	+	0.323359i
$582$		0			0
$583$	−1.00000	+	1.73205i	−0.0414158	+	0.0717342i
$584$	4.00000	+	6.92820i	0.165521	+	0.286691i
$585$	18.0000	+	31.1769i	0.744208	+	1.28901i
$586$	−13.0000	+	22.5167i	−0.537025	+	0.930155i
$587$	−28.0000			−1.15568			−0.577842	−	0.816149i	$-0.696105\pi$
$587$	−28.0000			−1.15568			−0.577842	+	0.816149i	$0.696105\pi$
$588$	19.5000	−	7.79423i	0.804166	−	0.321429i
$589$	24.0000			0.988903
$590$	−3.00000	+	5.19615i	−0.123508	+	0.213922i
$591$	−27.0000	−	46.7654i	−1.11063	−	1.92367i
$592$	1.00000	+	1.73205i	0.0410997	+	0.0711868i
$593$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$593$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$594$	−9.00000			−0.369274
$595$	−20.0000	−	6.92820i	−0.819920	−	0.284029i
$596$	−15.0000			−0.614424
$597$		0			0
$598$	21.0000	+	36.3731i	0.858754	+	1.48741i
$599$	17.0000	+	29.4449i	0.694601	+	1.20308i	0.970315	+	0.241845i	$0.0777525\pi$
$599$	17.0000	+	29.4449i	0.694601	+	1.20308i	−0.275714	+	0.961240i	$0.588914\pi$
$600$	−1.50000	+	2.59808i	−0.0612372	+	0.106066i
$601$	−34.0000			−1.38689			−0.693444	−	0.720510i	$-0.743908\pi$
$601$	−34.0000			−1.38689			−0.693444	+	0.720510i	$0.743908\pi$
$602$	−2.00000	+	1.73205i	−0.0815139	+	0.0705931i
$603$	6.00000			0.244339
$604$	8.00000	−	13.8564i	0.325515	−	0.563809i
$605$	−0.500000	−	0.866025i	−0.0203279	−	0.0352089i
$606$	−7.50000	−	12.9904i	−0.304667	−	0.527698i
$607$	5.50000	−	9.52628i	0.223238	−	0.386660i	−0.732551	−	0.680712i	$-0.761671\pi$
$607$	5.50000	−	9.52628i	0.223238	−	0.386660i	0.955789	+	0.294052i	$0.0950039\pi$
$608$	4.00000			0.162221
$609$	−13.5000	−	70.1481i	−0.547048	−	2.84254i
$610$	5.00000			0.202444
$611$	−24.0000	+	41.5692i	−0.970936	+	1.68171i
$612$	24.0000	+	41.5692i	0.970143	+	1.68034i
$613$	−11.0000	−	19.0526i	−0.444286	−	0.769526i	0.553716	−	0.832705i	$-0.313209\pi$
$613$	−11.0000	−	19.0526i	−0.444286	−	0.769526i	−0.998002	+	0.0631797i	$0.979876\pi$
$614$	3.50000	−	6.06218i	0.141249	−	0.244650i
$615$	−9.00000			−0.362915
$616$	−0.500000	−	2.59808i	−0.0201456	−	0.104679i
$617$	28.0000			1.12724			0.563619	−	0.826035i	$-0.309409\pi$
$617$	28.0000			1.12724			0.563619	+	0.826035i	$0.309409\pi$
$618$	19.5000	−	33.7750i	0.784405	−	1.35863i
$619$	−5.00000	−	8.66025i	−0.200967	−	0.348085i	0.747873	−	0.663842i	$-0.231075\pi$
$619$	−5.00000	−	8.66025i	−0.200967	−	0.348085i	−0.948840	+	0.315757i	$0.897742\pi$
$620$	3.00000	+	5.19615i	0.120483	+	0.208683i
$621$	−31.5000	+	54.5596i	−1.26405	+	2.18940i
$622$	18.0000			0.721734
$623$	−2.00000	+	1.73205i	−0.0801283	+	0.0693932i
$624$	18.0000			0.720577
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	8.00000	+	13.8564i	0.319744	+	0.553813i
$627$	6.00000	+	10.3923i	0.239617	+	0.415029i
$628$	−2.00000	+	3.46410i	−0.0798087	+	0.138233i
$629$	16.0000			0.637962
$630$	−15.0000	−	5.19615i	−0.597614	−	0.207020i
$631$	−10.0000			−0.398094			−0.199047	−	0.979990i	$-0.563785\pi$
$631$	−10.0000			−0.398094			−0.199047	+	0.979990i	$0.563785\pi$
$632$	5.00000	−	8.66025i	0.198889	−	0.344486i
$633$	−21.0000	−	36.3731i	−0.834675	−	1.44570i
$634$	4.00000	+	6.92820i	0.158860	+	0.275154i
$635$	10.0000	−	17.3205i	0.396838	−	0.687343i
$636$	6.00000			0.237915
$637$	−33.0000	−	25.9808i	−1.30751	−	1.02940i
$638$	−9.00000			−0.356313
$639$	−12.0000	+	20.7846i	−0.474713	+	0.822226i
$640$	0.500000	+	0.866025i	0.0197642	+	0.0342327i
$641$	−4.50000	−	7.79423i	−0.177739	−	0.307854i	0.763367	−	0.645966i	$-0.223545\pi$
$641$	−4.50000	−	7.79423i	−0.177739	−	0.307854i	−0.941106	+	0.338112i	$0.890212\pi$
$642$	25.5000	−	44.1673i	1.00640	−	1.74314i
$643$	−4.00000			−0.157745			−0.0788723	−	0.996885i	$-0.525132\pi$
$643$	−4.00000			−0.157745			−0.0788723	+	0.996885i	$0.525132\pi$
$644$	−17.5000	−	6.06218i	−0.689597	−	0.238883i
$645$	3.00000			0.118125
$646$	16.0000	−	27.7128i	0.629512	−	1.09035i
$647$	−19.5000	−	33.7750i	−0.766624	−	1.32783i	−0.939384	−	0.342868i	$-0.888602\pi$
$647$	−19.5000	−	33.7750i	−0.766624	−	1.32783i	0.172760	−	0.984964i	$-0.444732\pi$
$648$	4.50000	+	7.79423i	0.176777	+	0.306186i
$649$	−3.00000	+	5.19615i	−0.117760	+	0.203967i
$650$	6.00000			0.235339
$651$	−36.0000	+	31.1769i	−1.41095	+	1.22192i
$652$	8.00000			0.313304
$653$	9.00000	−	15.5885i	0.352197	−	0.610023i	−0.634437	−	0.772975i	$-0.718768\pi$
$653$	9.00000	−	15.5885i	0.352197	−	0.610023i	0.986634	+	0.162951i	$0.0521013\pi$
$654$	−7.50000	−	12.9904i	−0.293273	−	0.507964i
$655$	9.00000	+	15.5885i	0.351659	+	0.609091i
$656$	−1.50000	+	2.59808i	−0.0585652	+	0.101438i
$657$	48.0000			1.87266
$658$	−4.00000	−	20.7846i	−0.155936	−	0.810268i
$659$	−12.0000			−0.467454			−0.233727	−	0.972302i	$-0.575092\pi$
$659$	−12.0000			−0.467454			−0.233727	+	0.972302i	$0.575092\pi$
$660$	−1.50000	+	2.59808i	−0.0583874	+	0.101130i
$661$	−12.5000	−	21.6506i	−0.486194	−	0.842112i	0.513680	−	0.857982i	$-0.328282\pi$
$661$	−12.5000	−	21.6506i	−0.486194	−	0.842112i	−0.999874	+	0.0158695i	$0.994948\pi$
$662$	16.0000	+	27.7128i	0.621858	+	1.07709i
$663$	72.0000	−	124.708i	2.79625	−	4.84324i
$664$	−9.00000			−0.349268
$665$	2.00000	+	10.3923i	0.0775567	+	0.402996i
$666$	12.0000			0.464991
$667$	−31.5000	+	54.5596i	−1.21968	+	2.11256i
$668$	−1.50000	−	2.59808i	−0.0580367	−	0.100523i
$669$	−24.0000	−	41.5692i	−0.927894	−	1.60716i
$670$	0.500000	−	0.866025i	0.0193167	−	0.0334575i
$671$	5.00000			0.193023
$672$	−6.00000	+	5.19615i	−0.231455	+	0.200446i
$673$	26.0000			1.00223			0.501113	−	0.865382i	$-0.332924\pi$
$673$	26.0000			1.00223			0.501113	+	0.865382i	$0.332924\pi$
$674$	−10.0000	+	17.3205i	−0.385186	+	0.667161i
$675$	4.50000	+	7.79423i	0.173205	+	0.300000i
$676$	−11.5000	−	19.9186i	−0.442308	−	0.766099i
$677$	16.0000	−	27.7128i	0.614930	−	1.06509i	−0.375467	−	0.926836i	$-0.622518\pi$
$677$	16.0000	−	27.7128i	0.614930	−	1.06509i	0.990397	−	0.138254i	$-0.0441491\pi$
$678$	36.0000			1.38257
$679$		0			0
$680$	8.00000			0.306786
$681$	−30.0000	+	51.9615i	−1.14960	+	1.99117i
$682$	3.00000	+	5.19615i	0.114876	+	0.198971i
$683$	1.50000	+	2.59808i	0.0573959	+	0.0994126i	0.893296	−	0.449469i	$-0.148387\pi$
$683$	1.50000	+	2.59808i	0.0573959	+	0.0994126i	−0.835900	+	0.548882i	$0.815054\pi$
$684$	12.0000	−	20.7846i	0.458831	−	0.794719i
$685$	6.00000			0.229248
$686$	18.5000	−	0.866025i	0.706333	−	0.0330650i
$687$	18.0000			0.686743
$688$	0.500000	−	0.866025i	0.0190623	−	0.0330169i
$689$	−6.00000	−	10.3923i	−0.228582	−	0.395915i
$690$	10.5000	+	18.1865i	0.399728	+	0.692349i
$691$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$691$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$692$	10.0000			0.380143
$693$	−15.0000	−	5.19615i	−0.569803	−	0.197386i
$694$	13.0000			0.493473
$695$	1.00000	−	1.73205i	0.0379322	−	0.0657004i
$696$	13.5000	+	23.3827i	0.511716	+	0.886318i
$697$	12.0000	+	20.7846i	0.454532	+	0.787273i
$698$	−6.50000	+	11.2583i	−0.246029	+	0.426134i
$699$	−78.0000			−2.95023
$700$	−2.00000	+	1.73205i	−0.0755929	+	0.0654654i
$701$	−21.0000			−0.793159			−0.396580	−	0.918000i	$-0.629803\pi$
$701$	−21.0000			−0.793159			−0.396580	+	0.918000i	$0.629803\pi$
$702$	27.0000	−	46.7654i	1.01905	−	1.76505i
$703$	−4.00000	−	6.92820i	−0.150863	−	0.261302i
$704$	0.500000	+	0.866025i	0.0188445	+	0.0326396i
$705$	−12.0000	+	20.7846i	−0.451946	+	0.782794i
$706$	8.00000			0.301084
$707$	−2.50000	−	12.9904i	−0.0940222	−	0.488554i
$708$	18.0000			0.676481
$709$	−0.500000	+	0.866025i	−0.0187779	+	0.0325243i	−0.875262	−	0.483650i	$-0.839311\pi$
$709$	−0.500000	+	0.866025i	−0.0187779	+	0.0325243i	0.856484	+	0.516174i	$0.172644\pi$
$710$	2.00000	+	3.46410i	0.0750587	+	0.130005i
$711$	−30.0000	−	51.9615i	−1.12509	−	1.94871i
$712$	0.500000	−	0.866025i	0.0187383	−	0.0324557i
$713$	42.0000			1.57291
$714$	12.0000	+	62.3538i	0.449089	+	2.33353i
$715$	6.00000			0.224387
$716$	−4.00000	+	6.92820i	−0.149487	+	0.258919i
$717$	−9.00000	−	15.5885i	−0.336111	−	0.582162i
$718$	−8.00000	−	13.8564i	−0.298557	−	0.517116i
$719$	−22.0000	+	38.1051i	−0.820462	+	1.42108i	0.0848774	+	0.996391i	$0.472950\pi$
$719$	−22.0000	+	38.1051i	−0.820462	+	1.42108i	−0.905339	+	0.424690i	$0.860383\pi$
$720$	6.00000			0.223607
$721$	26.0000	−	22.5167i	0.968291	−	0.838564i
$722$	3.00000			0.111648
$723$	−15.0000	+	25.9808i	−0.557856	+	0.966235i
$724$	−1.50000	−	2.59808i	−0.0557471	−	0.0965567i
$725$	4.50000	+	7.79423i	0.167126	+	0.289470i
$726$	−1.50000	+	2.59808i	−0.0556702	+	0.0964237i
$727$	21.0000			0.778847			0.389423	−	0.921059i	$-0.372674\pi$
$727$	21.0000			0.778847			0.389423	+	0.921059i	$0.372674\pi$
$728$	15.0000	+	5.19615i	0.555937	+	0.192582i
$729$	−27.0000			−1.00000
$730$	4.00000	−	6.92820i	0.148047	−	0.256424i
$731$	−4.00000	−	6.92820i	−0.147945	−	0.256249i
$732$	−7.50000	−	12.9904i	−0.277208	−	0.480138i
$733$	−7.00000	+	12.1244i	−0.258551	+	0.447823i	−0.965854	−	0.259087i	$-0.916578\pi$
$733$	−7.00000	+	12.1244i	−0.258551	+	0.447823i	0.707303	+	0.706910i	$0.249912\pi$
$734$	−11.0000			−0.406017
$735$	−16.5000	−	12.9904i	−0.608612	−	0.479157i
$736$	7.00000			0.258023
$737$	0.500000	−	0.866025i	0.0184177	−	0.0319005i
$738$	9.00000	+	15.5885i	0.331295	+	0.573819i
$739$	6.00000	+	10.3923i	0.220714	+	0.382287i	0.955025	−	0.296526i	$-0.0958281\pi$
$739$	6.00000	+	10.3923i	0.220714	+	0.382287i	−0.734311	+	0.678813i	$0.762495\pi$
$740$	1.00000	−	1.73205i	0.0367607	−	0.0636715i
$741$	−72.0000			−2.64499
$742$	5.00000	+	1.73205i	0.183556	+	0.0635856i
$743$	−39.0000			−1.43077			−0.715386	−	0.698730i	$-0.753749\pi$
$743$	−39.0000			−1.43077			−0.715386	+	0.698730i	$0.753749\pi$
$744$	9.00000	−	15.5885i	0.329956	−	0.571501i
$745$	7.50000	+	12.9904i	0.274779	+	0.475931i
$746$	−16.0000	−	27.7128i	−0.585802	−	1.01464i
$747$	−27.0000	+	46.7654i	−0.987878	+	1.71106i
$748$	8.00000			0.292509
$749$	34.0000	−	29.4449i	1.24233	−	1.07589i
$750$	3.00000			0.109545
$751$	7.00000	−	12.1244i	0.255434	−	0.442424i	−0.709580	−	0.704625i	$-0.751115\pi$
$751$	7.00000	−	12.1244i	0.255434	−	0.442424i	0.965013	+	0.262201i	$0.0844484\pi$
$752$	4.00000	+	6.92820i	0.145865	+	0.252646i
$753$	3.00000	+	5.19615i	0.109326	+	0.189358i
$754$	27.0000	−	46.7654i	0.983282	−	1.70309i
$755$	−16.0000			−0.582300
$756$	4.50000	+	23.3827i	0.163663	+	0.850420i
$757$	6.00000			0.218074			0.109037	−	0.994038i	$-0.465223\pi$
$757$	6.00000			0.218074			0.109037	+	0.994038i	$0.465223\pi$
$758$	−12.0000	+	20.7846i	−0.435860	+	0.754931i
$759$	10.5000	+	18.1865i	0.381126	+	0.660129i
$760$	−2.00000	−	3.46410i	−0.0725476	−	0.125656i
$761$	−17.0000	+	29.4449i	−0.616250	+	1.06738i	0.373914	+	0.927463i	$0.378015\pi$
$761$	−17.0000	+	29.4449i	−0.616250	+	1.06738i	−0.990164	+	0.139912i	$0.955318\pi$
$762$	−60.0000			−2.17357
$763$	−2.50000	−	12.9904i	−0.0905061	−	0.470283i
$764$	−16.0000			−0.578860
$765$	24.0000	−	41.5692i	0.867722	−	1.50294i
$766$	−3.50000	−	6.06218i	−0.126460	−	0.219035i
$767$	−18.0000	−	31.1769i	−0.649942	−	1.12573i
$768$	1.50000	−	2.59808i	0.0541266	−	0.0937500i
$769$	22.0000			0.793340			0.396670	−	0.917961i	$-0.370166\pi$
$769$	22.0000			0.793340			0.396670	+	0.917961i	$0.370166\pi$
$770$	−2.00000	+	1.73205i	−0.0720750	+	0.0624188i
$771$	18.0000			0.648254
$772$	−9.00000	+	15.5885i	−0.323917	+	0.561041i
$773$	12.0000	+	20.7846i	0.431610	+	0.747570i	0.997012	−	0.0772449i	$-0.0246123\pi$
$773$	12.0000	+	20.7846i	0.431610	+	0.747570i	−0.565402	+	0.824815i	$0.691279\pi$
$774$	−3.00000	−	5.19615i	−0.107833	−	0.186772i
$775$	3.00000	−	5.19615i	0.107763	−	0.186651i
$776$		0			0
$777$	15.0000	+	5.19615i	0.538122	+	0.186411i
$778$	30.0000			1.07555
$779$	6.00000	−	10.3923i	0.214972	−	0.372343i
$780$	−9.00000	−	15.5885i	−0.322252	−	0.558156i
$781$	2.00000	+	3.46410i	0.0715656	+	0.123955i
$782$	28.0000	−	48.4974i	1.00128	−	1.73426i
$783$	81.0000			2.89470
$784$	−6.50000	+	2.59808i	−0.232143	+	0.0927884i
$785$	4.00000			0.142766
$786$	27.0000	−	46.7654i	0.963058	−	1.66807i
$787$	8.50000	+	14.7224i	0.302992	+	0.524798i	0.976812	−	0.214097i	$-0.0686810\pi$
$787$	8.50000	+	14.7224i	0.302992	+	0.524798i	−0.673820	+	0.738896i	$0.735348\pi$
$788$	9.00000	+	15.5885i	0.320612	+	0.555316i
$789$	19.5000	−	33.7750i	0.694218	−	1.20242i
$790$	−10.0000			−0.355784
$791$	30.0000	+	10.3923i	1.06668	+	0.369508i
$792$	6.00000			0.213201
$793$	−15.0000	+	25.9808i	−0.532666	+	0.922604i
$794$	10.0000	+	17.3205i	0.354887	+	0.614682i
$795$	−3.00000	−	5.19615i	−0.106399	−	0.184289i
$796$		0			0
$797$	8.00000			0.283375			0.141687	−	0.989911i	$-0.454747\pi$
$797$	8.00000			0.283375			0.141687	+	0.989911i	$0.454747\pi$
$798$	24.0000	−	20.7846i	0.849591	−	0.735767i
$799$	64.0000			2.26416
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$	−3.00000	−	5.19615i	−0.106000	−	0.183597i
$802$	−2.50000	−	4.33013i	−0.0882781	−	0.152902i
$803$	4.00000	−	6.92820i	0.141157	−	0.244491i
$804$	−3.00000			−0.105802
$805$	3.50000	+	18.1865i	0.123359	+	0.640991i
$806$	−36.0000			−1.26805
$807$	10.5000	−	18.1865i	0.369618	−	0.640196i
$808$	2.50000	+	4.33013i	0.0879497	+	0.152333i
$809$	6.50000	+	11.2583i	0.228528	+	0.395822i	0.957372	−	0.288858i	$-0.0932755\pi$
$809$	6.50000	+	11.2583i	0.228528	+	0.395822i	−0.728844	+	0.684680i	$0.759942\pi$
$810$	4.50000	−	7.79423i	0.158114	−	0.273861i
$811$	52.0000			1.82597			0.912983	−	0.407997i	$-0.133772\pi$
$811$	52.0000			1.82597			0.912983	+	0.407997i	$0.133772\pi$
$812$	4.50000	+	23.3827i	0.157919	+	0.820571i
$813$		0			0
$814$	1.00000	−	1.73205i	0.0350500	−	0.0607083i
$815$	−4.00000	−	6.92820i	−0.140114	−	0.242684i
$816$	−12.0000	−	20.7846i	−0.420084	−	0.727607i
$817$	−2.00000	+	3.46410i	−0.0699711	+	0.121194i
$818$	−13.0000			−0.454534
$819$	72.0000	−	62.3538i	2.51588	−	2.17882i
$820$	3.00000			0.104765
$821$	15.0000	−	25.9808i	0.523504	−	0.906735i	−0.476122	−	0.879379i	$-0.657958\pi$
$821$	15.0000	−	25.9808i	0.523504	−	0.906735i	0.999626	−	0.0273557i	$-0.00870868\pi$
$822$	−9.00000	−	15.5885i	−0.313911	−	0.543710i
$823$	−6.50000	−	11.2583i	−0.226576	−	0.392441i	0.730215	−	0.683217i	$-0.239420\pi$
$823$	−6.50000	−	11.2583i	−0.226576	−	0.392441i	−0.956791	+	0.290776i	$0.906086\pi$
$824$	−6.50000	+	11.2583i	−0.226438	+	0.392203i
$825$	3.00000			0.104447
$826$	15.0000	+	5.19615i	0.521917	+	0.180797i
$827$	−27.0000			−0.938882			−0.469441	−	0.882964i	$-0.655545\pi$
$827$	−27.0000			−0.938882			−0.469441	+	0.882964i	$0.655545\pi$
$828$	21.0000	−	36.3731i	0.729800	−	1.26405i
$829$	27.0000	+	46.7654i	0.937749	+	1.62423i	0.769657	+	0.638457i	$0.220427\pi$
$829$	27.0000	+	46.7654i	0.937749	+	1.62423i	0.168091	+	0.985771i	$0.446240\pi$
$830$	4.50000	+	7.79423i	0.156197	+	0.270542i
$831$	3.00000	−	5.19615i	0.104069	−	0.180253i
$832$	−6.00000			−0.208013
$833$	−8.00000	+	55.4256i	−0.277184	+	1.92038i
$834$	−6.00000			−0.207763
$835$	−1.50000	+	2.59808i	−0.0519096	+	0.0899101i
$836$	−2.00000	−	3.46410i	−0.0691714	−	0.119808i
$837$	−27.0000	−	46.7654i	−0.933257	−	1.61645i
$838$	15.0000	−	25.9808i	0.518166	−	0.897491i
$839$	−46.0000			−1.58810			−0.794048	−	0.607855i	$-0.792030\pi$
$839$	−46.0000			−1.58810			−0.794048	+	0.607855i	$0.792030\pi$
$840$	7.50000	+	2.59808i	0.258775	+	0.0896421i
$841$	52.0000			1.79310
$842$	12.5000	−	21.6506i	0.430778	−	0.746130i
$843$	45.0000	+	77.9423i	1.54988	+	2.68447i
$844$	7.00000	+	12.1244i	0.240950	+	0.417338i
$845$	−11.5000	+	19.9186i	−0.395612	+	0.685220i
$846$	48.0000			1.65027
$847$	−2.00000	+	1.73205i	−0.0687208	+	0.0595140i
$848$	−2.00000			−0.0686803
$849$	6.00000	−	10.3923i	0.205919	−	0.356663i
$850$	−4.00000	−	6.92820i	−0.137199	−	0.237635i
$851$	−7.00000	−	12.1244i	−0.239957	−	0.415618i
$852$	6.00000	−	10.3923i	0.205557	−	0.356034i
$853$		0			0			−	1.00000i	$-0.5\pi$
$853$		0			0				1.00000i	$0.5\pi$
$854$	−2.50000	−	12.9904i	−0.0855482	−	0.444522i
$855$	−24.0000			−0.820783
$856$	−8.50000	+	14.7224i	−0.290524	+	0.503202i
$857$	12.0000	+	20.7846i	0.409912	+	0.709989i	0.994880	−	0.101068i	$-0.0322260\pi$
$857$	12.0000	+	20.7846i	0.409912	+	0.709989i	−0.584967	+	0.811057i	$0.698893\pi$
$858$	−9.00000	−	15.5885i	−0.307255	−	0.532181i
$859$	1.00000	−	1.73205i	0.0341196	−	0.0590968i	−0.848461	−	0.529257i	$-0.822471\pi$
$859$	1.00000	−	1.73205i	0.0341196	−	0.0590968i	0.882581	+	0.470160i	$0.155804\pi$
$860$	−1.00000			−0.0340997
$861$	4.50000	+	23.3827i	0.153360	+	0.796880i
$862$	4.00000			0.136241
$863$	12.5000	−	21.6506i	0.425505	−	0.736996i	−0.570962	−	0.820976i	$-0.693430\pi$
$863$	12.5000	−	21.6506i	0.425505	−	0.736996i	0.996467	+	0.0839800i	$0.0267632\pi$
$864$	−4.50000	−	7.79423i	−0.153093	−	0.265165i
$865$	−5.00000	−	8.66025i	−0.170005	−	0.294457i
$866$	−15.0000	+	25.9808i	−0.509721	+	0.882862i
$867$	−141.000			−4.78861
$868$	12.0000	−	10.3923i	0.407307	−	0.352738i
$869$	−10.0000			−0.339227
$870$	13.5000	−	23.3827i	0.457693	−	0.792747i
$871$	3.00000	+	5.19615i	0.101651	+	0.176065i
$872$	2.50000	+	4.33013i	0.0846607	+	0.146637i
$873$		0			0
$874$	−28.0000			−0.947114
$875$	2.50000	+	0.866025i	0.0845154	+	0.0292770i
$876$	−24.0000			−0.810885
$877$	10.0000	−	17.3205i	0.337676	−	0.584872i	−0.646319	−	0.763067i	$-0.723693\pi$
$877$	10.0000	−	17.3205i	0.337676	−	0.584872i	0.983995	+	0.178195i	$0.0570259\pi$
$878$	15.0000	+	25.9808i	0.506225	+	0.876808i
$879$	−39.0000	−	67.5500i	−1.31544	−	2.27840i
$880$	0.500000	−	0.866025i	0.0168550	−	0.0291937i
$881$	29.0000			0.977035			0.488517	−	0.872554i	$-0.337538\pi$
$881$	29.0000			0.977035			0.488517	+	0.872554i	$0.337538\pi$
$882$	−6.00000	+	41.5692i	−0.202031	+	1.39971i
$883$	−4.00000			−0.134611			−0.0673054	−	0.997732i	$-0.521440\pi$
$883$	−4.00000			−0.134611			−0.0673054	+	0.997732i	$0.521440\pi$
$884$	−24.0000	+	41.5692i	−0.807207	+	1.39812i
$885$	−9.00000	−	15.5885i	−0.302532	−	0.524000i
$886$	6.50000	+	11.2583i	0.218372	+	0.378231i
$887$	13.5000	−	23.3827i	0.453286	−	0.785114i	−0.545302	−	0.838240i	$-0.683585\pi$
$887$	13.5000	−	23.3827i	0.453286	−	0.785114i	0.998588	+	0.0531258i	$0.0169184\pi$
$888$	−6.00000			−0.201347
$889$	−50.0000	−	17.3205i	−1.67695	−	0.580911i
$890$	−1.00000			−0.0335201
$891$	4.50000	−	7.79423i	0.150756	−	0.261116i
$892$	8.00000	+	13.8564i	0.267860	+	0.463947i
$893$	−16.0000	−	27.7128i	−0.535420	−	0.927374i
$894$	22.5000	−	38.9711i	0.752513	−	1.30339i
$895$	8.00000			0.267411
$896$	2.00000	−	1.73205i	0.0668153	−	0.0578638i
$897$	−126.000			−4.20702
$898$	−12.5000	+	21.6506i	−0.417130	+	0.722491i
$899$	−27.0000	−	46.7654i	−0.900500	−	1.55971i
$900$	−3.00000	−	5.19615i	−0.100000	−	0.173205i
$901$	−8.00000	+	13.8564i	−0.266519	+	0.461624i
$902$	3.00000			0.0998891
$903$	−1.50000	−	7.79423i	−0.0499169	−	0.259376i
$904$	−12.0000			−0.399114
$905$	−1.50000	+	2.59808i	−0.0498617	+	0.0863630i
$906$	24.0000	+	41.5692i	0.797347	+	1.38104i
$907$	0.500000	+	0.866025i	0.0166022	+	0.0287559i	0.874207	−	0.485553i	$-0.161382\pi$
$907$	0.500000	+	0.866025i	0.0166022	+	0.0287559i	−0.857605	+	0.514309i	$0.828048\pi$
$908$	10.0000	−	17.3205i	0.331862	−	0.574801i
$909$	30.0000			0.995037
$910$	−3.00000	−	15.5885i	−0.0994490	−	0.516752i
$911$	−34.0000			−1.12647			−0.563235	−	0.826297i	$-0.690443\pi$
$911$	−34.0000			−1.12647			−0.563235	+	0.826297i	$0.690443\pi$
$912$	−6.00000	+	10.3923i	−0.198680	+	0.344124i
$913$	4.50000	+	7.79423i	0.148928	+	0.257951i
$914$	−4.00000	−	6.92820i	−0.132308	−	0.229165i
$915$	−7.50000	+	12.9904i	−0.247942	+	0.429449i
$916$	−6.00000			−0.198246
$917$	36.0000	−	31.1769i	1.18882	−	1.02955i
$918$	−72.0000			−2.37635
$919$	2.00000	−	3.46410i	0.0659739	−	0.114270i	−0.831152	−	0.556046i	$-0.812318\pi$
$919$	2.00000	−	3.46410i	0.0659739	−	0.114270i	0.897126	+	0.441776i	$0.145651\pi$
$920$	−3.50000	−	6.06218i	−0.115392	−	0.199864i
$921$	10.5000	+	18.1865i	0.345987	+	0.599267i
$922$	−9.00000	+	15.5885i	−0.296399	+	0.513378i
$923$	−24.0000			−0.789970
$924$	7.50000	+	2.59808i	0.246732	+	0.0854704i
$925$	−2.00000			−0.0657596
$926$	5.50000	−	9.52628i	0.180741	−	0.313053i
$927$	39.0000	+	67.5500i	1.28093	+	2.21863i
$928$	−4.50000	−	7.79423i	−0.147720	−	0.255858i
$929$	−13.5000	+	23.3827i	−0.442921	+	0.767161i	−0.997905	−	0.0646999i	$-0.979391\pi$
$929$	−13.5000	+	23.3827i	−0.442921	+	0.767161i	0.554984	+	0.831861i	$0.312724\pi$
$930$	−18.0000			−0.590243
$931$	26.0000	−	10.3923i	0.852116	−	0.340594i
$932$	26.0000			0.851658
$933$	−27.0000	+	46.7654i	−0.883940	+	1.53103i
$934$	−13.5000	−	23.3827i	−0.441733	−	0.765105i
$935$	−4.00000	−	6.92820i	−0.130814	−	0.226576i
$936$	−18.0000	+	31.1769i	−0.588348	+	1.01905i
$937$	28.0000			0.914720			0.457360	−	0.889282i	$-0.348795\pi$
$937$	28.0000			0.914720			0.457360	+	0.889282i	$0.348795\pi$
$938$	−2.50000	−	0.866025i	−0.0816279	−	0.0282767i
$939$	−48.0000			−1.56642
$940$	4.00000	−	6.92820i	0.130466	−	0.225973i
$941$	5.00000	+	8.66025i	0.162995	+	0.282316i	0.935942	−	0.352155i	$-0.114551\pi$
$941$	5.00000	+	8.66025i	0.162995	+	0.282316i	−0.772946	+	0.634472i	$0.781218\pi$
$942$	−6.00000	−	10.3923i	−0.195491	−	0.338600i
$943$	10.5000	−	18.1865i	0.341927	−	0.592235i
$944$	−6.00000			−0.195283
$945$	18.0000	−	15.5885i	0.585540	−	0.507093i
$946$	−1.00000			−0.0325128
$947$	25.5000	−	44.1673i	0.828639	−	1.43524i	−0.0704677	−	0.997514i	$-0.522449\pi$
$947$	25.5000	−	44.1673i	0.828639	−	1.43524i	0.899106	−	0.437730i	$-0.144217\pi$
$948$	15.0000	+	25.9808i	0.487177	+	0.843816i
$949$	24.0000	+	41.5692i	0.779073	+	1.34939i
$950$	−2.00000	+	3.46410i	−0.0648886	+	0.112390i
$951$	−24.0000			−0.778253
$952$	−4.00000	−	20.7846i	−0.129641	−	0.673633i
$953$	−14.0000			−0.453504			−0.226752	−	0.973952i	$-0.572811\pi$
$953$	−14.0000			−0.453504			−0.226752	+	0.973952i	$0.572811\pi$
$954$	−6.00000	+	10.3923i	−0.194257	+	0.336463i
$955$	8.00000	+	13.8564i	0.258874	+	0.448383i
$956$	3.00000	+	5.19615i	0.0970269	+	0.168056i
$957$	13.5000	−	23.3827i	0.436393	−	0.755855i
$958$	42.0000			1.35696
$959$	−3.00000	−	15.5885i	−0.0968751	−	0.503378i
$960$	−3.00000			−0.0968246
$961$	−2.50000	+	4.33013i	−0.0806452	+	0.139682i
$962$	6.00000	+	10.3923i	0.193448	+	0.335061i
$963$	51.0000	+	88.3346i	1.64345	+	2.84654i
$964$	5.00000	−	8.66025i	0.161039	−	0.278928i
$965$	18.0000			0.579441
$966$	42.0000	−	36.3731i	1.35133	−	1.17028i
$967$	−59.0000			−1.89731			−0.948656	−	0.316310i	$-0.897556\pi$
$967$	−59.0000			−1.89731			−0.948656	+	0.316310i	$0.897556\pi$
$968$	0.500000	−	0.866025i	0.0160706	−	0.0278351i
$969$	48.0000	+	83.1384i	1.54198	+	2.67079i
$970$		0			0
$971$	−16.0000	+	27.7128i	−0.513464	+	0.889346i	0.486414	+	0.873729i	$0.338305\pi$
$971$	−16.0000	+	27.7128i	−0.513464	+	0.889346i	−0.999878	+	0.0156178i	$0.995028\pi$
$972$		0			0
$973$	−5.00000	−	1.73205i	−0.160293	−	0.0555270i
$974$	4.00000			0.128168
$975$	−9.00000	+	15.5885i	−0.288231	+	0.499230i
$976$	2.50000	+	4.33013i	0.0800230	+	0.138604i
$977$	−12.0000	−	20.7846i	−0.383914	−	0.664959i	0.607704	−	0.794164i	$-0.292091\pi$
$977$	−12.0000	−	20.7846i	−0.383914	−	0.664959i	−0.991618	+	0.129205i	$0.958757\pi$
$978$	−12.0000	+	20.7846i	−0.383718	+	0.664619i
$979$	−1.00000			−0.0319601
$980$	5.50000	+	4.33013i	0.175691	+	0.138321i
$981$	30.0000			0.957826
$982$	−11.0000	+	19.0526i	−0.351024	+	0.607992i
$983$	18.5000	+	32.0429i	0.590058	+	1.02201i	0.994224	+	0.107325i	$0.0342286\pi$
$983$	18.5000	+	32.0429i	0.590058	+	1.02201i	−0.404166	+	0.914686i	$0.632438\pi$
$984$	−4.50000	−	7.79423i	−0.143455	−	0.248471i
$985$	9.00000	−	15.5885i	0.286764	−	0.496690i
$986$	−72.0000			−2.29295
$987$	60.0000	+	20.7846i	1.90982	+	0.661581i
$988$	24.0000			0.763542
$989$	−3.50000	+	6.06218i	−0.111294	+	0.192766i
$990$	−3.00000	−	5.19615i	−0.0953463	−	0.165145i
$991$	−10.0000	−	17.3205i	−0.317660	−	0.550204i	0.662339	−	0.749204i	$-0.269564\pi$
$991$	−10.0000	−	17.3205i	−0.317660	−	0.550204i	−0.979999	+	0.199000i	$0.936231\pi$
$992$	−3.00000	+	5.19615i	−0.0952501	+	0.164978i
$993$	−96.0000			−3.04647
$994$	8.00000	−	6.92820i	0.253745	−	0.219749i
$995$		0			0
$996$	13.5000	−	23.3827i	0.427764	−	0.740909i
$997$	−14.0000	−	24.2487i	−0.443384	−	0.767964i	0.554554	−	0.832148i	$-0.312889\pi$
$997$	−14.0000	−	24.2487i	−0.443384	−	0.767964i	−0.997938	+	0.0641836i	$0.979556\pi$
$998$	2.00000	+	3.46410i	0.0633089	+	0.109654i
$999$	−9.00000	+	15.5885i	−0.284747	+	0.493197i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.i.i.331.1	yes	2
7.2	even	3		5390.2.a.b.1.1		1
7.4	even	3	inner	770.2.i.i.221.1	✓	2
7.5	odd	6		5390.2.a.s.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.i.i.221.1	✓	2	7.4	even	3	inner
770.2.i.i.331.1	yes	2	1.1	even	1	trivial
5390.2.a.b.1.1		1	7.2	even	3
5390.2.a.s.1.1		1	7.5	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:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +3.00000 q^{6} +(2.50000 + 0.866025i) q^{7} -1.00000 q^{8} +(-3.00000 + 5.19615i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +3.00000 q^{6} +(2.50000 + 0.866025i) q^{7} -1.00000 q^{8} +(-3.00000 + 5.19615i) q^{9} +(0.500000 + 0.866025i) q^{10} +(0.500000 + 0.866025i) q^{11} +(1.50000 - 2.59808i) q^{12} -6.00000 q^{13} +(2.00000 - 1.73205i) q^{14} -3.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(4.00000 + 6.92820i) q^{17} +(3.00000 + 5.19615i) q^{18} +(2.00000 - 3.46410i) q^{19} +1.00000 q^{20} +(1.50000 + 7.79423i) q^{21} +1.00000 q^{22} +(3.50000 - 6.06218i) q^{23} +(-1.50000 - 2.59808i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-3.00000 + 5.19615i) q^{26} -9.00000 q^{27} +(-0.500000 - 2.59808i) q^{28} -9.00000 q^{29} +(-1.50000 + 2.59808i) q^{30} +(3.00000 + 5.19615i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.50000 + 2.59808i) q^{33} +8.00000 q^{34} +(-2.00000 + 1.73205i) q^{35} +6.00000 q^{36} +(1.00000 - 1.73205i) q^{37} +(-2.00000 - 3.46410i) q^{38} +(-9.00000 - 15.5885i) q^{39} +(0.500000 - 0.866025i) q^{40} +3.00000 q^{41} +(7.50000 + 2.59808i) q^{42} -1.00000 q^{43} +(0.500000 - 0.866025i) q^{44} +(-3.00000 - 5.19615i) q^{45} +(-3.50000 - 6.06218i) q^{46} +(4.00000 - 6.92820i) q^{47} -3.00000 q^{48} +(5.50000 + 4.33013i) q^{49} -1.00000 q^{50} +(-12.0000 + 20.7846i) q^{51} +(3.00000 + 5.19615i) q^{52} +(1.00000 + 1.73205i) q^{53} +(-4.50000 + 7.79423i) q^{54} -1.00000 q^{55} +(-2.50000 - 0.866025i) q^{56} +12.0000 q^{57} +(-4.50000 + 7.79423i) q^{58} +(3.00000 + 5.19615i) q^{59} +(1.50000 + 2.59808i) q^{60} +(2.50000 - 4.33013i) q^{61} +6.00000 q^{62} +(-12.0000 + 10.3923i) q^{63} +1.00000 q^{64} +(3.00000 - 5.19615i) q^{65} +(1.50000 + 2.59808i) q^{66} +(-0.500000 - 0.866025i) q^{67} +(4.00000 - 6.92820i) q^{68} +21.0000 q^{69} +(0.500000 + 2.59808i) q^{70} +4.00000 q^{71} +(3.00000 - 5.19615i) q^{72} +(-4.00000 - 6.92820i) q^{73} +(-1.00000 - 1.73205i) q^{74} +(1.50000 - 2.59808i) q^{75} -4.00000 q^{76} +(0.500000 + 2.59808i) q^{77} -18.0000 q^{78} +(-5.00000 + 8.66025i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(1.50000 - 2.59808i) q^{82} +9.00000 q^{83} +(6.00000 - 5.19615i) q^{84} -8.00000 q^{85} +(-0.500000 + 0.866025i) q^{86} +(-13.5000 - 23.3827i) q^{87} +(-0.500000 - 0.866025i) q^{88} +(-0.500000 + 0.866025i) q^{89} -6.00000 q^{90} +(-15.0000 - 5.19615i) q^{91} -7.00000 q^{92} +(-9.00000 + 15.5885i) q^{93} +(-4.00000 - 6.92820i) q^{94} +(2.00000 + 3.46410i) q^{95} +(-1.50000 + 2.59808i) q^{96} +(6.50000 - 2.59808i) q^{98} -6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + 3 q^{3} - q^{4} - q^{5} + 6 q^{6} + 5 q^{7} - 2 q^{8} - 6 q^{9}+O(q^{10}) \) 2 * q + q^2 + 3 * q^3 - q^4 - q^5 + 6 * q^6 + 5 * q^7 - 2 * q^8 - 6 * q^9	\( 2 q + q^{2} + 3 q^{3} - q^{4} - q^{5} + 6 q^{6} + 5 q^{7} - 2 q^{8} - 6 q^{9} + q^{10} + q^{11} + 3 q^{12} - 12 q^{13} + 4 q^{14} - 6 q^{15} - q^{16} + 8 q^{17} + 6 q^{18} + 4 q^{19} + 2 q^{20} + 3 q^{21} + 2 q^{22} + 7 q^{23} - 3 q^{24} - q^{25} - 6 q^{26} - 18 q^{27} - q^{28} - 18 q^{29} - 3 q^{30} + 6 q^{31} + q^{32} - 3 q^{33} + 16 q^{34} - 4 q^{35} + 12 q^{36} + 2 q^{37} - 4 q^{38} - 18 q^{39} + q^{40} + 6 q^{41} + 15 q^{42} - 2 q^{43} + q^{44} - 6 q^{45} - 7 q^{46} + 8 q^{47} - 6 q^{48} + 11 q^{49} - 2 q^{50} - 24 q^{51} + 6 q^{52} + 2 q^{53} - 9 q^{54} - 2 q^{55} - 5 q^{56} + 24 q^{57} - 9 q^{58} + 6 q^{59} + 3 q^{60} + 5 q^{61} + 12 q^{62} - 24 q^{63} + 2 q^{64} + 6 q^{65} + 3 q^{66} - q^{67} + 8 q^{68} + 42 q^{69} + q^{70} + 8 q^{71} + 6 q^{72} - 8 q^{73} - 2 q^{74} + 3 q^{75} - 8 q^{76} + q^{77} - 36 q^{78} - 10 q^{79} - q^{80} - 9 q^{81} + 3 q^{82} + 18 q^{83} + 12 q^{84} - 16 q^{85} - q^{86} - 27 q^{87} - q^{88} - q^{89} - 12 q^{90} - 30 q^{91} - 14 q^{92} - 18 q^{93} - 8 q^{94} + 4 q^{95} - 3 q^{96} + 13 q^{98} - 12 q^{99}+O(q^{100}) \) 2 * q + q^2 + 3 * q^3 - q^4 - q^5 + 6 * q^6 + 5 * q^7 - 2 * q^8 - 6 * q^9 + q^10 + q^11 + 3 * q^12 - 12 * q^13 + 4 * q^14 - 6 * q^15 - q^16 + 8 * q^17 + 6 * q^18 + 4 * q^19 + 2 * q^20 + 3 * q^21 + 2 * q^22 + 7 * q^23 - 3 * q^24 - q^25 - 6 * q^26 - 18 * q^27 - q^28 - 18 * q^29 - 3 * q^30 + 6 * q^31 + q^32 - 3 * q^33 + 16 * q^34 - 4 * q^35 + 12 * q^36 + 2 * q^37 - 4 * q^38 - 18 * q^39 + q^40 + 6 * q^41 + 15 * q^42 - 2 * q^43 + q^44 - 6 * q^45 - 7 * q^46 + 8 * q^47 - 6 * q^48 + 11 * q^49 - 2 * q^50 - 24 * q^51 + 6 * q^52 + 2 * q^53 - 9 * q^54 - 2 * q^55 - 5 * q^56 + 24 * q^57 - 9 * q^58 + 6 * q^59 + 3 * q^60 + 5 * q^61 + 12 * q^62 - 24 * q^63 + 2 * q^64 + 6 * q^65 + 3 * q^66 - q^67 + 8 * q^68 + 42 * q^69 + q^70 + 8 * q^71 + 6 * q^72 - 8 * q^73 - 2 * q^74 + 3 * q^75 - 8 * q^76 + q^77 - 36 * q^78 - 10 * q^79 - q^80 - 9 * q^81 + 3 * q^82 + 18 * q^83 + 12 * q^84 - 16 * q^85 - q^86 - 27 * q^87 - q^88 - q^89 - 12 * q^90 - 30 * q^91 - 14 * q^92 - 18 * q^93 - 8 * q^94 + 4 * q^95 - 3 * q^96 + 13 * q^98 - 12 * q^99

Introduction

L-functions

Modular forms

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