LMFDB - Embedded newform 62.2.c.a.5.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [62,2,Mod(5,62)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(62, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("62.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 62 = 2 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	62.c (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:	$0.495072492532$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			5.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	62.5
Dual form			62.2.c.a.25.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(-0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(1.50000 + 2.59808i) q^{5} +(0.500000 - 0.866025i) q^{6} +(0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(-0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(1.50000 + 2.59808i) q^{5} +(0.500000 - 0.866025i) q^{6} +(0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +(-1.50000 - 2.59808i) q^{10} +(-1.50000 - 2.59808i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(-2.50000 - 4.33013i) q^{13} +(-0.500000 + 0.866025i) q^{14} -3.00000 q^{15} +1.00000 q^{16} +(-1.50000 + 2.59808i) q^{17} +(-1.00000 - 1.73205i) q^{18} +(3.50000 - 6.06218i) q^{19} +(1.50000 + 2.59808i) q^{20} +(0.500000 + 0.866025i) q^{21} +(1.50000 + 2.59808i) q^{22} +(0.500000 - 0.866025i) q^{24} +(-2.00000 + 3.46410i) q^{25} +(2.50000 + 4.33013i) q^{26} -5.00000 q^{27} +(0.500000 - 0.866025i) q^{28} +6.00000 q^{29} +3.00000 q^{30} +(-2.00000 + 5.19615i) q^{31} -1.00000 q^{32} +3.00000 q^{33} +(1.50000 - 2.59808i) q^{34} +3.00000 q^{35} +(1.00000 + 1.73205i) q^{36} +(3.50000 - 6.06218i) q^{37} +(-3.50000 + 6.06218i) q^{38} +5.00000 q^{39} +(-1.50000 - 2.59808i) q^{40} +(-1.50000 - 2.59808i) q^{41} +(-0.500000 - 0.866025i) q^{42} +(-2.50000 + 4.33013i) q^{43} +(-1.50000 - 2.59808i) q^{44} +(-3.00000 + 5.19615i) q^{45} -12.0000 q^{47} +(-0.500000 + 0.866025i) q^{48} +(3.00000 + 5.19615i) q^{49} +(2.00000 - 3.46410i) q^{50} +(-1.50000 - 2.59808i) q^{51} +(-2.50000 - 4.33013i) q^{52} +(-4.50000 - 7.79423i) q^{53} +5.00000 q^{54} +(4.50000 - 7.79423i) q^{55} +(-0.500000 + 0.866025i) q^{56} +(3.50000 + 6.06218i) q^{57} -6.00000 q^{58} +(1.50000 - 2.59808i) q^{59} -3.00000 q^{60} -10.0000 q^{61} +(2.00000 - 5.19615i) q^{62} +2.00000 q^{63} +1.00000 q^{64} +(7.50000 - 12.9904i) q^{65} -3.00000 q^{66} +(6.50000 + 11.2583i) q^{67} +(-1.50000 + 2.59808i) q^{68} -3.00000 q^{70} +(1.50000 + 2.59808i) q^{71} +(-1.00000 - 1.73205i) q^{72} +(6.50000 + 11.2583i) q^{73} +(-3.50000 + 6.06218i) q^{74} +(-2.00000 - 3.46410i) q^{75} +(3.50000 - 6.06218i) q^{76} -3.00000 q^{77} -5.00000 q^{78} +(0.500000 - 0.866025i) q^{79} +(1.50000 + 2.59808i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(1.50000 + 2.59808i) q^{82} +(4.50000 + 7.79423i) q^{83} +(0.500000 + 0.866025i) q^{84} -9.00000 q^{85} +(2.50000 - 4.33013i) q^{86} +(-3.00000 + 5.19615i) q^{87} +(1.50000 + 2.59808i) q^{88} +6.00000 q^{89} +(3.00000 - 5.19615i) q^{90} -5.00000 q^{91} +(-3.50000 - 4.33013i) q^{93} +12.0000 q^{94} +21.0000 q^{95} +(0.500000 - 0.866025i) q^{96} +2.00000 q^{97} +(-3.00000 - 5.19615i) q^{98} +(3.00000 - 5.19615i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - q^{3} + 2 q^{4} + 3 q^{5} + q^{6} + q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 - q^3 + 2 * q^4 + 3 * q^5 + q^6 + q^7 - 2 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} - q^{3} + 2 q^{4} + 3 q^{5} + q^{6} + q^{7} - 2 q^{8} + 2 q^{9} - 3 q^{10} - 3 q^{11} - q^{12} - 5 q^{13} - q^{14} - 6 q^{15} + 2 q^{16} - 3 q^{17} - 2 q^{18} + 7 q^{19} + 3 q^{20} + q^{21} + 3 q^{22} + q^{24} - 4 q^{25} + 5 q^{26} - 10 q^{27} + q^{28} + 12 q^{29} + 6 q^{30} - 4 q^{31} - 2 q^{32} + 6 q^{33} + 3 q^{34} + 6 q^{35} + 2 q^{36} + 7 q^{37} - 7 q^{38} + 10 q^{39} - 3 q^{40} - 3 q^{41} - q^{42} - 5 q^{43} - 3 q^{44} - 6 q^{45} - 24 q^{47} - q^{48} + 6 q^{49} + 4 q^{50} - 3 q^{51} - 5 q^{52} - 9 q^{53} + 10 q^{54} + 9 q^{55} - q^{56} + 7 q^{57} - 12 q^{58} + 3 q^{59} - 6 q^{60} - 20 q^{61} + 4 q^{62} + 4 q^{63} + 2 q^{64} + 15 q^{65} - 6 q^{66} + 13 q^{67} - 3 q^{68} - 6 q^{70} + 3 q^{71} - 2 q^{72} + 13 q^{73} - 7 q^{74} - 4 q^{75} + 7 q^{76} - 6 q^{77} - 10 q^{78} + q^{79} + 3 q^{80} - q^{81} + 3 q^{82} + 9 q^{83} + q^{84} - 18 q^{85} + 5 q^{86} - 6 q^{87} + 3 q^{88} + 12 q^{89} + 6 q^{90} - 10 q^{91} - 7 q^{93} + 24 q^{94} + 42 q^{95} + q^{96} + 4 q^{97} - 6 q^{98} + 6 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - q^3 + 2 * q^4 + 3 * q^5 + q^6 + q^7 - 2 * q^8 + 2 * q^9 - 3 * q^10 - 3 * q^11 - q^12 - 5 * q^13 - q^14 - 6 * q^15 + 2 * q^16 - 3 * q^17 - 2 * q^18 + 7 * q^19 + 3 * q^20 + q^21 + 3 * q^22 + q^24 - 4 * q^25 + 5 * q^26 - 10 * q^27 + q^28 + 12 * q^29 + 6 * q^30 - 4 * q^31 - 2 * q^32 + 6 * q^33 + 3 * q^34 + 6 * q^35 + 2 * q^36 + 7 * q^37 - 7 * q^38 + 10 * q^39 - 3 * q^40 - 3 * q^41 - q^42 - 5 * q^43 - 3 * q^44 - 6 * q^45 - 24 * q^47 - q^48 + 6 * q^49 + 4 * q^50 - 3 * q^51 - 5 * q^52 - 9 * q^53 + 10 * q^54 + 9 * q^55 - q^56 + 7 * q^57 - 12 * q^58 + 3 * q^59 - 6 * q^60 - 20 * q^61 + 4 * q^62 + 4 * q^63 + 2 * q^64 + 15 * q^65 - 6 * q^66 + 13 * q^67 - 3 * q^68 - 6 * q^70 + 3 * q^71 - 2 * q^72 + 13 * q^73 - 7 * q^74 - 4 * q^75 + 7 * q^76 - 6 * q^77 - 10 * q^78 + q^79 + 3 * q^80 - q^81 + 3 * q^82 + 9 * q^83 + q^84 - 18 * q^85 + 5 * q^86 - 6 * q^87 + 3 * q^88 + 12 * q^89 + 6 * q^90 - 10 * q^91 - 7 * q^93 + 24 * q^94 + 42 * q^95 + q^96 + 4 * q^97 - 6 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/62\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i	−0.973494	−	0.228714i	$-0.926548\pi$
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i	0.684819	+	0.728714i	$0.259881\pi$
$4$	1.00000			0.500000
$5$	1.50000	+	2.59808i	0.670820	+	1.16190i	0.977672	+	0.210138i	$0.0673912\pi$
$5$	1.50000	+	2.59808i	0.670820	+	1.16190i	−0.306851	+	0.951757i	$0.599275\pi$
$6$	0.500000	−	0.866025i	0.204124	−	0.353553i
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i	−0.755929	−	0.654654i	$-0.772814\pi$
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i	0.944911	+	0.327327i	$0.106148\pi$
$8$	−1.00000			−0.353553
$9$	1.00000	+	1.73205i	0.333333	+	0.577350i
$10$	−1.50000	−	2.59808i	−0.474342	−	0.821584i
$11$	−1.50000	−	2.59808i	−0.452267	−	0.783349i	0.546259	−	0.837616i	$-0.316051\pi$
$11$	−1.50000	−	2.59808i	−0.452267	−	0.783349i	−0.998526	+	0.0542666i	$0.982718\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	−2.50000	−	4.33013i	−0.693375	−	1.20096i	−0.970725	−	0.240192i	$-0.922790\pi$
$13$	−2.50000	−	4.33013i	−0.693375	−	1.20096i	0.277350	−	0.960769i	$-0.410544\pi$
$14$	−0.500000	+	0.866025i	−0.133631	+	0.231455i
$15$	−3.00000			−0.774597
$16$	1.00000			0.250000
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	−0.988583	−	0.150675i	$-0.951855\pi$
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	0.624780	+	0.780801i	$0.285189\pi$
$18$	−1.00000	−	1.73205i	−0.235702	−	0.408248i
$19$	3.50000	−	6.06218i	0.802955	−	1.39076i	−0.114708	−	0.993399i	$-0.536593\pi$
$19$	3.50000	−	6.06218i	0.802955	−	1.39076i	0.917663	−	0.397360i	$-0.130073\pi$
$20$	1.50000	+	2.59808i	0.335410	+	0.580948i
$21$	0.500000	+	0.866025i	0.109109	+	0.188982i
$22$	1.50000	+	2.59808i	0.319801	+	0.553912i
$23$		0			0			−	1.00000i	$-0.5\pi$
$23$		0			0				1.00000i	$0.5\pi$
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$	−2.00000	+	3.46410i	−0.400000	+	0.692820i
$26$	2.50000	+	4.33013i	0.490290	+	0.849208i
$27$	−5.00000			−0.962250
$28$	0.500000	−	0.866025i	0.0944911	−	0.163663i
$29$	6.00000			1.11417			0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000			1.11417			0.557086	+	0.830455i	$0.311919\pi$
$30$	3.00000			0.547723
$31$	−2.00000	+	5.19615i	−0.359211	+	0.933257i
$31$	−2.00000	+	5.19615i	−0.359211	+	0.933257i
$32$	−1.00000			−0.176777
$33$	3.00000			0.522233
$34$	1.50000	−	2.59808i	0.257248	−	0.445566i
$35$	3.00000			0.507093
$36$	1.00000	+	1.73205i	0.166667	+	0.288675i
$37$	3.50000	−	6.06218i	0.575396	−	0.996616i	−0.420602	−	0.907245i	$-0.638181\pi$
$37$	3.50000	−	6.06218i	0.575396	−	0.996616i	0.995998	−	0.0893706i	$-0.0284856\pi$
$38$	−3.50000	+	6.06218i	−0.567775	+	0.983415i
$39$	5.00000			0.800641
$40$	−1.50000	−	2.59808i	−0.237171	−	0.410792i
$41$	−1.50000	−	2.59808i	−0.234261	−	0.405751i	0.724797	−	0.688963i	$-0.241934\pi$
$41$	−1.50000	−	2.59808i	−0.234261	−	0.405751i	−0.959058	+	0.283211i	$0.908600\pi$
$42$	−0.500000	−	0.866025i	−0.0771517	−	0.133631i
$43$	−2.50000	+	4.33013i	−0.381246	+	0.660338i	−0.991241	−	0.132068i	$-0.957838\pi$
$43$	−2.50000	+	4.33013i	−0.381246	+	0.660338i	0.609994	+	0.792406i	$0.291172\pi$
$44$	−1.50000	−	2.59808i	−0.226134	−	0.391675i
$45$	−3.00000	+	5.19615i	−0.447214	+	0.774597i
$46$		0			0
$47$	−12.0000			−1.75038			−0.875190	−	0.483779i	$-0.839264\pi$
$47$	−12.0000			−1.75038			−0.875190	+	0.483779i	$0.839264\pi$
$48$	−0.500000	+	0.866025i	−0.0721688	+	0.125000i
$49$	3.00000	+	5.19615i	0.428571	+	0.742307i
$50$	2.00000	−	3.46410i	0.282843	−	0.489898i
$51$	−1.50000	−	2.59808i	−0.210042	−	0.363803i
$52$	−2.50000	−	4.33013i	−0.346688	−	0.600481i
$53$	−4.50000	−	7.79423i	−0.618123	−	1.07062i	−0.989828	−	0.142269i	$-0.954560\pi$
$53$	−4.50000	−	7.79423i	−0.618123	−	1.07062i	0.371706	−	0.928351i	$-0.378773\pi$
$54$	5.00000			0.680414
$55$	4.50000	−	7.79423i	0.606780	−	1.05097i
$56$	−0.500000	+	0.866025i	−0.0668153	+	0.115728i
$57$	3.50000	+	6.06218i	0.463586	+	0.802955i
$58$	−6.00000			−0.787839
$59$	1.50000	−	2.59808i	0.195283	−	0.338241i	−0.751710	−	0.659494i	$-0.770771\pi$
$59$	1.50000	−	2.59808i	0.195283	−	0.338241i	0.946993	+	0.321253i	$0.104104\pi$
$60$	−3.00000			−0.387298
$61$	−10.0000			−1.28037			−0.640184	−	0.768221i	$-0.721142\pi$
$61$	−10.0000			−1.28037			−0.640184	+	0.768221i	$0.721142\pi$
$62$	2.00000	−	5.19615i	0.254000	−	0.659912i
$63$	2.00000			0.251976
$64$	1.00000			0.125000
$65$	7.50000	−	12.9904i	0.930261	−	1.61126i
$66$	−3.00000			−0.369274
$67$	6.50000	+	11.2583i	0.794101	+	1.37542i	0.923408	+	0.383819i	$0.125391\pi$
$67$	6.50000	+	11.2583i	0.794101	+	1.37542i	−0.129307	+	0.991605i	$0.541275\pi$
$68$	−1.50000	+	2.59808i	−0.181902	+	0.315063i
$69$		0			0
$70$	−3.00000			−0.358569
$71$	1.50000	+	2.59808i	0.178017	+	0.308335i	0.941201	−	0.337846i	$-0.109698\pi$
$71$	1.50000	+	2.59808i	0.178017	+	0.308335i	−0.763184	+	0.646181i	$0.776365\pi$
$72$	−1.00000	−	1.73205i	−0.117851	−	0.204124i
$73$	6.50000	+	11.2583i	0.760767	+	1.31769i	0.942455	+	0.334332i	$0.108511\pi$
$73$	6.50000	+	11.2583i	0.760767	+	1.31769i	−0.181688	+	0.983356i	$0.558156\pi$
$74$	−3.50000	+	6.06218i	−0.406867	+	0.704714i
$75$	−2.00000	−	3.46410i	−0.230940	−	0.400000i
$76$	3.50000	−	6.06218i	0.401478	−	0.695379i
$77$	−3.00000			−0.341882
$78$	−5.00000			−0.566139
$79$	0.500000	−	0.866025i	0.0562544	−	0.0974355i	−0.836527	−	0.547926i	$-0.815418\pi$
$79$	0.500000	−	0.866025i	0.0562544	−	0.0974355i	0.892781	+	0.450490i	$0.148751\pi$
$80$	1.50000	+	2.59808i	0.167705	+	0.290474i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	1.50000	+	2.59808i	0.165647	+	0.286910i
$83$	4.50000	+	7.79423i	0.493939	+	0.855528i	0.999976	−	0.00698436i	$-0.00222321\pi$
$83$	4.50000	+	7.79423i	0.493939	+	0.855528i	−0.506036	+	0.862512i	$0.668890\pi$
$84$	0.500000	+	0.866025i	0.0545545	+	0.0944911i
$85$	−9.00000			−0.976187
$86$	2.50000	−	4.33013i	0.269582	−	0.466930i
$87$	−3.00000	+	5.19615i	−0.321634	+	0.557086i
$88$	1.50000	+	2.59808i	0.159901	+	0.276956i
$89$	6.00000			0.635999			0.317999	−	0.948091i	$-0.396989\pi$
$89$	6.00000			0.635999			0.317999	+	0.948091i	$0.396989\pi$
$90$	3.00000	−	5.19615i	0.316228	−	0.547723i
$91$	−5.00000			−0.524142
$92$		0			0
$93$	−3.50000	−	4.33013i	−0.362933	−	0.449013i
$94$	12.0000			1.23771
$95$	21.0000			2.15455
$96$	0.500000	−	0.866025i	0.0510310	−	0.0883883i
$97$	2.00000			0.203069			0.101535	−	0.994832i	$-0.467625\pi$
$97$	2.00000			0.203069			0.101535	+	0.994832i	$0.467625\pi$
$98$	−3.00000	−	5.19615i	−0.303046	−	0.524891i
$99$	3.00000	−	5.19615i	0.301511	−	0.522233i
$100$	−2.00000	+	3.46410i	−0.200000	+	0.346410i
$101$	−18.0000			−1.79107			−0.895533	−	0.444994i	$-0.853206\pi$
$101$	−18.0000			−1.79107			−0.895533	+	0.444994i	$0.853206\pi$
$102$	1.50000	+	2.59808i	0.148522	+	0.257248i
$103$	−2.50000	−	4.33013i	−0.246332	−	0.426660i	0.716173	−	0.697923i	$-0.245892\pi$
$103$	−2.50000	−	4.33013i	−0.246332	−	0.426660i	−0.962505	+	0.271263i	$0.912559\pi$
$104$	2.50000	+	4.33013i	0.245145	+	0.424604i
$105$	−1.50000	+	2.59808i	−0.146385	+	0.253546i
$106$	4.50000	+	7.79423i	0.437079	+	0.757042i
$107$	1.50000	−	2.59808i	0.145010	−	0.251166i	−0.784366	−	0.620298i	$-0.787012\pi$
$107$	1.50000	−	2.59808i	0.145010	−	0.251166i	0.929377	+	0.369132i	$0.120345\pi$
$108$	−5.00000			−0.481125
$109$	−10.0000			−0.957826			−0.478913	−	0.877862i	$-0.658969\pi$
$109$	−10.0000			−0.957826			−0.478913	+	0.877862i	$0.658969\pi$
$110$	−4.50000	+	7.79423i	−0.429058	+	0.743151i
$111$	3.50000	+	6.06218i	0.332205	+	0.575396i
$112$	0.500000	−	0.866025i	0.0472456	−	0.0818317i
$113$	−1.50000	−	2.59808i	−0.141108	−	0.244406i	0.786806	−	0.617200i	$-0.211733\pi$
$113$	−1.50000	−	2.59808i	−0.141108	−	0.244406i	−0.927914	+	0.372794i	$0.878400\pi$
$114$	−3.50000	−	6.06218i	−0.327805	−	0.567775i
$115$		0			0
$116$	6.00000			0.557086
$117$	5.00000	−	8.66025i	0.462250	−	0.800641i
$118$	−1.50000	+	2.59808i	−0.138086	+	0.239172i
$119$	1.50000	+	2.59808i	0.137505	+	0.238165i
$120$	3.00000			0.273861
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$	10.0000			0.905357
$123$	3.00000			0.270501
$124$	−2.00000	+	5.19615i	−0.179605	+	0.466628i
$125$	3.00000			0.268328
$126$	−2.00000			−0.178174
$127$	0.500000	−	0.866025i	0.0443678	−	0.0768473i	−0.842989	−	0.537931i	$-0.819206\pi$
$127$	0.500000	−	0.866025i	0.0443678	−	0.0768473i	0.887357	+	0.461084i	$0.152539\pi$
$128$	−1.00000			−0.0883883
$129$	−2.50000	−	4.33013i	−0.220113	−	0.381246i
$130$	−7.50000	+	12.9904i	−0.657794	+	1.13933i
$131$	−4.50000	+	7.79423i	−0.393167	+	0.680985i	−0.992865	−	0.119241i	$-0.961954\pi$
$131$	−4.50000	+	7.79423i	−0.393167	+	0.680985i	0.599699	+	0.800226i	$0.295287\pi$
$132$	3.00000			0.261116
$133$	−3.50000	−	6.06218i	−0.303488	−	0.525657i
$134$	−6.50000	−	11.2583i	−0.561514	−	0.972572i
$135$	−7.50000	−	12.9904i	−0.645497	−	1.11803i
$136$	1.50000	−	2.59808i	0.128624	−	0.222783i
$137$	−7.50000	−	12.9904i	−0.640768	−	1.10984i	−0.985262	−	0.171054i	$-0.945283\pi$
$137$	−7.50000	−	12.9904i	−0.640768	−	1.10984i	0.344493	−	0.938789i	$-0.388051\pi$
$138$		0			0
$139$	−4.00000			−0.339276			−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000			−0.339276			−0.169638	+	0.985506i	$0.554260\pi$
$140$	3.00000			0.253546
$141$	6.00000	−	10.3923i	0.505291	−	0.875190i
$142$	−1.50000	−	2.59808i	−0.125877	−	0.218026i
$143$	−7.50000	+	12.9904i	−0.627182	+	1.08631i
$144$	1.00000	+	1.73205i	0.0833333	+	0.144338i
$145$	9.00000	+	15.5885i	0.747409	+	1.29455i
$146$	−6.50000	−	11.2583i	−0.537944	−	0.931746i
$147$	−6.00000			−0.494872
$148$	3.50000	−	6.06218i	0.287698	−	0.498308i
$149$	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	$-0.0439449\pi$
$150$	2.00000	+	3.46410i	0.163299	+	0.282843i
$151$	−16.0000			−1.30206			−0.651031	−	0.759051i	$-0.725663\pi$
$151$	−16.0000			−1.30206			−0.651031	+	0.759051i	$0.725663\pi$
$152$	−3.50000	+	6.06218i	−0.283887	+	0.491708i
$153$	−6.00000			−0.485071
$154$	3.00000			0.241747
$155$	−16.5000	+	2.59808i	−1.32531	+	0.208683i
$156$	5.00000			0.400320
$157$	2.00000			0.159617			0.0798087	−	0.996810i	$-0.474569\pi$
$157$	2.00000			0.159617			0.0798087	+	0.996810i	$0.474569\pi$
$158$	−0.500000	+	0.866025i	−0.0397779	+	0.0688973i
$159$	9.00000			0.713746
$160$	−1.50000	−	2.59808i	−0.118585	−	0.205396i
$161$		0			0
$162$	0.500000	−	0.866025i	0.0392837	−	0.0680414i
$163$	20.0000			1.56652			0.783260	−	0.621694i	$-0.213555\pi$
$163$	20.0000			1.56652			0.783260	+	0.621694i	$0.213555\pi$
$164$	−1.50000	−	2.59808i	−0.117130	−	0.202876i
$165$	4.50000	+	7.79423i	0.350325	+	0.606780i
$166$	−4.50000	−	7.79423i	−0.349268	−	0.604949i
$167$	4.50000	−	7.79423i	0.348220	−	0.603136i	−0.637713	−	0.770274i	$-0.720119\pi$
$167$	4.50000	−	7.79423i	0.348220	−	0.603136i	0.985933	+	0.167139i	$0.0534527\pi$
$168$	−0.500000	−	0.866025i	−0.0385758	−	0.0668153i
$169$	−6.00000	+	10.3923i	−0.461538	+	0.799408i
$170$	9.00000			0.690268
$171$	14.0000			1.07061
$172$	−2.50000	+	4.33013i	−0.190623	+	0.330169i
$173$	7.50000	+	12.9904i	0.570214	+	0.987640i	0.996544	+	0.0830722i	$0.0264732\pi$
$173$	7.50000	+	12.9904i	0.570214	+	0.987640i	−0.426329	+	0.904568i	$0.640193\pi$
$174$	3.00000	−	5.19615i	0.227429	−	0.393919i
$175$	2.00000	+	3.46410i	0.151186	+	0.261861i
$176$	−1.50000	−	2.59808i	−0.113067	−	0.195837i
$177$	1.50000	+	2.59808i	0.112747	+	0.195283i
$178$	−6.00000			−0.449719
$179$	−10.5000	+	18.1865i	−0.784807	+	1.35933i	0.144308	+	0.989533i	$0.453905\pi$
$179$	−10.5000	+	18.1865i	−0.784807	+	1.35933i	−0.929114	+	0.369792i	$0.879429\pi$
$180$	−3.00000	+	5.19615i	−0.223607	+	0.387298i
$181$	3.50000	+	6.06218i	0.260153	+	0.450598i	0.966282	−	0.257485i	$-0.0828937\pi$
$181$	3.50000	+	6.06218i	0.260153	+	0.450598i	−0.706129	+	0.708083i	$0.749560\pi$
$182$	5.00000			0.370625
$183$	5.00000	−	8.66025i	0.369611	−	0.640184i
$184$		0			0
$185$	21.0000			1.54395
$186$	3.50000	+	4.33013i	0.256632	+	0.317500i
$187$	9.00000			0.658145
$188$	−12.0000			−0.875190
$189$	−2.50000	+	4.33013i	−0.181848	+	0.314970i
$190$	−21.0000			−1.52350
$191$	1.50000	+	2.59808i	0.108536	+	0.187990i	0.915177	−	0.403051i	$-0.132050\pi$
$191$	1.50000	+	2.59808i	0.108536	+	0.187990i	−0.806641	+	0.591041i	$0.798717\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	0.500000	−	0.866025i	0.0359908	−	0.0623379i	−0.847469	−	0.530845i	$-0.821875\pi$
$193$	0.500000	−	0.866025i	0.0359908	−	0.0623379i	0.883460	+	0.468507i	$0.155208\pi$
$194$	−2.00000			−0.143592
$195$	7.50000	+	12.9904i	0.537086	+	0.930261i
$196$	3.00000	+	5.19615i	0.214286	+	0.371154i
$197$	1.50000	+	2.59808i	0.106871	+	0.185105i	0.914501	−	0.404584i	$-0.132584\pi$
$197$	1.50000	+	2.59808i	0.106871	+	0.185105i	−0.807630	+	0.589689i	$0.799250\pi$
$198$	−3.00000	+	5.19615i	−0.213201	+	0.369274i
$199$	3.50000	+	6.06218i	0.248108	+	0.429736i	0.963001	−	0.269498i	$-0.0868577\pi$
$199$	3.50000	+	6.06218i	0.248108	+	0.429736i	−0.714893	+	0.699234i	$0.753524\pi$
$200$	2.00000	−	3.46410i	0.141421	−	0.244949i
$201$	−13.0000			−0.916949
$202$	18.0000			1.26648
$203$	3.00000	−	5.19615i	0.210559	−	0.364698i
$204$	−1.50000	−	2.59808i	−0.105021	−	0.181902i
$205$	4.50000	−	7.79423i	0.314294	−	0.544373i
$206$	2.50000	+	4.33013i	0.174183	+	0.301694i
$207$		0			0
$208$	−2.50000	−	4.33013i	−0.173344	−	0.300240i
$209$	−21.0000			−1.45260
$210$	1.50000	−	2.59808i	0.103510	−	0.179284i
$211$	9.50000	−	16.4545i	0.654007	−	1.13277i	−0.328135	−	0.944631i	$-0.606420\pi$
$211$	9.50000	−	16.4545i	0.654007	−	1.13277i	0.982142	−	0.188142i	$-0.0602466\pi$
$212$	−4.50000	−	7.79423i	−0.309061	−	0.535310i
$213$	−3.00000			−0.205557
$214$	−1.50000	+	2.59808i	−0.102538	+	0.177601i
$215$	−15.0000			−1.02299
$216$	5.00000			0.340207
$217$	3.50000	+	4.33013i	0.237595	+	0.293948i
$218$	10.0000			0.677285
$219$	−13.0000			−0.878459
$220$	4.50000	−	7.79423i	0.303390	−	0.525487i
$221$	15.0000			1.00901
$222$	−3.50000	−	6.06218i	−0.234905	−	0.406867i
$223$	6.50000	−	11.2583i	0.435272	−	0.753914i	−0.562046	−	0.827106i	$-0.689985\pi$
$223$	6.50000	−	11.2583i	0.435272	−	0.753914i	0.997318	+	0.0731927i	$0.0233188\pi$
$224$	−0.500000	+	0.866025i	−0.0334077	+	0.0578638i
$225$	−8.00000			−0.533333
$226$	1.50000	+	2.59808i	0.0997785	+	0.172821i
$227$	−1.50000	−	2.59808i	−0.0995585	−	0.172440i	0.811943	−	0.583736i	$-0.198410\pi$
$227$	−1.50000	−	2.59808i	−0.0995585	−	0.172440i	−0.911502	+	0.411296i	$0.865076\pi$
$228$	3.50000	+	6.06218i	0.231793	+	0.401478i
$229$	3.50000	−	6.06218i	0.231287	−	0.400600i	−0.726900	−	0.686743i	$-0.759040\pi$
$229$	3.50000	−	6.06218i	0.231287	−	0.400600i	0.958187	+	0.286143i	$0.0923732\pi$
$230$		0			0
$231$	1.50000	−	2.59808i	0.0986928	−	0.170941i
$232$	−6.00000			−0.393919
$233$	6.00000			0.393073			0.196537	−	0.980497i	$-0.437031\pi$
$233$	6.00000			0.393073			0.196537	+	0.980497i	$0.437031\pi$
$234$	−5.00000	+	8.66025i	−0.326860	+	0.566139i
$235$	−18.0000	−	31.1769i	−1.17419	−	2.03376i
$236$	1.50000	−	2.59808i	0.0976417	−	0.169120i
$237$	0.500000	+	0.866025i	0.0324785	+	0.0562544i
$238$	−1.50000	−	2.59808i	−0.0972306	−	0.168408i
$239$	1.50000	+	2.59808i	0.0970269	+	0.168056i	0.910453	−	0.413613i	$-0.135733\pi$
$239$	1.50000	+	2.59808i	0.0970269	+	0.168056i	−0.813426	+	0.581669i	$0.802400\pi$
$240$	−3.00000			−0.193649
$241$	−5.50000	+	9.52628i	−0.354286	+	0.613642i	−0.986996	−	0.160748i	$-0.948609\pi$
$241$	−5.50000	+	9.52628i	−0.354286	+	0.613642i	0.632709	+	0.774389i	$0.281943\pi$
$242$	−1.00000	+	1.73205i	−0.0642824	+	0.111340i
$243$	−8.00000	−	13.8564i	−0.513200	−	0.888889i
$244$	−10.0000			−0.640184
$245$	−9.00000	+	15.5885i	−0.574989	+	0.995910i
$246$	−3.00000			−0.191273
$247$	−35.0000			−2.22700
$248$	2.00000	−	5.19615i	0.127000	−	0.329956i
$249$	−9.00000			−0.570352
$250$	−3.00000			−0.189737
$251$	−4.50000	+	7.79423i	−0.284037	+	0.491967i	−0.972375	−	0.233423i	$-0.925007\pi$
$251$	−4.50000	+	7.79423i	−0.284037	+	0.491967i	0.688338	+	0.725390i	$0.258341\pi$
$252$	2.00000			0.125988
$253$		0			0
$254$	−0.500000	+	0.866025i	−0.0313728	+	0.0543393i
$255$	4.50000	−	7.79423i	0.281801	−	0.488094i
$256$	1.00000			0.0625000
$257$	4.50000	+	7.79423i	0.280702	+	0.486191i	0.971558	−	0.236802i	$-0.0760993\pi$
$257$	4.50000	+	7.79423i	0.280702	+	0.486191i	−0.690856	+	0.722993i	$0.742766\pi$
$258$	2.50000	+	4.33013i	0.155643	+	0.269582i
$259$	−3.50000	−	6.06218i	−0.217479	−	0.376685i
$260$	7.50000	−	12.9904i	0.465130	−	0.805629i
$261$	6.00000	+	10.3923i	0.371391	+	0.643268i
$262$	4.50000	−	7.79423i	0.278011	−	0.481529i
$263$	12.0000			0.739952			0.369976	−	0.929041i	$-0.379366\pi$
$263$	12.0000			0.739952			0.369976	+	0.929041i	$0.379366\pi$
$264$	−3.00000			−0.184637
$265$	13.5000	−	23.3827i	0.829298	−	1.43639i
$266$	3.50000	+	6.06218i	0.214599	+	0.371696i
$267$	−3.00000	+	5.19615i	−0.183597	+	0.317999i
$268$	6.50000	+	11.2583i	0.397051	+	0.687712i
$269$	−4.50000	−	7.79423i	−0.274370	−	0.475223i	0.695606	−	0.718423i	$-0.255136\pi$
$269$	−4.50000	−	7.79423i	−0.274370	−	0.475223i	−0.969976	+	0.243201i	$0.921803\pi$
$270$	7.50000	+	12.9904i	0.456435	+	0.790569i
$271$	20.0000			1.21491			0.607457	−	0.794353i	$-0.292190\pi$
$271$	20.0000			1.21491			0.607457	+	0.794353i	$0.292190\pi$
$272$	−1.50000	+	2.59808i	−0.0909509	+	0.157532i
$273$	2.50000	−	4.33013i	0.151307	−	0.262071i
$274$	7.50000	+	12.9904i	0.453092	+	0.784778i
$275$	12.0000			0.723627
$276$		0			0
$277$	14.0000			0.841178			0.420589	−	0.907251i	$-0.361823\pi$
$277$	14.0000			0.841178			0.420589	+	0.907251i	$0.361823\pi$
$278$	4.00000			0.239904
$279$	−11.0000	+	1.73205i	−0.658553	+	0.103695i
$280$	−3.00000			−0.179284
$281$	6.00000			0.357930			0.178965	−	0.983855i	$-0.442725\pi$
$281$	6.00000			0.357930			0.178965	+	0.983855i	$0.442725\pi$
$282$	−6.00000	+	10.3923i	−0.357295	+	0.618853i
$283$	−16.0000			−0.951101			−0.475551	−	0.879688i	$-0.657751\pi$
$283$	−16.0000			−0.951101			−0.475551	+	0.879688i	$0.657751\pi$
$284$	1.50000	+	2.59808i	0.0890086	+	0.154167i
$285$	−10.5000	+	18.1865i	−0.621966	+	1.07728i
$286$	7.50000	−	12.9904i	0.443484	−	0.768137i
$287$	−3.00000			−0.177084
$288$	−1.00000	−	1.73205i	−0.0589256	−	0.102062i
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$	−9.00000	−	15.5885i	−0.528498	−	0.915386i
$291$	−1.00000	+	1.73205i	−0.0586210	+	0.101535i
$292$	6.50000	+	11.2583i	0.380384	+	0.658844i
$293$	1.50000	−	2.59808i	0.0876309	−	0.151781i	−0.818878	−	0.573967i	$-0.805404\pi$
$293$	1.50000	−	2.59808i	0.0876309	−	0.151781i	0.906509	+	0.422186i	$0.138737\pi$
$294$	6.00000			0.349927
$295$	9.00000			0.524000
$296$	−3.50000	+	6.06218i	−0.203433	+	0.352357i
$297$	7.50000	+	12.9904i	0.435194	+	0.753778i
$298$	−7.50000	+	12.9904i	−0.434463	+	0.752513i
$299$		0			0
$300$	−2.00000	−	3.46410i	−0.115470	−	0.200000i
$301$	2.50000	+	4.33013i	0.144098	+	0.249584i
$302$	16.0000			0.920697
$303$	9.00000	−	15.5885i	0.517036	−	0.895533i
$304$	3.50000	−	6.06218i	0.200739	−	0.347690i
$305$	−15.0000	−	25.9808i	−0.858898	−	1.48765i
$306$	6.00000			0.342997
$307$	−8.50000	+	14.7224i	−0.485121	+	0.840254i	−0.999854	−	0.0170968i	$-0.994558\pi$
$307$	−8.50000	+	14.7224i	−0.485121	+	0.840254i	0.514733	+	0.857350i	$0.327891\pi$
$308$	−3.00000			−0.170941
$309$	5.00000			0.284440
$310$	16.5000	−	2.59808i	0.937137	−	0.147561i
$311$	−24.0000			−1.36092			−0.680458	−	0.732787i	$-0.738219\pi$
$311$	−24.0000			−1.36092			−0.680458	+	0.732787i	$0.738219\pi$
$312$	−5.00000			−0.283069
$313$	−5.50000	+	9.52628i	−0.310878	+	0.538457i	−0.978553	−	0.205996i	$-0.933957\pi$
$313$	−5.50000	+	9.52628i	−0.310878	+	0.538457i	0.667674	+	0.744453i	$0.267290\pi$
$314$	−2.00000			−0.112867
$315$	3.00000	+	5.19615i	0.169031	+	0.292770i
$316$	0.500000	−	0.866025i	0.0281272	−	0.0487177i
$317$	1.50000	−	2.59808i	0.0842484	−	0.145922i	−0.820822	−	0.571184i	$-0.806484\pi$
$317$	1.50000	−	2.59808i	0.0842484	−	0.145922i	0.905071	+	0.425261i	$0.139818\pi$
$318$	−9.00000			−0.504695
$319$	−9.00000	−	15.5885i	−0.503903	−	0.872786i
$320$	1.50000	+	2.59808i	0.0838525	+	0.145237i
$321$	1.50000	+	2.59808i	0.0837218	+	0.145010i
$322$		0			0
$323$	10.5000	+	18.1865i	0.584236	+	1.01193i
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	20.0000			1.10940
$326$	−20.0000			−1.10770
$327$	5.00000	−	8.66025i	0.276501	−	0.478913i
$328$	1.50000	+	2.59808i	0.0828236	+	0.143455i
$329$	−6.00000	+	10.3923i	−0.330791	+	0.572946i
$330$	−4.50000	−	7.79423i	−0.247717	−	0.429058i
$331$	−5.50000	−	9.52628i	−0.302307	−	0.523612i	0.674351	−	0.738411i	$-0.264424\pi$
$331$	−5.50000	−	9.52628i	−0.302307	−	0.523612i	−0.976658	+	0.214799i	$0.931090\pi$
$332$	4.50000	+	7.79423i	0.246970	+	0.427764i
$333$	14.0000			0.767195
$334$	−4.50000	+	7.79423i	−0.246229	+	0.426481i
$335$	−19.5000	+	33.7750i	−1.06540	+	1.84532i
$336$	0.500000	+	0.866025i	0.0272772	+	0.0472456i
$337$	14.0000			0.762629			0.381314	−	0.924445i	$-0.375472\pi$
$337$	14.0000			0.762629			0.381314	+	0.924445i	$0.375472\pi$
$338$	6.00000	−	10.3923i	0.326357	−	0.565267i
$339$	3.00000			0.162938
$340$	−9.00000			−0.488094
$341$	16.5000	−	2.59808i	0.893525	−	0.140694i
$342$	−14.0000			−0.757033
$343$	13.0000			0.701934
$344$	2.50000	−	4.33013i	0.134791	−	0.233465i
$345$		0			0
$346$	−7.50000	−	12.9904i	−0.403202	−	0.698367i
$347$	13.5000	−	23.3827i	0.724718	−	1.25525i	−0.234372	−	0.972147i	$-0.575303\pi$
$347$	13.5000	−	23.3827i	0.724718	−	1.25525i	0.959090	−	0.283101i	$-0.0913633\pi$
$348$	−3.00000	+	5.19615i	−0.160817	+	0.278543i
$349$	−10.0000			−0.535288			−0.267644	−	0.963518i	$-0.586245\pi$
$349$	−10.0000			−0.535288			−0.267644	+	0.963518i	$0.586245\pi$
$350$	−2.00000	−	3.46410i	−0.106904	−	0.185164i
$351$	12.5000	+	21.6506i	0.667201	+	1.15563i
$352$	1.50000	+	2.59808i	0.0799503	+	0.138478i
$353$	10.5000	−	18.1865i	0.558859	−	0.967972i	−0.438733	−	0.898617i	$-0.644573\pi$
$353$	10.5000	−	18.1865i	0.558859	−	0.967972i	0.997592	−	0.0693543i	$-0.0220939\pi$
$354$	−1.50000	−	2.59808i	−0.0797241	−	0.138086i
$355$	−4.50000	+	7.79423i	−0.238835	+	0.413675i
$356$	6.00000			0.317999
$357$	−3.00000			−0.158777
$358$	10.5000	−	18.1865i	0.554942	−	0.961188i
$359$	1.50000	+	2.59808i	0.0791670	+	0.137121i	0.902891	−	0.429870i	$-0.141441\pi$
$359$	1.50000	+	2.59808i	0.0791670	+	0.137121i	−0.823724	+	0.566991i	$0.808107\pi$
$360$	3.00000	−	5.19615i	0.158114	−	0.273861i
$361$	−15.0000	−	25.9808i	−0.789474	−	1.36741i
$362$	−3.50000	−	6.06218i	−0.183956	−	0.318621i
$363$	1.00000	+	1.73205i	0.0524864	+	0.0909091i
$364$	−5.00000			−0.262071
$365$	−19.5000	+	33.7750i	−1.02068	+	1.76786i
$366$	−5.00000	+	8.66025i	−0.261354	+	0.452679i
$367$	3.50000	+	6.06218i	0.182699	+	0.316443i	0.942799	−	0.333363i	$-0.108183\pi$
$367$	3.50000	+	6.06218i	0.182699	+	0.316443i	−0.760100	+	0.649806i	$0.774850\pi$
$368$		0			0
$369$	3.00000	−	5.19615i	0.156174	−	0.270501i
$370$	−21.0000			−1.09174
$371$	−9.00000			−0.467257
$372$	−3.50000	−	4.33013i	−0.181467	−	0.224507i
$373$	−22.0000			−1.13912			−0.569558	−	0.821951i	$-0.692886\pi$
$373$	−22.0000			−1.13912			−0.569558	+	0.821951i	$0.692886\pi$
$374$	−9.00000			−0.465379
$375$	−1.50000	+	2.59808i	−0.0774597	+	0.134164i
$376$	12.0000			0.618853
$377$	−15.0000	−	25.9808i	−0.772539	−	1.33808i
$378$	2.50000	−	4.33013i	0.128586	−	0.222718i
$379$	15.5000	−	26.8468i	0.796182	−	1.37903i	−0.125905	−	0.992042i	$-0.540183\pi$
$379$	15.5000	−	26.8468i	0.796182	−	1.37903i	0.922086	−	0.386985i	$-0.126483\pi$
$380$	21.0000			1.07728
$381$	0.500000	+	0.866025i	0.0256158	+	0.0443678i
$382$	−1.50000	−	2.59808i	−0.0767467	−	0.132929i
$383$	13.5000	+	23.3827i	0.689818	+	1.19480i	0.971897	+	0.235408i	$0.0756427\pi$
$383$	13.5000	+	23.3827i	0.689818	+	1.19480i	−0.282079	+	0.959391i	$0.591024\pi$
$384$	0.500000	−	0.866025i	0.0255155	−	0.0441942i
$385$	−4.50000	−	7.79423i	−0.229341	−	0.397231i
$386$	−0.500000	+	0.866025i	−0.0254493	+	0.0440795i
$387$	−10.0000			−0.508329
$388$	2.00000			0.101535
$389$	−16.5000	+	28.5788i	−0.836583	+	1.44900i	0.0561516	+	0.998422i	$0.482117\pi$
$389$	−16.5000	+	28.5788i	−0.836583	+	1.44900i	−0.892735	+	0.450582i	$0.851216\pi$
$390$	−7.50000	−	12.9904i	−0.379777	−	0.657794i
$391$		0			0
$392$	−3.00000	−	5.19615i	−0.151523	−	0.262445i
$393$	−4.50000	−	7.79423i	−0.226995	−	0.393167i
$394$	−1.50000	−	2.59808i	−0.0755689	−	0.130889i
$395$	3.00000			0.150946
$396$	3.00000	−	5.19615i	0.150756	−	0.261116i
$397$	3.50000	−	6.06218i	0.175660	−	0.304252i	−0.764730	−	0.644351i	$-0.777127\pi$
$397$	3.50000	−	6.06218i	0.175660	−	0.304252i	0.940389	+	0.340099i	$0.110461\pi$
$398$	−3.50000	−	6.06218i	−0.175439	−	0.303870i
$399$	7.00000			0.350438
$400$	−2.00000	+	3.46410i	−0.100000	+	0.173205i
$401$	18.0000			0.898877			0.449439	−	0.893311i	$-0.351624\pi$
$401$	18.0000			0.898877			0.449439	+	0.893311i	$0.351624\pi$
$402$	13.0000			0.648381
$403$	27.5000	−	4.33013i	1.36987	−	0.215699i
$404$	−18.0000			−0.895533
$405$	−3.00000			−0.149071
$406$	−3.00000	+	5.19615i	−0.148888	+	0.257881i
$407$	−21.0000			−1.04093
$408$	1.50000	+	2.59808i	0.0742611	+	0.128624i
$409$	−11.5000	+	19.9186i	−0.568638	+	0.984911i	0.428063	+	0.903749i	$0.359196\pi$
$409$	−11.5000	+	19.9186i	−0.568638	+	0.984911i	−0.996701	+	0.0811615i	$0.974137\pi$
$410$	−4.50000	+	7.79423i	−0.222239	+	0.384930i
$411$	15.0000			0.739895
$412$	−2.50000	−	4.33013i	−0.123166	−	0.213330i
$413$	−1.50000	−	2.59808i	−0.0738102	−	0.127843i
$414$		0			0
$415$	−13.5000	+	23.3827i	−0.662689	+	1.14781i
$416$	2.50000	+	4.33013i	0.122573	+	0.212302i
$417$	2.00000	−	3.46410i	0.0979404	−	0.169638i
$418$	21.0000			1.02714
$419$	36.0000			1.75872			0.879358	−	0.476162i	$-0.157972\pi$
$419$	36.0000			1.75872			0.879358	+	0.476162i	$0.157972\pi$
$420$	−1.50000	+	2.59808i	−0.0731925	+	0.126773i
$421$	−8.50000	−	14.7224i	−0.414265	−	0.717527i	0.581086	−	0.813842i	$-0.302628\pi$
$421$	−8.50000	−	14.7224i	−0.414265	−	0.717527i	−0.995351	+	0.0963145i	$0.969295\pi$
$422$	−9.50000	+	16.4545i	−0.462453	+	0.800992i
$423$	−12.0000	−	20.7846i	−0.583460	−	1.01058i
$424$	4.50000	+	7.79423i	0.218539	+	0.378521i
$425$	−6.00000	−	10.3923i	−0.291043	−	0.504101i
$426$	3.00000			0.145350
$427$	−5.00000	+	8.66025i	−0.241967	+	0.419099i
$428$	1.50000	−	2.59808i	0.0725052	−	0.125583i
$429$	−7.50000	−	12.9904i	−0.362103	−	0.627182i
$430$	15.0000			0.723364
$431$	10.5000	−	18.1865i	0.505767	−	0.876014i	−0.494211	−	0.869342i	$-0.664543\pi$
$431$	10.5000	−	18.1865i	0.505767	−	0.876014i	0.999978	−	0.00667224i	$-0.00212386\pi$
$432$	−5.00000			−0.240563
$433$	−10.0000			−0.480569			−0.240285	−	0.970702i	$-0.577241\pi$
$433$	−10.0000			−0.480569			−0.240285	+	0.970702i	$0.577241\pi$
$434$	−3.50000	−	4.33013i	−0.168005	−	0.207853i
$435$	−18.0000			−0.863034
$436$	−10.0000			−0.478913
$437$		0			0
$438$	13.0000			0.621164
$439$	−2.50000	−	4.33013i	−0.119318	−	0.206666i	0.800179	−	0.599761i	$-0.204738\pi$
$439$	−2.50000	−	4.33013i	−0.119318	−	0.206666i	−0.919498	+	0.393095i	$0.871404\pi$
$440$	−4.50000	+	7.79423i	−0.214529	+	0.371575i
$441$	−6.00000	+	10.3923i	−0.285714	+	0.494872i
$442$	−15.0000			−0.713477
$443$	10.5000	+	18.1865i	0.498870	+	0.864068i	0.999999	−	0.00130426i	$-0.000415158\pi$
$443$	10.5000	+	18.1865i	0.498870	+	0.864068i	−0.501129	+	0.865373i	$0.667082\pi$
$444$	3.50000	+	6.06218i	0.166103	+	0.287698i
$445$	9.00000	+	15.5885i	0.426641	+	0.738964i
$446$	−6.50000	+	11.2583i	−0.307784	+	0.533097i
$447$	7.50000	+	12.9904i	0.354738	+	0.614424i
$448$	0.500000	−	0.866025i	0.0236228	−	0.0409159i
$449$	6.00000			0.283158			0.141579	−	0.989927i	$-0.454782\pi$
$449$	6.00000			0.283158			0.141579	+	0.989927i	$0.454782\pi$
$450$	8.00000			0.377124
$451$	−4.50000	+	7.79423i	−0.211897	+	0.367016i
$452$	−1.50000	−	2.59808i	−0.0705541	−	0.122203i
$453$	8.00000	−	13.8564i	0.375873	−	0.651031i
$454$	1.50000	+	2.59808i	0.0703985	+	0.121934i
$455$	−7.50000	−	12.9904i	−0.351605	−	0.608998i
$456$	−3.50000	−	6.06218i	−0.163903	−	0.283887i
$457$	14.0000			0.654892			0.327446	−	0.944870i	$-0.393812\pi$
$457$	14.0000			0.654892			0.327446	+	0.944870i	$0.393812\pi$
$458$	−3.50000	+	6.06218i	−0.163544	+	0.283267i
$459$	7.50000	−	12.9904i	0.350070	−	0.606339i
$460$		0			0
$461$	18.0000			0.838344			0.419172	−	0.907907i	$-0.362320\pi$
$461$	18.0000			0.838344			0.419172	+	0.907907i	$0.362320\pi$
$462$	−1.50000	+	2.59808i	−0.0697863	+	0.120873i
$463$	8.00000			0.371792			0.185896	−	0.982569i	$-0.440481\pi$
$463$	8.00000			0.371792			0.185896	+	0.982569i	$0.440481\pi$
$464$	6.00000			0.278543
$465$	6.00000	−	15.5885i	0.278243	−	0.722897i
$466$	−6.00000			−0.277945
$467$	−36.0000			−1.66588			−0.832941	−	0.553362i	$-0.813345\pi$
$467$	−36.0000			−1.66588			−0.832941	+	0.553362i	$0.813345\pi$
$468$	5.00000	−	8.66025i	0.231125	−	0.400320i
$469$	13.0000			0.600284
$470$	18.0000	+	31.1769i	0.830278	+	1.43808i
$471$	−1.00000	+	1.73205i	−0.0460776	+	0.0798087i
$472$	−1.50000	+	2.59808i	−0.0690431	+	0.119586i
$473$	15.0000			0.689701
$474$	−0.500000	−	0.866025i	−0.0229658	−	0.0397779i
$475$	14.0000	+	24.2487i	0.642364	+	1.11261i
$476$	1.50000	+	2.59808i	0.0687524	+	0.119083i
$477$	9.00000	−	15.5885i	0.412082	−	0.713746i
$478$	−1.50000	−	2.59808i	−0.0686084	−	0.118833i
$479$	−1.50000	+	2.59808i	−0.0685367	+	0.118709i	−0.898257	−	0.439470i	$-0.855166\pi$
$479$	−1.50000	+	2.59808i	−0.0685367	+	0.118709i	0.829721	+	0.558179i	$0.188500\pi$
$480$	3.00000			0.136931
$481$	−35.0000			−1.59586
$482$	5.50000	−	9.52628i	0.250518	−	0.433910i
$483$		0			0
$484$	1.00000	−	1.73205i	0.0454545	−	0.0787296i
$485$	3.00000	+	5.19615i	0.136223	+	0.235945i
$486$	8.00000	+	13.8564i	0.362887	+	0.628539i
$487$	15.5000	+	26.8468i	0.702372	+	1.21654i	0.967632	+	0.252367i	$0.0812090\pi$
$487$	15.5000	+	26.8468i	0.702372	+	1.21654i	−0.265260	+	0.964177i	$0.585458\pi$
$488$	10.0000			0.452679
$489$	−10.0000	+	17.3205i	−0.452216	+	0.783260i
$490$	9.00000	−	15.5885i	0.406579	−	0.704215i
$491$	−13.5000	−	23.3827i	−0.609246	−	1.05525i	−0.991365	−	0.131132i	$-0.958139\pi$
$491$	−13.5000	−	23.3827i	−0.609246	−	1.05525i	0.382118	−	0.924113i	$-0.375195\pi$
$492$	3.00000			0.135250
$493$	−9.00000	+	15.5885i	−0.405340	+	0.702069i
$494$	35.0000			1.57472
$495$	18.0000			0.809040
$496$	−2.00000	+	5.19615i	−0.0898027	+	0.233314i
$497$	3.00000			0.134568
$498$	9.00000			0.403300
$499$	−20.5000	+	35.5070i	−0.917706	+	1.58951i	−0.114816	+	0.993387i	$0.536628\pi$
$499$	−20.5000	+	35.5070i	−0.917706	+	1.58951i	−0.802890	+	0.596127i	$0.796706\pi$
$500$	3.00000			0.134164
$501$	4.50000	+	7.79423i	0.201045	+	0.348220i
$502$	4.50000	−	7.79423i	0.200845	−	0.347873i
$503$	4.50000	−	7.79423i	0.200645	−	0.347527i	−0.748091	−	0.663596i	$-0.769030\pi$
$503$	4.50000	−	7.79423i	0.200645	−	0.347527i	0.948736	+	0.316068i	$0.102363\pi$
$504$	−2.00000			−0.0890871
$505$	−27.0000	−	46.7654i	−1.20148	−	2.08103i
$506$		0			0
$507$	−6.00000	−	10.3923i	−0.266469	−	0.461538i
$508$	0.500000	−	0.866025i	0.0221839	−	0.0384237i
$509$	−10.5000	−	18.1865i	−0.465404	−	0.806104i	0.533815	−	0.845601i	$-0.320758\pi$
$509$	−10.5000	−	18.1865i	−0.465404	−	0.806104i	−0.999220	+	0.0394971i	$0.987424\pi$
$510$	−4.50000	+	7.79423i	−0.199263	+	0.345134i
$511$	13.0000			0.575086
$512$	−1.00000			−0.0441942
$513$	−17.5000	+	30.3109i	−0.772644	+	1.33826i
$514$	−4.50000	−	7.79423i	−0.198486	−	0.343789i
$515$	7.50000	−	12.9904i	0.330489	−	0.572425i
$516$	−2.50000	−	4.33013i	−0.110056	−	0.190623i
$517$	18.0000	+	31.1769i	0.791639	+	1.37116i
$518$	3.50000	+	6.06218i	0.153781	+	0.266357i
$519$	−15.0000			−0.658427
$520$	−7.50000	+	12.9904i	−0.328897	+	0.569666i
$521$	4.50000	−	7.79423i	0.197149	−	0.341471i	−0.750454	−	0.660922i	$-0.770165\pi$
$521$	4.50000	−	7.79423i	0.197149	−	0.341471i	0.947603	+	0.319451i	$0.103499\pi$
$522$	−6.00000	−	10.3923i	−0.262613	−	0.454859i
$523$	−16.0000			−0.699631			−0.349816	−	0.936819i	$-0.613756\pi$
$523$	−16.0000			−0.699631			−0.349816	+	0.936819i	$0.613756\pi$
$524$	−4.50000	+	7.79423i	−0.196583	+	0.340492i
$525$	−4.00000			−0.174574
$526$	−12.0000			−0.523225
$527$	−10.5000	−	12.9904i	−0.457387	−	0.565870i
$528$	3.00000			0.130558
$529$	−23.0000			−1.00000
$530$	−13.5000	+	23.3827i	−0.586403	+	1.01568i
$531$	6.00000			0.260378
$532$	−3.50000	−	6.06218i	−0.151744	−	0.262829i
$533$	−7.50000	+	12.9904i	−0.324861	+	0.562676i
$534$	3.00000	−	5.19615i	0.129823	−	0.224860i
$535$	9.00000			0.389104
$536$	−6.50000	−	11.2583i	−0.280757	−	0.486286i
$537$	−10.5000	−	18.1865i	−0.453108	−	0.784807i
$538$	4.50000	+	7.79423i	0.194009	+	0.336033i
$539$	9.00000	−	15.5885i	0.387657	−	0.671442i
$540$	−7.50000	−	12.9904i	−0.322749	−	0.559017i
$541$	15.5000	−	26.8468i	0.666397	−	1.15423i	−0.312507	−	0.949915i	$-0.601169\pi$
$541$	15.5000	−	26.8468i	0.666397	−	1.15423i	0.978905	−	0.204318i	$-0.0654977\pi$
$542$	−20.0000			−0.859074
$543$	−7.00000			−0.300399
$544$	1.50000	−	2.59808i	0.0643120	−	0.111392i
$545$	−15.0000	−	25.9808i	−0.642529	−	1.11289i
$546$	−2.50000	+	4.33013i	−0.106990	+	0.185312i
$547$	18.5000	+	32.0429i	0.791003	+	1.37006i	0.925347	+	0.379122i	$0.123774\pi$
$547$	18.5000	+	32.0429i	0.791003	+	1.37006i	−0.134344	+	0.990935i	$0.542893\pi$
$548$	−7.50000	−	12.9904i	−0.320384	−	0.554922i
$549$	−10.0000	−	17.3205i	−0.426790	−	0.739221i
$550$	−12.0000			−0.511682
$551$	21.0000	−	36.3731i	0.894630	−	1.54954i
$552$		0			0
$553$	−0.500000	−	0.866025i	−0.0212622	−	0.0368271i
$554$	−14.0000			−0.594803
$555$	−10.5000	+	18.1865i	−0.445700	+	0.771975i
$556$	−4.00000			−0.169638
$557$	18.0000			0.762684			0.381342	−	0.924434i	$-0.375462\pi$
$557$	18.0000			0.762684			0.381342	+	0.924434i	$0.375462\pi$
$558$	11.0000	−	1.73205i	0.465667	−	0.0733236i
$559$	25.0000			1.05739
$560$	3.00000			0.126773
$561$	−4.50000	+	7.79423i	−0.189990	+	0.329073i
$562$	−6.00000			−0.253095
$563$	−13.5000	−	23.3827i	−0.568957	−	0.985463i	−0.996669	−	0.0815478i	$-0.974014\pi$
$563$	−13.5000	−	23.3827i	−0.568957	−	0.985463i	0.427712	−	0.903915i	$-0.359320\pi$
$564$	6.00000	−	10.3923i	0.252646	−	0.437595i
$565$	4.50000	−	7.79423i	0.189316	−	0.327906i
$566$	16.0000			0.672530
$567$	0.500000	+	0.866025i	0.0209980	+	0.0363696i
$568$	−1.50000	−	2.59808i	−0.0629386	−	0.109013i
$569$	−13.5000	−	23.3827i	−0.565949	−	0.980253i	−0.996961	−	0.0779066i	$-0.975176\pi$
$569$	−13.5000	−	23.3827i	−0.565949	−	0.980253i	0.431011	−	0.902347i	$-0.358157\pi$
$570$	10.5000	−	18.1865i	0.439797	−	0.761750i
$571$	−11.5000	−	19.9186i	−0.481260	−	0.833567i	0.518509	−	0.855072i	$-0.326487\pi$
$571$	−11.5000	−	19.9186i	−0.481260	−	0.833567i	−0.999769	+	0.0215055i	$0.993154\pi$
$572$	−7.50000	+	12.9904i	−0.313591	+	0.543155i
$573$	−3.00000			−0.125327
$574$	3.00000			0.125218
$575$		0			0
$576$	1.00000	+	1.73205i	0.0416667	+	0.0721688i
$577$	−5.50000	+	9.52628i	−0.228968	+	0.396584i	−0.957503	−	0.288425i	$-0.906868\pi$
$577$	−5.50000	+	9.52628i	−0.228968	+	0.396584i	0.728535	+	0.685009i	$0.240202\pi$
$578$	−4.00000	−	6.92820i	−0.166378	−	0.288175i
$579$	0.500000	+	0.866025i	0.0207793	+	0.0359908i
$580$	9.00000	+	15.5885i	0.373705	+	0.647275i
$581$	9.00000			0.373383
$582$	1.00000	−	1.73205i	0.0414513	−	0.0717958i
$583$	−13.5000	+	23.3827i	−0.559113	+	0.968412i
$584$	−6.50000	−	11.2583i	−0.268972	−	0.465873i
$585$	30.0000			1.24035
$586$	−1.50000	+	2.59808i	−0.0619644	+	0.107326i
$587$	−12.0000			−0.495293			−0.247647	−	0.968850i	$-0.579657\pi$
$587$	−12.0000			−0.495293			−0.247647	+	0.968850i	$0.579657\pi$
$588$	−6.00000			−0.247436
$589$	24.5000	+	30.3109i	1.00950	+	1.24894i
$590$	−9.00000			−0.370524
$591$	−3.00000			−0.123404
$592$	3.50000	−	6.06218i	0.143849	−	0.249154i
$593$	6.00000			0.246390			0.123195	−	0.992382i	$-0.460686\pi$
$593$	6.00000			0.246390			0.123195	+	0.992382i	$0.460686\pi$
$594$	−7.50000	−	12.9904i	−0.307729	−	0.533002i
$595$	−4.50000	+	7.79423i	−0.184482	+	0.319532i
$596$	7.50000	−	12.9904i	0.307212	−	0.532107i
$597$	−7.00000			−0.286491
$598$		0			0
$599$	−10.5000	−	18.1865i	−0.429018	−	0.743082i	0.567768	−	0.823189i	$-0.307807\pi$
$599$	−10.5000	−	18.1865i	−0.429018	−	0.743082i	−0.996786	+	0.0801071i	$0.974474\pi$
$600$	2.00000	+	3.46410i	0.0816497	+	0.141421i
$601$	−17.5000	+	30.3109i	−0.713840	+	1.23641i	0.249565	+	0.968358i	$0.419712\pi$
$601$	−17.5000	+	30.3109i	−0.713840	+	1.23641i	−0.963405	+	0.268049i	$0.913621\pi$
$602$	−2.50000	−	4.33013i	−0.101892	−	0.176483i
$603$	−13.0000	+	22.5167i	−0.529401	+	0.916949i
$604$	−16.0000			−0.651031
$605$	6.00000			0.243935
$606$	−9.00000	+	15.5885i	−0.365600	+	0.633238i
$607$	−8.50000	−	14.7224i	−0.345004	−	0.597565i	0.640350	−	0.768083i	$-0.278789\pi$
$607$	−8.50000	−	14.7224i	−0.345004	−	0.597565i	−0.985355	+	0.170518i	$0.945456\pi$
$608$	−3.50000	+	6.06218i	−0.141944	+	0.245854i
$609$	3.00000	+	5.19615i	0.121566	+	0.210559i
$610$	15.0000	+	25.9808i	0.607332	+	1.05193i
$611$	30.0000	+	51.9615i	1.21367	+	2.10214i
$612$	−6.00000			−0.242536
$613$	−14.5000	+	25.1147i	−0.585649	+	1.01437i	0.409145	+	0.912470i	$0.365827\pi$
$613$	−14.5000	+	25.1147i	−0.585649	+	1.01437i	−0.994794	+	0.101905i	$0.967506\pi$
$614$	8.50000	−	14.7224i	0.343032	−	0.594149i
$615$	4.50000	+	7.79423i	0.181458	+	0.314294i
$616$	3.00000			0.120873
$617$	4.50000	−	7.79423i	0.181163	−	0.313784i	−0.761114	−	0.648618i	$-0.775347\pi$
$617$	4.50000	−	7.79423i	0.181163	−	0.313784i	0.942277	+	0.334835i	$0.108680\pi$
$618$	−5.00000			−0.201129
$619$	44.0000			1.76851			0.884255	−	0.467005i	$-0.154667\pi$
$619$	44.0000			1.76851			0.884255	+	0.467005i	$0.154667\pi$
$620$	−16.5000	+	2.59808i	−0.662656	+	0.104341i
$621$		0			0
$622$	24.0000			0.962312
$623$	3.00000	−	5.19615i	0.120192	−	0.208179i
$624$	5.00000			0.200160
$625$	14.5000	+	25.1147i	0.580000	+	1.00459i
$626$	5.50000	−	9.52628i	0.219824	−	0.380747i
$627$	10.5000	−	18.1865i	0.419330	−	0.726300i
$628$	2.00000			0.0798087
$629$	10.5000	+	18.1865i	0.418662	+	0.725145i
$630$	−3.00000	−	5.19615i	−0.119523	−	0.207020i
$631$	3.50000	+	6.06218i	0.139333	+	0.241331i	0.927244	−	0.374457i	$-0.122171\pi$
$631$	3.50000	+	6.06218i	0.139333	+	0.241331i	−0.787911	+	0.615789i	$0.788838\pi$
$632$	−0.500000	+	0.866025i	−0.0198889	+	0.0344486i
$633$	9.50000	+	16.4545i	0.377591	+	0.654007i
$634$	−1.50000	+	2.59808i	−0.0595726	+	0.103183i
$635$	3.00000			0.119051
$636$	9.00000			0.356873
$637$	15.0000	−	25.9808i	0.594322	−	1.02940i
$638$	9.00000	+	15.5885i	0.356313	+	0.617153i
$639$	−3.00000	+	5.19615i	−0.118678	+	0.205557i
$640$	−1.50000	−	2.59808i	−0.0592927	−	0.102698i
$641$	4.50000	+	7.79423i	0.177739	+	0.307854i	0.941106	−	0.338112i	$-0.109788\pi$
$641$	4.50000	+	7.79423i	0.177739	+	0.307854i	−0.763367	+	0.645966i	$0.776455\pi$
$642$	−1.50000	−	2.59808i	−0.0592003	−	0.102538i
$643$	−16.0000			−0.630978			−0.315489	−	0.948929i	$-0.602169\pi$
$643$	−16.0000			−0.630978			−0.315489	+	0.948929i	$0.602169\pi$
$644$		0			0
$645$	7.50000	−	12.9904i	0.295312	−	0.511496i
$646$	−10.5000	−	18.1865i	−0.413117	−	0.715540i
$647$	12.0000			0.471769			0.235884	−	0.971781i	$-0.424201\pi$
$647$	12.0000			0.471769			0.235884	+	0.971781i	$0.424201\pi$
$648$	0.500000	−	0.866025i	0.0196419	−	0.0340207i
$649$	−9.00000			−0.353281
$650$	−20.0000			−0.784465
$651$	−5.50000	+	0.866025i	−0.215562	+	0.0339422i
$652$	20.0000			0.783260
$653$	6.00000			0.234798			0.117399	−	0.993085i	$-0.462544\pi$
$653$	6.00000			0.234798			0.117399	+	0.993085i	$0.462544\pi$
$654$	−5.00000	+	8.66025i	−0.195515	+	0.338643i
$655$	−27.0000			−1.05498
$656$	−1.50000	−	2.59808i	−0.0585652	−	0.101438i
$657$	−13.0000	+	22.5167i	−0.507178	+	0.878459i
$658$	6.00000	−	10.3923i	0.233904	−	0.405134i
$659$	36.0000			1.40236			0.701180	−	0.712984i	$-0.252657\pi$
$659$	36.0000			1.40236			0.701180	+	0.712984i	$0.252657\pi$
$660$	4.50000	+	7.79423i	0.175162	+	0.303390i
$661$	−2.50000	−	4.33013i	−0.0972387	−	0.168422i	0.813302	−	0.581842i	$-0.197668\pi$
$661$	−2.50000	−	4.33013i	−0.0972387	−	0.168422i	−0.910541	+	0.413419i	$0.864334\pi$
$662$	5.50000	+	9.52628i	0.213764	+	0.370249i
$663$	−7.50000	+	12.9904i	−0.291276	+	0.504505i
$664$	−4.50000	−	7.79423i	−0.174634	−	0.302475i
$665$	10.5000	−	18.1865i	0.407173	−	0.705244i
$666$	−14.0000			−0.542489
$667$		0			0
$668$	4.50000	−	7.79423i	0.174110	−	0.301568i
$669$	6.50000	+	11.2583i	0.251305	+	0.435272i
$670$	19.5000	−	33.7750i	0.753351	−	1.30484i
$671$	15.0000	+	25.9808i	0.579069	+	1.00298i
$672$	−0.500000	−	0.866025i	−0.0192879	−	0.0334077i
$673$	−17.5000	−	30.3109i	−0.674575	−	1.16840i	−0.976593	−	0.215096i	$-0.930993\pi$
$673$	−17.5000	−	30.3109i	−0.674575	−	1.16840i	0.302017	−	0.953302i	$-0.402340\pi$
$674$	−14.0000			−0.539260
$675$	10.0000	−	17.3205i	0.384900	−	0.666667i
$676$	−6.00000	+	10.3923i	−0.230769	+	0.399704i
$677$	7.50000	+	12.9904i	0.288248	+	0.499261i	0.973392	−	0.229147i	$-0.0735938\pi$
$677$	7.50000	+	12.9904i	0.288248	+	0.499261i	−0.685143	+	0.728408i	$0.740260\pi$
$678$	−3.00000			−0.115214
$679$	1.00000	−	1.73205i	0.0383765	−	0.0664700i
$680$	9.00000			0.345134
$681$	3.00000			0.114960
$682$	−16.5000	+	2.59808i	−0.631818	+	0.0994855i
$683$	−12.0000			−0.459167			−0.229584	−	0.973289i	$-0.573736\pi$
$683$	−12.0000			−0.459167			−0.229584	+	0.973289i	$0.573736\pi$
$684$	14.0000			0.535303
$685$	22.5000	−	38.9711i	0.859681	−	1.48901i
$686$	−13.0000			−0.496342
$687$	3.50000	+	6.06218i	0.133533	+	0.231287i
$688$	−2.50000	+	4.33013i	−0.0953116	+	0.165085i
$689$	−22.5000	+	38.9711i	−0.857182	+	1.48468i
$690$		0			0
$691$	−17.5000	−	30.3109i	−0.665731	−	1.15308i	−0.979086	−	0.203445i	$-0.934786\pi$
$691$	−17.5000	−	30.3109i	−0.665731	−	1.15308i	0.313355	−	0.949636i	$-0.398547\pi$
$692$	7.50000	+	12.9904i	0.285107	+	0.493820i
$693$	−3.00000	−	5.19615i	−0.113961	−	0.197386i
$694$	−13.5000	+	23.3827i	−0.512453	+	0.887595i
$695$	−6.00000	−	10.3923i	−0.227593	−	0.394203i
$696$	3.00000	−	5.19615i	0.113715	−	0.196960i
$697$	9.00000			0.340899
$698$	10.0000			0.378506
$699$	−3.00000	+	5.19615i	−0.113470	+	0.196537i
$700$	2.00000	+	3.46410i	0.0755929	+	0.130931i
$701$	−16.5000	+	28.5788i	−0.623196	+	1.07941i	0.365690	+	0.930737i	$0.380833\pi$
$701$	−16.5000	+	28.5788i	−0.623196	+	1.07941i	−0.988887	+	0.148671i	$0.952500\pi$
$702$	−12.5000	−	21.6506i	−0.471782	−	0.817151i
$703$	−24.5000	−	42.4352i	−0.924035	−	1.60048i
$704$	−1.50000	−	2.59808i	−0.0565334	−	0.0979187i
$705$	36.0000			1.35584
$706$	−10.5000	+	18.1865i	−0.395173	+	0.684459i
$707$	−9.00000	+	15.5885i	−0.338480	+	0.586264i
$708$	1.50000	+	2.59808i	0.0563735	+	0.0976417i
$709$	−34.0000			−1.27690			−0.638448	−	0.769665i	$-0.720423\pi$
$709$	−34.0000			−1.27690			−0.638448	+	0.769665i	$0.720423\pi$
$710$	4.50000	−	7.79423i	0.168882	−	0.292512i
$711$	2.00000			0.0750059
$712$	−6.00000			−0.224860
$713$		0			0
$714$	3.00000			0.112272
$715$	−45.0000			−1.68290
$716$	−10.5000	+	18.1865i	−0.392403	+	0.679663i
$717$	−3.00000			−0.112037
$718$	−1.50000	−	2.59808i	−0.0559795	−	0.0969593i
$719$	22.5000	−	38.9711i	0.839108	−	1.45338i	−0.0515326	−	0.998671i	$-0.516411\pi$
$719$	22.5000	−	38.9711i	0.839108	−	1.45338i	0.890641	−	0.454707i	$-0.150256\pi$
$720$	−3.00000	+	5.19615i	−0.111803	+	0.193649i
$721$	−5.00000			−0.186210
$722$	15.0000	+	25.9808i	0.558242	+	0.966904i
$723$	−5.50000	−	9.52628i	−0.204547	−	0.354286i
$724$	3.50000	+	6.06218i	0.130076	+	0.225299i
$725$	−12.0000	+	20.7846i	−0.445669	+	0.771921i
$726$	−1.00000	−	1.73205i	−0.0371135	−	0.0642824i
$727$	6.50000	−	11.2583i	0.241072	−	0.417548i	−0.719948	−	0.694028i	$-0.755834\pi$
$727$	6.50000	−	11.2583i	0.241072	−	0.417548i	0.961020	+	0.276479i	$0.0891678\pi$
$728$	5.00000			0.185312
$729$	13.0000			0.481481
$730$	19.5000	−	33.7750i	0.721727	−	1.25007i
$731$	−7.50000	−	12.9904i	−0.277398	−	0.480467i
$732$	5.00000	−	8.66025i	0.184805	−	0.320092i
$733$	−14.5000	−	25.1147i	−0.535570	−	0.927634i	−0.999136	−	0.0415715i	$-0.986764\pi$
$733$	−14.5000	−	25.1147i	−0.535570	−	0.927634i	0.463566	−	0.886062i	$-0.346570\pi$
$734$	−3.50000	−	6.06218i	−0.129187	−	0.223759i
$735$	−9.00000	−	15.5885i	−0.331970	−	0.574989i
$736$		0			0
$737$	19.5000	−	33.7750i	0.718292	−	1.24412i
$738$	−3.00000	+	5.19615i	−0.110432	+	0.191273i
$739$	18.5000	+	32.0429i	0.680534	+	1.17872i	0.974818	+	0.223001i	$0.0715853\pi$
$739$	18.5000	+	32.0429i	0.680534	+	1.17872i	−0.294285	+	0.955718i	$0.595081\pi$
$740$	21.0000			0.771975
$741$	17.5000	−	30.3109i	0.642879	−	1.11350i
$742$	9.00000			0.330400
$743$	−48.0000			−1.76095			−0.880475	−	0.474093i	$-0.842776\pi$
$743$	−48.0000			−1.76095			−0.880475	+	0.474093i	$0.842776\pi$
$744$	3.50000	+	4.33013i	0.128316	+	0.158750i
$745$	45.0000			1.64867
$746$	22.0000			0.805477
$747$	−9.00000	+	15.5885i	−0.329293	+	0.570352i
$748$	9.00000			0.329073
$749$	−1.50000	−	2.59808i	−0.0548088	−	0.0949316i
$750$	1.50000	−	2.59808i	0.0547723	−	0.0948683i
$751$	−17.5000	+	30.3109i	−0.638584	+	1.10606i	0.347160	+	0.937806i	$0.387146\pi$
$751$	−17.5000	+	30.3109i	−0.638584	+	1.10606i	−0.985744	+	0.168254i	$0.946187\pi$
$752$	−12.0000			−0.437595
$753$	−4.50000	−	7.79423i	−0.163989	−	0.284037i
$754$	15.0000	+	25.9808i	0.546268	+	0.946164i
$755$	−24.0000	−	41.5692i	−0.873449	−	1.51286i
$756$	−2.50000	+	4.33013i	−0.0909241	+	0.157485i
$757$	21.5000	+	37.2391i	0.781431	+	1.35348i	0.931108	+	0.364743i	$0.118843\pi$
$757$	21.5000	+	37.2391i	0.781431	+	1.35348i	−0.149677	+	0.988735i	$0.547824\pi$
$758$	−15.5000	+	26.8468i	−0.562985	+	0.975119i
$759$		0			0
$760$	−21.0000			−0.761750
$761$	−19.5000	+	33.7750i	−0.706874	+	1.22434i	0.259136	+	0.965841i	$0.416562\pi$
$761$	−19.5000	+	33.7750i	−0.706874	+	1.22434i	−0.966011	+	0.258502i	$0.916771\pi$
$762$	−0.500000	−	0.866025i	−0.0181131	−	0.0313728i
$763$	−5.00000	+	8.66025i	−0.181012	+	0.313522i
$764$	1.50000	+	2.59808i	0.0542681	+	0.0939951i
$765$	−9.00000	−	15.5885i	−0.325396	−	0.563602i
$766$	−13.5000	−	23.3827i	−0.487775	−	0.844851i
$767$	−15.0000			−0.541619
$768$	−0.500000	+	0.866025i	−0.0180422	+	0.0312500i
$769$	24.5000	−	42.4352i	0.883493	−	1.53025i	0.0360609	−	0.999350i	$-0.488519\pi$
$769$	24.5000	−	42.4352i	0.883493	−	1.53025i	0.847432	−	0.530904i	$-0.178148\pi$
$770$	4.50000	+	7.79423i	0.162169	+	0.280885i
$771$	−9.00000			−0.324127
$772$	0.500000	−	0.866025i	0.0179954	−	0.0311689i
$773$	−42.0000			−1.51064			−0.755318	−	0.655359i	$-0.772517\pi$
$773$	−42.0000			−1.51064			−0.755318	+	0.655359i	$0.772517\pi$
$774$	10.0000			0.359443
$775$	−14.0000	−	17.3205i	−0.502895	−	0.622171i
$776$	−2.00000			−0.0717958
$777$	7.00000			0.251124
$778$	16.5000	−	28.5788i	0.591554	−	1.02460i
$779$	−21.0000			−0.752403
$780$	7.50000	+	12.9904i	0.268543	+	0.465130i
$781$	4.50000	−	7.79423i	0.161023	−	0.278899i
$782$		0			0
$783$	−30.0000			−1.07211
$784$	3.00000	+	5.19615i	0.107143	+	0.185577i
$785$	3.00000	+	5.19615i	0.107075	+	0.185459i
$786$	4.50000	+	7.79423i	0.160510	+	0.278011i
$787$	15.5000	−	26.8468i	0.552515	−	0.956985i	−0.445577	−	0.895244i	$-0.647001\pi$
$787$	15.5000	−	26.8468i	0.552515	−	0.956985i	0.998092	−	0.0617409i	$-0.0196653\pi$
$788$	1.50000	+	2.59808i	0.0534353	+	0.0925526i
$789$	−6.00000	+	10.3923i	−0.213606	+	0.369976i
$790$	−3.00000			−0.106735
$791$	−3.00000			−0.106668
$792$	−3.00000	+	5.19615i	−0.106600	+	0.184637i
$793$	25.0000	+	43.3013i	0.887776	+	1.53767i
$794$	−3.50000	+	6.06218i	−0.124210	+	0.215139i
$795$	13.5000	+	23.3827i	0.478796	+	0.829298i
$796$	3.50000	+	6.06218i	0.124054	+	0.214868i
$797$	1.50000	+	2.59808i	0.0531327	+	0.0920286i	0.891368	−	0.453279i	$-0.149746\pi$
$797$	1.50000	+	2.59808i	0.0531327	+	0.0920286i	−0.838236	+	0.545308i	$0.816413\pi$
$798$	−7.00000			−0.247797
$799$	18.0000	−	31.1769i	0.636794	−	1.10296i
$800$	2.00000	−	3.46410i	0.0707107	−	0.122474i
$801$	6.00000	+	10.3923i	0.212000	+	0.367194i
$802$	−18.0000			−0.635602
$803$	19.5000	−	33.7750i	0.688140	−	1.19189i
$804$	−13.0000			−0.458475
$805$		0			0
$806$	−27.5000	+	4.33013i	−0.968646	+	0.152522i
$807$	9.00000			0.316815
$808$	18.0000			0.633238
$809$	10.5000	−	18.1865i	0.369160	−	0.639404i	−0.620274	−	0.784385i	$-0.712979\pi$
$809$	10.5000	−	18.1865i	0.369160	−	0.639404i	0.989434	+	0.144981i	$0.0463120\pi$
$810$	3.00000			0.105409
$811$	−17.5000	−	30.3109i	−0.614508	−	1.06436i	−0.990471	−	0.137724i	$-0.956021\pi$
$811$	−17.5000	−	30.3109i	−0.614508	−	1.06436i	0.375962	−	0.926635i	$-0.377312\pi$
$812$	3.00000	−	5.19615i	0.105279	−	0.182349i
$813$	−10.0000	+	17.3205i	−0.350715	+	0.607457i
$814$	21.0000			0.736050
$815$	30.0000	+	51.9615i	1.05085	+	1.82013i
$816$	−1.50000	−	2.59808i	−0.0525105	−	0.0909509i
$817$	17.5000	+	30.3109i	0.612247	+	1.06044i
$818$	11.5000	−	19.9186i	0.402088	−	0.696437i
$819$	−5.00000	−	8.66025i	−0.174714	−	0.302614i
$820$	4.50000	−	7.79423i	0.157147	−	0.272186i
$821$	6.00000			0.209401			0.104701	−	0.994504i	$-0.466612\pi$
$821$	6.00000			0.209401			0.104701	+	0.994504i	$0.466612\pi$
$822$	−15.0000			−0.523185
$823$	6.50000	−	11.2583i	0.226576	−	0.392441i	−0.730215	−	0.683217i	$-0.760580\pi$
$823$	6.50000	−	11.2583i	0.226576	−	0.392441i	0.956791	+	0.290776i	$0.0939136\pi$
$824$	2.50000	+	4.33013i	0.0870916	+	0.150847i
$825$	−6.00000	+	10.3923i	−0.208893	+	0.361814i
$826$	1.50000	+	2.59808i	0.0521917	+	0.0903986i
$827$	4.50000	+	7.79423i	0.156480	+	0.271032i	0.933597	−	0.358325i	$-0.116652\pi$
$827$	4.50000	+	7.79423i	0.156480	+	0.271032i	−0.777117	+	0.629356i	$0.783319\pi$
$828$		0			0
$829$	2.00000			0.0694629			0.0347314	−	0.999397i	$-0.488942\pi$
$829$	2.00000			0.0694629			0.0347314	+	0.999397i	$0.488942\pi$
$830$	13.5000	−	23.3827i	0.468592	−	0.811625i
$831$	−7.00000	+	12.1244i	−0.242827	+	0.420589i
$832$	−2.50000	−	4.33013i	−0.0866719	−	0.150120i
$833$	−18.0000			−0.623663
$834$	−2.00000	+	3.46410i	−0.0692543	+	0.119952i
$835$	27.0000			0.934374
$836$	−21.0000			−0.726300
$837$	10.0000	−	25.9808i	0.345651	−	0.898027i
$838$	−36.0000			−1.24360
$839$	24.0000			0.828572			0.414286	−	0.910147i	$-0.364031\pi$
$839$	24.0000			0.828572			0.414286	+	0.910147i	$0.364031\pi$
$840$	1.50000	−	2.59808i	0.0517549	−	0.0896421i
$841$	7.00000			0.241379
$842$	8.50000	+	14.7224i	0.292929	+	0.507369i
$843$	−3.00000	+	5.19615i	−0.103325	+	0.178965i
$844$	9.50000	−	16.4545i	0.327003	−	0.566387i
$845$	−36.0000			−1.23844
$846$	12.0000	+	20.7846i	0.412568	+	0.714590i
$847$	−1.00000	−	1.73205i	−0.0343604	−	0.0595140i
$848$	−4.50000	−	7.79423i	−0.154531	−	0.267655i
$849$	8.00000	−	13.8564i	0.274559	−	0.475551i
$850$	6.00000	+	10.3923i	0.205798	+	0.356453i
$851$		0			0
$852$	−3.00000			−0.102778
$853$	−34.0000			−1.16414			−0.582069	−	0.813139i	$-0.697757\pi$
$853$	−34.0000			−1.16414			−0.582069	+	0.813139i	$0.697757\pi$
$854$	5.00000	−	8.66025i	0.171096	−	0.296348i
$855$	21.0000	+	36.3731i	0.718185	+	1.24393i
$856$	−1.50000	+	2.59808i	−0.0512689	+	0.0888004i
$857$	−1.50000	−	2.59808i	−0.0512390	−	0.0887486i	0.839268	−	0.543718i	$-0.182984\pi$
$857$	−1.50000	−	2.59808i	−0.0512390	−	0.0887486i	−0.890507	+	0.454969i	$0.849650\pi$
$858$	7.50000	+	12.9904i	0.256046	+	0.443484i
$859$	0.500000	+	0.866025i	0.0170598	+	0.0295484i	0.874429	−	0.485153i	$-0.161236\pi$
$859$	0.500000	+	0.866025i	0.0170598	+	0.0295484i	−0.857369	+	0.514701i	$0.827903\pi$
$860$	−15.0000			−0.511496
$861$	1.50000	−	2.59808i	0.0511199	−	0.0885422i
$862$	−10.5000	+	18.1865i	−0.357631	+	0.619436i
$863$	25.5000	+	44.1673i	0.868030	+	1.50347i	0.864007	+	0.503480i	$0.167947\pi$
$863$	25.5000	+	44.1673i	0.868030	+	1.50347i	0.00402340	+	0.999992i	$0.498719\pi$
$864$	5.00000			0.170103
$865$	−22.5000	+	38.9711i	−0.765023	+	1.32506i
$866$	10.0000			0.339814
$867$	−8.00000			−0.271694
$868$	3.50000	+	4.33013i	0.118798	+	0.146974i
$869$	−3.00000			−0.101768
$870$	18.0000			0.610257
$871$	32.5000	−	56.2917i	1.10122	−	1.90737i
$872$	10.0000			0.338643
$873$	2.00000	+	3.46410i	0.0676897	+	0.117242i
$874$		0			0
$875$	1.50000	−	2.59808i	0.0507093	−	0.0878310i
$876$	−13.0000			−0.439229
$877$	−8.50000	−	14.7224i	−0.287025	−	0.497141i	0.686074	−	0.727532i	$-0.259333\pi$
$877$	−8.50000	−	14.7224i	−0.287025	−	0.497141i	−0.973098	+	0.230391i	$0.925999\pi$
$878$	2.50000	+	4.33013i	0.0843709	+	0.146135i
$879$	1.50000	+	2.59808i	0.0505937	+	0.0876309i
$880$	4.50000	−	7.79423i	0.151695	−	0.262743i
$881$	22.5000	+	38.9711i	0.758044	+	1.31297i	0.943847	+	0.330384i	$0.107178\pi$
$881$	22.5000	+	38.9711i	0.758044	+	1.31297i	−0.185802	+	0.982587i	$0.559488\pi$
$882$	6.00000	−	10.3923i	0.202031	−	0.349927i
$883$	20.0000			0.673054			0.336527	−	0.941674i	$-0.390748\pi$
$883$	20.0000			0.673054			0.336527	+	0.941674i	$0.390748\pi$
$884$	15.0000			0.504505
$885$	−4.50000	+	7.79423i	−0.151266	+	0.262000i
$886$	−10.5000	−	18.1865i	−0.352754	−	0.610989i
$887$	16.5000	−	28.5788i	0.554016	−	0.959583i	−0.443964	−	0.896045i	$-0.646428\pi$
$887$	16.5000	−	28.5788i	0.554016	−	0.959583i	0.997979	−	0.0635387i	$-0.0202386\pi$
$888$	−3.50000	−	6.06218i	−0.117452	−	0.203433i
$889$	−0.500000	−	0.866025i	−0.0167695	−	0.0290456i
$890$	−9.00000	−	15.5885i	−0.301681	−	0.522526i
$891$	3.00000			0.100504
$892$	6.50000	−	11.2583i	0.217636	−	0.376957i
$893$	−42.0000	+	72.7461i	−1.40548	+	2.43436i
$894$	−7.50000	−	12.9904i	−0.250838	−	0.434463i
$895$	−63.0000			−2.10586
$896$	−0.500000	+	0.866025i	−0.0167038	+	0.0289319i
$897$		0			0
$898$	−6.00000			−0.200223
$899$	−12.0000	+	31.1769i	−0.400222	+	1.03981i
$900$	−8.00000			−0.266667
$901$	27.0000			0.899500
$902$	4.50000	−	7.79423i	0.149834	−	0.259519i
$903$	−5.00000			−0.166390
$904$	1.50000	+	2.59808i	0.0498893	+	0.0864107i
$905$	−10.5000	+	18.1865i	−0.349032	+	0.604541i
$906$	−8.00000	+	13.8564i	−0.265782	+	0.460348i
$907$	−28.0000			−0.929725			−0.464862	−	0.885383i	$-0.653896\pi$
$907$	−28.0000			−0.929725			−0.464862	+	0.885383i	$0.653896\pi$
$908$	−1.50000	−	2.59808i	−0.0497792	−	0.0862202i
$909$	−18.0000	−	31.1769i	−0.597022	−	1.03407i
$910$	7.50000	+	12.9904i	0.248623	+	0.430627i
$911$	10.5000	−	18.1865i	0.347881	−	0.602547i	−0.637992	−	0.770043i	$-0.720235\pi$
$911$	10.5000	−	18.1865i	0.347881	−	0.602547i	0.985873	+	0.167496i	$0.0535682\pi$
$912$	3.50000	+	6.06218i	0.115897	+	0.200739i
$913$	13.5000	−	23.3827i	0.446785	−	0.773854i
$914$	−14.0000			−0.463079
$915$	30.0000			0.991769
$916$	3.50000	−	6.06218i	0.115643	−	0.200300i
$917$	4.50000	+	7.79423i	0.148603	+	0.257388i
$918$	−7.50000	+	12.9904i	−0.247537	+	0.428746i
$919$	27.5000	+	47.6314i	0.907141	+	1.57121i	0.818017	+	0.575194i	$0.195074\pi$
$919$	27.5000	+	47.6314i	0.907141	+	1.57121i	0.0891245	+	0.996020i	$0.471593\pi$
$920$		0			0
$921$	−8.50000	−	14.7224i	−0.280085	−	0.485121i
$922$	−18.0000			−0.592798
$923$	7.50000	−	12.9904i	0.246866	−	0.427584i
$924$	1.50000	−	2.59808i	0.0493464	−	0.0854704i
$925$	14.0000	+	24.2487i	0.460317	+	0.797293i
$926$	−8.00000			−0.262896
$927$	5.00000	−	8.66025i	0.164222	−	0.284440i
$928$	−6.00000			−0.196960
$929$	54.0000			1.77168			0.885841	−	0.463988i	$-0.153582\pi$
$929$	54.0000			1.77168			0.885841	+	0.463988i	$0.153582\pi$
$930$	−6.00000	+	15.5885i	−0.196748	+	0.511166i
$931$	42.0000			1.37649
$932$	6.00000			0.196537
$933$	12.0000	−	20.7846i	0.392862	−	0.680458i
$934$	36.0000			1.17796
$935$	13.5000	+	23.3827i	0.441497	+	0.764696i
$936$	−5.00000	+	8.66025i	−0.163430	+	0.283069i
$937$	6.50000	−	11.2583i	0.212346	−	0.367794i	−0.740102	−	0.672494i	$-0.765223\pi$
$937$	6.50000	−	11.2583i	0.212346	−	0.367794i	0.952448	+	0.304700i	$0.0985564\pi$
$938$	−13.0000			−0.424465
$939$	−5.50000	−	9.52628i	−0.179486	−	0.310878i
$940$	−18.0000	−	31.1769i	−0.587095	−	1.01688i
$941$	−10.5000	−	18.1865i	−0.342290	−	0.592864i	0.642567	−	0.766229i	$-0.277869\pi$
$941$	−10.5000	−	18.1865i	−0.342290	−	0.592864i	−0.984858	+	0.173365i	$0.944536\pi$
$942$	1.00000	−	1.73205i	0.0325818	−	0.0564333i
$943$		0			0
$944$	1.50000	−	2.59808i	0.0488208	−	0.0845602i
$945$	−15.0000			−0.487950
$946$	−15.0000			−0.487692
$947$	1.50000	−	2.59808i	0.0487435	−	0.0844261i	−0.840624	−	0.541619i	$-0.817812\pi$
$947$	1.50000	−	2.59808i	0.0487435	−	0.0844261i	0.889368	+	0.457193i	$0.151145\pi$
$948$	0.500000	+	0.866025i	0.0162392	+	0.0281272i
$949$	32.5000	−	56.2917i	1.05499	−	1.82730i
$950$	−14.0000	−	24.2487i	−0.454220	−	0.786732i
$951$	1.50000	+	2.59808i	0.0486408	+	0.0842484i
$952$	−1.50000	−	2.59808i	−0.0486153	−	0.0842041i
$953$	6.00000			0.194359			0.0971795	−	0.995267i	$-0.469018\pi$
$953$	6.00000			0.194359			0.0971795	+	0.995267i	$0.469018\pi$
$954$	−9.00000	+	15.5885i	−0.291386	+	0.504695i
$955$	−4.50000	+	7.79423i	−0.145617	+	0.252215i
$956$	1.50000	+	2.59808i	0.0485135	+	0.0840278i
$957$	18.0000			0.581857
$958$	1.50000	−	2.59808i	0.0484628	−	0.0839400i
$959$	−15.0000			−0.484375
$960$	−3.00000			−0.0968246
$961$	−23.0000	−	20.7846i	−0.741935	−	0.670471i
$962$	35.0000			1.12845
$963$	6.00000			0.193347
$964$	−5.50000	+	9.52628i	−0.177143	+	0.306821i
$965$	3.00000			0.0965734
$966$		0			0
$967$	−11.5000	+	19.9186i	−0.369815	+	0.640538i	−0.989536	−	0.144283i	$-0.953912\pi$
$967$	−11.5000	+	19.9186i	−0.369815	+	0.640538i	0.619721	+	0.784822i	$0.287246\pi$
$968$	−1.00000	+	1.73205i	−0.0321412	+	0.0556702i
$969$	−21.0000			−0.674617
$970$	−3.00000	−	5.19615i	−0.0963242	−	0.166838i
$971$	−1.50000	−	2.59808i	−0.0481373	−	0.0833762i	0.840953	−	0.541108i	$-0.181995\pi$
$971$	−1.50000	−	2.59808i	−0.0481373	−	0.0833762i	−0.889090	+	0.457732i	$0.848662\pi$
$972$	−8.00000	−	13.8564i	−0.256600	−	0.444444i
$973$	−2.00000	+	3.46410i	−0.0641171	+	0.111054i
$974$	−15.5000	−	26.8468i	−0.496652	−	0.860227i
$975$	−10.0000	+	17.3205i	−0.320256	+	0.554700i
$976$	−10.0000			−0.320092
$977$	−30.0000			−0.959785			−0.479893	−	0.877327i	$-0.659324\pi$
$977$	−30.0000			−0.959785			−0.479893	+	0.877327i	$0.659324\pi$
$978$	10.0000	−	17.3205i	0.319765	−	0.553849i
$979$	−9.00000	−	15.5885i	−0.287641	−	0.498209i
$980$	−9.00000	+	15.5885i	−0.287494	+	0.497955i
$981$	−10.0000	−	17.3205i	−0.319275	−	0.553001i
$982$	13.5000	+	23.3827i	0.430802	+	0.746171i
$983$	−4.50000	−	7.79423i	−0.143528	−	0.248597i	0.785295	−	0.619122i	$-0.212511\pi$
$983$	−4.50000	−	7.79423i	−0.143528	−	0.248597i	−0.928823	+	0.370525i	$0.879178\pi$
$984$	−3.00000			−0.0956365
$985$	−4.50000	+	7.79423i	−0.143382	+	0.248345i
$986$	9.00000	−	15.5885i	0.286618	−	0.496438i
$987$	−6.00000	−	10.3923i	−0.190982	−	0.330791i
$988$	−35.0000			−1.11350
$989$		0			0
$990$	−18.0000			−0.572078
$991$	−40.0000			−1.27064			−0.635321	−	0.772248i	$-0.719132\pi$
$991$	−40.0000			−1.27064			−0.635321	+	0.772248i	$0.719132\pi$
$992$	2.00000	−	5.19615i	0.0635001	−	0.164978i
$993$	11.0000			0.349074
$994$	−3.00000			−0.0951542
$995$	−10.5000	+	18.1865i	−0.332872	+	0.576552i
$996$	−9.00000			−0.285176
$997$	−8.50000	−	14.7224i	−0.269198	−	0.466264i	0.699457	−	0.714675i	$-0.253425\pi$
$997$	−8.50000	−	14.7224i	−0.269198	−	0.466264i	−0.968655	+	0.248410i	$0.920092\pi$
$998$	20.5000	−	35.5070i	0.648916	−	1.12396i
$999$	−17.5000	+	30.3109i	−0.553675	+	0.958994i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	62.2.c.a.5.1	✓	2
3.2	odd	2		558.2.e.c.253.1		2
4.3	odd	2		496.2.i.e.129.1		2
5.2	odd	4		1550.2.p.d.749.1		4
5.3	odd	4		1550.2.p.d.749.2		4
5.4	even	2		1550.2.e.g.501.1		2
31.5	even	3		1922.2.a.b.1.1		1
31.25	even	3	inner	62.2.c.a.25.1	yes	2
31.26	odd	6		1922.2.a.a.1.1		1
93.56	odd	6		558.2.e.c.397.1		2
124.87	odd	6		496.2.i.e.273.1		2
155.87	odd	12		1550.2.p.d.149.1		4
155.118	odd	12		1550.2.p.d.149.2		4
155.149	even	6		1550.2.e.g.1451.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
62.2.c.a.5.1	✓	2	1.1	even	1	trivial
62.2.c.a.25.1	yes	2	31.25	even	3	inner
496.2.i.e.129.1		2	4.3	odd	2
496.2.i.e.273.1		2	124.87	odd	6
558.2.e.c.253.1		2	3.2	odd	2
558.2.e.c.397.1		2	93.56	odd	6
1550.2.e.g.501.1		2	5.4	even	2
1550.2.e.g.1451.1		2	155.149	even	6
1550.2.p.d.149.1		4	155.87	odd	12
1550.2.p.d.149.2		4	155.118	odd	12
1550.2.p.d.749.1		4	5.2	odd	4
1550.2.p.d.749.2		4	5.3	odd	4
1922.2.a.a.1.1		1	31.26	odd	6
1922.2.a.b.1.1		1	31.5	even	3

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:	\( N \)	\(=\)	\( 62 = 2 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	62.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(-0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(1.50000 + 2.59808i) q^{5} +(0.500000 - 0.866025i) q^{6} +(0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(-0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(1.50000 + 2.59808i) q^{5} +(0.500000 - 0.866025i) q^{6} +(0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +(-1.50000 - 2.59808i) q^{10} +(-1.50000 - 2.59808i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(-2.50000 - 4.33013i) q^{13} +(-0.500000 + 0.866025i) q^{14} -3.00000 q^{15} +1.00000 q^{16} +(-1.50000 + 2.59808i) q^{17} +(-1.00000 - 1.73205i) q^{18} +(3.50000 - 6.06218i) q^{19} +(1.50000 + 2.59808i) q^{20} +(0.500000 + 0.866025i) q^{21} +(1.50000 + 2.59808i) q^{22} +(0.500000 - 0.866025i) q^{24} +(-2.00000 + 3.46410i) q^{25} +(2.50000 + 4.33013i) q^{26} -5.00000 q^{27} +(0.500000 - 0.866025i) q^{28} +6.00000 q^{29} +3.00000 q^{30} +(-2.00000 + 5.19615i) q^{31} -1.00000 q^{32} +3.00000 q^{33} +(1.50000 - 2.59808i) q^{34} +3.00000 q^{35} +(1.00000 + 1.73205i) q^{36} +(3.50000 - 6.06218i) q^{37} +(-3.50000 + 6.06218i) q^{38} +5.00000 q^{39} +(-1.50000 - 2.59808i) q^{40} +(-1.50000 - 2.59808i) q^{41} +(-0.500000 - 0.866025i) q^{42} +(-2.50000 + 4.33013i) q^{43} +(-1.50000 - 2.59808i) q^{44} +(-3.00000 + 5.19615i) q^{45} -12.0000 q^{47} +(-0.500000 + 0.866025i) q^{48} +(3.00000 + 5.19615i) q^{49} +(2.00000 - 3.46410i) q^{50} +(-1.50000 - 2.59808i) q^{51} +(-2.50000 - 4.33013i) q^{52} +(-4.50000 - 7.79423i) q^{53} +5.00000 q^{54} +(4.50000 - 7.79423i) q^{55} +(-0.500000 + 0.866025i) q^{56} +(3.50000 + 6.06218i) q^{57} -6.00000 q^{58} +(1.50000 - 2.59808i) q^{59} -3.00000 q^{60} -10.0000 q^{61} +(2.00000 - 5.19615i) q^{62} +2.00000 q^{63} +1.00000 q^{64} +(7.50000 - 12.9904i) q^{65} -3.00000 q^{66} +(6.50000 + 11.2583i) q^{67} +(-1.50000 + 2.59808i) q^{68} -3.00000 q^{70} +(1.50000 + 2.59808i) q^{71} +(-1.00000 - 1.73205i) q^{72} +(6.50000 + 11.2583i) q^{73} +(-3.50000 + 6.06218i) q^{74} +(-2.00000 - 3.46410i) q^{75} +(3.50000 - 6.06218i) q^{76} -3.00000 q^{77} -5.00000 q^{78} +(0.500000 - 0.866025i) q^{79} +(1.50000 + 2.59808i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(1.50000 + 2.59808i) q^{82} +(4.50000 + 7.79423i) q^{83} +(0.500000 + 0.866025i) q^{84} -9.00000 q^{85} +(2.50000 - 4.33013i) q^{86} +(-3.00000 + 5.19615i) q^{87} +(1.50000 + 2.59808i) q^{88} +6.00000 q^{89} +(3.00000 - 5.19615i) q^{90} -5.00000 q^{91} +(-3.50000 - 4.33013i) q^{93} +12.0000 q^{94} +21.0000 q^{95} +(0.500000 - 0.866025i) q^{96} +2.00000 q^{97} +(-3.00000 - 5.19615i) q^{98} +(3.00000 - 5.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - q^{3} + 2 q^{4} + 3 q^{5} + q^{6} + q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 - q^3 + 2 * q^4 + 3 * q^5 + q^6 + q^7 - 2 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} - q^{3} + 2 q^{4} + 3 q^{5} + q^{6} + q^{7} - 2 q^{8} + 2 q^{9} - 3 q^{10} - 3 q^{11} - q^{12} - 5 q^{13} - q^{14} - 6 q^{15} + 2 q^{16} - 3 q^{17} - 2 q^{18} + 7 q^{19} + 3 q^{20} + q^{21} + 3 q^{22} + q^{24} - 4 q^{25} + 5 q^{26} - 10 q^{27} + q^{28} + 12 q^{29} + 6 q^{30} - 4 q^{31} - 2 q^{32} + 6 q^{33} + 3 q^{34} + 6 q^{35} + 2 q^{36} + 7 q^{37} - 7 q^{38} + 10 q^{39} - 3 q^{40} - 3 q^{41} - q^{42} - 5 q^{43} - 3 q^{44} - 6 q^{45} - 24 q^{47} - q^{48} + 6 q^{49} + 4 q^{50} - 3 q^{51} - 5 q^{52} - 9 q^{53} + 10 q^{54} + 9 q^{55} - q^{56} + 7 q^{57} - 12 q^{58} + 3 q^{59} - 6 q^{60} - 20 q^{61} + 4 q^{62} + 4 q^{63} + 2 q^{64} + 15 q^{65} - 6 q^{66} + 13 q^{67} - 3 q^{68} - 6 q^{70} + 3 q^{71} - 2 q^{72} + 13 q^{73} - 7 q^{74} - 4 q^{75} + 7 q^{76} - 6 q^{77} - 10 q^{78} + q^{79} + 3 q^{80} - q^{81} + 3 q^{82} + 9 q^{83} + q^{84} - 18 q^{85} + 5 q^{86} - 6 q^{87} + 3 q^{88} + 12 q^{89} + 6 q^{90} - 10 q^{91} - 7 q^{93} + 24 q^{94} + 42 q^{95} + q^{96} + 4 q^{97} - 6 q^{98} + 6 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - q^3 + 2 * q^4 + 3 * q^5 + q^6 + q^7 - 2 * q^8 + 2 * q^9 - 3 * q^10 - 3 * q^11 - q^12 - 5 * q^13 - q^14 - 6 * q^15 + 2 * q^16 - 3 * q^17 - 2 * q^18 + 7 * q^19 + 3 * q^20 + q^21 + 3 * q^22 + q^24 - 4 * q^25 + 5 * q^26 - 10 * q^27 + q^28 + 12 * q^29 + 6 * q^30 - 4 * q^31 - 2 * q^32 + 6 * q^33 + 3 * q^34 + 6 * q^35 + 2 * q^36 + 7 * q^37 - 7 * q^38 + 10 * q^39 - 3 * q^40 - 3 * q^41 - q^42 - 5 * q^43 - 3 * q^44 - 6 * q^45 - 24 * q^47 - q^48 + 6 * q^49 + 4 * q^50 - 3 * q^51 - 5 * q^52 - 9 * q^53 + 10 * q^54 + 9 * q^55 - q^56 + 7 * q^57 - 12 * q^58 + 3 * q^59 - 6 * q^60 - 20 * q^61 + 4 * q^62 + 4 * q^63 + 2 * q^64 + 15 * q^65 - 6 * q^66 + 13 * q^67 - 3 * q^68 - 6 * q^70 + 3 * q^71 - 2 * q^72 + 13 * q^73 - 7 * q^74 - 4 * q^75 + 7 * q^76 - 6 * q^77 - 10 * q^78 + q^79 + 3 * q^80 - q^81 + 3 * q^82 + 9 * q^83 + q^84 - 18 * q^85 + 5 * q^86 - 6 * q^87 + 3 * q^88 + 12 * q^89 + 6 * q^90 - 10 * q^91 - 7 * q^93 + 24 * q^94 + 42 * q^95 + q^96 + 4 * q^97 - 6 * q^98 + 6 * q^99

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