LMFDB - Embedded newform 42.2.e.a.25.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [42,2,Mod(25,42)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(42, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("42.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 42 = 2 \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	42.e (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:	$0.335371688489$
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			25.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	42.25
Dual form			42.2.e.a.37.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} -1.00000 q^{6} +(0.500000 + 2.59808i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} -1.00000 q^{6} +(0.500000 + 2.59808i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(-2.50000 + 4.33013i) q^{11} +(0.500000 + 0.866025i) q^{12} +(2.00000 - 1.73205i) q^{14} -1.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.00000 - 3.46410i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(-4.00000 - 6.92820i) q^{19} +1.00000 q^{20} +(2.50000 + 0.866025i) q^{21} +5.00000 q^{22} +(2.00000 + 3.46410i) q^{23} +(0.500000 - 0.866025i) q^{24} +(2.00000 - 3.46410i) q^{25} -1.00000 q^{27} +(-2.50000 - 0.866025i) q^{28} -5.00000 q^{29} +(0.500000 + 0.866025i) q^{30} +(-1.50000 + 2.59808i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(2.50000 + 4.33013i) q^{33} -4.00000 q^{34} +(2.00000 - 1.73205i) q^{35} +1.00000 q^{36} +(2.00000 + 3.46410i) q^{37} +(-4.00000 + 6.92820i) q^{38} +(-0.500000 - 0.866025i) q^{40} +(-0.500000 - 2.59808i) q^{42} +2.00000 q^{43} +(-2.50000 - 4.33013i) q^{44} +(-0.500000 + 0.866025i) q^{45} +(2.00000 - 3.46410i) q^{46} +(3.00000 + 5.19615i) q^{47} -1.00000 q^{48} +(-6.50000 + 2.59808i) q^{49} -4.00000 q^{50} +(-2.00000 - 3.46410i) q^{51} +(4.50000 - 7.79423i) q^{53} +(0.500000 + 0.866025i) q^{54} +5.00000 q^{55} +(0.500000 + 2.59808i) q^{56} -8.00000 q^{57} +(2.50000 + 4.33013i) q^{58} +(5.50000 - 9.52628i) q^{59} +(0.500000 - 0.866025i) q^{60} +(3.00000 + 5.19615i) q^{61} +3.00000 q^{62} +(2.00000 - 1.73205i) q^{63} +1.00000 q^{64} +(2.50000 - 4.33013i) q^{66} +(1.00000 - 1.73205i) q^{67} +(2.00000 + 3.46410i) q^{68} +4.00000 q^{69} +(-2.50000 - 0.866025i) q^{70} +2.00000 q^{71} +(-0.500000 - 0.866025i) q^{72} +(-5.00000 + 8.66025i) q^{73} +(2.00000 - 3.46410i) q^{74} +(-2.00000 - 3.46410i) q^{75} +8.00000 q^{76} +(-12.5000 - 4.33013i) q^{77} +(-1.50000 - 2.59808i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} -7.00000 q^{83} +(-2.00000 + 1.73205i) q^{84} -4.00000 q^{85} +(-1.00000 - 1.73205i) q^{86} +(-2.50000 + 4.33013i) q^{87} +(-2.50000 + 4.33013i) q^{88} +(3.00000 + 5.19615i) q^{89} +1.00000 q^{90} -4.00000 q^{92} +(1.50000 + 2.59808i) q^{93} +(3.00000 - 5.19615i) q^{94} +(-4.00000 + 6.92820i) q^{95} +(0.500000 + 0.866025i) q^{96} +7.00000 q^{97} +(5.50000 + 4.33013i) q^{98} +5.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} + q^{3} - q^{4} - q^{5} - 2 q^{6} + q^{7} + 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q - q^2 + q^3 - q^4 - q^5 - 2 * q^6 + q^7 + 2 * q^8 - q^9	$ 2 q - q^{2} + q^{3} - q^{4} - q^{5} - 2 q^{6} + q^{7} + 2 q^{8} - q^{9} - q^{10} - 5 q^{11} + q^{12} + 4 q^{14} - 2 q^{15} - q^{16} + 4 q^{17} - q^{18} - 8 q^{19} + 2 q^{20} + 5 q^{21} + 10 q^{22} + 4 q^{23} + q^{24} + 4 q^{25} - 2 q^{27} - 5 q^{28} - 10 q^{29} + q^{30} - 3 q^{31} - q^{32} + 5 q^{33} - 8 q^{34} + 4 q^{35} + 2 q^{36} + 4 q^{37} - 8 q^{38} - q^{40} - q^{42} + 4 q^{43} - 5 q^{44} - q^{45} + 4 q^{46} + 6 q^{47} - 2 q^{48} - 13 q^{49} - 8 q^{50} - 4 q^{51} + 9 q^{53} + q^{54} + 10 q^{55} + q^{56} - 16 q^{57} + 5 q^{58} + 11 q^{59} + q^{60} + 6 q^{61} + 6 q^{62} + 4 q^{63} + 2 q^{64} + 5 q^{66} + 2 q^{67} + 4 q^{68} + 8 q^{69} - 5 q^{70} + 4 q^{71} - q^{72} - 10 q^{73} + 4 q^{74} - 4 q^{75} + 16 q^{76} - 25 q^{77} - 3 q^{79} - q^{80} - q^{81} - 14 q^{83} - 4 q^{84} - 8 q^{85} - 2 q^{86} - 5 q^{87} - 5 q^{88} + 6 q^{89} + 2 q^{90} - 8 q^{92} + 3 q^{93} + 6 q^{94} - 8 q^{95} + q^{96} + 14 q^{97} + 11 q^{98} + 10 q^{99}+O(q^{100}) $ 2 * q - q^2 + q^3 - q^4 - q^5 - 2 * q^6 + q^7 + 2 * q^8 - q^9 - q^10 - 5 * q^11 + q^12 + 4 * q^14 - 2 * q^15 - q^16 + 4 * q^17 - q^18 - 8 * q^19 + 2 * q^20 + 5 * q^21 + 10 * q^22 + 4 * q^23 + q^24 + 4 * q^25 - 2 * q^27 - 5 * q^28 - 10 * q^29 + q^30 - 3 * q^31 - q^32 + 5 * q^33 - 8 * q^34 + 4 * q^35 + 2 * q^36 + 4 * q^37 - 8 * q^38 - q^40 - q^42 + 4 * q^43 - 5 * q^44 - q^45 + 4 * q^46 + 6 * q^47 - 2 * q^48 - 13 * q^49 - 8 * q^50 - 4 * q^51 + 9 * q^53 + q^54 + 10 * q^55 + q^56 - 16 * q^57 + 5 * q^58 + 11 * q^59 + q^60 + 6 * q^61 + 6 * q^62 + 4 * q^63 + 2 * q^64 + 5 * q^66 + 2 * q^67 + 4 * q^68 + 8 * q^69 - 5 * q^70 + 4 * q^71 - q^72 - 10 * q^73 + 4 * q^74 - 4 * q^75 + 16 * q^76 - 25 * q^77 - 3 * q^79 - q^80 - q^81 - 14 * q^83 - 4 * q^84 - 8 * q^85 - 2 * q^86 - 5 * q^87 - 5 * q^88 + 6 * q^89 + 2 * q^90 - 8 * q^92 + 3 * q^93 + 6 * q^94 - 8 * q^95 + q^96 + 14 * q^97 + 11 * q^98 + 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/42\mathbb{Z}\right)^\times$.

$n$	$29$	$31$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i	0.732294	−	0.680989i	$-0.238450\pi$
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i	−0.955901	+	0.293691i	$0.905116\pi$
$6$	−1.00000			−0.408248
$7$	0.500000	+	2.59808i	0.188982	+	0.981981i
$7$	0.500000	+	2.59808i	0.188982	+	0.981981i
$8$	1.00000			0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−0.500000	+	0.866025i	−0.158114	+	0.273861i
$11$	−2.50000	+	4.33013i	−0.753778	+	1.30558i	0.192201	+	0.981356i	$0.438437\pi$
$11$	−2.50000	+	4.33013i	−0.753778	+	1.30558i	−0.945979	+	0.324227i	$0.894896\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$		0			0			−	1.00000i	$-0.5\pi$
$13$		0			0				1.00000i	$0.5\pi$
$14$	2.00000	−	1.73205i	0.534522	−	0.462910i
$15$	−1.00000			−0.258199
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.00000	−	3.46410i	0.485071	−	0.840168i	−0.514782	−	0.857321i	$-0.672127\pi$
$17$	2.00000	−	3.46410i	0.485071	−	0.840168i	0.999853	+	0.0171533i	$0.00546033\pi$
$18$	−0.500000	+	0.866025i	−0.117851	+	0.204124i
$19$	−4.00000	−	6.92820i	−0.917663	−	1.58944i	−0.802955	−	0.596040i	$-0.796740\pi$
$19$	−4.00000	−	6.92820i	−0.917663	−	1.58944i	−0.114708	−	0.993399i	$-0.536593\pi$
$20$	1.00000			0.223607
$21$	2.50000	+	0.866025i	0.545545	+	0.188982i
$22$	5.00000			1.06600
$23$	2.00000	+	3.46410i	0.417029	+	0.722315i	0.995639	−	0.0932891i	$-0.0297381\pi$
$23$	2.00000	+	3.46410i	0.417029	+	0.722315i	−0.578610	+	0.815604i	$0.696405\pi$
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$	2.00000	−	3.46410i	0.400000	−	0.692820i
$26$		0			0
$27$	−1.00000			−0.192450
$28$	−2.50000	−	0.866025i	−0.472456	−	0.163663i
$29$	−5.00000			−0.928477			−0.464238	−	0.885710i	$-0.653672\pi$
$29$	−5.00000			−0.928477			−0.464238	+	0.885710i	$0.653672\pi$
$30$	0.500000	+	0.866025i	0.0912871	+	0.158114i
$31$	−1.50000	+	2.59808i	−0.269408	+	0.466628i	−0.968709	−	0.248199i	$-0.920161\pi$
$31$	−1.50000	+	2.59808i	−0.269408	+	0.466628i	0.699301	+	0.714827i	$0.253495\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	2.50000	+	4.33013i	0.435194	+	0.753778i
$34$	−4.00000			−0.685994
$35$	2.00000	−	1.73205i	0.338062	−	0.292770i
$36$	1.00000			0.166667
$37$	2.00000	+	3.46410i	0.328798	+	0.569495i	0.982274	−	0.187453i	$-0.0600231\pi$
$37$	2.00000	+	3.46410i	0.328798	+	0.569495i	−0.653476	+	0.756948i	$0.726690\pi$
$38$	−4.00000	+	6.92820i	−0.648886	+	1.12390i
$39$		0			0
$40$	−0.500000	−	0.866025i	−0.0790569	−	0.136931i
$41$		0			0			−	1.00000i	$-0.5\pi$
$41$		0			0				1.00000i	$0.5\pi$
$42$	−0.500000	−	2.59808i	−0.0771517	−	0.400892i
$43$	2.00000			0.304997			0.152499	−	0.988304i	$-0.451268\pi$
$43$	2.00000			0.304997			0.152499	+	0.988304i	$0.451268\pi$
$44$	−2.50000	−	4.33013i	−0.376889	−	0.652791i
$45$	−0.500000	+	0.866025i	−0.0745356	+	0.129099i
$46$	2.00000	−	3.46410i	0.294884	−	0.510754i
$47$	3.00000	+	5.19615i	0.437595	+	0.757937i	0.997503	−	0.0706177i	$-0.0224970\pi$
$47$	3.00000	+	5.19615i	0.437595	+	0.757937i	−0.559908	+	0.828554i	$0.689164\pi$
$48$	−1.00000			−0.144338
$49$	−6.50000	+	2.59808i	−0.928571	+	0.371154i
$50$	−4.00000			−0.565685
$51$	−2.00000	−	3.46410i	−0.280056	−	0.485071i
$52$		0			0
$53$	4.50000	−	7.79423i	0.618123	−	1.07062i	−0.371706	−	0.928351i	$-0.621227\pi$
$53$	4.50000	−	7.79423i	0.618123	−	1.07062i	0.989828	−	0.142269i	$-0.0454398\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$	5.00000			0.674200
$56$	0.500000	+	2.59808i	0.0668153	+	0.347183i
$57$	−8.00000			−1.05963
$58$	2.50000	+	4.33013i	0.328266	+	0.568574i
$59$	5.50000	−	9.52628i	0.716039	−	1.24022i	−0.246518	−	0.969138i	$-0.579287\pi$
$59$	5.50000	−	9.52628i	0.716039	−	1.24022i	0.962557	−	0.271078i	$-0.0873801\pi$
$60$	0.500000	−	0.866025i	0.0645497	−	0.111803i
$61$	3.00000	+	5.19615i	0.384111	+	0.665299i	0.991645	−	0.128994i	$-0.0411748\pi$
$61$	3.00000	+	5.19615i	0.384111	+	0.665299i	−0.607535	+	0.794293i	$0.707841\pi$
$62$	3.00000			0.381000
$63$	2.00000	−	1.73205i	0.251976	−	0.218218i
$64$	1.00000			0.125000
$65$		0			0
$66$	2.50000	−	4.33013i	0.307729	−	0.533002i
$67$	1.00000	−	1.73205i	0.122169	−	0.211604i	−0.798454	−	0.602056i	$-0.794348\pi$
$67$	1.00000	−	1.73205i	0.122169	−	0.211604i	0.920623	+	0.390453i	$0.127682\pi$
$68$	2.00000	+	3.46410i	0.242536	+	0.420084i
$69$	4.00000			0.481543
$70$	−2.50000	−	0.866025i	−0.298807	−	0.103510i
$71$	2.00000			0.237356			0.118678	−	0.992933i	$-0.462134\pi$
$71$	2.00000			0.237356			0.118678	+	0.992933i	$0.462134\pi$
$72$	−0.500000	−	0.866025i	−0.0589256	−	0.102062i
$73$	−5.00000	+	8.66025i	−0.585206	+	1.01361i	0.409644	+	0.912245i	$0.365653\pi$
$73$	−5.00000	+	8.66025i	−0.585206	+	1.01361i	−0.994850	+	0.101361i	$0.967680\pi$
$74$	2.00000	−	3.46410i	0.232495	−	0.402694i
$75$	−2.00000	−	3.46410i	−0.230940	−	0.400000i
$76$	8.00000			0.917663
$77$	−12.5000	−	4.33013i	−1.42451	−	0.493464i
$78$		0			0
$79$	−1.50000	−	2.59808i	−0.168763	−	0.292306i	0.769222	−	0.638982i	$-0.220644\pi$
$79$	−1.50000	−	2.59808i	−0.168763	−	0.292306i	−0.937985	+	0.346675i	$0.887311\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	−7.00000			−0.768350			−0.384175	−	0.923260i	$-0.625514\pi$
$83$	−7.00000			−0.768350			−0.384175	+	0.923260i	$0.625514\pi$
$84$	−2.00000	+	1.73205i	−0.218218	+	0.188982i
$85$	−4.00000			−0.433861
$86$	−1.00000	−	1.73205i	−0.107833	−	0.186772i
$87$	−2.50000	+	4.33013i	−0.268028	+	0.464238i
$88$	−2.50000	+	4.33013i	−0.266501	+	0.461593i
$89$	3.00000	+	5.19615i	0.317999	+	0.550791i	0.980071	−	0.198650i	$-0.0636557\pi$
$89$	3.00000	+	5.19615i	0.317999	+	0.550791i	−0.662071	+	0.749441i	$0.730322\pi$
$90$	1.00000			0.105409
$91$		0			0
$92$	−4.00000			−0.417029
$93$	1.50000	+	2.59808i	0.155543	+	0.269408i
$94$	3.00000	−	5.19615i	0.309426	−	0.535942i
$95$	−4.00000	+	6.92820i	−0.410391	+	0.710819i
$96$	0.500000	+	0.866025i	0.0510310	+	0.0883883i
$97$	7.00000			0.710742			0.355371	−	0.934725i	$-0.384354\pi$
$97$	7.00000			0.710742			0.355371	+	0.934725i	$0.384354\pi$
$98$	5.50000	+	4.33013i	0.555584	+	0.437409i
$99$	5.00000			0.502519
$100$	2.00000	+	3.46410i	0.200000	+	0.346410i
$101$	−5.00000	+	8.66025i	−0.497519	+	0.861727i	−0.999996	−	0.00286291i	$-0.999089\pi$
$101$	−5.00000	+	8.66025i	−0.497519	+	0.861727i	0.502477	+	0.864590i	$0.332422\pi$
$102$	−2.00000	+	3.46410i	−0.198030	+	0.342997i
$103$	−4.00000	−	6.92820i	−0.394132	−	0.682656i	0.598858	−	0.800855i	$-0.295621\pi$
$103$	−4.00000	−	6.92820i	−0.394132	−	0.682656i	−0.992990	+	0.118199i	$0.962288\pi$
$104$		0			0
$105$	−0.500000	−	2.59808i	−0.0487950	−	0.253546i
$106$	−9.00000			−0.874157
$107$	−1.50000	−	2.59808i	−0.145010	−	0.251166i	0.784366	−	0.620298i	$-0.212988\pi$
$107$	−1.50000	−	2.59808i	−0.145010	−	0.251166i	−0.929377	+	0.369132i	$0.879655\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	1.00000	−	1.73205i	0.0957826	−	0.165900i	−0.814152	−	0.580651i	$-0.802798\pi$
$109$	1.00000	−	1.73205i	0.0957826	−	0.165900i	0.909935	+	0.414751i	$0.136131\pi$
$110$	−2.50000	−	4.33013i	−0.238366	−	0.412861i
$111$	4.00000			0.379663
$112$	2.00000	−	1.73205i	0.188982	−	0.163663i
$113$	16.0000			1.50515			0.752577	−	0.658505i	$-0.228811\pi$
$113$	16.0000			1.50515			0.752577	+	0.658505i	$0.228811\pi$
$114$	4.00000	+	6.92820i	0.374634	+	0.648886i
$115$	2.00000	−	3.46410i	0.186501	−	0.323029i
$116$	2.50000	−	4.33013i	0.232119	−	0.402042i
$117$		0			0
$118$	−11.0000			−1.01263
$119$	10.0000	+	3.46410i	0.916698	+	0.317554i
$120$	−1.00000			−0.0912871
$121$	−7.00000	−	12.1244i	−0.636364	−	1.10221i
$122$	3.00000	−	5.19615i	0.271607	−	0.470438i
$123$		0			0
$124$	−1.50000	−	2.59808i	−0.134704	−	0.233314i
$125$	−9.00000			−0.804984
$126$	−2.50000	−	0.866025i	−0.222718	−	0.0771517i
$127$	9.00000			0.798621			0.399310	−	0.916816i	$-0.369250\pi$
$127$	9.00000			0.798621			0.399310	+	0.916816i	$0.369250\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	1.00000	−	1.73205i	0.0880451	−	0.152499i
$130$		0			0
$131$	−0.500000	−	0.866025i	−0.0436852	−	0.0756650i	0.843356	−	0.537355i	$-0.180577\pi$
$131$	−0.500000	−	0.866025i	−0.0436852	−	0.0756650i	−0.887041	+	0.461690i	$0.847243\pi$
$132$	−5.00000			−0.435194
$133$	16.0000	−	13.8564i	1.38738	−	1.20150i
$134$	−2.00000			−0.172774
$135$	0.500000	+	0.866025i	0.0430331	+	0.0745356i
$136$	2.00000	−	3.46410i	0.171499	−	0.297044i
$137$	1.00000	−	1.73205i	0.0854358	−	0.147979i	−0.820141	−	0.572161i	$-0.806105\pi$
$137$	1.00000	−	1.73205i	0.0854358	−	0.147979i	0.905577	+	0.424182i	$0.139438\pi$
$138$	−2.00000	−	3.46410i	−0.170251	−	0.294884i
$139$	−14.0000			−1.18746			−0.593732	−	0.804663i	$-0.702346\pi$
$139$	−14.0000			−1.18746			−0.593732	+	0.804663i	$0.702346\pi$
$140$	0.500000	+	2.59808i	0.0422577	+	0.219578i
$141$	6.00000			0.505291
$142$	−1.00000	−	1.73205i	−0.0839181	−	0.145350i
$143$		0			0
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	2.50000	+	4.33013i	0.207614	+	0.359597i
$146$	10.0000			0.827606
$147$	−1.00000	+	6.92820i	−0.0824786	+	0.571429i
$148$	−4.00000			−0.328798
$149$	9.00000	+	15.5885i	0.737309	+	1.27706i	0.953703	+	0.300750i	$0.0972370\pi$
$149$	9.00000	+	15.5885i	0.737309	+	1.27706i	−0.216394	+	0.976306i	$0.569430\pi$
$150$	−2.00000	+	3.46410i	−0.163299	+	0.282843i
$151$	−9.50000	+	16.4545i	−0.773099	+	1.33905i	0.162758	+	0.986666i	$0.447961\pi$
$151$	−9.50000	+	16.4545i	−0.773099	+	1.33905i	−0.935857	+	0.352381i	$0.885372\pi$
$152$	−4.00000	−	6.92820i	−0.324443	−	0.561951i
$153$	−4.00000			−0.323381
$154$	2.50000	+	12.9904i	0.201456	+	1.04679i
$155$	3.00000			0.240966
$156$		0			0
$157$	2.00000	−	3.46410i	0.159617	−	0.276465i	−0.775113	−	0.631822i	$-0.782307\pi$
$157$	2.00000	−	3.46410i	0.159617	−	0.276465i	0.934731	+	0.355357i	$0.115641\pi$
$158$	−1.50000	+	2.59808i	−0.119334	+	0.206692i
$159$	−4.50000	−	7.79423i	−0.356873	−	0.618123i
$160$	1.00000			0.0790569
$161$	−8.00000	+	6.92820i	−0.630488	+	0.546019i
$162$	1.00000			0.0785674
$163$	2.00000	+	3.46410i	0.156652	+	0.271329i	0.933659	−	0.358162i	$-0.116597\pi$
$163$	2.00000	+	3.46410i	0.156652	+	0.271329i	−0.777007	+	0.629492i	$0.783263\pi$
$164$		0			0
$165$	2.50000	−	4.33013i	0.194625	−	0.337100i
$166$	3.50000	+	6.06218i	0.271653	+	0.470516i
$167$	−14.0000			−1.08335			−0.541676	−	0.840587i	$-0.682210\pi$
$167$	−14.0000			−1.08335			−0.541676	+	0.840587i	$0.682210\pi$
$168$	2.50000	+	0.866025i	0.192879	+	0.0668153i
$169$	−13.0000			−1.00000
$170$	2.00000	+	3.46410i	0.153393	+	0.265684i
$171$	−4.00000	+	6.92820i	−0.305888	+	0.529813i
$172$	−1.00000	+	1.73205i	−0.0762493	+	0.132068i
$173$	−11.0000	−	19.0526i	−0.836315	−	1.44854i	−0.892956	−	0.450145i	$-0.851372\pi$
$173$	−11.0000	−	19.0526i	−0.836315	−	1.44854i	0.0566411	−	0.998395i	$-0.481961\pi$
$174$	5.00000			0.379049
$175$	10.0000	+	3.46410i	0.755929	+	0.261861i
$176$	5.00000			0.376889
$177$	−5.50000	−	9.52628i	−0.413405	−	0.716039i
$178$	3.00000	−	5.19615i	0.224860	−	0.389468i
$179$	−6.00000	+	10.3923i	−0.448461	+	0.776757i	−0.998286	−	0.0585225i	$-0.981361\pi$
$179$	−6.00000	+	10.3923i	−0.448461	+	0.776757i	0.549825	+	0.835280i	$0.314694\pi$
$180$	−0.500000	−	0.866025i	−0.0372678	−	0.0645497i
$181$		0			0			−	1.00000i	$-0.5\pi$
$181$		0			0				1.00000i	$0.5\pi$
$182$		0			0
$183$	6.00000			0.443533
$184$	2.00000	+	3.46410i	0.147442	+	0.255377i
$185$	2.00000	−	3.46410i	0.147043	−	0.254686i
$186$	1.50000	−	2.59808i	0.109985	−	0.190500i
$187$	10.0000	+	17.3205i	0.731272	+	1.26660i
$188$	−6.00000			−0.437595
$189$	−0.500000	−	2.59808i	−0.0363696	−	0.188982i
$190$	8.00000			0.580381
$191$	−12.0000	−	20.7846i	−0.868290	−	1.50392i	−0.863743	−	0.503932i	$-0.831886\pi$
$191$	−12.0000	−	20.7846i	−0.868290	−	1.50392i	−0.00454614	−	0.999990i	$-0.501447\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	−2.50000	+	4.33013i	−0.179954	+	0.311689i	−0.941865	−	0.335993i	$-0.890928\pi$
$193$	−2.50000	+	4.33013i	−0.179954	+	0.311689i	0.761911	+	0.647682i	$0.224262\pi$
$194$	−3.50000	−	6.06218i	−0.251285	−	0.435239i
$195$		0			0
$196$	1.00000	−	6.92820i	0.0714286	−	0.494872i
$197$	2.00000			0.142494			0.0712470	−	0.997459i	$-0.477302\pi$
$197$	2.00000			0.142494			0.0712470	+	0.997459i	$0.477302\pi$
$198$	−2.50000	−	4.33013i	−0.177667	−	0.307729i
$199$	2.00000	−	3.46410i	0.141776	−	0.245564i	−0.786389	−	0.617731i	$-0.788052\pi$
$199$	2.00000	−	3.46410i	0.141776	−	0.245564i	0.928166	+	0.372168i	$0.121385\pi$
$200$	2.00000	−	3.46410i	0.141421	−	0.244949i
$201$	−1.00000	−	1.73205i	−0.0705346	−	0.122169i
$202$	10.0000			0.703598
$203$	−2.50000	−	12.9904i	−0.175466	−	0.911746i
$204$	4.00000			0.280056
$205$		0			0
$206$	−4.00000	+	6.92820i	−0.278693	+	0.482711i
$207$	2.00000	−	3.46410i	0.139010	−	0.240772i
$208$		0			0
$209$	40.0000			2.76686
$210$	−2.00000	+	1.73205i	−0.138013	+	0.119523i
$211$	2.00000			0.137686			0.0688428	−	0.997628i	$-0.478069\pi$
$211$	2.00000			0.137686			0.0688428	+	0.997628i	$0.478069\pi$
$212$	4.50000	+	7.79423i	0.309061	+	0.535310i
$213$	1.00000	−	1.73205i	0.0685189	−	0.118678i
$214$	−1.50000	+	2.59808i	−0.102538	+	0.177601i
$215$	−1.00000	−	1.73205i	−0.0681994	−	0.118125i
$216$	−1.00000			−0.0680414
$217$	−7.50000	−	2.59808i	−0.509133	−	0.176369i
$218$	−2.00000			−0.135457
$219$	5.00000	+	8.66025i	0.337869	+	0.585206i
$220$	−2.50000	+	4.33013i	−0.168550	+	0.291937i
$221$		0			0
$222$	−2.00000	−	3.46410i	−0.134231	−	0.232495i
$223$	−7.00000			−0.468755			−0.234377	−	0.972146i	$-0.575305\pi$
$223$	−7.00000			−0.468755			−0.234377	+	0.972146i	$0.575305\pi$
$224$	−2.50000	−	0.866025i	−0.167038	−	0.0578638i
$225$	−4.00000			−0.266667
$226$	−8.00000	−	13.8564i	−0.532152	−	0.921714i
$227$	−1.50000	+	2.59808i	−0.0995585	+	0.172440i	−0.911502	−	0.411296i	$-0.865076\pi$
$227$	−1.50000	+	2.59808i	−0.0995585	+	0.172440i	0.811943	+	0.583736i	$0.198410\pi$
$228$	4.00000	−	6.92820i	0.264906	−	0.458831i
$229$	10.0000	+	17.3205i	0.660819	+	1.14457i	0.980401	+	0.197013i	$0.0631241\pi$
$229$	10.0000	+	17.3205i	0.660819	+	1.14457i	−0.319582	+	0.947559i	$0.603543\pi$
$230$	−4.00000			−0.263752
$231$	−10.0000	+	8.66025i	−0.657952	+	0.569803i
$232$	−5.00000			−0.328266
$233$	2.00000	+	3.46410i	0.131024	+	0.226941i	0.924072	−	0.382219i	$-0.124840\pi$
$233$	2.00000	+	3.46410i	0.131024	+	0.226941i	−0.793047	+	0.609160i	$0.791507\pi$
$234$		0			0
$235$	3.00000	−	5.19615i	0.195698	−	0.338960i
$236$	5.50000	+	9.52628i	0.358020	+	0.620108i
$237$	−3.00000			−0.194871
$238$	−2.00000	−	10.3923i	−0.129641	−	0.673633i
$239$	−12.0000			−0.776215			−0.388108	−	0.921614i	$-0.626871\pi$
$239$	−12.0000			−0.776215			−0.388108	+	0.921614i	$0.626871\pi$
$240$	0.500000	+	0.866025i	0.0322749	+	0.0559017i
$241$	12.5000	−	21.6506i	0.805196	−	1.39464i	−0.110963	−	0.993825i	$-0.535394\pi$
$241$	12.5000	−	21.6506i	0.805196	−	1.39464i	0.916159	−	0.400815i	$-0.131273\pi$
$242$	−7.00000	+	12.1244i	−0.449977	+	0.779383i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−6.00000			−0.384111
$245$	5.50000	+	4.33013i	0.351382	+	0.276642i
$246$		0			0
$247$		0			0
$248$	−1.50000	+	2.59808i	−0.0952501	+	0.164978i
$249$	−3.50000	+	6.06218i	−0.221803	+	0.384175i
$250$	4.50000	+	7.79423i	0.284605	+	0.492950i
$251$	21.0000			1.32551			0.662754	−	0.748837i	$-0.269387\pi$
$251$	21.0000			1.32551			0.662754	+	0.748837i	$0.269387\pi$
$252$	0.500000	+	2.59808i	0.0314970	+	0.163663i
$253$	−20.0000			−1.25739
$254$	−4.50000	−	7.79423i	−0.282355	−	0.489053i
$255$	−2.00000	+	3.46410i	−0.125245	+	0.216930i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	3.00000	+	5.19615i	0.187135	+	0.324127i	0.944294	−	0.329104i	$-0.106747\pi$
$257$	3.00000	+	5.19615i	0.187135	+	0.324127i	−0.757159	+	0.653231i	$0.773413\pi$
$258$	−2.00000			−0.124515
$259$	−8.00000	+	6.92820i	−0.497096	+	0.430498i
$260$		0			0
$261$	2.50000	+	4.33013i	0.154746	+	0.268028i
$262$	−0.500000	+	0.866025i	−0.0308901	+	0.0535032i
$263$	15.0000	−	25.9808i	0.924940	−	1.60204i	0.133281	−	0.991078i	$-0.457449\pi$
$263$	15.0000	−	25.9808i	0.924940	−	1.60204i	0.791658	−	0.610964i	$-0.209218\pi$
$264$	2.50000	+	4.33013i	0.153864	+	0.266501i
$265$	−9.00000			−0.552866
$266$	−20.0000	−	6.92820i	−1.22628	−	0.424795i
$267$	6.00000			0.367194
$268$	1.00000	+	1.73205i	0.0610847	+	0.105802i
$269$	−15.5000	+	26.8468i	−0.945052	+	1.63688i	−0.189404	+	0.981899i	$0.560656\pi$
$269$	−15.5000	+	26.8468i	−0.945052	+	1.63688i	−0.755648	+	0.654978i	$0.772678\pi$
$270$	0.500000	−	0.866025i	0.0304290	−	0.0527046i
$271$	−7.50000	−	12.9904i	−0.455593	−	0.789109i	0.543130	−	0.839649i	$-0.317239\pi$
$271$	−7.50000	−	12.9904i	−0.455593	−	0.789109i	−0.998722	+	0.0505395i	$0.983906\pi$
$272$	−4.00000			−0.242536
$273$		0			0
$274$	−2.00000			−0.120824
$275$	10.0000	+	17.3205i	0.603023	+	1.04447i
$276$	−2.00000	+	3.46410i	−0.120386	+	0.208514i
$277$	8.00000	−	13.8564i	0.480673	−	0.832551i	−0.519081	−	0.854725i	$-0.673726\pi$
$277$	8.00000	−	13.8564i	0.480673	−	0.832551i	0.999754	+	0.0221745i	$0.00705893\pi$
$278$	7.00000	+	12.1244i	0.419832	+	0.727171i
$279$	3.00000			0.179605
$280$	2.00000	−	1.73205i	0.119523	−	0.103510i
$281$	2.00000			0.119310			0.0596550	−	0.998219i	$-0.481000\pi$
$281$	2.00000			0.119310			0.0596550	+	0.998219i	$0.481000\pi$
$282$	−3.00000	−	5.19615i	−0.178647	−	0.309426i
$283$	−5.00000	+	8.66025i	−0.297219	+	0.514799i	−0.975499	−	0.220005i	$-0.929393\pi$
$283$	−5.00000	+	8.66025i	−0.297219	+	0.514799i	0.678280	+	0.734804i	$0.262726\pi$
$284$	−1.00000	+	1.73205i	−0.0593391	+	0.102778i
$285$	4.00000	+	6.92820i	0.236940	+	0.410391i
$286$		0			0
$287$		0			0
$288$	1.00000			0.0589256
$289$	0.500000	+	0.866025i	0.0294118	+	0.0509427i
$290$	2.50000	−	4.33013i	0.146805	−	0.254274i
$291$	3.50000	−	6.06218i	0.205174	−	0.355371i
$292$	−5.00000	−	8.66025i	−0.292603	−	0.506803i
$293$	−21.0000			−1.22683			−0.613417	−	0.789760i	$-0.710205\pi$
$293$	−21.0000			−1.22683			−0.613417	+	0.789760i	$0.710205\pi$
$294$	6.50000	−	2.59808i	0.379088	−	0.151523i
$295$	−11.0000			−0.640445
$296$	2.00000	+	3.46410i	0.116248	+	0.201347i
$297$	2.50000	−	4.33013i	0.145065	−	0.251259i
$298$	9.00000	−	15.5885i	0.521356	−	0.903015i
$299$		0			0
$300$	4.00000			0.230940
$301$	1.00000	+	5.19615i	0.0576390	+	0.299501i
$302$	19.0000			1.09333
$303$	5.00000	+	8.66025i	0.287242	+	0.497519i
$304$	−4.00000	+	6.92820i	−0.229416	+	0.397360i
$305$	3.00000	−	5.19615i	0.171780	−	0.297531i
$306$	2.00000	+	3.46410i	0.114332	+	0.198030i
$307$	28.0000			1.59804			0.799022	−	0.601302i	$-0.205351\pi$
$307$	28.0000			1.59804			0.799022	+	0.601302i	$0.205351\pi$
$308$	10.0000	−	8.66025i	0.569803	−	0.493464i
$309$	−8.00000			−0.455104
$310$	−1.50000	−	2.59808i	−0.0851943	−	0.147561i
$311$	16.0000	−	27.7128i	0.907277	−	1.57145i	0.0894452	−	0.995992i	$-0.471491\pi$
$311$	16.0000	−	27.7128i	0.907277	−	1.57145i	0.817832	−	0.575458i	$-0.195176\pi$
$312$		0			0
$313$	−0.500000	−	0.866025i	−0.0282617	−	0.0489506i	0.851549	−	0.524276i	$-0.175664\pi$
$313$	−0.500000	−	0.866025i	−0.0282617	−	0.0489506i	−0.879810	+	0.475325i	$0.842331\pi$
$314$	−4.00000			−0.225733
$315$	−2.50000	−	0.866025i	−0.140859	−	0.0487950i
$316$	3.00000			0.168763
$317$	−1.50000	−	2.59808i	−0.0842484	−	0.145922i	0.820822	−	0.571184i	$-0.193516\pi$
$317$	−1.50000	−	2.59808i	−0.0842484	−	0.145922i	−0.905071	+	0.425261i	$0.860182\pi$
$318$	−4.50000	+	7.79423i	−0.252347	+	0.437079i
$319$	12.5000	−	21.6506i	0.699866	−	1.21220i
$320$	−0.500000	−	0.866025i	−0.0279508	−	0.0484123i
$321$	−3.00000			−0.167444
$322$	10.0000	+	3.46410i	0.557278	+	0.193047i
$323$	−32.0000			−1.78053
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$		0			0
$326$	2.00000	−	3.46410i	0.110770	−	0.191859i
$327$	−1.00000	−	1.73205i	−0.0553001	−	0.0957826i
$328$		0			0
$329$	−12.0000	+	10.3923i	−0.661581	+	0.572946i
$330$	−5.00000			−0.275241
$331$	2.00000	+	3.46410i	0.109930	+	0.190404i	0.915742	−	0.401768i	$-0.131604\pi$
$331$	2.00000	+	3.46410i	0.109930	+	0.190404i	−0.805812	+	0.592172i	$0.798271\pi$
$332$	3.50000	−	6.06218i	0.192087	−	0.332705i
$333$	2.00000	−	3.46410i	0.109599	−	0.189832i
$334$	7.00000	+	12.1244i	0.383023	+	0.663415i
$335$	−2.00000			−0.109272
$336$	−0.500000	−	2.59808i	−0.0272772	−	0.141737i
$337$	9.00000			0.490261			0.245131	−	0.969490i	$-0.421169\pi$
$337$	9.00000			0.490261			0.245131	+	0.969490i	$0.421169\pi$
$338$	6.50000	+	11.2583i	0.353553	+	0.612372i
$339$	8.00000	−	13.8564i	0.434500	−	0.752577i
$340$	2.00000	−	3.46410i	0.108465	−	0.187867i
$341$	−7.50000	−	12.9904i	−0.406148	−	0.703469i
$342$	8.00000			0.432590
$343$	−10.0000	−	15.5885i	−0.539949	−	0.841698i
$344$	2.00000			0.107833
$345$	−2.00000	−	3.46410i	−0.107676	−	0.186501i
$346$	−11.0000	+	19.0526i	−0.591364	+	1.02427i
$347$	−6.00000	+	10.3923i	−0.322097	+	0.557888i	−0.980921	−	0.194409i	$-0.937721\pi$
$347$	−6.00000	+	10.3923i	−0.322097	+	0.557888i	0.658824	+	0.752297i	$0.271054\pi$
$348$	−2.50000	−	4.33013i	−0.134014	−	0.232119i
$349$	−14.0000			−0.749403			−0.374701	−	0.927146i	$-0.622255\pi$
$349$	−14.0000			−0.749403			−0.374701	+	0.927146i	$0.622255\pi$
$350$	−2.00000	−	10.3923i	−0.106904	−	0.555492i
$351$		0			0
$352$	−2.50000	−	4.33013i	−0.133250	−	0.230797i
$353$	−12.0000	+	20.7846i	−0.638696	+	1.10625i	0.347024	+	0.937856i	$0.387192\pi$
$353$	−12.0000	+	20.7846i	−0.638696	+	1.10625i	−0.985719	+	0.168397i	$0.946141\pi$
$354$	−5.50000	+	9.52628i	−0.292322	+	0.506316i
$355$	−1.00000	−	1.73205i	−0.0530745	−	0.0919277i
$356$	−6.00000			−0.317999
$357$	8.00000	−	6.92820i	0.423405	−	0.366679i
$358$	12.0000			0.634220
$359$	−5.00000	−	8.66025i	−0.263890	−	0.457071i	0.703382	−	0.710812i	$-0.251672\pi$
$359$	−5.00000	−	8.66025i	−0.263890	−	0.457071i	−0.967272	+	0.253741i	$0.918339\pi$
$360$	−0.500000	+	0.866025i	−0.0263523	+	0.0456435i
$361$	−22.5000	+	38.9711i	−1.18421	+	2.05111i
$362$		0			0
$363$	−14.0000			−0.734809
$364$		0			0
$365$	10.0000			0.523424
$366$	−3.00000	−	5.19615i	−0.156813	−	0.271607i
$367$	−8.50000	+	14.7224i	−0.443696	+	0.768505i	−0.997960	−	0.0638362i	$-0.979666\pi$
$367$	−8.50000	+	14.7224i	−0.443696	+	0.768505i	0.554264	+	0.832341i	$0.313000\pi$
$368$	2.00000	−	3.46410i	0.104257	−	0.180579i
$369$		0			0
$370$	−4.00000			−0.207950
$371$	22.5000	+	7.79423i	1.16814	+	0.404656i
$372$	−3.00000			−0.155543
$373$	16.0000	+	27.7128i	0.828449	+	1.43492i	0.899255	+	0.437425i	$0.144109\pi$
$373$	16.0000	+	27.7128i	0.828449	+	1.43492i	−0.0708063	+	0.997490i	$0.522557\pi$
$374$	10.0000	−	17.3205i	0.517088	−	0.895622i
$375$	−4.50000	+	7.79423i	−0.232379	+	0.402492i
$376$	3.00000	+	5.19615i	0.154713	+	0.267971i
$377$		0			0
$378$	−2.00000	+	1.73205i	−0.102869	+	0.0890871i
$379$	16.0000			0.821865			0.410932	−	0.911666i	$-0.365203\pi$
$379$	16.0000			0.821865			0.410932	+	0.911666i	$0.365203\pi$
$380$	−4.00000	−	6.92820i	−0.205196	−	0.355409i
$381$	4.50000	−	7.79423i	0.230542	−	0.399310i
$382$	−12.0000	+	20.7846i	−0.613973	+	1.06343i
$383$	17.0000	+	29.4449i	0.868659	+	1.50456i	0.863367	+	0.504576i	$0.168351\pi$
$383$	17.0000	+	29.4449i	0.868659	+	1.50456i	0.00529229	+	0.999986i	$0.498315\pi$
$384$	−1.00000			−0.0510310
$385$	2.50000	+	12.9904i	0.127412	+	0.662051i
$386$	5.00000			0.254493
$387$	−1.00000	−	1.73205i	−0.0508329	−	0.0880451i
$388$	−3.50000	+	6.06218i	−0.177686	+	0.307760i
$389$	1.00000	−	1.73205i	0.0507020	−	0.0878185i	−0.839561	−	0.543266i	$-0.817187\pi$
$389$	1.00000	−	1.73205i	0.0507020	−	0.0878185i	0.890263	+	0.455448i	$0.150521\pi$
$390$		0			0
$391$	16.0000			0.809155
$392$	−6.50000	+	2.59808i	−0.328300	+	0.131223i
$393$	−1.00000			−0.0504433
$394$	−1.00000	−	1.73205i	−0.0503793	−	0.0872595i
$395$	−1.50000	+	2.59808i	−0.0754732	+	0.130723i
$396$	−2.50000	+	4.33013i	−0.125630	+	0.217597i
$397$	−18.0000	−	31.1769i	−0.903394	−	1.56472i	−0.823058	−	0.567957i	$-0.807734\pi$
$397$	−18.0000	−	31.1769i	−0.903394	−	1.56472i	−0.0803356	−	0.996768i	$-0.525599\pi$
$398$	−4.00000			−0.200502
$399$	−4.00000	−	20.7846i	−0.200250	−	1.04053i
$400$	−4.00000			−0.200000
$401$	−12.0000	−	20.7846i	−0.599251	−	1.03793i	−0.992932	−	0.118686i	$-0.962132\pi$
$401$	−12.0000	−	20.7846i	−0.599251	−	1.03793i	0.393680	−	0.919247i	$-0.371202\pi$
$402$	−1.00000	+	1.73205i	−0.0498755	+	0.0863868i
$403$		0			0
$404$	−5.00000	−	8.66025i	−0.248759	−	0.430864i
$405$	1.00000			0.0496904
$406$	−10.0000	+	8.66025i	−0.496292	+	0.429801i
$407$	−20.0000			−0.991363
$408$	−2.00000	−	3.46410i	−0.0990148	−	0.171499i
$409$	12.5000	−	21.6506i	0.618085	−	1.07056i	−0.371750	−	0.928333i	$-0.621242\pi$
$409$	12.5000	−	21.6506i	0.618085	−	1.07056i	0.989835	−	0.142222i	$-0.0454247\pi$
$410$		0			0
$411$	−1.00000	−	1.73205i	−0.0493264	−	0.0854358i
$412$	8.00000			0.394132
$413$	27.5000	+	9.52628i	1.35319	+	0.468758i
$414$	−4.00000			−0.196589
$415$	3.50000	+	6.06218i	0.171808	+	0.297581i
$416$		0			0
$417$	−7.00000	+	12.1244i	−0.342791	+	0.593732i
$418$	−20.0000	−	34.6410i	−0.978232	−	1.69435i
$419$		0			0			−	1.00000i	$-0.5\pi$
$419$		0			0				1.00000i	$0.5\pi$
$420$	2.50000	+	0.866025i	0.121988	+	0.0422577i
$421$	30.0000			1.46211			0.731055	−	0.682318i	$-0.239028\pi$
$421$	30.0000			1.46211			0.731055	+	0.682318i	$0.239028\pi$
$422$	−1.00000	−	1.73205i	−0.0486792	−	0.0843149i
$423$	3.00000	−	5.19615i	0.145865	−	0.252646i
$424$	4.50000	−	7.79423i	0.218539	−	0.378521i
$425$	−8.00000	−	13.8564i	−0.388057	−	0.672134i
$426$	−2.00000			−0.0969003
$427$	−12.0000	+	10.3923i	−0.580721	+	0.502919i
$428$	3.00000			0.145010
$429$		0			0
$430$	−1.00000	+	1.73205i	−0.0482243	+	0.0835269i
$431$	−6.00000	+	10.3923i	−0.289010	+	0.500580i	−0.973574	−	0.228373i	$-0.926659\pi$
$431$	−6.00000	+	10.3923i	−0.289010	+	0.500580i	0.684564	+	0.728953i	$0.259993\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	14.0000			0.672797			0.336399	−	0.941720i	$-0.390791\pi$
$433$	14.0000			0.672797			0.336399	+	0.941720i	$0.390791\pi$
$434$	1.50000	+	7.79423i	0.0720023	+	0.374135i
$435$	5.00000			0.239732
$436$	1.00000	+	1.73205i	0.0478913	+	0.0829502i
$437$	16.0000	−	27.7128i	0.765384	−	1.32568i
$438$	5.00000	−	8.66025i	0.238909	−	0.413803i
$439$	−7.50000	−	12.9904i	−0.357955	−	0.619997i	0.629664	−	0.776868i	$-0.283193\pi$
$439$	−7.50000	−	12.9904i	−0.357955	−	0.619997i	−0.987619	+	0.156871i	$0.949859\pi$
$440$	5.00000			0.238366
$441$	5.50000	+	4.33013i	0.261905	+	0.206197i
$442$		0			0
$443$	−8.50000	−	14.7224i	−0.403847	−	0.699484i	0.590339	−	0.807155i	$-0.298994\pi$
$443$	−8.50000	−	14.7224i	−0.403847	−	0.699484i	−0.994187	+	0.107671i	$0.965661\pi$
$444$	−2.00000	+	3.46410i	−0.0949158	+	0.164399i
$445$	3.00000	−	5.19615i	0.142214	−	0.246321i
$446$	3.50000	+	6.06218i	0.165730	+	0.287052i
$447$	18.0000			0.851371
$448$	0.500000	+	2.59808i	0.0236228	+	0.122748i
$449$	16.0000			0.755087			0.377543	−	0.925992i	$-0.376769\pi$
$449$	16.0000			0.755087			0.377543	+	0.925992i	$0.376769\pi$
$450$	2.00000	+	3.46410i	0.0942809	+	0.163299i
$451$		0			0
$452$	−8.00000	+	13.8564i	−0.376288	+	0.651751i
$453$	9.50000	+	16.4545i	0.446349	+	0.773099i
$454$	3.00000			0.140797
$455$		0			0
$456$	−8.00000			−0.374634
$457$	−15.5000	−	26.8468i	−0.725059	−	1.25584i	−0.958950	−	0.283577i	$-0.908479\pi$
$457$	−15.5000	−	26.8468i	−0.725059	−	1.25584i	0.233890	−	0.972263i	$-0.424854\pi$
$458$	10.0000	−	17.3205i	0.467269	−	0.809334i
$459$	−2.00000	+	3.46410i	−0.0933520	+	0.161690i
$460$	2.00000	+	3.46410i	0.0932505	+	0.161515i
$461$	−14.0000			−0.652045			−0.326023	−	0.945362i	$-0.605709\pi$
$461$	−14.0000			−0.652045			−0.326023	+	0.945362i	$0.605709\pi$
$462$	12.5000	+	4.33013i	0.581553	+	0.201456i
$463$	16.0000			0.743583			0.371792	−	0.928316i	$-0.378744\pi$
$463$	16.0000			0.743583			0.371792	+	0.928316i	$0.378744\pi$
$464$	2.50000	+	4.33013i	0.116060	+	0.201021i
$465$	1.50000	−	2.59808i	0.0695608	−	0.120483i
$466$	2.00000	−	3.46410i	0.0926482	−	0.160471i
$467$	10.0000	+	17.3205i	0.462745	+	0.801498i	0.999097	−	0.0424970i	$-0.0135313\pi$
$467$	10.0000	+	17.3205i	0.462745	+	0.801498i	−0.536352	+	0.843995i	$0.680198\pi$
$468$		0			0
$469$	5.00000	+	1.73205i	0.230879	+	0.0799787i
$470$	−6.00000			−0.276759
$471$	−2.00000	−	3.46410i	−0.0921551	−	0.159617i
$472$	5.50000	−	9.52628i	0.253158	−	0.438483i
$473$	−5.00000	+	8.66025i	−0.229900	+	0.398199i
$474$	1.50000	+	2.59808i	0.0688973	+	0.119334i
$475$	−32.0000			−1.46826
$476$	−8.00000	+	6.92820i	−0.366679	+	0.317554i
$477$	−9.00000			−0.412082
$478$	6.00000	+	10.3923i	0.274434	+	0.475333i
$479$	−19.0000	+	32.9090i	−0.868132	+	1.50365i	−0.00422900	+	0.999991i	$0.501346\pi$
$479$	−19.0000	+	32.9090i	−0.868132	+	1.50365i	−0.863903	+	0.503658i	$0.831987\pi$
$480$	0.500000	−	0.866025i	0.0228218	−	0.0395285i
$481$		0			0
$482$	−25.0000			−1.13872
$483$	2.00000	+	10.3923i	0.0910032	+	0.472866i
$484$	14.0000			0.636364
$485$	−3.50000	−	6.06218i	−0.158927	−	0.275269i
$486$	0.500000	−	0.866025i	0.0226805	−	0.0392837i
$487$	−2.50000	+	4.33013i	−0.113286	+	0.196217i	−0.917093	−	0.398673i	$-0.869471\pi$
$487$	−2.50000	+	4.33013i	−0.113286	+	0.196217i	0.803807	+	0.594890i	$0.202804\pi$
$488$	3.00000	+	5.19615i	0.135804	+	0.235219i
$489$	4.00000			0.180886
$490$	1.00000	−	6.92820i	0.0451754	−	0.312984i
$491$	9.00000			0.406164			0.203082	−	0.979162i	$-0.434904\pi$
$491$	9.00000			0.406164			0.203082	+	0.979162i	$0.434904\pi$
$492$		0			0
$493$	−10.0000	+	17.3205i	−0.450377	+	0.780076i
$494$		0			0
$495$	−2.50000	−	4.33013i	−0.112367	−	0.194625i
$496$	3.00000			0.134704
$497$	1.00000	+	5.19615i	0.0448561	+	0.233079i
$498$	7.00000			0.313678
$499$	−5.00000	−	8.66025i	−0.223831	−	0.387686i	0.732137	−	0.681157i	$-0.238523\pi$
$499$	−5.00000	−	8.66025i	−0.223831	−	0.387686i	−0.955968	+	0.293471i	$0.905190\pi$
$500$	4.50000	−	7.79423i	0.201246	−	0.348569i
$501$	−7.00000	+	12.1244i	−0.312737	+	0.541676i
$502$	−10.5000	−	18.1865i	−0.468638	−	0.811705i
$503$		0			0			−	1.00000i	$-0.5\pi$
$503$		0			0				1.00000i	$0.5\pi$
$504$	2.00000	−	1.73205i	0.0890871	−	0.0771517i
$505$	10.0000			0.444994
$506$	10.0000	+	17.3205i	0.444554	+	0.769991i
$507$	−6.50000	+	11.2583i	−0.288675	+	0.500000i
$508$	−4.50000	+	7.79423i	−0.199655	+	0.345813i
$509$	−7.50000	−	12.9904i	−0.332432	−	0.575789i	0.650556	−	0.759458i	$-0.274536\pi$
$509$	−7.50000	−	12.9904i	−0.332432	−	0.575789i	−0.982988	+	0.183669i	$0.941202\pi$
$510$	4.00000			0.177123
$511$	−25.0000	−	8.66025i	−1.10593	−	0.383107i
$512$	1.00000			0.0441942
$513$	4.00000	+	6.92820i	0.176604	+	0.305888i
$514$	3.00000	−	5.19615i	0.132324	−	0.229192i
$515$	−4.00000	+	6.92820i	−0.176261	+	0.305293i
$516$	1.00000	+	1.73205i	0.0440225	+	0.0762493i
$517$	−30.0000			−1.31940
$518$	10.0000	+	3.46410i	0.439375	+	0.152204i
$519$	−22.0000			−0.965693
$520$		0			0
$521$	9.00000	−	15.5885i	0.394297	−	0.682943i	−0.598714	−	0.800963i	$-0.704321\pi$
$521$	9.00000	−	15.5885i	0.394297	−	0.682943i	0.993011	+	0.118020i	$0.0376547\pi$
$522$	2.50000	−	4.33013i	0.109422	−	0.189525i
$523$	−4.00000	−	6.92820i	−0.174908	−	0.302949i	0.765222	−	0.643767i	$-0.222629\pi$
$523$	−4.00000	−	6.92820i	−0.174908	−	0.302949i	−0.940129	+	0.340818i	$0.889296\pi$
$524$	1.00000			0.0436852
$525$	8.00000	−	6.92820i	0.349149	−	0.302372i
$526$	−30.0000			−1.30806
$527$	6.00000	+	10.3923i	0.261364	+	0.452696i
$528$	2.50000	−	4.33013i	0.108799	−	0.188445i
$529$	3.50000	−	6.06218i	0.152174	−	0.263573i
$530$	4.50000	+	7.79423i	0.195468	+	0.338560i
$531$	−11.0000			−0.477359
$532$	4.00000	+	20.7846i	0.173422	+	0.901127i
$533$		0			0
$534$	−3.00000	−	5.19615i	−0.129823	−	0.224860i
$535$	−1.50000	+	2.59808i	−0.0648507	+	0.112325i
$536$	1.00000	−	1.73205i	0.0431934	−	0.0748132i
$537$	6.00000	+	10.3923i	0.258919	+	0.448461i
$538$	31.0000			1.33650
$539$	5.00000	−	34.6410i	0.215365	−	1.49209i
$540$	−1.00000			−0.0430331
$541$	9.00000	+	15.5885i	0.386940	+	0.670200i	0.992036	−	0.125952i	$-0.0401986\pi$
$541$	9.00000	+	15.5885i	0.386940	+	0.670200i	−0.605096	+	0.796152i	$0.706865\pi$
$542$	−7.50000	+	12.9904i	−0.322153	+	0.557985i
$543$		0			0
$544$	2.00000	+	3.46410i	0.0857493	+	0.148522i
$545$	−2.00000			−0.0856706
$546$		0			0
$547$	−12.0000			−0.513083			−0.256541	−	0.966533i	$-0.582583\pi$
$547$	−12.0000			−0.513083			−0.256541	+	0.966533i	$0.582583\pi$
$548$	1.00000	+	1.73205i	0.0427179	+	0.0739895i
$549$	3.00000	−	5.19615i	0.128037	−	0.221766i
$550$	10.0000	−	17.3205i	0.426401	−	0.738549i
$551$	20.0000	+	34.6410i	0.852029	+	1.47576i
$552$	4.00000			0.170251
$553$	6.00000	−	5.19615i	0.255146	−	0.220963i
$554$	−16.0000			−0.679775
$555$	−2.00000	−	3.46410i	−0.0848953	−	0.147043i
$556$	7.00000	−	12.1244i	0.296866	−	0.514187i
$557$	11.5000	−	19.9186i	0.487271	−	0.843978i	−0.512622	−	0.858614i	$-0.671326\pi$
$557$	11.5000	−	19.9186i	0.487271	−	0.843978i	0.999893	+	0.0146368i	$0.00465919\pi$
$558$	−1.50000	−	2.59808i	−0.0635001	−	0.109985i
$559$		0			0
$560$	−2.50000	−	0.866025i	−0.105644	−	0.0365963i
$561$	20.0000			0.844401
$562$	−1.00000	−	1.73205i	−0.0421825	−	0.0730622i
$563$	−8.50000	+	14.7224i	−0.358232	+	0.620477i	−0.987666	−	0.156578i	$-0.949954\pi$
$563$	−8.50000	+	14.7224i	−0.358232	+	0.620477i	0.629433	+	0.777055i	$0.283287\pi$
$564$	−3.00000	+	5.19615i	−0.126323	+	0.218797i
$565$	−8.00000	−	13.8564i	−0.336563	−	0.582943i
$566$	10.0000			0.420331
$567$	−2.50000	−	0.866025i	−0.104990	−	0.0363696i
$568$	2.00000			0.0839181
$569$	−12.0000	−	20.7846i	−0.503066	−	0.871336i	−0.999994	−	0.00354413i	$-0.998872\pi$
$569$	−12.0000	−	20.7846i	−0.503066	−	0.871336i	0.496928	−	0.867792i	$-0.334461\pi$
$570$	4.00000	−	6.92820i	0.167542	−	0.290191i
$571$	15.0000	−	25.9808i	0.627730	−	1.08726i	−0.360276	−	0.932846i	$-0.617317\pi$
$571$	15.0000	−	25.9808i	0.627730	−	1.08726i	0.988006	−	0.154415i	$-0.0493493\pi$
$572$		0			0
$573$	−24.0000			−1.00261
$574$		0			0
$575$	16.0000			0.667246
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−15.5000	+	26.8468i	−0.645273	+	1.11765i	0.338965	+	0.940799i	$0.389923\pi$
$577$	−15.5000	+	26.8468i	−0.645273	+	1.11765i	−0.984238	+	0.176847i	$0.943410\pi$
$578$	0.500000	−	0.866025i	0.0207973	−	0.0360219i
$579$	2.50000	+	4.33013i	0.103896	+	0.179954i
$580$	−5.00000			−0.207614
$581$	−3.50000	−	18.1865i	−0.145204	−	0.754505i
$582$	−7.00000			−0.290159
$583$	22.5000	+	38.9711i	0.931855	+	1.61402i
$584$	−5.00000	+	8.66025i	−0.206901	+	0.358364i
$585$		0			0
$586$	10.5000	+	18.1865i	0.433751	+	0.751279i
$587$	35.0000			1.44460			0.722302	−	0.691577i	$-0.243084\pi$
$587$	35.0000			1.44460			0.722302	+	0.691577i	$0.243084\pi$
$588$	−5.50000	−	4.33013i	−0.226816	−	0.178571i
$589$	24.0000			0.988903
$590$	5.50000	+	9.52628i	0.226431	+	0.392191i
$591$	1.00000	−	1.73205i	0.0411345	−	0.0712470i
$592$	2.00000	−	3.46410i	0.0821995	−	0.142374i
$593$	−18.0000	−	31.1769i	−0.739171	−	1.28028i	−0.952869	−	0.303383i	$-0.901884\pi$
$593$	−18.0000	−	31.1769i	−0.739171	−	1.28028i	0.213697	−	0.976900i	$-0.431449\pi$
$594$	−5.00000			−0.205152
$595$	−2.00000	−	10.3923i	−0.0819920	−	0.426043i
$596$	−18.0000			−0.737309
$597$	−2.00000	−	3.46410i	−0.0818546	−	0.141776i
$598$		0			0
$599$	15.0000	−	25.9808i	0.612883	−	1.06155i	−0.377869	−	0.925859i	$-0.623343\pi$
$599$	15.0000	−	25.9808i	0.612883	−	1.06155i	0.990752	−	0.135686i	$-0.0433238\pi$
$600$	−2.00000	−	3.46410i	−0.0816497	−	0.141421i
$601$	35.0000			1.42768			0.713840	−	0.700309i	$-0.246954\pi$
$601$	35.0000			1.42768			0.713840	+	0.700309i	$0.246954\pi$
$602$	4.00000	−	3.46410i	0.163028	−	0.141186i
$603$	−2.00000			−0.0814463
$604$	−9.50000	−	16.4545i	−0.386550	−	0.669523i
$605$	−7.00000	+	12.1244i	−0.284590	+	0.492925i
$606$	5.00000	−	8.66025i	0.203111	−	0.351799i
$607$	13.5000	+	23.3827i	0.547948	+	0.949074i	0.998415	+	0.0562808i	$0.0179242\pi$
$607$	13.5000	+	23.3827i	0.547948	+	0.949074i	−0.450467	+	0.892793i	$0.648742\pi$
$608$	8.00000			0.324443
$609$	−12.5000	−	4.33013i	−0.506526	−	0.175466i
$610$	−6.00000			−0.242933
$611$		0			0
$612$	2.00000	−	3.46410i	0.0808452	−	0.140028i
$613$	−6.00000	+	10.3923i	−0.242338	+	0.419741i	−0.961380	−	0.275225i	$-0.911248\pi$
$613$	−6.00000	+	10.3923i	−0.242338	+	0.419741i	0.719042	+	0.694967i	$0.244581\pi$
$614$	−14.0000	−	24.2487i	−0.564994	−	0.978598i
$615$		0			0
$616$	−12.5000	−	4.33013i	−0.503639	−	0.174466i
$617$	2.00000			0.0805170			0.0402585	−	0.999189i	$-0.487182\pi$
$617$	2.00000			0.0805170			0.0402585	+	0.999189i	$0.487182\pi$
$618$	4.00000	+	6.92820i	0.160904	+	0.278693i
$619$	−5.00000	+	8.66025i	−0.200967	+	0.348085i	−0.948840	−	0.315757i	$-0.897742\pi$
$619$	−5.00000	+	8.66025i	−0.200967	+	0.348085i	0.747873	+	0.663842i	$0.231075\pi$
$620$	−1.50000	+	2.59808i	−0.0602414	+	0.104341i
$621$	−2.00000	−	3.46410i	−0.0802572	−	0.139010i
$622$	−32.0000			−1.28308
$623$	−12.0000	+	10.3923i	−0.480770	+	0.416359i
$624$		0			0
$625$	−5.50000	−	9.52628i	−0.220000	−	0.381051i
$626$	−0.500000	+	0.866025i	−0.0199840	+	0.0346133i
$627$	20.0000	−	34.6410i	0.798723	−	1.38343i
$628$	2.00000	+	3.46410i	0.0798087	+	0.138233i
$629$	16.0000			0.637962
$630$	0.500000	+	2.59808i	0.0199205	+	0.103510i
$631$	−19.0000			−0.756378			−0.378189	−	0.925728i	$-0.623453\pi$
$631$	−19.0000			−0.756378			−0.378189	+	0.925728i	$0.623453\pi$
$632$	−1.50000	−	2.59808i	−0.0596668	−	0.103346i
$633$	1.00000	−	1.73205i	0.0397464	−	0.0688428i
$634$	−1.50000	+	2.59808i	−0.0595726	+	0.103183i
$635$	−4.50000	−	7.79423i	−0.178577	−	0.309305i
$636$	9.00000			0.356873
$637$		0			0
$638$	−25.0000			−0.989759
$639$	−1.00000	−	1.73205i	−0.0395594	−	0.0685189i
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	−13.0000	+	22.5167i	−0.513469	+	0.889355i	0.486409	+	0.873731i	$0.338307\pi$
$641$	−13.0000	+	22.5167i	−0.513469	+	0.889355i	−0.999878	+	0.0156233i	$0.995027\pi$
$642$	1.50000	+	2.59808i	0.0592003	+	0.102538i
$643$	14.0000			0.552106			0.276053	−	0.961142i	$-0.410973\pi$
$643$	14.0000			0.552106			0.276053	+	0.961142i	$0.410973\pi$
$644$	−2.00000	−	10.3923i	−0.0788110	−	0.409514i
$645$	−2.00000			−0.0787499
$646$	16.0000	+	27.7128i	0.629512	+	1.09035i
$647$	9.00000	−	15.5885i	0.353827	−	0.612845i	−0.633090	−	0.774078i	$-0.718214\pi$
$647$	9.00000	−	15.5885i	0.353827	−	0.612845i	0.986916	+	0.161233i	$0.0515470\pi$
$648$	−0.500000	+	0.866025i	−0.0196419	+	0.0340207i
$649$	27.5000	+	47.6314i	1.07947	+	1.86970i
$650$		0			0
$651$	−6.00000	+	5.19615i	−0.235159	+	0.203653i
$652$	−4.00000			−0.156652
$653$	19.5000	+	33.7750i	0.763094	+	1.32172i	0.941248	+	0.337715i	$0.109654\pi$
$653$	19.5000	+	33.7750i	0.763094	+	1.32172i	−0.178154	+	0.984003i	$0.557013\pi$
$654$	−1.00000	+	1.73205i	−0.0391031	+	0.0677285i
$655$	−0.500000	+	0.866025i	−0.0195366	+	0.0338384i
$656$		0			0
$657$	10.0000			0.390137
$658$	15.0000	+	5.19615i	0.584761	+	0.202567i
$659$	−40.0000			−1.55818			−0.779089	−	0.626913i	$-0.784318\pi$
$659$	−40.0000			−1.55818			−0.779089	+	0.626913i	$0.784318\pi$
$660$	2.50000	+	4.33013i	0.0973124	+	0.168550i
$661$	−5.00000	+	8.66025i	−0.194477	+	0.336845i	−0.946729	−	0.322031i	$-0.895634\pi$
$661$	−5.00000	+	8.66025i	−0.194477	+	0.336845i	0.752252	+	0.658876i	$0.228968\pi$
$662$	2.00000	−	3.46410i	0.0777322	−	0.134636i
$663$		0			0
$664$	−7.00000			−0.271653
$665$	−20.0000	−	6.92820i	−0.775567	−	0.268664i
$666$	−4.00000			−0.154997
$667$	−10.0000	−	17.3205i	−0.387202	−	0.670653i
$668$	7.00000	−	12.1244i	0.270838	−	0.469105i
$669$	−3.50000	+	6.06218i	−0.135318	+	0.234377i
$670$	1.00000	+	1.73205i	0.0386334	+	0.0669150i
$671$	−30.0000			−1.15814
$672$	−2.00000	+	1.73205i	−0.0771517	+	0.0668153i
$673$	−19.0000			−0.732396			−0.366198	−	0.930537i	$-0.619341\pi$
$673$	−19.0000			−0.732396			−0.366198	+	0.930537i	$0.619341\pi$
$674$	−4.50000	−	7.79423i	−0.173334	−	0.300222i
$675$	−2.00000	+	3.46410i	−0.0769800	+	0.133333i
$676$	6.50000	−	11.2583i	0.250000	−	0.433013i
$677$	13.5000	+	23.3827i	0.518847	+	0.898670i	0.999760	+	0.0219013i	$0.00697196\pi$
$677$	13.5000	+	23.3827i	0.518847	+	0.898670i	−0.480913	+	0.876768i	$0.659695\pi$
$678$	−16.0000			−0.614476
$679$	3.50000	+	18.1865i	0.134318	+	0.697935i
$680$	−4.00000			−0.153393
$681$	1.50000	+	2.59808i	0.0574801	+	0.0995585i
$682$	−7.50000	+	12.9904i	−0.287190	+	0.497427i
$683$	4.50000	−	7.79423i	0.172188	−	0.298238i	−0.766997	−	0.641651i	$-0.778250\pi$
$683$	4.50000	−	7.79423i	0.172188	−	0.298238i	0.939184	+	0.343413i	$0.111583\pi$
$684$	−4.00000	−	6.92820i	−0.152944	−	0.264906i
$685$	−2.00000			−0.0764161
$686$	−8.50000	+	16.4545i	−0.324532	+	0.628235i
$687$	20.0000			0.763048
$688$	−1.00000	−	1.73205i	−0.0381246	−	0.0660338i
$689$		0			0
$690$	−2.00000	+	3.46410i	−0.0761387	+	0.131876i
$691$	−4.00000	−	6.92820i	−0.152167	−	0.263561i	0.779857	−	0.625958i	$-0.215292\pi$
$691$	−4.00000	−	6.92820i	−0.152167	−	0.263561i	−0.932024	+	0.362397i	$0.881959\pi$
$692$	22.0000			0.836315
$693$	2.50000	+	12.9904i	0.0949671	+	0.493464i
$694$	12.0000			0.455514
$695$	7.00000	+	12.1244i	0.265525	+	0.459903i
$696$	−2.50000	+	4.33013i	−0.0947623	+	0.164133i
$697$		0			0
$698$	7.00000	+	12.1244i	0.264954	+	0.458914i
$699$	4.00000			0.151294
$700$	−8.00000	+	6.92820i	−0.302372	+	0.261861i
$701$	−5.00000			−0.188847			−0.0944237	−	0.995532i	$-0.530101\pi$
$701$	−5.00000			−0.188847			−0.0944237	+	0.995532i	$0.530101\pi$
$702$		0			0
$703$	16.0000	−	27.7128i	0.603451	−	1.04521i
$704$	−2.50000	+	4.33013i	−0.0942223	+	0.163198i
$705$	−3.00000	−	5.19615i	−0.112987	−	0.195698i
$706$	24.0000			0.903252
$707$	−25.0000	−	8.66025i	−0.940222	−	0.325702i
$708$	11.0000			0.413405
$709$	−19.0000	−	32.9090i	−0.713560	−	1.23592i	−0.963512	−	0.267664i	$-0.913748\pi$
$709$	−19.0000	−	32.9090i	−0.713560	−	1.23592i	0.249952	−	0.968258i	$-0.419585\pi$
$710$	−1.00000	+	1.73205i	−0.0375293	+	0.0650027i
$711$	−1.50000	+	2.59808i	−0.0562544	+	0.0974355i
$712$	3.00000	+	5.19615i	0.112430	+	0.194734i
$713$	−12.0000			−0.449404
$714$	−10.0000	−	3.46410i	−0.374241	−	0.129641i
$715$		0			0
$716$	−6.00000	−	10.3923i	−0.224231	−	0.388379i
$717$	−6.00000	+	10.3923i	−0.224074	+	0.388108i
$718$	−5.00000	+	8.66025i	−0.186598	+	0.323198i
$719$	3.00000	+	5.19615i	0.111881	+	0.193784i	0.916529	−	0.399969i	$-0.130979\pi$
$719$	3.00000	+	5.19615i	0.111881	+	0.193784i	−0.804648	+	0.593753i	$0.797646\pi$
$720$	1.00000			0.0372678
$721$	16.0000	−	13.8564i	0.595871	−	0.516040i
$722$	45.0000			1.67473
$723$	−12.5000	−	21.6506i	−0.464880	−	0.805196i
$724$		0			0
$725$	−10.0000	+	17.3205i	−0.371391	+	0.643268i
$726$	7.00000	+	12.1244i	0.259794	+	0.449977i
$727$	7.00000			0.259616			0.129808	−	0.991539i	$-0.458564\pi$
$727$	7.00000			0.259616			0.129808	+	0.991539i	$0.458564\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	−5.00000	−	8.66025i	−0.185058	−	0.320530i
$731$	4.00000	−	6.92820i	0.147945	−	0.256249i
$732$	−3.00000	+	5.19615i	−0.110883	+	0.192055i
$733$	3.00000	+	5.19615i	0.110808	+	0.191924i	0.916096	−	0.400959i	$-0.131323\pi$
$733$	3.00000	+	5.19615i	0.110808	+	0.191924i	−0.805289	+	0.592883i	$0.797990\pi$
$734$	17.0000			0.627481
$735$	6.50000	−	2.59808i	0.239756	−	0.0958315i
$736$	−4.00000			−0.147442
$737$	5.00000	+	8.66025i	0.184177	+	0.319005i
$738$		0			0
$739$	15.0000	−	25.9808i	0.551784	−	0.955718i	−0.446362	−	0.894852i	$-0.647281\pi$
$739$	15.0000	−	25.9808i	0.551784	−	0.955718i	0.998146	−	0.0608653i	$-0.0193860\pi$
$740$	2.00000	+	3.46410i	0.0735215	+	0.127343i
$741$		0			0
$742$	−4.50000	−	23.3827i	−0.165200	−	0.858405i
$743$	30.0000			1.10059			0.550297	−	0.834969i	$-0.314515\pi$
$743$	30.0000			1.10059			0.550297	+	0.834969i	$0.314515\pi$
$744$	1.50000	+	2.59808i	0.0549927	+	0.0952501i
$745$	9.00000	−	15.5885i	0.329734	−	0.571117i
$746$	16.0000	−	27.7128i	0.585802	−	1.01464i
$747$	3.50000	+	6.06218i	0.128058	+	0.221803i
$748$	−20.0000			−0.731272
$749$	6.00000	−	5.19615i	0.219235	−	0.189863i
$750$	9.00000			0.328634
$751$	−22.5000	−	38.9711i	−0.821037	−	1.42208i	−0.904911	−	0.425601i	$-0.860063\pi$
$751$	−22.5000	−	38.9711i	−0.821037	−	1.42208i	0.0838743	−	0.996476i	$-0.473271\pi$
$752$	3.00000	−	5.19615i	0.109399	−	0.189484i
$753$	10.5000	−	18.1865i	0.382641	−	0.662754i
$754$		0			0
$755$	19.0000			0.691481
$756$	2.50000	+	0.866025i	0.0909241	+	0.0314970i
$757$	−54.0000			−1.96266			−0.981332	−	0.192323i	$-0.938398\pi$
$757$	−54.0000			−1.96266			−0.981332	+	0.192323i	$0.938398\pi$
$758$	−8.00000	−	13.8564i	−0.290573	−	0.503287i
$759$	−10.0000	+	17.3205i	−0.362977	+	0.628695i
$760$	−4.00000	+	6.92820i	−0.145095	+	0.251312i
$761$	−4.00000	−	6.92820i	−0.145000	−	0.251147i	0.784373	−	0.620289i	$-0.212985\pi$
$761$	−4.00000	−	6.92820i	−0.145000	−	0.251147i	−0.929373	+	0.369142i	$0.879652\pi$
$762$	−9.00000			−0.326036
$763$	5.00000	+	1.73205i	0.181012	+	0.0627044i
$764$	24.0000			0.868290
$765$	2.00000	+	3.46410i	0.0723102	+	0.125245i
$766$	17.0000	−	29.4449i	0.614235	−	1.06389i
$767$		0			0
$768$	0.500000	+	0.866025i	0.0180422	+	0.0312500i
$769$	−35.0000			−1.26213			−0.631066	−	0.775729i	$-0.717382\pi$
$769$	−35.0000			−1.26213			−0.631066	+	0.775729i	$0.717382\pi$
$770$	10.0000	−	8.66025i	0.360375	−	0.312094i
$771$	6.00000			0.216085
$772$	−2.50000	−	4.33013i	−0.0899770	−	0.155845i
$773$	−5.00000	+	8.66025i	−0.179838	+	0.311488i	−0.941825	−	0.336104i	$-0.890891\pi$
$773$	−5.00000	+	8.66025i	−0.179838	+	0.311488i	0.761987	+	0.647592i	$0.224224\pi$
$774$	−1.00000	+	1.73205i	−0.0359443	+	0.0622573i
$775$	6.00000	+	10.3923i	0.215526	+	0.373303i
$776$	7.00000			0.251285
$777$	2.00000	+	10.3923i	0.0717496	+	0.372822i
$778$	−2.00000			−0.0717035
$779$		0			0
$780$		0			0
$781$	−5.00000	+	8.66025i	−0.178914	+	0.309888i
$782$	−8.00000	−	13.8564i	−0.286079	−	0.495504i
$783$	5.00000			0.178685
$784$	5.50000	+	4.33013i	0.196429	+	0.154647i
$785$	−4.00000			−0.142766
$786$	0.500000	+	0.866025i	0.0178344	+	0.0308901i
$787$	9.00000	−	15.5885i	0.320815	−	0.555668i	−0.659841	−	0.751405i	$-0.729376\pi$
$787$	9.00000	−	15.5885i	0.320815	−	0.555668i	0.980656	+	0.195737i	$0.0627098\pi$
$788$	−1.00000	+	1.73205i	−0.0356235	+	0.0617018i
$789$	−15.0000	−	25.9808i	−0.534014	−	0.924940i
$790$	3.00000			0.106735
$791$	8.00000	+	41.5692i	0.284447	+	1.47803i
$792$	5.00000			0.177667
$793$		0			0
$794$	−18.0000	+	31.1769i	−0.638796	+	1.10643i
$795$	−4.50000	+	7.79423i	−0.159599	+	0.276433i
$796$	2.00000	+	3.46410i	0.0708881	+	0.122782i
$797$	21.0000			0.743858			0.371929	−	0.928261i	$-0.378696\pi$
$797$	21.0000			0.743858			0.371929	+	0.928261i	$0.378696\pi$
$798$	−16.0000	+	13.8564i	−0.566394	+	0.490511i
$799$	24.0000			0.849059
$800$	2.00000	+	3.46410i	0.0707107	+	0.122474i
$801$	3.00000	−	5.19615i	0.106000	−	0.183597i
$802$	−12.0000	+	20.7846i	−0.423735	+	0.733930i
$803$	−25.0000	−	43.3013i	−0.882231	−	1.52807i
$804$	2.00000			0.0705346
$805$	10.0000	+	3.46410i	0.352454	+	0.122094i
$806$		0			0
$807$	15.5000	+	26.8468i	0.545626	+	0.945052i
$808$	−5.00000	+	8.66025i	−0.175899	+	0.304667i
$809$	−20.0000	+	34.6410i	−0.703163	+	1.21791i	0.264188	+	0.964471i	$0.414896\pi$
$809$	−20.0000	+	34.6410i	−0.703163	+	1.21791i	−0.967351	+	0.253442i	$0.918437\pi$
$810$	−0.500000	−	0.866025i	−0.0175682	−	0.0304290i
$811$	−14.0000			−0.491606			−0.245803	−	0.969320i	$-0.579052\pi$
$811$	−14.0000			−0.491606			−0.245803	+	0.969320i	$0.579052\pi$
$812$	12.5000	+	4.33013i	0.438664	+	0.151958i
$813$	−15.0000			−0.526073
$814$	10.0000	+	17.3205i	0.350500	+	0.607083i
$815$	2.00000	−	3.46410i	0.0700569	−	0.121342i
$816$	−2.00000	+	3.46410i	−0.0700140	+	0.121268i
$817$	−8.00000	−	13.8564i	−0.279885	−	0.484774i
$818$	−25.0000			−0.874105
$819$		0			0
$820$		0			0
$821$	12.5000	+	21.6506i	0.436253	+	0.755612i	0.997397	−	0.0721058i	$-0.0229719\pi$
$821$	12.5000	+	21.6506i	0.436253	+	0.755612i	−0.561144	+	0.827718i	$0.689639\pi$
$822$	−1.00000	+	1.73205i	−0.0348790	+	0.0604122i
$823$	−20.0000	+	34.6410i	−0.697156	+	1.20751i	0.272292	+	0.962215i	$0.412218\pi$
$823$	−20.0000	+	34.6410i	−0.697156	+	1.20751i	−0.969448	+	0.245295i	$0.921115\pi$
$824$	−4.00000	−	6.92820i	−0.139347	−	0.241355i
$825$	20.0000			0.696311
$826$	−5.50000	−	28.5788i	−0.191369	−	0.994385i
$827$	9.00000			0.312961			0.156480	−	0.987681i	$-0.449985\pi$
$827$	9.00000			0.312961			0.156480	+	0.987681i	$0.449985\pi$
$828$	2.00000	+	3.46410i	0.0695048	+	0.120386i
$829$	16.0000	−	27.7128i	0.555703	−	0.962506i	−0.442145	−	0.896943i	$-0.645783\pi$
$829$	16.0000	−	27.7128i	0.555703	−	0.962506i	0.997848	−	0.0655624i	$-0.0208842\pi$
$830$	3.50000	−	6.06218i	0.121487	−	0.210421i
$831$	−8.00000	−	13.8564i	−0.277517	−	0.480673i
$832$		0			0
$833$	−4.00000	+	27.7128i	−0.138592	+	0.960192i
$834$	14.0000			0.484780
$835$	7.00000	+	12.1244i	0.242245	+	0.419581i
$836$	−20.0000	+	34.6410i	−0.691714	+	1.19808i
$837$	1.50000	−	2.59808i	0.0518476	−	0.0898027i
$838$		0			0
$839$	−28.0000			−0.966667			−0.483334	−	0.875436i	$-0.660574\pi$
$839$	−28.0000			−0.966667			−0.483334	+	0.875436i	$0.660574\pi$
$840$	−0.500000	−	2.59808i	−0.0172516	−	0.0896421i
$841$	−4.00000			−0.137931
$842$	−15.0000	−	25.9808i	−0.516934	−	0.895356i
$843$	1.00000	−	1.73205i	0.0344418	−	0.0596550i
$844$	−1.00000	+	1.73205i	−0.0344214	+	0.0596196i
$845$	6.50000	+	11.2583i	0.223607	+	0.387298i
$846$	−6.00000			−0.206284
$847$	28.0000	−	24.2487i	0.962091	−	0.833196i
$848$	−9.00000			−0.309061
$849$	5.00000	+	8.66025i	0.171600	+	0.297219i
$850$	−8.00000	+	13.8564i	−0.274398	+	0.475271i
$851$	−8.00000	+	13.8564i	−0.274236	+	0.474991i
$852$	1.00000	+	1.73205i	0.0342594	+	0.0593391i
$853$	14.0000			0.479351			0.239675	−	0.970853i	$-0.422959\pi$
$853$	14.0000			0.479351			0.239675	+	0.970853i	$0.422959\pi$
$854$	15.0000	+	5.19615i	0.513289	+	0.177809i
$855$	8.00000			0.273594
$856$	−1.50000	−	2.59808i	−0.0512689	−	0.0888004i
$857$	9.00000	−	15.5885i	0.307434	−	0.532492i	−0.670366	−	0.742030i	$-0.733863\pi$
$857$	9.00000	−	15.5885i	0.307434	−	0.532492i	0.977800	+	0.209539i	$0.0671963\pi$
$858$		0			0
$859$	17.0000	+	29.4449i	0.580033	+	1.00465i	0.995475	+	0.0950262i	$0.0302935\pi$
$859$	17.0000	+	29.4449i	0.580033	+	1.00465i	−0.415442	+	0.909620i	$0.636373\pi$
$860$	2.00000			0.0681994
$861$		0			0
$862$	12.0000			0.408722
$863$	−5.00000	−	8.66025i	−0.170202	−	0.294798i	0.768288	−	0.640104i	$-0.221109\pi$
$863$	−5.00000	−	8.66025i	−0.170202	−	0.294798i	−0.938490	+	0.345305i	$0.887775\pi$
$864$	0.500000	−	0.866025i	0.0170103	−	0.0294628i
$865$	−11.0000	+	19.0526i	−0.374011	+	0.647806i
$866$	−7.00000	−	12.1244i	−0.237870	−	0.412002i
$867$	1.00000			0.0339618
$868$	6.00000	−	5.19615i	0.203653	−	0.176369i
$869$	15.0000			0.508840
$870$	−2.50000	−	4.33013i	−0.0847579	−	0.146805i
$871$		0			0
$872$	1.00000	−	1.73205i	0.0338643	−	0.0586546i
$873$	−3.50000	−	6.06218i	−0.118457	−	0.205174i
$874$	−32.0000			−1.08242
$875$	−4.50000	−	23.3827i	−0.152128	−	0.790479i
$876$	−10.0000			−0.337869
$877$	16.0000	+	27.7128i	0.540282	+	0.935795i	0.998888	+	0.0471555i	$0.0150156\pi$
$877$	16.0000	+	27.7128i	0.540282	+	0.935795i	−0.458606	+	0.888640i	$0.651651\pi$
$878$	−7.50000	+	12.9904i	−0.253113	+	0.438404i
$879$	−10.5000	+	18.1865i	−0.354156	+	0.613417i
$880$	−2.50000	−	4.33013i	−0.0842750	−	0.145969i
$881$	−42.0000			−1.41502			−0.707508	−	0.706705i	$-0.750181\pi$
$881$	−42.0000			−1.41502			−0.707508	+	0.706705i	$0.750181\pi$
$882$	1.00000	−	6.92820i	0.0336718	−	0.233285i
$883$	−40.0000			−1.34611			−0.673054	−	0.739594i	$-0.735018\pi$
$883$	−40.0000			−1.34611			−0.673054	+	0.739594i	$0.735018\pi$
$884$		0			0
$885$	−5.50000	+	9.52628i	−0.184880	+	0.320222i
$886$	−8.50000	+	14.7224i	−0.285563	+	0.494610i
$887$	−18.0000	−	31.1769i	−0.604381	−	1.04682i	−0.992149	−	0.125061i	$-0.960087\pi$
$887$	−18.0000	−	31.1769i	−0.604381	−	1.04682i	0.387768	−	0.921757i	$-0.373246\pi$
$888$	4.00000			0.134231
$889$	4.50000	+	23.3827i	0.150925	+	0.784230i
$890$	−6.00000			−0.201120
$891$	−2.50000	−	4.33013i	−0.0837532	−	0.145065i
$892$	3.50000	−	6.06218i	0.117189	−	0.202977i
$893$	24.0000	−	41.5692i	0.803129	−	1.39106i
$894$	−9.00000	−	15.5885i	−0.301005	−	0.521356i
$895$	12.0000			0.401116
$896$	2.00000	−	1.73205i	0.0668153	−	0.0578638i
$897$		0			0
$898$	−8.00000	−	13.8564i	−0.266963	−	0.462394i
$899$	7.50000	−	12.9904i	0.250139	−	0.433253i
$900$	2.00000	−	3.46410i	0.0666667	−	0.115470i
$901$	−18.0000	−	31.1769i	−0.599667	−	1.03865i
$902$		0			0
$903$	5.00000	+	1.73205i	0.166390	+	0.0576390i
$904$	16.0000			0.532152
$905$		0			0
$906$	9.50000	−	16.4545i	0.315616	−	0.546664i
$907$	−6.00000	+	10.3923i	−0.199227	+	0.345071i	−0.948278	−	0.317441i	$-0.897176\pi$
$907$	−6.00000	+	10.3923i	−0.199227	+	0.345071i	0.749051	+	0.662512i	$0.230510\pi$
$908$	−1.50000	−	2.59808i	−0.0497792	−	0.0862202i
$909$	10.0000			0.331679
$910$		0			0
$911$	30.0000			0.993944			0.496972	−	0.867766i	$-0.334445\pi$
$911$	30.0000			0.993944			0.496972	+	0.867766i	$0.334445\pi$
$912$	4.00000	+	6.92820i	0.132453	+	0.229416i
$913$	17.5000	−	30.3109i	0.579165	−	1.00314i
$914$	−15.5000	+	26.8468i	−0.512694	+	0.888013i
$915$	−3.00000	−	5.19615i	−0.0991769	−	0.171780i
$916$	−20.0000			−0.660819
$917$	2.00000	−	1.73205i	0.0660458	−	0.0571974i
$918$	4.00000			0.132020
$919$	16.0000	+	27.7128i	0.527791	+	0.914161i	0.999475	+	0.0323936i	$0.0103130\pi$
$919$	16.0000	+	27.7128i	0.527791	+	0.914161i	−0.471684	+	0.881768i	$0.656354\pi$
$920$	2.00000	−	3.46410i	0.0659380	−	0.114208i
$921$	14.0000	−	24.2487i	0.461316	−	0.799022i
$922$	7.00000	+	12.1244i	0.230533	+	0.399294i
$923$		0			0
$924$	−2.50000	−	12.9904i	−0.0822440	−	0.427352i
$925$	16.0000			0.526077
$926$	−8.00000	−	13.8564i	−0.262896	−	0.455350i
$927$	−4.00000	+	6.92820i	−0.131377	+	0.227552i
$928$	2.50000	−	4.33013i	0.0820665	−	0.142143i
$929$	3.00000	+	5.19615i	0.0984268	+	0.170480i	0.911034	−	0.412332i	$-0.135286\pi$
$929$	3.00000	+	5.19615i	0.0984268	+	0.170480i	−0.812607	+	0.582812i	$0.801952\pi$
$930$	−3.00000			−0.0983739
$931$	44.0000	+	34.6410i	1.44204	+	1.13531i
$932$	−4.00000			−0.131024
$933$	−16.0000	−	27.7128i	−0.523816	−	0.907277i
$934$	10.0000	−	17.3205i	0.327210	−	0.566744i
$935$	10.0000	−	17.3205i	0.327035	−	0.566441i
$936$		0			0
$937$	35.0000			1.14340			0.571700	−	0.820463i	$-0.306284\pi$
$937$	35.0000			1.14340			0.571700	+	0.820463i	$0.306284\pi$
$938$	−1.00000	−	5.19615i	−0.0326512	−	0.169660i
$939$	−1.00000			−0.0326338
$940$	3.00000	+	5.19615i	0.0978492	+	0.169480i
$941$	5.50000	−	9.52628i	0.179295	−	0.310548i	−0.762344	−	0.647172i	$-0.775952\pi$
$941$	5.50000	−	9.52628i	0.179295	−	0.310548i	0.941639	+	0.336624i	$0.109285\pi$
$942$	−2.00000	+	3.46410i	−0.0651635	+	0.112867i
$943$		0			0
$944$	−11.0000			−0.358020
$945$	−2.00000	+	1.73205i	−0.0650600	+	0.0563436i
$946$	10.0000			0.325128
$947$	16.0000	+	27.7128i	0.519930	+	0.900545i	0.999732	+	0.0231683i	$0.00737536\pi$
$947$	16.0000	+	27.7128i	0.519930	+	0.900545i	−0.479801	+	0.877377i	$0.659291\pi$
$948$	1.50000	−	2.59808i	0.0487177	−	0.0843816i
$949$		0			0
$950$	16.0000	+	27.7128i	0.519109	+	0.899122i
$951$	−3.00000			−0.0972817
$952$	10.0000	+	3.46410i	0.324102	+	0.112272i
$953$	2.00000			0.0647864			0.0323932	−	0.999475i	$-0.489687\pi$
$953$	2.00000			0.0647864			0.0323932	+	0.999475i	$0.489687\pi$
$954$	4.50000	+	7.79423i	0.145693	+	0.252347i
$955$	−12.0000	+	20.7846i	−0.388311	+	0.672574i
$956$	6.00000	−	10.3923i	0.194054	−	0.336111i
$957$	−12.5000	−	21.6506i	−0.404068	−	0.699866i
$958$	38.0000			1.22772
$959$	5.00000	+	1.73205i	0.161458	+	0.0559308i
$960$	−1.00000			−0.0322749
$961$	11.0000	+	19.0526i	0.354839	+	0.614599i
$962$		0			0
$963$	−1.50000	+	2.59808i	−0.0483368	+	0.0837218i
$964$	12.5000	+	21.6506i	0.402598	+	0.697320i
$965$	5.00000			0.160956
$966$	8.00000	−	6.92820i	0.257396	−	0.222911i
$967$	−61.0000			−1.96163			−0.980814	−	0.194946i	$-0.937547\pi$
$967$	−61.0000			−1.96163			−0.980814	+	0.194946i	$0.937547\pi$
$968$	−7.00000	−	12.1244i	−0.224989	−	0.389692i
$969$	−16.0000	+	27.7128i	−0.513994	+	0.890264i
$970$	−3.50000	+	6.06218i	−0.112378	+	0.194645i
$971$	−7.50000	−	12.9904i	−0.240686	−	0.416881i	0.720224	−	0.693742i	$-0.244039\pi$
$971$	−7.50000	−	12.9904i	−0.240686	−	0.416881i	−0.960910	+	0.276861i	$0.910706\pi$
$972$	−1.00000			−0.0320750
$973$	−7.00000	−	36.3731i	−0.224410	−	1.16607i
$974$	5.00000			0.160210
$975$		0			0
$976$	3.00000	−	5.19615i	0.0960277	−	0.166325i
$977$	15.0000	−	25.9808i	0.479893	−	0.831198i	−0.519841	−	0.854263i	$-0.674009\pi$
$977$	15.0000	−	25.9808i	0.479893	−	0.831198i	0.999734	+	0.0230645i	$0.00734232\pi$
$978$	−2.00000	−	3.46410i	−0.0639529	−	0.110770i
$979$	−30.0000			−0.958804
$980$	−6.50000	+	2.59808i	−0.207635	+	0.0829925i
$981$	−2.00000			−0.0638551
$982$	−4.50000	−	7.79423i	−0.143601	−	0.248724i
$983$	30.0000	−	51.9615i	0.956851	−	1.65732i	0.226778	−	0.973946i	$-0.427181\pi$
$983$	30.0000	−	51.9615i	0.956851	−	1.65732i	0.730073	−	0.683369i	$-0.239486\pi$
$984$		0			0
$985$	−1.00000	−	1.73205i	−0.0318626	−	0.0551877i
$986$	20.0000			0.636930
$987$	3.00000	+	15.5885i	0.0954911	+	0.496186i
$988$		0			0
$989$	4.00000	+	6.92820i	0.127193	+	0.220304i
$990$	−2.50000	+	4.33013i	−0.0794552	+	0.137620i
$991$	−23.5000	+	40.7032i	−0.746502	+	1.29298i	0.202988	+	0.979181i	$0.434935\pi$
$991$	−23.5000	+	40.7032i	−0.746502	+	1.29298i	−0.949490	+	0.313798i	$0.898398\pi$
$992$	−1.50000	−	2.59808i	−0.0476250	−	0.0824890i
$993$	4.00000			0.126936
$994$	4.00000	−	3.46410i	0.126872	−	0.109875i
$995$	−4.00000			−0.126809
$996$	−3.50000	−	6.06218i	−0.110902	−	0.192087i
$997$	−19.0000	+	32.9090i	−0.601736	+	1.04224i	0.390822	+	0.920466i	$0.372191\pi$
$997$	−19.0000	+	32.9090i	−0.601736	+	1.04224i	−0.992558	+	0.121771i	$0.961143\pi$
$998$	−5.00000	+	8.66025i	−0.158272	+	0.274136i
$999$	−2.00000	−	3.46410i	−0.0632772	−	0.109599i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	42.2.e.a.25.1	✓	2
3.2	odd	2		126.2.g.c.109.1		2
4.3	odd	2		336.2.q.b.193.1		2
5.2	odd	4		1050.2.o.a.949.2		4
5.3	odd	4		1050.2.o.a.949.1		4
5.4	even	2		1050.2.i.l.151.1		2
7.2	even	3	inner	42.2.e.a.37.1	yes	2
7.3	odd	6		294.2.a.f.1.1		1
7.4	even	3		294.2.a.e.1.1		1
7.5	odd	6		294.2.e.b.79.1		2
7.6	odd	2		294.2.e.b.67.1		2
8.3	odd	2		1344.2.q.s.193.1		2
8.5	even	2		1344.2.q.g.193.1		2
9.2	odd	6		1134.2.h.l.109.1		2
9.4	even	3		1134.2.e.l.865.1		2
9.5	odd	6		1134.2.e.e.865.1		2
9.7	even	3		1134.2.h.e.109.1		2
12.11	even	2		1008.2.s.k.865.1		2
21.2	odd	6		126.2.g.c.37.1		2
21.5	even	6		882.2.g.i.667.1		2
21.11	odd	6		882.2.a.c.1.1		1
21.17	even	6		882.2.a.d.1.1		1
21.20	even	2		882.2.g.i.361.1		2
28.3	even	6		2352.2.a.f.1.1		1
28.11	odd	6		2352.2.a.t.1.1		1
28.19	even	6		2352.2.q.u.961.1		2
28.23	odd	6		336.2.q.b.289.1		2
28.27	even	2		2352.2.q.u.1537.1		2
35.2	odd	12		1050.2.o.a.499.1		4
35.4	even	6		7350.2.a.bl.1.1		1
35.9	even	6		1050.2.i.l.751.1		2
35.23	odd	12		1050.2.o.a.499.2		4
35.24	odd	6		7350.2.a.q.1.1		1
56.3	even	6		9408.2.a.cr.1.1		1
56.11	odd	6		9408.2.a.q.1.1		1
56.37	even	6		1344.2.q.g.961.1		2
56.45	odd	6		9408.2.a.z.1.1		1
56.51	odd	6		1344.2.q.s.961.1		2
56.53	even	6		9408.2.a.ce.1.1		1
63.2	odd	6		1134.2.e.e.919.1		2
63.16	even	3		1134.2.e.l.919.1		2
63.23	odd	6		1134.2.h.l.541.1		2
63.58	even	3		1134.2.h.e.541.1		2
84.11	even	6		7056.2.a.w.1.1		1
84.23	even	6		1008.2.s.k.289.1		2
84.59	odd	6		7056.2.a.bl.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.2.e.a.25.1	✓	2	1.1	even	1	trivial
42.2.e.a.37.1	yes	2	7.2	even	3	inner
126.2.g.c.37.1		2	21.2	odd	6
126.2.g.c.109.1		2	3.2	odd	2
294.2.a.e.1.1		1	7.4	even	3
294.2.a.f.1.1		1	7.3	odd	6
294.2.e.b.67.1		2	7.6	odd	2
294.2.e.b.79.1		2	7.5	odd	6
336.2.q.b.193.1		2	4.3	odd	2
336.2.q.b.289.1		2	28.23	odd	6
882.2.a.c.1.1		1	21.11	odd	6
882.2.a.d.1.1		1	21.17	even	6
882.2.g.i.361.1		2	21.20	even	2
882.2.g.i.667.1		2	21.5	even	6
1008.2.s.k.289.1		2	84.23	even	6
1008.2.s.k.865.1		2	12.11	even	2
1050.2.i.l.151.1		2	5.4	even	2
1050.2.i.l.751.1		2	35.9	even	6
1050.2.o.a.499.1		4	35.2	odd	12
1050.2.o.a.499.2		4	35.23	odd	12
1050.2.o.a.949.1		4	5.3	odd	4
1050.2.o.a.949.2		4	5.2	odd	4
1134.2.e.e.865.1		2	9.5	odd	6
1134.2.e.e.919.1		2	63.2	odd	6
1134.2.e.l.865.1		2	9.4	even	3
1134.2.e.l.919.1		2	63.16	even	3
1134.2.h.e.109.1		2	9.7	even	3
1134.2.h.e.541.1		2	63.58	even	3
1134.2.h.l.109.1		2	9.2	odd	6
1134.2.h.l.541.1		2	63.23	odd	6
1344.2.q.g.193.1		2	8.5	even	2
1344.2.q.g.961.1		2	56.37	even	6
1344.2.q.s.193.1		2	8.3	odd	2
1344.2.q.s.961.1		2	56.51	odd	6
2352.2.a.f.1.1		1	28.3	even	6
2352.2.a.t.1.1		1	28.11	odd	6
2352.2.q.u.961.1		2	28.19	even	6
2352.2.q.u.1537.1		2	28.27	even	2
7056.2.a.w.1.1		1	84.11	even	6
7056.2.a.bl.1.1		1	84.59	odd	6
7350.2.a.q.1.1		1	35.24	odd	6
7350.2.a.bl.1.1		1	35.4	even	6
9408.2.a.q.1.1		1	56.11	odd	6
9408.2.a.z.1.1		1	56.45	odd	6
9408.2.a.ce.1.1		1	56.53	even	6
9408.2.a.cr.1.1		1	56.3	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 42 = 2 \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	42.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} -1.00000 q^{6} +(0.500000 + 2.59808i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} -1.00000 q^{6} +(0.500000 + 2.59808i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(-2.50000 + 4.33013i) q^{11} +(0.500000 + 0.866025i) q^{12} +(2.00000 - 1.73205i) q^{14} -1.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.00000 - 3.46410i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(-4.00000 - 6.92820i) q^{19} +1.00000 q^{20} +(2.50000 + 0.866025i) q^{21} +5.00000 q^{22} +(2.00000 + 3.46410i) q^{23} +(0.500000 - 0.866025i) q^{24} +(2.00000 - 3.46410i) q^{25} -1.00000 q^{27} +(-2.50000 - 0.866025i) q^{28} -5.00000 q^{29} +(0.500000 + 0.866025i) q^{30} +(-1.50000 + 2.59808i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(2.50000 + 4.33013i) q^{33} -4.00000 q^{34} +(2.00000 - 1.73205i) q^{35} +1.00000 q^{36} +(2.00000 + 3.46410i) q^{37} +(-4.00000 + 6.92820i) q^{38} +(-0.500000 - 0.866025i) q^{40} +(-0.500000 - 2.59808i) q^{42} +2.00000 q^{43} +(-2.50000 - 4.33013i) q^{44} +(-0.500000 + 0.866025i) q^{45} +(2.00000 - 3.46410i) q^{46} +(3.00000 + 5.19615i) q^{47} -1.00000 q^{48} +(-6.50000 + 2.59808i) q^{49} -4.00000 q^{50} +(-2.00000 - 3.46410i) q^{51} +(4.50000 - 7.79423i) q^{53} +(0.500000 + 0.866025i) q^{54} +5.00000 q^{55} +(0.500000 + 2.59808i) q^{56} -8.00000 q^{57} +(2.50000 + 4.33013i) q^{58} +(5.50000 - 9.52628i) q^{59} +(0.500000 - 0.866025i) q^{60} +(3.00000 + 5.19615i) q^{61} +3.00000 q^{62} +(2.00000 - 1.73205i) q^{63} +1.00000 q^{64} +(2.50000 - 4.33013i) q^{66} +(1.00000 - 1.73205i) q^{67} +(2.00000 + 3.46410i) q^{68} +4.00000 q^{69} +(-2.50000 - 0.866025i) q^{70} +2.00000 q^{71} +(-0.500000 - 0.866025i) q^{72} +(-5.00000 + 8.66025i) q^{73} +(2.00000 - 3.46410i) q^{74} +(-2.00000 - 3.46410i) q^{75} +8.00000 q^{76} +(-12.5000 - 4.33013i) q^{77} +(-1.50000 - 2.59808i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} -7.00000 q^{83} +(-2.00000 + 1.73205i) q^{84} -4.00000 q^{85} +(-1.00000 - 1.73205i) q^{86} +(-2.50000 + 4.33013i) q^{87} +(-2.50000 + 4.33013i) q^{88} +(3.00000 + 5.19615i) q^{89} +1.00000 q^{90} -4.00000 q^{92} +(1.50000 + 2.59808i) q^{93} +(3.00000 - 5.19615i) q^{94} +(-4.00000 + 6.92820i) q^{95} +(0.500000 + 0.866025i) q^{96} +7.00000 q^{97} +(5.50000 + 4.33013i) q^{98} +5.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} + q^{3} - q^{4} - q^{5} - 2 q^{6} + q^{7} + 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q - q^2 + q^3 - q^4 - q^5 - 2 * q^6 + q^7 + 2 * q^8 - q^9	\( 2 q - q^{2} + q^{3} - q^{4} - q^{5} - 2 q^{6} + q^{7} + 2 q^{8} - q^{9} - q^{10} - 5 q^{11} + q^{12} + 4 q^{14} - 2 q^{15} - q^{16} + 4 q^{17} - q^{18} - 8 q^{19} + 2 q^{20} + 5 q^{21} + 10 q^{22} + 4 q^{23} + q^{24} + 4 q^{25} - 2 q^{27} - 5 q^{28} - 10 q^{29} + q^{30} - 3 q^{31} - q^{32} + 5 q^{33} - 8 q^{34} + 4 q^{35} + 2 q^{36} + 4 q^{37} - 8 q^{38} - q^{40} - q^{42} + 4 q^{43} - 5 q^{44} - q^{45} + 4 q^{46} + 6 q^{47} - 2 q^{48} - 13 q^{49} - 8 q^{50} - 4 q^{51} + 9 q^{53} + q^{54} + 10 q^{55} + q^{56} - 16 q^{57} + 5 q^{58} + 11 q^{59} + q^{60} + 6 q^{61} + 6 q^{62} + 4 q^{63} + 2 q^{64} + 5 q^{66} + 2 q^{67} + 4 q^{68} + 8 q^{69} - 5 q^{70} + 4 q^{71} - q^{72} - 10 q^{73} + 4 q^{74} - 4 q^{75} + 16 q^{76} - 25 q^{77} - 3 q^{79} - q^{80} - q^{81} - 14 q^{83} - 4 q^{84} - 8 q^{85} - 2 q^{86} - 5 q^{87} - 5 q^{88} + 6 q^{89} + 2 q^{90} - 8 q^{92} + 3 q^{93} + 6 q^{94} - 8 q^{95} + q^{96} + 14 q^{97} + 11 q^{98} + 10 q^{99}+O(q^{100}) \) 2 * q - q^2 + q^3 - q^4 - q^5 - 2 * q^6 + q^7 + 2 * q^8 - q^9 - q^10 - 5 * q^11 + q^12 + 4 * q^14 - 2 * q^15 - q^16 + 4 * q^17 - q^18 - 8 * q^19 + 2 * q^20 + 5 * q^21 + 10 * q^22 + 4 * q^23 + q^24 + 4 * q^25 - 2 * q^27 - 5 * q^28 - 10 * q^29 + q^30 - 3 * q^31 - q^32 + 5 * q^33 - 8 * q^34 + 4 * q^35 + 2 * q^36 + 4 * q^37 - 8 * q^38 - q^40 - q^42 + 4 * q^43 - 5 * q^44 - q^45 + 4 * q^46 + 6 * q^47 - 2 * q^48 - 13 * q^49 - 8 * q^50 - 4 * q^51 + 9 * q^53 + q^54 + 10 * q^55 + q^56 - 16 * q^57 + 5 * q^58 + 11 * q^59 + q^60 + 6 * q^61 + 6 * q^62 + 4 * q^63 + 2 * q^64 + 5 * q^66 + 2 * q^67 + 4 * q^68 + 8 * q^69 - 5 * q^70 + 4 * q^71 - q^72 - 10 * q^73 + 4 * q^74 - 4 * q^75 + 16 * q^76 - 25 * q^77 - 3 * q^79 - q^80 - q^81 - 14 * q^83 - 4 * q^84 - 8 * q^85 - 2 * q^86 - 5 * q^87 - 5 * q^88 + 6 * q^89 + 2 * q^90 - 8 * q^92 + 3 * q^93 + 6 * q^94 - 8 * q^95 + q^96 + 14 * q^97 + 11 * q^98 + 10 * q^99

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