LMFDB - Embedded newform 966.2.i.c.415.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(277,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("966.277");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.71354883526$
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			415.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	966.415
Dual form			966.2.i.c.277.1

$q$-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} +(1.50000 + 2.59808i) q^{11} +(0.500000 - 0.866025i) q^{12} +2.00000 q^{13} +(-2.00000 - 1.73205i) q^{14} -1.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.00000 + 1.73205i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(1.00000 - 1.73205i) q^{19} +1.00000 q^{20} +(-2.50000 + 0.866025i) q^{21} -3.00000 q^{22} +(-0.500000 + 0.866025i) q^{23} +(0.500000 + 0.866025i) q^{24} +(2.00000 + 3.46410i) q^{25} +(-1.00000 + 1.73205i) q^{26} -1.00000 q^{27} +(2.50000 - 0.866025i) q^{28} -7.00000 q^{29} +(0.500000 - 0.866025i) q^{30} +(-3.50000 - 6.06218i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.50000 + 2.59808i) q^{33} -2.00000 q^{34} +(-2.00000 - 1.73205i) q^{35} +1.00000 q^{36} +(1.00000 - 1.73205i) q^{37} +(1.00000 + 1.73205i) q^{38} +(1.00000 + 1.73205i) q^{39} +(-0.500000 + 0.866025i) q^{40} -2.00000 q^{41} +(0.500000 - 2.59808i) q^{42} -6.00000 q^{43} +(1.50000 - 2.59808i) q^{44} +(-0.500000 - 0.866025i) q^{45} +(-0.500000 - 0.866025i) q^{46} +(-3.00000 + 5.19615i) q^{47} -1.00000 q^{48} +(-6.50000 - 2.59808i) q^{49} -4.00000 q^{50} +(-1.00000 + 1.73205i) q^{51} +(-1.00000 - 1.73205i) q^{52} +(4.50000 + 7.79423i) q^{53} +(0.500000 - 0.866025i) q^{54} -3.00000 q^{55} +(-0.500000 + 2.59808i) q^{56} +2.00000 q^{57} +(3.50000 - 6.06218i) q^{58} +(4.50000 + 7.79423i) q^{59} +(0.500000 + 0.866025i) q^{60} +(-3.00000 + 5.19615i) q^{61} +7.00000 q^{62} +(-2.00000 - 1.73205i) q^{63} +1.00000 q^{64} +(-1.00000 + 1.73205i) q^{65} +(-1.50000 - 2.59808i) q^{66} +(-5.00000 - 8.66025i) q^{67} +(1.00000 - 1.73205i) q^{68} -1.00000 q^{69} +(2.50000 - 0.866025i) q^{70} -8.00000 q^{71} +(-0.500000 + 0.866025i) q^{72} +(5.00000 + 8.66025i) q^{73} +(1.00000 + 1.73205i) q^{74} +(-2.00000 + 3.46410i) q^{75} -2.00000 q^{76} +(-7.50000 + 2.59808i) q^{77} -2.00000 q^{78} +(7.50000 - 12.9904i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.00000 - 1.73205i) q^{82} +1.00000 q^{83} +(2.00000 + 1.73205i) q^{84} -2.00000 q^{85} +(3.00000 - 5.19615i) q^{86} +(-3.50000 - 6.06218i) q^{87} +(1.50000 + 2.59808i) q^{88} +1.00000 q^{90} +(-1.00000 + 5.19615i) q^{91} +1.00000 q^{92} +(3.50000 - 6.06218i) q^{93} +(-3.00000 - 5.19615i) q^{94} +(1.00000 + 1.73205i) q^{95} +(0.500000 - 0.866025i) q^{96} +5.00000 q^{97} +(5.50000 - 4.33013i) q^{98} -3.00000 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	\( 2 q - q^{2} + q^{3} - q^{4} - q^{5} - 2 q^{6} - q^{7} + 2 q^{8} - q^{9} - q^{10} + 3 q^{11} + q^{12} + 4 q^{13} - 4 q^{14} - 2 q^{15} - q^{16} + 2 q^{17} - q^{18} + 2 q^{19} + 2 q^{20} - 5 q^{21} - 6 q^{22} - q^{23} + q^{24} + 4 q^{25} - 2 q^{26} - 2 q^{27} + 5 q^{28} - 14 q^{29} + q^{30} - 7 q^{31} - q^{32} - 3 q^{33} - 4 q^{34} - 4 q^{35} + 2 q^{36} + 2 q^{37} + 2 q^{38} + 2 q^{39} - q^{40} - 4 q^{41} + q^{42} - 12 q^{43} + 3 q^{44} - q^{45} - q^{46} - 6 q^{47} - 2 q^{48} - 13 q^{49} - 8 q^{50} - 2 q^{51} - 2 q^{52} + 9 q^{53} + q^{54} - 6 q^{55} - q^{56} + 4 q^{57} + 7 q^{58} + 9 q^{59} + q^{60} - 6 q^{61} + 14 q^{62} - 4 q^{63} + 2 q^{64} - 2 q^{65} - 3 q^{66} - 10 q^{67} + 2 q^{68} - 2 q^{69} + 5 q^{70} - 16 q^{71} - q^{72} + 10 q^{73} + 2 q^{74} - 4 q^{75} - 4 q^{76} - 15 q^{77} - 4 q^{78} + 15 q^{79} - q^{80} - q^{81} + 2 q^{82} + 2 q^{83} + 4 q^{84} - 4 q^{85} + 6 q^{86} - 7 q^{87} + 3 q^{88} + 2 q^{90} - 2 q^{91} + 2 q^{92} + 7 q^{93} - 6 q^{94} + 2 q^{95} + q^{96} + 10 q^{97} + 11 q^{98} - 6 q^{99}+O(q^{100}) \) 2 * q - q^2 + q^3 - q^4 - q^5 - 2 * q^6 - q^7 + 2 * q^8 - q^9 - q^10 + 3 * q^11 + q^12 + 4 * q^13 - 4 * q^14 - 2 * q^15 - q^16 + 2 * q^17 - q^18 + 2 * q^19 + 2 * q^20 - 5 * q^21 - 6 * q^22 - q^23 + q^24 + 4 * q^25 - 2 * q^26 - 2 * q^27 + 5 * q^28 - 14 * q^29 + q^30 - 7 * q^31 - q^32 - 3 * q^33 - 4 * q^34 - 4 * q^35 + 2 * q^36 + 2 * q^37 + 2 * q^38 + 2 * q^39 - q^40 - 4 * q^41 + q^42 - 12 * q^43 + 3 * q^44 - q^45 - q^46 - 6 * q^47 - 2 * q^48 - 13 * q^49 - 8 * q^50 - 2 * q^51 - 2 * q^52 + 9 * q^53 + q^54 - 6 * q^55 - q^56 + 4 * q^57 + 7 * q^58 + 9 * q^59 + q^60 - 6 * q^61 + 14 * q^62 - 4 * q^63 + 2 * q^64 - 2 * q^65 - 3 * q^66 - 10 * q^67 + 2 * q^68 - 2 * q^69 + 5 * q^70 - 16 * q^71 - q^72 + 10 * q^73 + 2 * q^74 - 4 * q^75 - 4 * q^76 - 15 * q^77 - 4 * q^78 + 15 * q^79 - q^80 - q^81 + 2 * q^82 + 2 * q^83 + 4 * q^84 - 4 * q^85 + 6 * q^86 - 7 * q^87 + 3 * q^88 + 2 * q^90 - 2 * q^91 + 2 * q^92 + 7 * q^93 - 6 * q^94 + 2 * q^95 + q^96 + 10 * q^97 + 11 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i	−0.955901	−	0.293691i	$-0.905116\pi$
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i	0.732294	+	0.680989i	$0.238450\pi$
$6$	−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
$11$	1.50000	+	2.59808i	0.452267	+	0.783349i	0.998526	−	0.0542666i	$-0.0172821\pi$
$11$	1.50000	+	2.59808i	0.452267	+	0.783349i	−0.546259	+	0.837616i	$0.683949\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	2.00000			0.554700			0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000			0.554700			0.277350	+	0.960769i	$0.410544\pi$
$14$	−2.00000	−	1.73205i	−0.534522	−	0.462910i
$15$	−1.00000			−0.258199
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.00000	+	1.73205i	0.242536	+	0.420084i	0.961436	−	0.275029i	$-0.0886875\pi$
$17$	1.00000	+	1.73205i	0.242536	+	0.420084i	−0.718900	+	0.695113i	$0.755354\pi$
$18$	−0.500000	−	0.866025i	−0.117851	−	0.204124i
$19$	1.00000	−	1.73205i	0.229416	−	0.397360i	−0.728219	−	0.685344i	$-0.759652\pi$
$19$	1.00000	−	1.73205i	0.229416	−	0.397360i	0.957635	+	0.287984i	$0.0929851\pi$
$20$	1.00000			0.223607
$21$	−2.50000	+	0.866025i	−0.545545	+	0.188982i
$22$	−3.00000			−0.639602
$23$	−0.500000	+	0.866025i	−0.104257	+	0.180579i
$23$	−0.500000	+	0.866025i	−0.104257	+	0.180579i
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	2.00000	+	3.46410i	0.400000	+	0.692820i
$26$	−1.00000	+	1.73205i	−0.196116	+	0.339683i
$27$	−1.00000			−0.192450
$28$	2.50000	−	0.866025i	0.472456	−	0.163663i
$29$	−7.00000			−1.29987			−0.649934	−	0.759991i	$-0.725203\pi$
$29$	−7.00000			−1.29987			−0.649934	+	0.759991i	$0.725203\pi$
$30$	0.500000	−	0.866025i	0.0912871	−	0.158114i
$31$	−3.50000	−	6.06218i	−0.628619	−	1.08880i	−0.987829	−	0.155543i	$-0.950287\pi$
$31$	−3.50000	−	6.06218i	−0.628619	−	1.08880i	0.359211	−	0.933257i	$-0.383046\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−1.50000	+	2.59808i	−0.261116	+	0.452267i
$34$	−2.00000			−0.342997
$35$	−2.00000	−	1.73205i	−0.338062	−	0.292770i
$36$	1.00000			0.166667
$37$	1.00000	−	1.73205i	0.164399	−	0.284747i	−0.772043	−	0.635571i	$-0.780765\pi$
$37$	1.00000	−	1.73205i	0.164399	−	0.284747i	0.936442	+	0.350823i	$0.114098\pi$
$38$	1.00000	+	1.73205i	0.162221	+	0.280976i
$39$	1.00000	+	1.73205i	0.160128	+	0.277350i
$40$	−0.500000	+	0.866025i	−0.0790569	+	0.136931i
$41$	−2.00000			−0.312348			−0.156174	−	0.987730i	$-0.549916\pi$
$41$	−2.00000			−0.312348			−0.156174	+	0.987730i	$0.549916\pi$
$42$	0.500000	−	2.59808i	0.0771517	−	0.400892i
$43$	−6.00000			−0.914991			−0.457496	−	0.889212i	$-0.651253\pi$
$43$	−6.00000			−0.914991			−0.457496	+	0.889212i	$0.651253\pi$
$44$	1.50000	−	2.59808i	0.226134	−	0.391675i
$45$	−0.500000	−	0.866025i	−0.0745356	−	0.129099i
$46$	−0.500000	−	0.866025i	−0.0737210	−	0.127688i
$47$	−3.00000	+	5.19615i	−0.437595	+	0.757937i	−0.997503	−	0.0706177i	$-0.977503\pi$
$47$	−3.00000	+	5.19615i	−0.437595	+	0.757937i	0.559908	+	0.828554i	$0.310836\pi$
$48$	−1.00000			−0.144338
$49$	−6.50000	−	2.59808i	−0.928571	−	0.371154i
$50$	−4.00000			−0.565685
$51$	−1.00000	+	1.73205i	−0.140028	+	0.242536i
$52$	−1.00000	−	1.73205i	−0.138675	−	0.240192i
$53$	4.50000	+	7.79423i	0.618123	+	1.07062i	0.989828	+	0.142269i	$0.0454398\pi$
$53$	4.50000	+	7.79423i	0.618123	+	1.07062i	−0.371706	+	0.928351i	$0.621227\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$	−3.00000			−0.404520
$56$	−0.500000	+	2.59808i	−0.0668153	+	0.347183i
$57$	2.00000			0.264906
$58$	3.50000	−	6.06218i	0.459573	−	0.796003i
$59$	4.50000	+	7.79423i	0.585850	+	1.01472i	0.994769	+	0.102151i	$0.0325726\pi$
$59$	4.50000	+	7.79423i	0.585850	+	1.01472i	−0.408919	+	0.912571i	$0.634094\pi$
$60$	0.500000	+	0.866025i	0.0645497	+	0.111803i
$61$	−3.00000	+	5.19615i	−0.384111	+	0.665299i	−0.991645	−	0.128994i	$-0.958825\pi$
$61$	−3.00000	+	5.19615i	−0.384111	+	0.665299i	0.607535	+	0.794293i	$0.292159\pi$
$62$	7.00000			0.889001
$63$	−2.00000	−	1.73205i	−0.251976	−	0.218218i
$64$	1.00000			0.125000
$65$	−1.00000	+	1.73205i	−0.124035	+	0.214834i
$66$	−1.50000	−	2.59808i	−0.184637	−	0.319801i
$67$	−5.00000	−	8.66025i	−0.610847	−	1.05802i	−0.991098	−	0.133135i	$-0.957496\pi$
$67$	−5.00000	−	8.66025i	−0.610847	−	1.05802i	0.380251	−	0.924883i	$-0.375838\pi$
$68$	1.00000	−	1.73205i	0.121268	−	0.210042i
$69$	−1.00000			−0.120386
$70$	2.50000	−	0.866025i	0.298807	−	0.103510i
$71$	−8.00000			−0.949425			−0.474713	−	0.880141i	$-0.657448\pi$
$71$	−8.00000			−0.949425			−0.474713	+	0.880141i	$0.657448\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$	5.00000	+	8.66025i	0.585206	+	1.01361i	0.994850	+	0.101361i	$0.0323196\pi$
$73$	5.00000	+	8.66025i	0.585206	+	1.01361i	−0.409644	+	0.912245i	$0.634347\pi$
$74$	1.00000	+	1.73205i	0.116248	+	0.201347i
$75$	−2.00000	+	3.46410i	−0.230940	+	0.400000i
$76$	−2.00000			−0.229416
$77$	−7.50000	+	2.59808i	−0.854704	+	0.296078i
$78$	−2.00000			−0.226455
$79$	7.50000	−	12.9904i	0.843816	−	1.46153i	−0.0428296	−	0.999082i	$-0.513637\pi$
$79$	7.50000	−	12.9904i	0.843816	−	1.46153i	0.886646	−	0.462450i	$-0.153029\pi$
$80$	−0.500000	−	0.866025i	−0.0559017	−	0.0968246i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	1.00000	−	1.73205i	0.110432	−	0.191273i
$83$	1.00000			0.109764			0.0548821	−	0.998493i	$-0.482522\pi$
$83$	1.00000			0.109764			0.0548821	+	0.998493i	$0.482522\pi$
$84$	2.00000	+	1.73205i	0.218218	+	0.188982i
$85$	−2.00000			−0.216930
$86$	3.00000	−	5.19615i	0.323498	−	0.560316i
$87$	−3.50000	−	6.06218i	−0.375239	−	0.649934i
$88$	1.50000	+	2.59808i	0.159901	+	0.276956i
$89$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$89$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$90$	1.00000			0.105409
$91$	−1.00000	+	5.19615i	−0.104828	+	0.544705i
$92$	1.00000			0.104257
$93$	3.50000	−	6.06218i	0.362933	−	0.628619i
$94$	−3.00000	−	5.19615i	−0.309426	−	0.535942i
$95$	1.00000	+	1.73205i	0.102598	+	0.177705i
$96$	0.500000	−	0.866025i	0.0510310	−	0.0883883i
$97$	5.00000			0.507673			0.253837	−	0.967247i	$-0.418307\pi$
$97$	5.00000			0.507673			0.253837	+	0.967247i	$0.418307\pi$
$98$	5.50000	−	4.33013i	0.555584	−	0.437409i
$99$	−3.00000			−0.301511
$100$	2.00000	−	3.46410i	0.200000	−	0.346410i
$101$	5.00000	+	8.66025i	0.497519	+	0.861727i	0.999996	−	0.00286291i	$-0.000911295\pi$
$101$	5.00000	+	8.66025i	0.497519	+	0.861727i	−0.502477	+	0.864590i	$0.667578\pi$
$102$	−1.00000	−	1.73205i	−0.0990148	−	0.171499i
$103$	4.00000	−	6.92820i	0.394132	−	0.682656i	−0.598858	−	0.800855i	$-0.704379\pi$
$103$	4.00000	−	6.92820i	0.394132	−	0.682656i	0.992990	+	0.118199i	$0.0377120\pi$
$104$	2.00000			0.196116
$105$	0.500000	−	2.59808i	0.0487950	−	0.253546i
$106$	−9.00000			−0.874157
$107$	−1.50000	+	2.59808i	−0.145010	+	0.251166i	−0.929377	−	0.369132i	$-0.879655\pi$
$107$	−1.50000	+	2.59808i	−0.145010	+	0.251166i	0.784366	+	0.620298i	$0.212988\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$	−5.00000	−	8.66025i	−0.478913	−	0.829502i	0.520794	−	0.853682i	$-0.325636\pi$
$109$	−5.00000	−	8.66025i	−0.478913	−	0.829502i	−0.999708	+	0.0241802i	$0.992302\pi$
$110$	1.50000	−	2.59808i	0.143019	−	0.247717i
$111$	2.00000			0.189832
$112$	−2.00000	−	1.73205i	−0.188982	−	0.163663i
$113$	10.0000			0.940721			0.470360	−	0.882474i	$-0.344124\pi$
$113$	10.0000			0.940721			0.470360	+	0.882474i	$0.344124\pi$
$114$	−1.00000	+	1.73205i	−0.0936586	+	0.162221i
$115$	−0.500000	−	0.866025i	−0.0466252	−	0.0807573i
$116$	3.50000	+	6.06218i	0.324967	+	0.562859i
$117$	−1.00000	+	1.73205i	−0.0924500	+	0.160128i
$118$	−9.00000			−0.828517
$119$	−5.00000	+	1.73205i	−0.458349	+	0.158777i
$120$	−1.00000			−0.0912871
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$	−3.00000	−	5.19615i	−0.271607	−	0.470438i
$123$	−1.00000	−	1.73205i	−0.0901670	−	0.156174i
$124$	−3.50000	+	6.06218i	−0.314309	+	0.544400i
$125$	−9.00000			−0.804984
$126$	2.50000	−	0.866025i	0.222718	−	0.0771517i
$127$	−7.00000			−0.621150			−0.310575	−	0.950549i	$-0.600522\pi$
$127$	−7.00000			−0.621150			−0.310575	+	0.950549i	$0.600522\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−3.00000	−	5.19615i	−0.264135	−	0.457496i
$130$	−1.00000	−	1.73205i	−0.0877058	−	0.151911i
$131$	−3.50000	+	6.06218i	−0.305796	+	0.529655i	−0.977438	−	0.211221i	$-0.932256\pi$
$131$	−3.50000	+	6.06218i	−0.305796	+	0.529655i	0.671642	+	0.740876i	$0.265589\pi$
$132$	3.00000			0.261116
$133$	4.00000	+	3.46410i	0.346844	+	0.300376i
$134$	10.0000			0.863868
$135$	0.500000	−	0.866025i	0.0430331	−	0.0745356i
$136$	1.00000	+	1.73205i	0.0857493	+	0.148522i
$137$	3.00000	+	5.19615i	0.256307	+	0.443937i	0.965250	−	0.261329i	$-0.0841608\pi$
$137$	3.00000	+	5.19615i	0.256307	+	0.443937i	−0.708942	+	0.705266i	$0.750827\pi$
$138$	0.500000	−	0.866025i	0.0425628	−	0.0737210i
$139$	14.0000			1.18746			0.593732	−	0.804663i	$-0.297654\pi$
$139$	14.0000			1.18746			0.593732	+	0.804663i	$0.297654\pi$
$140$	−0.500000	+	2.59808i	−0.0422577	+	0.219578i
$141$	−6.00000			−0.505291
$142$	4.00000	−	6.92820i	0.335673	−	0.581402i
$143$	3.00000	+	5.19615i	0.250873	+	0.434524i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	3.50000	−	6.06218i	0.290659	−	0.503436i
$146$	−10.0000			−0.827606
$147$	−1.00000	−	6.92820i	−0.0824786	−	0.571429i
$148$	−2.00000			−0.164399
$149$	11.0000	−	19.0526i	0.901155	−	1.56085i	0.0751583	−	0.997172i	$-0.476054\pi$
$149$	11.0000	−	19.0526i	0.901155	−	1.56085i	0.825997	−	0.563675i	$-0.190613\pi$
$150$	−2.00000	−	3.46410i	−0.163299	−	0.282843i
$151$	2.50000	+	4.33013i	0.203447	+	0.352381i	0.949637	−	0.313353i	$-0.101452\pi$
$151$	2.50000	+	4.33013i	0.203447	+	0.352381i	−0.746190	+	0.665733i	$0.768119\pi$
$152$	1.00000	−	1.73205i	0.0811107	−	0.140488i
$153$	−2.00000			−0.161690
$154$	1.50000	−	7.79423i	0.120873	−	0.628077i
$155$	7.00000			0.562254
$156$	1.00000	−	1.73205i	0.0800641	−	0.138675i
$157$	−3.00000	−	5.19615i	−0.239426	−	0.414698i	0.721124	−	0.692806i	$-0.243626\pi$
$157$	−3.00000	−	5.19615i	−0.239426	−	0.414698i	−0.960550	+	0.278108i	$0.910293\pi$
$158$	7.50000	+	12.9904i	0.596668	+	1.03346i
$159$	−4.50000	+	7.79423i	−0.356873	+	0.618123i
$160$	1.00000			0.0790569
$161$	−2.00000	−	1.73205i	−0.157622	−	0.136505i
$162$	1.00000			0.0785674
$163$	−1.00000	+	1.73205i	−0.0783260	+	0.135665i	−0.902528	−	0.430632i	$-0.858291\pi$
$163$	−1.00000	+	1.73205i	−0.0783260	+	0.135665i	0.824202	+	0.566296i	$0.191624\pi$
$164$	1.00000	+	1.73205i	0.0780869	+	0.135250i
$165$	−1.50000	−	2.59808i	−0.116775	−	0.202260i
$166$	−0.500000	+	0.866025i	−0.0388075	+	0.0672166i
$167$	6.00000			0.464294			0.232147	−	0.972681i	$-0.425425\pi$
$167$	6.00000			0.464294			0.232147	+	0.972681i	$0.425425\pi$
$168$	−2.50000	+	0.866025i	−0.192879	+	0.0668153i
$169$	−9.00000			−0.692308
$170$	1.00000	−	1.73205i	0.0766965	−	0.132842i
$171$	1.00000	+	1.73205i	0.0764719	+	0.132453i
$172$	3.00000	+	5.19615i	0.228748	+	0.396203i
$173$	3.00000	−	5.19615i	0.228086	−	0.395056i	−0.729155	−	0.684349i	$-0.760087\pi$
$173$	3.00000	−	5.19615i	0.228086	−	0.395056i	0.957241	+	0.289292i	$0.0934200\pi$
$174$	7.00000			0.530669
$175$	−10.0000	+	3.46410i	−0.755929	+	0.261861i
$176$	−3.00000			−0.226134
$177$	−4.50000	+	7.79423i	−0.338241	+	0.585850i
$178$		0			0
$179$	6.00000	+	10.3923i	0.448461	+	0.776757i	0.998286	−	0.0585225i	$-0.0186389\pi$
$179$	6.00000	+	10.3923i	0.448461	+	0.776757i	−0.549825	+	0.835280i	$0.685306\pi$
$180$	−0.500000	+	0.866025i	−0.0372678	+	0.0645497i
$181$	16.0000			1.18927			0.594635	−	0.803996i	$-0.297296\pi$
$181$	16.0000			1.18927			0.594635	+	0.803996i	$0.297296\pi$
$182$	−4.00000	−	3.46410i	−0.296500	−	0.256776i
$183$	−6.00000			−0.443533
$184$	−0.500000	+	0.866025i	−0.0368605	+	0.0638442i
$185$	1.00000	+	1.73205i	0.0735215	+	0.127343i
$186$	3.50000	+	6.06218i	0.256632	+	0.444500i
$187$	−3.00000	+	5.19615i	−0.219382	+	0.379980i
$188$	6.00000			0.437595
$189$	0.500000	−	2.59808i	0.0363696	−	0.188982i
$190$	−2.00000			−0.145095
$191$	−5.00000	+	8.66025i	−0.361787	+	0.626634i	−0.988255	−	0.152813i	$-0.951167\pi$
$191$	−5.00000	+	8.66025i	−0.361787	+	0.626634i	0.626468	+	0.779447i	$0.284500\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	11.5000	+	19.9186i	0.827788	+	1.43377i	0.899770	+	0.436365i	$0.143734\pi$
$193$	11.5000	+	19.9186i	0.827788	+	1.43377i	−0.0719816	+	0.997406i	$0.522932\pi$
$194$	−2.50000	+	4.33013i	−0.179490	+	0.310885i
$195$	−2.00000			−0.143223
$196$	1.00000	+	6.92820i	0.0714286	+	0.494872i
$197$	14.0000			0.997459			0.498729	−	0.866758i	$-0.333800\pi$
$197$	14.0000			0.997459			0.498729	+	0.866758i	$0.333800\pi$
$198$	1.50000	−	2.59808i	0.106600	−	0.184637i
$199$	2.00000	+	3.46410i	0.141776	+	0.245564i	0.928166	−	0.372168i	$-0.121385\pi$
$199$	2.00000	+	3.46410i	0.141776	+	0.245564i	−0.786389	+	0.617731i	$0.788052\pi$
$200$	2.00000	+	3.46410i	0.141421	+	0.244949i
$201$	5.00000	−	8.66025i	0.352673	−	0.610847i
$202$	−10.0000			−0.703598
$203$	3.50000	−	18.1865i	0.245652	−	1.27644i
$204$	2.00000			0.140028
$205$	1.00000	−	1.73205i	0.0698430	−	0.120972i
$206$	4.00000	+	6.92820i	0.278693	+	0.482711i
$207$	−0.500000	−	0.866025i	−0.0347524	−	0.0601929i
$208$	−1.00000	+	1.73205i	−0.0693375	+	0.120096i
$209$	6.00000			0.415029
$210$	2.00000	+	1.73205i	0.138013	+	0.119523i
$211$	6.00000			0.413057			0.206529	−	0.978441i	$-0.433783\pi$
$211$	6.00000			0.413057			0.206529	+	0.978441i	$0.433783\pi$
$212$	4.50000	−	7.79423i	0.309061	−	0.535310i
$213$	−4.00000	−	6.92820i	−0.274075	−	0.474713i
$214$	−1.50000	−	2.59808i	−0.102538	−	0.177601i
$215$	3.00000	−	5.19615i	0.204598	−	0.354375i
$216$	−1.00000			−0.0680414
$217$	17.5000	−	6.06218i	1.18798	−	0.411527i
$218$	10.0000			0.677285
$219$	−5.00000	+	8.66025i	−0.337869	+	0.585206i
$220$	1.50000	+	2.59808i	0.101130	+	0.175162i
$221$	2.00000	+	3.46410i	0.134535	+	0.233021i
$222$	−1.00000	+	1.73205i	−0.0671156	+	0.116248i
$223$	13.0000			0.870544			0.435272	−	0.900299i	$-0.356652\pi$
$223$	13.0000			0.870544			0.435272	+	0.900299i	$0.356652\pi$
$224$	2.50000	−	0.866025i	0.167038	−	0.0578638i
$225$	−4.00000			−0.266667
$226$	−5.00000	+	8.66025i	−0.332595	+	0.576072i
$227$	4.50000	+	7.79423i	0.298675	+	0.517321i	0.975833	−	0.218517i	$-0.0701218\pi$
$227$	4.50000	+	7.79423i	0.298675	+	0.517321i	−0.677158	+	0.735838i	$0.736789\pi$
$228$	−1.00000	−	1.73205i	−0.0662266	−	0.114708i
$229$	−11.0000	+	19.0526i	−0.726900	+	1.25903i	0.231287	+	0.972886i	$0.425707\pi$
$229$	−11.0000	+	19.0526i	−0.726900	+	1.25903i	−0.958187	+	0.286143i	$0.907627\pi$
$230$	1.00000			0.0659380
$231$	−6.00000	−	5.19615i	−0.394771	−	0.341882i
$232$	−7.00000			−0.459573
$233$	3.00000	−	5.19615i	0.196537	−	0.340411i	−0.750867	−	0.660454i	$-0.770364\pi$
$233$	3.00000	−	5.19615i	0.196537	−	0.340411i	0.947403	+	0.320043i	$0.103697\pi$
$234$	−1.00000	−	1.73205i	−0.0653720	−	0.113228i
$235$	−3.00000	−	5.19615i	−0.195698	−	0.338960i
$236$	4.50000	−	7.79423i	0.292925	−	0.507361i
$237$	15.0000			0.974355
$238$	1.00000	−	5.19615i	0.0648204	−	0.336817i
$239$	−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
$241$	13.5000	+	23.3827i	0.869611	+	1.50621i	0.862394	+	0.506237i	$0.168964\pi$
$241$	13.5000	+	23.3827i	0.869611	+	1.50621i	0.00721719	+	0.999974i	$0.497703\pi$
$242$	1.00000	+	1.73205i	0.0642824	+	0.111340i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	6.00000			0.384111
$245$	5.50000	−	4.33013i	0.351382	−	0.276642i
$246$	2.00000			0.127515
$247$	2.00000	−	3.46410i	0.127257	−	0.220416i
$248$	−3.50000	−	6.06218i	−0.222250	−	0.384949i
$249$	0.500000	+	0.866025i	0.0316862	+	0.0548821i
$250$	4.50000	−	7.79423i	0.284605	−	0.492950i
$251$	−3.00000			−0.189358			−0.0946792	−	0.995508i	$-0.530183\pi$
$251$	−3.00000			−0.189358			−0.0946792	+	0.995508i	$0.530183\pi$
$252$	−0.500000	+	2.59808i	−0.0314970	+	0.163663i
$253$	−3.00000			−0.188608
$254$	3.50000	−	6.06218i	0.219610	−	0.380375i
$255$	−1.00000	−	1.73205i	−0.0626224	−	0.108465i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	2.00000	−	3.46410i	0.124757	−	0.216085i	−0.796881	−	0.604136i	$-0.793518\pi$
$257$	2.00000	−	3.46410i	0.124757	−	0.216085i	0.921638	+	0.388051i	$0.126852\pi$
$258$	6.00000			0.373544
$259$	4.00000	+	3.46410i	0.248548	+	0.215249i
$260$	2.00000			0.124035
$261$	3.50000	−	6.06218i	0.216645	−	0.375239i
$262$	−3.50000	−	6.06218i	−0.216231	−	0.374523i
$263$	1.00000	+	1.73205i	0.0616626	+	0.106803i	0.895209	−	0.445647i	$-0.147026\pi$
$263$	1.00000	+	1.73205i	0.0616626	+	0.106803i	−0.833546	+	0.552450i	$0.813693\pi$
$264$	−1.50000	+	2.59808i	−0.0923186	+	0.159901i
$265$	−9.00000			−0.552866
$266$	−5.00000	+	1.73205i	−0.306570	+	0.106199i
$267$		0			0
$268$	−5.00000	+	8.66025i	−0.305424	+	0.529009i
$269$	13.5000	+	23.3827i	0.823110	+	1.42567i	0.903356	+	0.428892i	$0.141096\pi$
$269$	13.5000	+	23.3827i	0.823110	+	1.42567i	−0.0802460	+	0.996775i	$0.525571\pi$
$270$	0.500000	+	0.866025i	0.0304290	+	0.0527046i
$271$	4.50000	−	7.79423i	0.273356	−	0.473466i	−0.696363	−	0.717689i	$-0.745200\pi$
$271$	4.50000	−	7.79423i	0.273356	−	0.473466i	0.969719	+	0.244224i	$0.0785331\pi$
$272$	−2.00000			−0.121268
$273$	−5.00000	+	1.73205i	−0.302614	+	0.104828i
$274$	−6.00000			−0.362473
$275$	−6.00000	+	10.3923i	−0.361814	+	0.626680i
$276$	0.500000	+	0.866025i	0.0300965	+	0.0521286i
$277$	4.00000	+	6.92820i	0.240337	+	0.416275i	0.960810	−	0.277207i	$-0.0894088\pi$
$277$	4.00000	+	6.92820i	0.240337	+	0.416275i	−0.720473	+	0.693482i	$0.756075\pi$
$278$	−7.00000	+	12.1244i	−0.419832	+	0.727171i
$279$	7.00000			0.419079
$280$	−2.00000	−	1.73205i	−0.119523	−	0.103510i
$281$	−4.00000			−0.238620			−0.119310	−	0.992857i	$-0.538068\pi$
$281$	−4.00000			−0.238620			−0.119310	+	0.992857i	$0.538068\pi$
$282$	3.00000	−	5.19615i	0.178647	−	0.309426i
$283$	−3.00000	−	5.19615i	−0.178331	−	0.308879i	0.762978	−	0.646425i	$-0.223737\pi$
$283$	−3.00000	−	5.19615i	−0.178331	−	0.308879i	−0.941309	+	0.337546i	$0.890403\pi$
$284$	4.00000	+	6.92820i	0.237356	+	0.411113i
$285$	−1.00000	+	1.73205i	−0.0592349	+	0.102598i
$286$	−6.00000			−0.354787
$287$	1.00000	−	5.19615i	0.0590281	−	0.306719i
$288$	1.00000			0.0589256
$289$	6.50000	−	11.2583i	0.382353	−	0.662255i
$290$	3.50000	+	6.06218i	0.205527	+	0.355983i
$291$	2.50000	+	4.33013i	0.146553	+	0.253837i
$292$	5.00000	−	8.66025i	0.292603	−	0.506803i
$293$	19.0000			1.10999			0.554996	−	0.831853i	$-0.312720\pi$
$293$	19.0000			1.10999			0.554996	+	0.831853i	$0.312720\pi$
$294$	6.50000	+	2.59808i	0.379088	+	0.151523i
$295$	−9.00000			−0.524000
$296$	1.00000	−	1.73205i	0.0581238	−	0.100673i
$297$	−1.50000	−	2.59808i	−0.0870388	−	0.150756i
$298$	11.0000	+	19.0526i	0.637213	+	1.10369i
$299$	−1.00000	+	1.73205i	−0.0578315	+	0.100167i
$300$	4.00000			0.230940
$301$	3.00000	−	15.5885i	0.172917	−	0.898504i
$302$	−5.00000			−0.287718
$303$	−5.00000	+	8.66025i	−0.287242	+	0.497519i
$304$	1.00000	+	1.73205i	0.0573539	+	0.0993399i
$305$	−3.00000	−	5.19615i	−0.171780	−	0.297531i
$306$	1.00000	−	1.73205i	0.0571662	−	0.0990148i
$307$	−2.00000			−0.114146			−0.0570730	−	0.998370i	$-0.518177\pi$
$307$	−2.00000			−0.114146			−0.0570730	+	0.998370i	$0.518177\pi$
$308$	6.00000	+	5.19615i	0.341882	+	0.296078i
$309$	8.00000			0.455104
$310$	−3.50000	+	6.06218i	−0.198787	+	0.344309i
$311$	1.00000	+	1.73205i	0.0567048	+	0.0982156i	0.892984	−	0.450088i	$-0.148607\pi$
$311$	1.00000	+	1.73205i	0.0567048	+	0.0982156i	−0.836280	+	0.548303i	$0.815274\pi$
$312$	1.00000	+	1.73205i	0.0566139	+	0.0980581i
$313$	12.5000	−	21.6506i	0.706542	−	1.22377i	−0.259590	−	0.965719i	$-0.583588\pi$
$313$	12.5000	−	21.6506i	0.706542	−	1.22377i	0.966132	−	0.258047i	$-0.0830791\pi$
$314$	6.00000			0.338600
$315$	2.50000	−	0.866025i	0.140859	−	0.0487950i
$316$	−15.0000			−0.843816
$317$	15.5000	−	26.8468i	0.870567	−	1.50787i	0.00915525	−	0.999958i	$-0.497086\pi$
$317$	15.5000	−	26.8468i	0.870567	−	1.50787i	0.861411	−	0.507908i	$-0.169581\pi$
$318$	−4.50000	−	7.79423i	−0.252347	−	0.437079i
$319$	−10.5000	−	18.1865i	−0.587887	−	1.01825i
$320$	−0.500000	+	0.866025i	−0.0279508	+	0.0484123i
$321$	−3.00000			−0.167444
$322$	2.50000	−	0.866025i	0.139320	−	0.0482617i
$323$	4.00000			0.222566
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	4.00000	+	6.92820i	0.221880	+	0.384308i
$326$	−1.00000	−	1.73205i	−0.0553849	−	0.0959294i
$327$	5.00000	−	8.66025i	0.276501	−	0.478913i
$328$	−2.00000			−0.110432
$329$	−12.0000	−	10.3923i	−0.661581	−	0.572946i
$330$	3.00000			0.165145
$331$	−5.00000	+	8.66025i	−0.274825	+	0.476011i	−0.970091	−	0.242742i	$-0.921953\pi$
$331$	−5.00000	+	8.66025i	−0.274825	+	0.476011i	0.695266	+	0.718752i	$0.255287\pi$
$332$	−0.500000	−	0.866025i	−0.0274411	−	0.0475293i
$333$	1.00000	+	1.73205i	0.0547997	+	0.0949158i
$334$	−3.00000	+	5.19615i	−0.164153	+	0.284321i
$335$	10.0000			0.546358
$336$	0.500000	−	2.59808i	0.0272772	−	0.141737i
$337$	−9.00000			−0.490261			−0.245131	−	0.969490i	$-0.578831\pi$
$337$	−9.00000			−0.490261			−0.245131	+	0.969490i	$0.578831\pi$
$338$	4.50000	−	7.79423i	0.244768	−	0.423950i
$339$	5.00000	+	8.66025i	0.271563	+	0.470360i
$340$	1.00000	+	1.73205i	0.0542326	+	0.0939336i
$341$	10.5000	−	18.1865i	0.568607	−	0.984856i
$342$	−2.00000			−0.108148
$343$	10.0000	−	15.5885i	0.539949	−	0.841698i
$344$	−6.00000			−0.323498
$345$	0.500000	−	0.866025i	0.0269191	−	0.0466252i
$346$	3.00000	+	5.19615i	0.161281	+	0.279347i
$347$	−18.0000	−	31.1769i	−0.966291	−	1.67366i	−0.706107	−	0.708105i	$-0.749550\pi$
$347$	−18.0000	−	31.1769i	−0.966291	−	1.67366i	−0.260184	−	0.965559i	$-0.583783\pi$
$348$	−3.50000	+	6.06218i	−0.187620	+	0.324967i
$349$	16.0000			0.856460			0.428230	−	0.903670i	$-0.359137\pi$
$349$	16.0000			0.856460			0.428230	+	0.903670i	$0.359137\pi$
$350$	2.00000	−	10.3923i	0.106904	−	0.555492i
$351$	−2.00000			−0.106752
$352$	1.50000	−	2.59808i	0.0799503	−	0.138478i
$353$	13.0000	+	22.5167i	0.691920	+	1.19844i	0.971208	+	0.238233i	$0.0765683\pi$
$353$	13.0000	+	22.5167i	0.691920	+	1.19844i	−0.279288	+	0.960207i	$0.590098\pi$
$354$	−4.50000	−	7.79423i	−0.239172	−	0.414259i
$355$	4.00000	−	6.92820i	0.212298	−	0.367711i
$356$		0			0
$357$	−4.00000	−	3.46410i	−0.211702	−	0.183340i
$358$	−12.0000			−0.634220
$359$	−15.0000	+	25.9808i	−0.791670	+	1.37121i	0.133263	+	0.991081i	$0.457455\pi$
$359$	−15.0000	+	25.9808i	−0.791670	+	1.37121i	−0.924932	+	0.380131i	$0.875879\pi$
$360$	−0.500000	−	0.866025i	−0.0263523	−	0.0456435i
$361$	7.50000	+	12.9904i	0.394737	+	0.683704i
$362$	−8.00000	+	13.8564i	−0.420471	+	0.728277i
$363$	2.00000			0.104973
$364$	5.00000	−	1.73205i	0.262071	−	0.0907841i
$365$	−10.0000			−0.523424
$366$	3.00000	−	5.19615i	0.156813	−	0.271607i
$367$	−3.50000	−	6.06218i	−0.182699	−	0.316443i	0.760100	−	0.649806i	$-0.225150\pi$
$367$	−3.50000	−	6.06218i	−0.182699	−	0.316443i	−0.942799	+	0.333363i	$0.891817\pi$
$368$	−0.500000	−	0.866025i	−0.0260643	−	0.0451447i
$369$	1.00000	−	1.73205i	0.0520579	−	0.0901670i
$370$	−2.00000			−0.103975
$371$	−22.5000	+	7.79423i	−1.16814	+	0.404656i
$372$	−7.00000			−0.362933
$373$	−16.0000	+	27.7128i	−0.828449	+	1.43492i	0.0708063	+	0.997490i	$0.477443\pi$
$373$	−16.0000	+	27.7128i	−0.828449	+	1.43492i	−0.899255	+	0.437425i	$0.855891\pi$
$374$	−3.00000	−	5.19615i	−0.155126	−	0.268687i
$375$	−4.50000	−	7.79423i	−0.232379	−	0.402492i
$376$	−3.00000	+	5.19615i	−0.154713	+	0.267971i
$377$	−14.0000			−0.721037
$378$	2.00000	+	1.73205i	0.102869	+	0.0890871i
$379$	−4.00000			−0.205466			−0.102733	−	0.994709i	$-0.532759\pi$
$379$	−4.00000			−0.205466			−0.102733	+	0.994709i	$0.532759\pi$
$380$	1.00000	−	1.73205i	0.0512989	−	0.0888523i
$381$	−3.50000	−	6.06218i	−0.179310	−	0.310575i
$382$	−5.00000	−	8.66025i	−0.255822	−	0.443097i
$383$	−4.00000	+	6.92820i	−0.204390	+	0.354015i	−0.949938	−	0.312437i	$-0.898855\pi$
$383$	−4.00000	+	6.92820i	−0.204390	+	0.354015i	0.745548	+	0.666452i	$0.232188\pi$
$384$	−1.00000			−0.0510310
$385$	1.50000	−	7.79423i	0.0764471	−	0.397231i
$386$	−23.0000			−1.17067
$387$	3.00000	−	5.19615i	0.152499	−	0.264135i
$388$	−2.50000	−	4.33013i	−0.126918	−	0.219829i
$389$	−19.0000	−	32.9090i	−0.963338	−	1.66855i	−0.714015	−	0.700130i	$-0.753125\pi$
$389$	−19.0000	−	32.9090i	−0.963338	−	1.66855i	−0.249323	−	0.968420i	$-0.580208\pi$
$390$	1.00000	−	1.73205i	0.0506370	−	0.0877058i
$391$	−2.00000			−0.101144
$392$	−6.50000	−	2.59808i	−0.328300	−	0.131223i
$393$	−7.00000			−0.353103
$394$	−7.00000	+	12.1244i	−0.352655	+	0.610816i
$395$	7.50000	+	12.9904i	0.377366	+	0.653617i
$396$	1.50000	+	2.59808i	0.0753778	+	0.130558i
$397$	19.0000	−	32.9090i	0.953583	−	1.65165i	0.216004	−	0.976392i	$-0.430698\pi$
$397$	19.0000	−	32.9090i	0.953583	−	1.65165i	0.737579	−	0.675261i	$-0.235969\pi$
$398$	−4.00000			−0.200502
$399$	−1.00000	+	5.19615i	−0.0500626	+	0.260133i
$400$	−4.00000			−0.200000
$401$	−2.00000	+	3.46410i	−0.0998752	+	0.172989i	−0.911633	−	0.411005i	$-0.865178\pi$
$401$	−2.00000	+	3.46410i	−0.0998752	+	0.172989i	0.811758	+	0.583994i	$0.198511\pi$
$402$	5.00000	+	8.66025i	0.249377	+	0.431934i
$403$	−7.00000	−	12.1244i	−0.348695	−	0.603957i
$404$	5.00000	−	8.66025i	0.248759	−	0.430864i
$405$	1.00000			0.0496904
$406$	14.0000	+	12.1244i	0.694808	+	0.601722i
$407$	6.00000			0.297409
$408$	−1.00000	+	1.73205i	−0.0495074	+	0.0857493i
$409$	14.5000	+	25.1147i	0.716979	+	1.24184i	0.962191	+	0.272374i	$0.0878089\pi$
$409$	14.5000	+	25.1147i	0.716979	+	1.24184i	−0.245212	+	0.969469i	$0.578858\pi$
$410$	1.00000	+	1.73205i	0.0493865	+	0.0855399i
$411$	−3.00000	+	5.19615i	−0.147979	+	0.256307i
$412$	−8.00000			−0.394132
$413$	−22.5000	+	7.79423i	−1.10715	+	0.383529i
$414$	1.00000			0.0491473
$415$	−0.500000	+	0.866025i	−0.0245440	+	0.0425115i
$416$	−1.00000	−	1.73205i	−0.0490290	−	0.0849208i
$417$	7.00000	+	12.1244i	0.342791	+	0.593732i
$418$	−3.00000	+	5.19615i	−0.146735	+	0.254152i
$419$	−36.0000			−1.75872			−0.879358	−	0.476162i	$-0.842028\pi$
$419$	−36.0000			−1.75872			−0.879358	+	0.476162i	$0.842028\pi$
$420$	−2.50000	+	0.866025i	−0.121988	+	0.0422577i
$421$	−18.0000			−0.877266			−0.438633	−	0.898666i	$-0.644537\pi$
$421$	−18.0000			−0.877266			−0.438633	+	0.898666i	$0.644537\pi$
$422$	−3.00000	+	5.19615i	−0.146038	+	0.252945i
$423$	−3.00000	−	5.19615i	−0.145865	−	0.252646i
$424$	4.50000	+	7.79423i	0.218539	+	0.378521i
$425$	−4.00000	+	6.92820i	−0.194029	+	0.336067i
$426$	8.00000			0.387601
$427$	−12.0000	−	10.3923i	−0.580721	−	0.502919i
$428$	3.00000			0.145010
$429$	−3.00000	+	5.19615i	−0.144841	+	0.250873i
$430$	3.00000	+	5.19615i	0.144673	+	0.250581i
$431$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$431$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	38.0000			1.82616			0.913082	−	0.407777i	$-0.133696\pi$
$433$	38.0000			1.82616			0.913082	+	0.407777i	$0.133696\pi$
$434$	−3.50000	+	18.1865i	−0.168005	+	0.872982i
$435$	7.00000			0.335624
$436$	−5.00000	+	8.66025i	−0.239457	+	0.414751i
$437$	1.00000	+	1.73205i	0.0478365	+	0.0828552i
$438$	−5.00000	−	8.66025i	−0.238909	−	0.413803i
$439$	−17.5000	+	30.3109i	−0.835229	+	1.44666i	0.0586141	+	0.998281i	$0.481332\pi$
$439$	−17.5000	+	30.3109i	−0.835229	+	1.44666i	−0.893843	+	0.448379i	$0.852001\pi$
$440$	−3.00000			−0.143019
$441$	5.50000	−	4.33013i	0.261905	−	0.206197i
$442$	−4.00000			−0.190261
$443$	14.5000	−	25.1147i	0.688916	−	1.19324i	−0.283273	−	0.959039i	$-0.591420\pi$
$443$	14.5000	−	25.1147i	0.688916	−	1.19324i	0.972189	−	0.234198i	$-0.0752464\pi$
$444$	−1.00000	−	1.73205i	−0.0474579	−	0.0821995i
$445$		0			0
$446$	−6.50000	+	11.2583i	−0.307784	+	0.533097i
$447$	22.0000			1.04056
$448$	−0.500000	+	2.59808i	−0.0236228	+	0.122748i
$449$	−30.0000			−1.41579			−0.707894	−	0.706319i	$-0.750354\pi$
$449$	−30.0000			−1.41579			−0.707894	+	0.706319i	$0.750354\pi$
$450$	2.00000	−	3.46410i	0.0942809	−	0.163299i
$451$	−3.00000	−	5.19615i	−0.141264	−	0.244677i
$452$	−5.00000	−	8.66025i	−0.235180	−	0.407344i
$453$	−2.50000	+	4.33013i	−0.117460	+	0.203447i
$454$	−9.00000			−0.422391
$455$	−4.00000	−	3.46410i	−0.187523	−	0.162400i
$456$	2.00000			0.0936586
$457$	−0.500000	+	0.866025i	−0.0233890	+	0.0405110i	−0.877483	−	0.479608i	$-0.840779\pi$
$457$	−0.500000	+	0.866025i	−0.0233890	+	0.0405110i	0.854094	+	0.520119i	$0.174112\pi$
$458$	−11.0000	−	19.0526i	−0.513996	−	0.890268i
$459$	−1.00000	−	1.73205i	−0.0466760	−	0.0808452i
$460$	−0.500000	+	0.866025i	−0.0233126	+	0.0403786i
$461$	2.00000			0.0931493			0.0465746	−	0.998915i	$-0.485169\pi$
$461$	2.00000			0.0931493			0.0465746	+	0.998915i	$0.485169\pi$
$462$	7.50000	−	2.59808i	0.348932	−	0.120873i
$463$	−8.00000			−0.371792			−0.185896	−	0.982569i	$-0.559519\pi$
$463$	−8.00000			−0.371792			−0.185896	+	0.982569i	$0.559519\pi$
$464$	3.50000	−	6.06218i	0.162483	−	0.281430i
$465$	3.50000	+	6.06218i	0.162309	+	0.281127i
$466$	3.00000	+	5.19615i	0.138972	+	0.240707i
$467$	−2.00000	+	3.46410i	−0.0925490	+	0.160300i	−0.908583	−	0.417704i	$-0.862835\pi$
$467$	−2.00000	+	3.46410i	−0.0925490	+	0.160300i	0.816034	+	0.578004i	$0.196168\pi$
$468$	2.00000			0.0924500
$469$	25.0000	−	8.66025i	1.15439	−	0.399893i
$470$	6.00000			0.276759
$471$	3.00000	−	5.19615i	0.138233	−	0.239426i
$472$	4.50000	+	7.79423i	0.207129	+	0.358758i
$473$	−9.00000	−	15.5885i	−0.413820	−	0.716758i
$474$	−7.50000	+	12.9904i	−0.344486	+	0.596668i
$475$	8.00000			0.367065
$476$	4.00000	+	3.46410i	0.183340	+	0.158777i
$477$	−9.00000			−0.412082
$478$	6.00000	−	10.3923i	0.274434	−	0.475333i
$479$	−14.0000	−	24.2487i	−0.639676	−	1.10795i	−0.985504	−	0.169654i	$-0.945735\pi$
$479$	−14.0000	−	24.2487i	−0.639676	−	1.10795i	0.345827	−	0.938298i	$-0.387598\pi$
$480$	0.500000	+	0.866025i	0.0228218	+	0.0395285i
$481$	2.00000	−	3.46410i	0.0911922	−	0.157949i
$482$	−27.0000			−1.22982
$483$	0.500000	−	2.59808i	0.0227508	−	0.118217i
$484$	−2.00000			−0.0909091
$485$	−2.50000	+	4.33013i	−0.113519	+	0.196621i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	7.50000	+	12.9904i	0.339857	+	0.588650i	0.984406	−	0.175913i	$-0.0562878\pi$
$487$	7.50000	+	12.9904i	0.339857	+	0.588650i	−0.644548	+	0.764564i	$0.722955\pi$
$488$	−3.00000	+	5.19615i	−0.135804	+	0.235219i
$489$	−2.00000			−0.0904431
$490$	1.00000	+	6.92820i	0.0451754	+	0.312984i
$491$	19.0000			0.857458			0.428729	−	0.903433i	$-0.358962\pi$
$491$	19.0000			0.857458			0.428729	+	0.903433i	$0.358962\pi$
$492$	−1.00000	+	1.73205i	−0.0450835	+	0.0780869i
$493$	−7.00000	−	12.1244i	−0.315264	−	0.546054i
$494$	2.00000	+	3.46410i	0.0899843	+	0.155857i
$495$	1.50000	−	2.59808i	0.0674200	−	0.116775i
$496$	7.00000			0.314309
$497$	4.00000	−	20.7846i	0.179425	−	0.932317i
$498$	−1.00000			−0.0448111
$499$	−3.00000	+	5.19615i	−0.134298	+	0.232612i	−0.925329	−	0.379165i	$-0.876211\pi$
$499$	−3.00000	+	5.19615i	−0.134298	+	0.232612i	0.791031	+	0.611776i	$0.209545\pi$
$500$	4.50000	+	7.79423i	0.201246	+	0.348569i
$501$	3.00000	+	5.19615i	0.134030	+	0.232147i
$502$	1.50000	−	2.59808i	0.0669483	−	0.115958i
$503$	−28.0000			−1.24846			−0.624229	−	0.781241i	$-0.714587\pi$
$503$	−28.0000			−1.24846			−0.624229	+	0.781241i	$0.714587\pi$
$504$	−2.00000	−	1.73205i	−0.0890871	−	0.0771517i
$505$	−10.0000			−0.444994
$506$	1.50000	−	2.59808i	0.0666831	−	0.115499i
$507$	−4.50000	−	7.79423i	−0.199852	−	0.346154i
$508$	3.50000	+	6.06218i	0.155287	+	0.268966i
$509$	−8.50000	+	14.7224i	−0.376756	+	0.652560i	−0.990588	−	0.136876i	$-0.956294\pi$
$509$	−8.50000	+	14.7224i	−0.376756	+	0.652560i	0.613832	+	0.789436i	$0.289627\pi$
$510$	2.00000			0.0885615
$511$	−25.0000	+	8.66025i	−1.10593	+	0.383107i
$512$	1.00000			0.0441942
$513$	−1.00000	+	1.73205i	−0.0441511	+	0.0764719i
$514$	2.00000	+	3.46410i	0.0882162	+	0.152795i
$515$	4.00000	+	6.92820i	0.176261	+	0.305293i
$516$	−3.00000	+	5.19615i	−0.132068	+	0.228748i
$517$	−18.0000			−0.791639
$518$	−5.00000	+	1.73205i	−0.219687	+	0.0761019i
$519$	6.00000			0.263371
$520$	−1.00000	+	1.73205i	−0.0438529	+	0.0759555i
$521$	9.00000	+	15.5885i	0.394297	+	0.682943i	0.993011	−	0.118020i	$-0.0376547\pi$
$521$	9.00000	+	15.5885i	0.394297	+	0.682943i	−0.598714	+	0.800963i	$0.704321\pi$
$522$	3.50000	+	6.06218i	0.153191	+	0.265334i
$523$	6.00000	−	10.3923i	0.262362	−	0.454424i	−0.704507	−	0.709697i	$-0.748832\pi$
$523$	6.00000	−	10.3923i	0.262362	−	0.454424i	0.966869	+	0.255273i	$0.0821653\pi$
$524$	7.00000			0.305796
$525$	−8.00000	−	6.92820i	−0.349149	−	0.302372i
$526$	−2.00000			−0.0872041
$527$	7.00000	−	12.1244i	0.304925	−	0.528145i
$528$	−1.50000	−	2.59808i	−0.0652791	−	0.113067i
$529$	−0.500000	−	0.866025i	−0.0217391	−	0.0376533i
$530$	4.50000	−	7.79423i	0.195468	−	0.338560i
$531$	−9.00000			−0.390567
$532$	1.00000	−	5.19615i	0.0433555	−	0.225282i
$533$	−4.00000			−0.173259
$534$		0			0
$535$	−1.50000	−	2.59808i	−0.0648507	−	0.112325i
$536$	−5.00000	−	8.66025i	−0.215967	−	0.374066i
$537$	−6.00000	+	10.3923i	−0.258919	+	0.448461i
$538$	−27.0000			−1.16405
$539$	−3.00000	−	20.7846i	−0.129219	−	0.895257i
$540$	−1.00000			−0.0430331
$541$	4.00000	−	6.92820i	0.171973	−	0.297867i	−0.767136	−	0.641484i	$-0.778319\pi$
$541$	4.00000	−	6.92820i	0.171973	−	0.297867i	0.939110	+	0.343617i	$0.111652\pi$
$542$	4.50000	+	7.79423i	0.193292	+	0.334791i
$543$	8.00000	+	13.8564i	0.343313	+	0.594635i
$544$	1.00000	−	1.73205i	0.0428746	−	0.0742611i
$545$	10.0000			0.428353
$546$	1.00000	−	5.19615i	0.0427960	−	0.222375i
$547$	−38.0000			−1.62476			−0.812381	−	0.583127i	$-0.801829\pi$
$547$	−38.0000			−1.62476			−0.812381	+	0.583127i	$0.801829\pi$
$548$	3.00000	−	5.19615i	0.128154	−	0.221969i
$549$	−3.00000	−	5.19615i	−0.128037	−	0.221766i
$550$	−6.00000	−	10.3923i	−0.255841	−	0.443129i
$551$	−7.00000	+	12.1244i	−0.298210	+	0.516515i
$552$	−1.00000			−0.0425628
$553$	30.0000	+	25.9808i	1.27573	+	1.10481i
$554$	−8.00000			−0.339887
$555$	−1.00000	+	1.73205i	−0.0424476	+	0.0735215i
$556$	−7.00000	−	12.1244i	−0.296866	−	0.514187i
$557$	−16.5000	−	28.5788i	−0.699127	−	1.21092i	−0.968769	−	0.247964i	$-0.920239\pi$
$557$	−16.5000	−	28.5788i	−0.699127	−	1.21092i	0.269642	−	0.962961i	$-0.413095\pi$
$558$	−3.50000	+	6.06218i	−0.148167	+	0.256632i
$559$	−12.0000			−0.507546
$560$	2.50000	−	0.866025i	0.105644	−	0.0365963i
$561$	−6.00000			−0.253320
$562$	2.00000	−	3.46410i	0.0843649	−	0.146124i
$563$	1.50000	+	2.59808i	0.0632175	+	0.109496i	0.895902	−	0.444252i	$-0.146530\pi$
$563$	1.50000	+	2.59808i	0.0632175	+	0.109496i	−0.832684	+	0.553748i	$0.813197\pi$
$564$	3.00000	+	5.19615i	0.126323	+	0.218797i
$565$	−5.00000	+	8.66025i	−0.210352	+	0.364340i
$566$	6.00000			0.252199
$567$	2.50000	−	0.866025i	0.104990	−	0.0363696i
$568$	−8.00000			−0.335673
$569$	18.0000	−	31.1769i	0.754599	−	1.30700i	−0.190974	−	0.981595i	$-0.561165\pi$
$569$	18.0000	−	31.1769i	0.754599	−	1.30700i	0.945573	−	0.325409i	$-0.105502\pi$
$570$	−1.00000	−	1.73205i	−0.0418854	−	0.0725476i
$571$	−10.0000	−	17.3205i	−0.418487	−	0.724841i	0.577301	−	0.816532i	$-0.304106\pi$
$571$	−10.0000	−	17.3205i	−0.418487	−	0.724841i	−0.995788	+	0.0916910i	$0.970773\pi$
$572$	3.00000	−	5.19615i	0.125436	−	0.217262i
$573$	−10.0000			−0.417756
$574$	4.00000	+	3.46410i	0.166957	+	0.144589i
$575$	−4.00000			−0.166812
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	16.5000	+	28.5788i	0.686904	+	1.18975i	0.972834	+	0.231502i	$0.0743641\pi$
$577$	16.5000	+	28.5788i	0.686904	+	1.18975i	−0.285930	+	0.958250i	$0.592303\pi$
$578$	6.50000	+	11.2583i	0.270364	+	0.468285i
$579$	−11.5000	+	19.9186i	−0.477924	+	0.827788i
$580$	−7.00000			−0.290659
$581$	−0.500000	+	2.59808i	−0.0207435	+	0.107786i
$582$	−5.00000			−0.207257
$583$	−13.5000	+	23.3827i	−0.559113	+	0.968412i
$584$	5.00000	+	8.66025i	0.206901	+	0.358364i
$585$	−1.00000	−	1.73205i	−0.0413449	−	0.0716115i
$586$	−9.50000	+	16.4545i	−0.392441	+	0.679728i
$587$	−3.00000			−0.123823			−0.0619116	−	0.998082i	$-0.519720\pi$
$587$	−3.00000			−0.123823			−0.0619116	+	0.998082i	$0.519720\pi$
$588$	−5.50000	+	4.33013i	−0.226816	+	0.178571i
$589$	−14.0000			−0.576860
$590$	4.50000	−	7.79423i	0.185262	−	0.320883i
$591$	7.00000	+	12.1244i	0.287942	+	0.498729i
$592$	1.00000	+	1.73205i	0.0410997	+	0.0711868i
$593$	6.00000	−	10.3923i	0.246390	−	0.426761i	−0.716131	−	0.697966i	$-0.754089\pi$
$593$	6.00000	−	10.3923i	0.246390	−	0.426761i	0.962522	+	0.271205i	$0.0874221\pi$
$594$	3.00000			0.123091
$595$	1.00000	−	5.19615i	0.0409960	−	0.213021i
$596$	−22.0000			−0.901155
$597$	−2.00000	+	3.46410i	−0.0818546	+	0.141776i
$598$	−1.00000	−	1.73205i	−0.0408930	−	0.0708288i
$599$	−12.0000	−	20.7846i	−0.490307	−	0.849236i	0.509631	−	0.860393i	$-0.329782\pi$
$599$	−12.0000	−	20.7846i	−0.490307	−	0.849236i	−0.999938	+	0.0111569i	$0.996449\pi$
$600$	−2.00000	+	3.46410i	−0.0816497	+	0.141421i
$601$	23.0000			0.938190			0.469095	−	0.883148i	$-0.344580\pi$
$601$	23.0000			0.938190			0.469095	+	0.883148i	$0.344580\pi$
$602$	12.0000	+	10.3923i	0.489083	+	0.423559i
$603$	10.0000			0.407231
$604$	2.50000	−	4.33013i	0.101724	−	0.176190i
$605$	1.00000	+	1.73205i	0.0406558	+	0.0704179i
$606$	−5.00000	−	8.66025i	−0.203111	−	0.351799i
$607$	−10.5000	+	18.1865i	−0.426182	+	0.738169i	−0.996530	−	0.0832344i	$-0.973475\pi$
$607$	−10.5000	+	18.1865i	−0.426182	+	0.738169i	0.570348	+	0.821403i	$0.306808\pi$
$608$	−2.00000			−0.0811107
$609$	17.5000	−	6.06218i	0.709136	−	0.245652i
$610$	6.00000			0.242933
$611$	−6.00000	+	10.3923i	−0.242734	+	0.420428i
$612$	1.00000	+	1.73205i	0.0404226	+	0.0700140i
$613$	−18.0000	−	31.1769i	−0.727013	−	1.25922i	−0.958140	−	0.286300i	$-0.907575\pi$
$613$	−18.0000	−	31.1769i	−0.727013	−	1.25922i	0.231127	−	0.972924i	$-0.425759\pi$
$614$	1.00000	−	1.73205i	0.0403567	−	0.0698999i
$615$	2.00000			0.0806478
$616$	−7.50000	+	2.59808i	−0.302184	+	0.104679i
$617$	−6.00000			−0.241551			−0.120775	−	0.992680i	$-0.538538\pi$
$617$	−6.00000			−0.241551			−0.120775	+	0.992680i	$0.538538\pi$
$618$	−4.00000	+	6.92820i	−0.160904	+	0.278693i
$619$	8.00000	+	13.8564i	0.321547	+	0.556936i	0.980807	−	0.194979i	$-0.0624638\pi$
$619$	8.00000	+	13.8564i	0.321547	+	0.556936i	−0.659260	+	0.751915i	$0.729130\pi$
$620$	−3.50000	−	6.06218i	−0.140563	−	0.243463i
$621$	0.500000	−	0.866025i	0.0200643	−	0.0347524i
$622$	−2.00000			−0.0801927
$623$		0			0
$624$	−2.00000			−0.0800641
$625$	−5.50000	+	9.52628i	−0.220000	+	0.381051i
$626$	12.5000	+	21.6506i	0.499600	+	0.865333i
$627$	3.00000	+	5.19615i	0.119808	+	0.207514i
$628$	−3.00000	+	5.19615i	−0.119713	+	0.207349i
$629$	4.00000			0.159490
$630$	−0.500000	+	2.59808i	−0.0199205	+	0.103510i
$631$	31.0000			1.23409			0.617045	−	0.786928i	$-0.288330\pi$
$631$	31.0000			1.23409			0.617045	+	0.786928i	$0.288330\pi$
$632$	7.50000	−	12.9904i	0.298334	−	0.516730i
$633$	3.00000	+	5.19615i	0.119239	+	0.206529i
$634$	15.5000	+	26.8468i	0.615584	+	1.06622i
$635$	3.50000	−	6.06218i	0.138893	−	0.240570i
$636$	9.00000			0.356873
$637$	−13.0000	−	5.19615i	−0.515079	−	0.205879i
$638$	21.0000			0.831398
$639$	4.00000	−	6.92820i	0.158238	−	0.274075i
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	6.00000	+	10.3923i	0.236986	+	0.410471i	0.959848	−	0.280521i	$-0.0905072\pi$
$641$	6.00000	+	10.3923i	0.236986	+	0.410471i	−0.722862	+	0.690992i	$0.757174\pi$
$642$	1.50000	−	2.59808i	0.0592003	−	0.102538i
$643$	4.00000			0.157745			0.0788723	−	0.996885i	$-0.474868\pi$
$643$	4.00000			0.157745			0.0788723	+	0.996885i	$0.474868\pi$
$644$	−0.500000	+	2.59808i	−0.0197028	+	0.102379i
$645$	6.00000			0.236250
$646$	−2.00000	+	3.46410i	−0.0786889	+	0.136293i
$647$	−19.0000	−	32.9090i	−0.746967	−	1.29378i	−0.949270	−	0.314462i	$-0.898176\pi$
$647$	−19.0000	−	32.9090i	−0.746967	−	1.29378i	0.202303	−	0.979323i	$-0.435157\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	−13.5000	+	23.3827i	−0.529921	+	0.917851i
$650$	−8.00000			−0.313786
$651$	14.0000	+	12.1244i	0.548703	+	0.475191i
$652$	2.00000			0.0783260
$653$	−5.50000	+	9.52628i	−0.215232	+	0.372792i	−0.953344	−	0.301885i	$-0.902384\pi$
$653$	−5.50000	+	9.52628i	−0.215232	+	0.372792i	0.738113	+	0.674678i	$0.235717\pi$
$654$	5.00000	+	8.66025i	0.195515	+	0.338643i
$655$	−3.50000	−	6.06218i	−0.136756	−	0.236869i
$656$	1.00000	−	1.73205i	0.0390434	−	0.0676252i
$657$	−10.0000			−0.390137
$658$	15.0000	−	5.19615i	0.584761	−	0.202567i
$659$	28.0000			1.09073			0.545363	−	0.838200i	$-0.316392\pi$
$659$	28.0000			1.09073			0.545363	+	0.838200i	$0.316392\pi$
$660$	−1.50000	+	2.59808i	−0.0583874	+	0.101130i
$661$	−19.0000	−	32.9090i	−0.739014	−	1.28001i	−0.952940	−	0.303160i	$-0.901958\pi$
$661$	−19.0000	−	32.9090i	−0.739014	−	1.28001i	0.213925	−	0.976850i	$-0.431375\pi$
$662$	−5.00000	−	8.66025i	−0.194331	−	0.336590i
$663$	−2.00000	+	3.46410i	−0.0776736	+	0.134535i
$664$	1.00000			0.0388075
$665$	−5.00000	+	1.73205i	−0.193892	+	0.0671660i
$666$	−2.00000			−0.0774984
$667$	3.50000	−	6.06218i	0.135521	−	0.234728i
$668$	−3.00000	−	5.19615i	−0.116073	−	0.201045i
$669$	6.50000	+	11.2583i	0.251305	+	0.435272i
$670$	−5.00000	+	8.66025i	−0.193167	+	0.334575i
$671$	−18.0000			−0.694882
$672$	2.00000	+	1.73205i	0.0771517	+	0.0668153i
$673$	25.0000			0.963679			0.481840	−	0.876259i	$-0.339969\pi$
$673$	25.0000			0.963679			0.481840	+	0.876259i	$0.339969\pi$
$674$	4.50000	−	7.79423i	0.173334	−	0.300222i
$675$	−2.00000	−	3.46410i	−0.0769800	−	0.133333i
$676$	4.50000	+	7.79423i	0.173077	+	0.299778i
$677$	17.5000	−	30.3109i	0.672580	−	1.16494i	−0.304590	−	0.952483i	$-0.598520\pi$
$677$	17.5000	−	30.3109i	0.672580	−	1.16494i	0.977170	−	0.212459i	$-0.0681471\pi$
$678$	−10.0000			−0.384048
$679$	−2.50000	+	12.9904i	−0.0959412	+	0.498525i
$680$	−2.00000			−0.0766965
$681$	−4.50000	+	7.79423i	−0.172440	+	0.298675i
$682$	10.5000	+	18.1865i	0.402066	+	0.696398i
$683$	11.5000	+	19.9186i	0.440035	+	0.762163i	0.997692	−	0.0679085i	$-0.0216326\pi$
$683$	11.5000	+	19.9186i	0.440035	+	0.762163i	−0.557656	+	0.830072i	$0.688299\pi$
$684$	1.00000	−	1.73205i	0.0382360	−	0.0662266i
$685$	−6.00000			−0.229248
$686$	8.50000	+	16.4545i	0.324532	+	0.628235i
$687$	−22.0000			−0.839352
$688$	3.00000	−	5.19615i	0.114374	−	0.198101i
$689$	9.00000	+	15.5885i	0.342873	+	0.593873i
$690$	0.500000	+	0.866025i	0.0190347	+	0.0329690i
$691$	11.0000	−	19.0526i	0.418460	−	0.724793i	−0.577325	−	0.816514i	$-0.695903\pi$
$691$	11.0000	−	19.0526i	0.418460	−	0.724793i	0.995785	+	0.0917209i	$0.0292368\pi$
$692$	−6.00000			−0.228086
$693$	1.50000	−	7.79423i	0.0569803	−	0.296078i
$694$	36.0000			1.36654
$695$	−7.00000	+	12.1244i	−0.265525	+	0.459903i
$696$	−3.50000	−	6.06218i	−0.132667	−	0.229786i
$697$	−2.00000	−	3.46410i	−0.0757554	−	0.131212i
$698$	−8.00000	+	13.8564i	−0.302804	+	0.524473i
$699$	6.00000			0.226941
$700$	8.00000	+	6.92820i	0.302372	+	0.261861i
$701$	−1.00000			−0.0377695			−0.0188847	−	0.999822i	$-0.506012\pi$
$701$	−1.00000			−0.0377695			−0.0188847	+	0.999822i	$0.506012\pi$
$702$	1.00000	−	1.73205i	0.0377426	−	0.0653720i
$703$	−2.00000	−	3.46410i	−0.0754314	−	0.130651i
$704$	1.50000	+	2.59808i	0.0565334	+	0.0979187i
$705$	3.00000	−	5.19615i	0.112987	−	0.195698i
$706$	−26.0000			−0.978523
$707$	−25.0000	+	8.66025i	−0.940222	+	0.325702i
$708$	9.00000			0.338241
$709$	14.0000	−	24.2487i	0.525781	−	0.910679i	−0.473768	−	0.880650i	$-0.657106\pi$
$709$	14.0000	−	24.2487i	0.525781	−	0.910679i	0.999549	−	0.0300298i	$-0.00956021\pi$
$710$	4.00000	+	6.92820i	0.150117	+	0.260011i
$711$	7.50000	+	12.9904i	0.281272	+	0.487177i
$712$		0			0
$713$	7.00000			0.262152
$714$	5.00000	−	1.73205i	0.187120	−	0.0648204i
$715$	−6.00000			−0.224387
$716$	6.00000	−	10.3923i	0.224231	−	0.388379i
$717$	−6.00000	−	10.3923i	−0.224074	−	0.388108i
$718$	−15.0000	−	25.9808i	−0.559795	−	0.969593i
$719$	15.0000	−	25.9808i	0.559406	−	0.968919i	−0.438141	−	0.898906i	$-0.644363\pi$
$719$	15.0000	−	25.9808i	0.559406	−	0.968919i	0.997546	−	0.0700124i	$-0.0223039\pi$
$720$	1.00000			0.0372678
$721$	16.0000	+	13.8564i	0.595871	+	0.516040i
$722$	−15.0000			−0.558242
$723$	−13.5000	+	23.3827i	−0.502070	+	0.869611i
$724$	−8.00000	−	13.8564i	−0.297318	−	0.514969i
$725$	−14.0000	−	24.2487i	−0.519947	−	0.900575i
$726$	−1.00000	+	1.73205i	−0.0371135	+	0.0642824i
$727$	5.00000			0.185440			0.0927199	−	0.995692i	$-0.470444\pi$
$727$	5.00000			0.185440			0.0927199	+	0.995692i	$0.470444\pi$
$728$	−1.00000	+	5.19615i	−0.0370625	+	0.192582i
$729$	1.00000			0.0370370
$730$	5.00000	−	8.66025i	0.185058	−	0.320530i
$731$	−6.00000	−	10.3923i	−0.221918	−	0.384373i
$732$	3.00000	+	5.19615i	0.110883	+	0.192055i
$733$	14.0000	−	24.2487i	0.517102	−	0.895647i	−0.482701	−	0.875785i	$-0.660344\pi$
$733$	14.0000	−	24.2487i	0.517102	−	0.895647i	0.999803	−	0.0198613i	$-0.00632248\pi$
$734$	7.00000			0.258375
$735$	6.50000	+	2.59808i	0.239756	+	0.0958315i
$736$	1.00000			0.0368605
$737$	15.0000	−	25.9808i	0.552532	−	0.957014i
$738$	1.00000	+	1.73205i	0.0368105	+	0.0637577i
$739$	7.00000	+	12.1244i	0.257499	+	0.446002i	0.965571	−	0.260138i	$-0.0837682\pi$
$739$	7.00000	+	12.1244i	0.257499	+	0.446002i	−0.708072	+	0.706140i	$0.750435\pi$
$740$	1.00000	−	1.73205i	0.0367607	−	0.0636715i
$741$	4.00000			0.146944
$742$	4.50000	−	23.3827i	0.165200	−	0.858405i
$743$	48.0000			1.76095			0.880475	−	0.474093i	$-0.157224\pi$
$743$	48.0000			1.76095			0.880475	+	0.474093i	$0.157224\pi$
$744$	3.50000	−	6.06218i	0.128316	−	0.222250i
$745$	11.0000	+	19.0526i	0.403009	+	0.698032i
$746$	−16.0000	−	27.7128i	−0.585802	−	1.01464i
$747$	−0.500000	+	0.866025i	−0.0182940	+	0.0316862i
$748$	6.00000			0.219382
$749$	−6.00000	−	5.19615i	−0.219235	−	0.189863i
$750$	9.00000			0.328634
$751$	−5.50000	+	9.52628i	−0.200698	+	0.347619i	−0.948753	−	0.316017i	$-0.897654\pi$
$751$	−5.50000	+	9.52628i	−0.200698	+	0.347619i	0.748056	+	0.663636i	$0.230988\pi$
$752$	−3.00000	−	5.19615i	−0.109399	−	0.189484i
$753$	−1.50000	−	2.59808i	−0.0546630	−	0.0946792i
$754$	7.00000	−	12.1244i	0.254925	−	0.441543i
$755$	−5.00000			−0.181969
$756$	−2.50000	+	0.866025i	−0.0909241	+	0.0314970i
$757$	8.00000			0.290765			0.145382	−	0.989376i	$-0.453559\pi$
$757$	8.00000			0.290765			0.145382	+	0.989376i	$0.453559\pi$
$758$	2.00000	−	3.46410i	0.0726433	−	0.125822i
$759$	−1.50000	−	2.59808i	−0.0544466	−	0.0943042i
$760$	1.00000	+	1.73205i	0.0362738	+	0.0628281i
$761$	−9.00000	+	15.5885i	−0.326250	+	0.565081i	−0.981764	−	0.190101i	$-0.939118\pi$
$761$	−9.00000	+	15.5885i	−0.326250	+	0.565081i	0.655515	+	0.755182i	$0.272452\pi$
$762$	7.00000			0.253583
$763$	25.0000	−	8.66025i	0.905061	−	0.313522i
$764$	10.0000			0.361787
$765$	1.00000	−	1.73205i	0.0361551	−	0.0626224i
$766$	−4.00000	−	6.92820i	−0.144526	−	0.250326i
$767$	9.00000	+	15.5885i	0.324971	+	0.562867i
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	15.0000			0.540914			0.270457	−	0.962732i	$-0.412825\pi$
$769$	15.0000			0.540914			0.270457	+	0.962732i	$0.412825\pi$
$770$	6.00000	+	5.19615i	0.216225	+	0.187256i
$771$	4.00000			0.144056
$772$	11.5000	−	19.9186i	0.413894	−	0.716886i
$773$	7.00000	+	12.1244i	0.251773	+	0.436083i	0.964014	−	0.265852i	$-0.0856532\pi$
$773$	7.00000	+	12.1244i	0.251773	+	0.436083i	−0.712241	+	0.701935i	$0.752320\pi$
$774$	3.00000	+	5.19615i	0.107833	+	0.186772i
$775$	14.0000	−	24.2487i	0.502895	−	0.871039i
$776$	5.00000			0.179490
$777$	−1.00000	+	5.19615i	−0.0358748	+	0.186411i
$778$	38.0000			1.36237
$779$	−2.00000	+	3.46410i	−0.0716574	+	0.124114i
$780$	1.00000	+	1.73205i	0.0358057	+	0.0620174i
$781$	−12.0000	−	20.7846i	−0.429394	−	0.743732i
$782$	1.00000	−	1.73205i	0.0357599	−	0.0619380i
$783$	7.00000			0.250160
$784$	5.50000	−	4.33013i	0.196429	−	0.154647i
$785$	6.00000			0.214149
$786$	3.50000	−	6.06218i	0.124841	−	0.216231i
$787$	7.00000	+	12.1244i	0.249523	+	0.432187i	0.963394	−	0.268091i	$-0.0863928\pi$
$787$	7.00000	+	12.1244i	0.249523	+	0.432187i	−0.713871	+	0.700278i	$0.753059\pi$
$788$	−7.00000	−	12.1244i	−0.249365	−	0.431912i
$789$	−1.00000	+	1.73205i	−0.0356009	+	0.0616626i
$790$	−15.0000			−0.533676
$791$	−5.00000	+	25.9808i	−0.177780	+	0.923770i
$792$	−3.00000			−0.106600
$793$	−6.00000	+	10.3923i	−0.213066	+	0.369042i
$794$	19.0000	+	32.9090i	0.674285	+	1.16790i
$795$	−4.50000	−	7.79423i	−0.159599	−	0.276433i
$796$	2.00000	−	3.46410i	0.0708881	−	0.122782i
$797$	−15.0000			−0.531327			−0.265664	−	0.964066i	$-0.585591\pi$
$797$	−15.0000			−0.531327			−0.265664	+	0.964066i	$0.585591\pi$
$798$	−4.00000	−	3.46410i	−0.141598	−	0.122628i
$799$	−12.0000			−0.424529
$800$	2.00000	−	3.46410i	0.0707107	−	0.122474i
$801$		0			0
$802$	−2.00000	−	3.46410i	−0.0706225	−	0.122322i
$803$	−15.0000	+	25.9808i	−0.529339	+	0.916841i
$804$	−10.0000			−0.352673
$805$	2.50000	−	0.866025i	0.0881134	−	0.0305234i
$806$	14.0000			0.493129
$807$	−13.5000	+	23.3827i	−0.475223	+	0.823110i
$808$	5.00000	+	8.66025i	0.175899	+	0.304667i
$809$	17.0000	+	29.4449i	0.597688	+	1.03523i	0.993161	+	0.116749i	$0.0372472\pi$
$809$	17.0000	+	29.4449i	0.597688	+	1.03523i	−0.395473	+	0.918477i	$0.629419\pi$
$810$	−0.500000	+	0.866025i	−0.0175682	+	0.0304290i
$811$	46.0000			1.61528			0.807639	−	0.589677i	$-0.200745\pi$
$811$	46.0000			1.61528			0.807639	+	0.589677i	$0.200745\pi$
$812$	−17.5000	+	6.06218i	−0.614130	+	0.212741i
$813$	9.00000			0.315644
$814$	−3.00000	+	5.19615i	−0.105150	+	0.182125i
$815$	−1.00000	−	1.73205i	−0.0350285	−	0.0606711i
$816$	−1.00000	−	1.73205i	−0.0350070	−	0.0606339i
$817$	−6.00000	+	10.3923i	−0.209913	+	0.363581i
$818$	−29.0000			−1.01396
$819$	−4.00000	−	3.46410i	−0.139771	−	0.121046i
$820$	−2.00000			−0.0698430
$821$	−8.50000	+	14.7224i	−0.296652	+	0.513816i	−0.975368	−	0.220585i	$-0.929203\pi$
$821$	−8.50000	+	14.7224i	−0.296652	+	0.513816i	0.678716	+	0.734401i	$0.262537\pi$
$822$	−3.00000	−	5.19615i	−0.104637	−	0.181237i
$823$	−8.00000	−	13.8564i	−0.278862	−	0.483004i	0.692240	−	0.721668i	$-0.256624\pi$
$823$	−8.00000	−	13.8564i	−0.278862	−	0.483004i	−0.971102	+	0.238664i	$0.923291\pi$
$824$	4.00000	−	6.92820i	0.139347	−	0.241355i
$825$	−12.0000			−0.417786
$826$	4.50000	−	23.3827i	0.156575	−	0.813588i
$827$	5.00000			0.173867			0.0869335	−	0.996214i	$-0.472293\pi$
$827$	5.00000			0.173867			0.0869335	+	0.996214i	$0.472293\pi$
$828$	−0.500000	+	0.866025i	−0.0173762	+	0.0300965i
$829$	10.0000	+	17.3205i	0.347314	+	0.601566i	0.985771	−	0.168091i	$-0.0537604\pi$
$829$	10.0000	+	17.3205i	0.347314	+	0.601566i	−0.638457	+	0.769657i	$0.720427\pi$
$830$	−0.500000	−	0.866025i	−0.0173553	−	0.0300602i
$831$	−4.00000	+	6.92820i	−0.138758	+	0.240337i
$832$	2.00000			0.0693375
$833$	−2.00000	−	13.8564i	−0.0692959	−	0.480096i
$834$	−14.0000			−0.484780
$835$	−3.00000	+	5.19615i	−0.103819	+	0.179820i
$836$	−3.00000	−	5.19615i	−0.103757	−	0.179713i
$837$	3.50000	+	6.06218i	0.120978	+	0.209540i
$838$	18.0000	−	31.1769i	0.621800	−	1.07699i
$839$	−26.0000			−0.897620			−0.448810	−	0.893627i	$-0.648152\pi$
$839$	−26.0000			−0.897620			−0.448810	+	0.893627i	$0.648152\pi$
$840$	0.500000	−	2.59808i	0.0172516	−	0.0896421i
$841$	20.0000			0.689655
$842$	9.00000	−	15.5885i	0.310160	−	0.537214i
$843$	−2.00000	−	3.46410i	−0.0688837	−	0.119310i
$844$	−3.00000	−	5.19615i	−0.103264	−	0.178859i
$845$	4.50000	−	7.79423i	0.154805	−	0.268130i
$846$	6.00000			0.206284
$847$	4.00000	+	3.46410i	0.137442	+	0.119028i
$848$	−9.00000			−0.309061
$849$	3.00000	−	5.19615i	0.102960	−	0.178331i
$850$	−4.00000	−	6.92820i	−0.137199	−	0.237635i
$851$	1.00000	+	1.73205i	0.0342796	+	0.0593739i
$852$	−4.00000	+	6.92820i	−0.137038	+	0.237356i
$853$	54.0000			1.84892			0.924462	−	0.381273i	$-0.124514\pi$
$853$	54.0000			1.84892			0.924462	+	0.381273i	$0.124514\pi$
$854$	15.0000	−	5.19615i	0.513289	−	0.177809i
$855$	−2.00000			−0.0683986
$856$	−1.50000	+	2.59808i	−0.0512689	+	0.0888004i
$857$	−8.00000	−	13.8564i	−0.273275	−	0.473326i	0.696424	−	0.717631i	$-0.254773\pi$
$857$	−8.00000	−	13.8564i	−0.273275	−	0.473326i	−0.969698	+	0.244305i	$0.921440\pi$
$858$	−3.00000	−	5.19615i	−0.102418	−	0.177394i
$859$	−20.0000	+	34.6410i	−0.682391	+	1.18194i	0.291858	+	0.956462i	$0.405727\pi$
$859$	−20.0000	+	34.6410i	−0.682391	+	1.18194i	−0.974249	+	0.225475i	$0.927607\pi$
$860$	−6.00000			−0.204598
$861$	5.00000	−	1.73205i	0.170400	−	0.0590281i
$862$		0			0
$863$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$863$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$864$	0.500000	+	0.866025i	0.0170103	+	0.0294628i
$865$	3.00000	+	5.19615i	0.102003	+	0.176674i
$866$	−19.0000	+	32.9090i	−0.645646	+	1.11829i
$867$	13.0000			0.441503
$868$	−14.0000	−	12.1244i	−0.475191	−	0.411527i
$869$	45.0000			1.52652
$870$	−3.50000	+	6.06218i	−0.118661	+	0.205527i
$871$	−10.0000	−	17.3205i	−0.338837	−	0.586883i
$872$	−5.00000	−	8.66025i	−0.169321	−	0.293273i
$873$	−2.50000	+	4.33013i	−0.0846122	+	0.146553i
$874$	−2.00000			−0.0676510
$875$	4.50000	−	23.3827i	0.152128	−	0.790479i
$876$	10.0000			0.337869
$877$	−25.0000	+	43.3013i	−0.844190	+	1.46218i	0.0421327	+	0.999112i	$0.486585\pi$
$877$	−25.0000	+	43.3013i	−0.844190	+	1.46218i	−0.886323	+	0.463068i	$0.846749\pi$
$878$	−17.5000	−	30.3109i	−0.590596	−	1.02294i
$879$	9.50000	+	16.4545i	0.320427	+	0.554996i
$880$	1.50000	−	2.59808i	0.0505650	−	0.0875811i
$881$	−18.0000			−0.606435			−0.303218	−	0.952921i	$-0.598061\pi$
$881$	−18.0000			−0.606435			−0.303218	+	0.952921i	$0.598061\pi$
$882$	1.00000	+	6.92820i	0.0336718	+	0.233285i
$883$	2.00000			0.0673054			0.0336527	−	0.999434i	$-0.489286\pi$
$883$	2.00000			0.0673054			0.0336527	+	0.999434i	$0.489286\pi$
$884$	2.00000	−	3.46410i	0.0672673	−	0.116510i
$885$	−4.50000	−	7.79423i	−0.151266	−	0.262000i
$886$	14.5000	+	25.1147i	0.487137	+	0.843746i
$887$	18.0000	−	31.1769i	0.604381	−	1.04682i	−0.387768	−	0.921757i	$-0.626754\pi$
$887$	18.0000	−	31.1769i	0.604381	−	1.04682i	0.992149	−	0.125061i	$-0.0399128\pi$
$888$	2.00000			0.0671156
$889$	3.50000	−	18.1865i	0.117386	−	0.609957i
$890$		0			0
$891$	1.50000	−	2.59808i	0.0502519	−	0.0870388i
$892$	−6.50000	−	11.2583i	−0.217636	−	0.376957i
$893$	6.00000	+	10.3923i	0.200782	+	0.347765i
$894$	−11.0000	+	19.0526i	−0.367895	+	0.637213i
$895$	−12.0000			−0.401116
$896$	−2.00000	−	1.73205i	−0.0668153	−	0.0578638i
$897$	−2.00000			−0.0667781
$898$	15.0000	−	25.9808i	0.500556	−	0.866989i
$899$	24.5000	+	42.4352i	0.817121	+	1.41529i
$900$	2.00000	+	3.46410i	0.0666667	+	0.115470i
$901$	−9.00000	+	15.5885i	−0.299833	+	0.519327i
$902$	6.00000			0.199778
$903$	15.0000	−	5.19615i	0.499169	−	0.172917i
$904$	10.0000			0.332595
$905$	−8.00000	+	13.8564i	−0.265929	+	0.460603i
$906$	−2.50000	−	4.33013i	−0.0830569	−	0.143859i
$907$	−23.0000	−	39.8372i	−0.763702	−	1.32277i	−0.940930	−	0.338602i	$-0.890046\pi$
$907$	−23.0000	−	39.8372i	−0.763702	−	1.32277i	0.177227	−	0.984170i	$-0.443287\pi$
$908$	4.50000	−	7.79423i	0.149338	−	0.258661i
$909$	−10.0000			−0.331679
$910$	5.00000	−	1.73205i	0.165748	−	0.0574169i
$911$	22.0000			0.728893			0.364446	−	0.931224i	$-0.381258\pi$
$911$	22.0000			0.728893			0.364446	+	0.931224i	$0.381258\pi$
$912$	−1.00000	+	1.73205i	−0.0331133	+	0.0573539i
$913$	1.50000	+	2.59808i	0.0496428	+	0.0859838i
$914$	−0.500000	−	0.866025i	−0.0165385	−	0.0286456i
$915$	3.00000	−	5.19615i	0.0991769	−	0.171780i
$916$	22.0000			0.726900
$917$	−14.0000	−	12.1244i	−0.462321	−	0.400381i
$918$	2.00000			0.0660098
$919$	−16.0000	+	27.7128i	−0.527791	+	0.914161i	0.471684	+	0.881768i	$0.343646\pi$
$919$	−16.0000	+	27.7128i	−0.527791	+	0.914161i	−0.999475	+	0.0323936i	$0.989687\pi$
$920$	−0.500000	−	0.866025i	−0.0164845	−	0.0285520i
$921$	−1.00000	−	1.73205i	−0.0329511	−	0.0570730i
$922$	−1.00000	+	1.73205i	−0.0329332	+	0.0570421i
$923$	−16.0000			−0.526646
$924$	−1.50000	+	7.79423i	−0.0493464	+	0.256411i
$925$	8.00000			0.263038
$926$	4.00000	−	6.92820i	0.131448	−	0.227675i
$927$	4.00000	+	6.92820i	0.131377	+	0.227552i
$928$	3.50000	+	6.06218i	0.114893	+	0.199001i
$929$	−16.0000	+	27.7128i	−0.524943	+	0.909228i	0.474635	+	0.880183i	$0.342580\pi$
$929$	−16.0000	+	27.7128i	−0.524943	+	0.909228i	−0.999578	+	0.0290452i	$0.990753\pi$
$930$	−7.00000			−0.229539
$931$	−11.0000	+	8.66025i	−0.360510	+	0.283828i
$932$	−6.00000			−0.196537
$933$	−1.00000	+	1.73205i	−0.0327385	+	0.0567048i
$934$	−2.00000	−	3.46410i	−0.0654420	−	0.113349i
$935$	−3.00000	−	5.19615i	−0.0981105	−	0.169932i
$936$	−1.00000	+	1.73205i	−0.0326860	+	0.0566139i
$937$	29.0000			0.947389			0.473694	−	0.880689i	$-0.342920\pi$
$937$	29.0000			0.947389			0.473694	+	0.880689i	$0.342920\pi$
$938$	−5.00000	+	25.9808i	−0.163256	+	0.848302i
$939$	25.0000			0.815844
$940$	−3.00000	+	5.19615i	−0.0978492	+	0.169480i
$941$	7.50000	+	12.9904i	0.244493	+	0.423474i	0.961989	−	0.273088i	$-0.0880451\pi$
$941$	7.50000	+	12.9904i	0.244493	+	0.423474i	−0.717496	+	0.696563i	$0.754712\pi$
$942$	3.00000	+	5.19615i	0.0977453	+	0.169300i
$943$	1.00000	−	1.73205i	0.0325645	−	0.0564033i
$944$	−9.00000			−0.292925
$945$	2.00000	+	1.73205i	0.0650600	+	0.0563436i
$946$	18.0000			0.585230
$947$	12.0000	−	20.7846i	0.389948	−	0.675409i	−0.602494	−	0.798123i	$-0.705826\pi$
$947$	12.0000	−	20.7846i	0.389948	−	0.675409i	0.992442	+	0.122714i	$0.0391598\pi$
$948$	−7.50000	−	12.9904i	−0.243589	−	0.421908i
$949$	10.0000	+	17.3205i	0.324614	+	0.562247i
$950$	−4.00000	+	6.92820i	−0.129777	+	0.224781i
$951$	31.0000			1.00524
$952$	−5.00000	+	1.73205i	−0.162051	+	0.0561361i
$953$	−26.0000			−0.842223			−0.421111	−	0.907009i	$-0.638360\pi$
$953$	−26.0000			−0.842223			−0.421111	+	0.907009i	$0.638360\pi$
$954$	4.50000	−	7.79423i	0.145693	−	0.252347i
$955$	−5.00000	−	8.66025i	−0.161796	−	0.280239i
$956$	6.00000	+	10.3923i	0.194054	+	0.336111i
$957$	10.5000	−	18.1865i	0.339417	−	0.587887i
$958$	28.0000			0.904639
$959$	−15.0000	+	5.19615i	−0.484375	+	0.167793i
$960$	−1.00000			−0.0322749
$961$	−9.00000	+	15.5885i	−0.290323	+	0.502853i
$962$	2.00000	+	3.46410i	0.0644826	+	0.111687i
$963$	−1.50000	−	2.59808i	−0.0483368	−	0.0837218i
$964$	13.5000	−	23.3827i	0.434806	−	0.753106i
$965$	−23.0000			−0.740396
$966$	2.00000	+	1.73205i	0.0643489	+	0.0557278i
$967$	−13.0000			−0.418052			−0.209026	−	0.977910i	$-0.567029\pi$
$967$	−13.0000			−0.418052			−0.209026	+	0.977910i	$0.567029\pi$
$968$	1.00000	−	1.73205i	0.0321412	−	0.0556702i
$969$	2.00000	+	3.46410i	0.0642493	+	0.111283i
$970$	−2.50000	−	4.33013i	−0.0802702	−	0.139032i
$971$	8.50000	−	14.7224i	0.272778	−	0.472465i	−0.696794	−	0.717271i	$-0.745391\pi$
$971$	8.50000	−	14.7224i	0.272778	−	0.472465i	0.969572	+	0.244806i	$0.0787242\pi$
$972$	−1.00000			−0.0320750
$973$	−7.00000	+	36.3731i	−0.224410	+	1.16607i
$974$	−15.0000			−0.480631
$975$	−4.00000	+	6.92820i	−0.128103	+	0.221880i
$976$	−3.00000	−	5.19615i	−0.0960277	−	0.166325i
$977$	−15.0000	−	25.9808i	−0.479893	−	0.831198i	0.519841	−	0.854263i	$-0.325991\pi$
$977$	−15.0000	−	25.9808i	−0.479893	−	0.831198i	−0.999734	+	0.0230645i	$0.992658\pi$
$978$	1.00000	−	1.73205i	0.0319765	−	0.0553849i
$979$		0			0
$980$	−6.50000	−	2.59808i	−0.207635	−	0.0829925i
$981$	10.0000			0.319275
$982$	−9.50000	+	16.4545i	−0.303157	+	0.525084i
$983$	25.0000	+	43.3013i	0.797376	+	1.38110i	0.921319	+	0.388807i	$0.127113\pi$
$983$	25.0000	+	43.3013i	0.797376	+	1.38110i	−0.123943	+	0.992289i	$0.539554\pi$
$984$	−1.00000	−	1.73205i	−0.0318788	−	0.0552158i
$985$	−7.00000	+	12.1244i	−0.223039	+	0.386314i
$986$	14.0000			0.445851
$987$	3.00000	−	15.5885i	0.0954911	−	0.496186i
$988$	−4.00000			−0.127257
$989$	3.00000	−	5.19615i	0.0953945	−	0.165228i
$990$	1.50000	+	2.59808i	0.0476731	+	0.0825723i
$991$	−1.50000	−	2.59808i	−0.0476491	−	0.0825306i	0.841217	−	0.540697i	$-0.181840\pi$
$991$	−1.50000	−	2.59808i	−0.0476491	−	0.0825306i	−0.888866	+	0.458167i	$0.848506\pi$
$992$	−3.50000	+	6.06218i	−0.111125	+	0.192474i
$993$	−10.0000			−0.317340
$994$	16.0000	+	13.8564i	0.507489	+	0.439499i
$995$	−4.00000			−0.126809
$996$	0.500000	−	0.866025i	0.0158431	−	0.0274411i
$997$	−18.0000	−	31.1769i	−0.570066	−	0.987383i	−0.996559	−	0.0828918i	$-0.973584\pi$
$997$	−18.0000	−	31.1769i	−0.570066	−	0.987383i	0.426493	−	0.904491i	$-0.359749\pi$
$998$	−3.00000	−	5.19615i	−0.0949633	−	0.164481i
$999$	−1.00000	+	1.73205i	−0.0316386	+	0.0547997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.i.c.415.1	yes	2
7.2	even	3		6762.2.a.bb.1.1		1
7.4	even	3	inner	966.2.i.c.277.1	✓	2
7.5	odd	6		6762.2.a.bh.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.i.c.277.1	✓	2	7.4	even	3	inner
966.2.i.c.415.1	yes	2	1.1	even	1	trivial
6762.2.a.bb.1.1		1	7.2	even	3
6762.2.a.bh.1.1		1	7.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.i (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} +(1.50000 + 2.59808i) q^{11} +(0.500000 - 0.866025i) q^{12} +2.00000 q^{13} +(-2.00000 - 1.73205i) q^{14} -1.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.00000 + 1.73205i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(1.00000 - 1.73205i) q^{19} +1.00000 q^{20} +(-2.50000 + 0.866025i) q^{21} -3.00000 q^{22} +(-0.500000 + 0.866025i) q^{23} +(0.500000 + 0.866025i) q^{24} +(2.00000 + 3.46410i) q^{25} +(-1.00000 + 1.73205i) q^{26} -1.00000 q^{27} +(2.50000 - 0.866025i) q^{28} -7.00000 q^{29} +(0.500000 - 0.866025i) q^{30} +(-3.50000 - 6.06218i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.50000 + 2.59808i) q^{33} -2.00000 q^{34} +(-2.00000 - 1.73205i) q^{35} +1.00000 q^{36} +(1.00000 - 1.73205i) q^{37} +(1.00000 + 1.73205i) q^{38} +(1.00000 + 1.73205i) q^{39} +(-0.500000 + 0.866025i) q^{40} -2.00000 q^{41} +(0.500000 - 2.59808i) q^{42} -6.00000 q^{43} +(1.50000 - 2.59808i) q^{44} +(-0.500000 - 0.866025i) q^{45} +(-0.500000 - 0.866025i) q^{46} +(-3.00000 + 5.19615i) q^{47} -1.00000 q^{48} +(-6.50000 - 2.59808i) q^{49} -4.00000 q^{50} +(-1.00000 + 1.73205i) q^{51} +(-1.00000 - 1.73205i) q^{52} +(4.50000 + 7.79423i) q^{53} +(0.500000 - 0.866025i) q^{54} -3.00000 q^{55} +(-0.500000 + 2.59808i) q^{56} +2.00000 q^{57} +(3.50000 - 6.06218i) q^{58} +(4.50000 + 7.79423i) q^{59} +(0.500000 + 0.866025i) q^{60} +(-3.00000 + 5.19615i) q^{61} +7.00000 q^{62} +(-2.00000 - 1.73205i) q^{63} +1.00000 q^{64} +(-1.00000 + 1.73205i) q^{65} +(-1.50000 - 2.59808i) q^{66} +(-5.00000 - 8.66025i) q^{67} +(1.00000 - 1.73205i) q^{68} -1.00000 q^{69} +(2.50000 - 0.866025i) q^{70} -8.00000 q^{71} +(-0.500000 + 0.866025i) q^{72} +(5.00000 + 8.66025i) q^{73} +(1.00000 + 1.73205i) q^{74} +(-2.00000 + 3.46410i) q^{75} -2.00000 q^{76} +(-7.50000 + 2.59808i) q^{77} -2.00000 q^{78} +(7.50000 - 12.9904i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.00000 - 1.73205i) q^{82} +1.00000 q^{83} +(2.00000 + 1.73205i) q^{84} -2.00000 q^{85} +(3.00000 - 5.19615i) q^{86} +(-3.50000 - 6.06218i) q^{87} +(1.50000 + 2.59808i) q^{88} +1.00000 q^{90} +(-1.00000 + 5.19615i) q^{91} +1.00000 q^{92} +(3.50000 - 6.06218i) q^{93} +(-3.00000 - 5.19615i) q^{94} +(1.00000 + 1.73205i) q^{95} +(0.500000 - 0.866025i) q^{96} +5.00000 q^{97} +(5.50000 - 4.33013i) q^{98} -3.00000 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	\( 2 q - q^{2} + q^{3} - q^{4} - q^{5} - 2 q^{6} - q^{7} + 2 q^{8} - q^{9} - q^{10} + 3 q^{11} + q^{12} + 4 q^{13} - 4 q^{14} - 2 q^{15} - q^{16} + 2 q^{17} - q^{18} + 2 q^{19} + 2 q^{20} - 5 q^{21} - 6 q^{22} - q^{23} + q^{24} + 4 q^{25} - 2 q^{26} - 2 q^{27} + 5 q^{28} - 14 q^{29} + q^{30} - 7 q^{31} - q^{32} - 3 q^{33} - 4 q^{34} - 4 q^{35} + 2 q^{36} + 2 q^{37} + 2 q^{38} + 2 q^{39} - q^{40} - 4 q^{41} + q^{42} - 12 q^{43} + 3 q^{44} - q^{45} - q^{46} - 6 q^{47} - 2 q^{48} - 13 q^{49} - 8 q^{50} - 2 q^{51} - 2 q^{52} + 9 q^{53} + q^{54} - 6 q^{55} - q^{56} + 4 q^{57} + 7 q^{58} + 9 q^{59} + q^{60} - 6 q^{61} + 14 q^{62} - 4 q^{63} + 2 q^{64} - 2 q^{65} - 3 q^{66} - 10 q^{67} + 2 q^{68} - 2 q^{69} + 5 q^{70} - 16 q^{71} - q^{72} + 10 q^{73} + 2 q^{74} - 4 q^{75} - 4 q^{76} - 15 q^{77} - 4 q^{78} + 15 q^{79} - q^{80} - q^{81} + 2 q^{82} + 2 q^{83} + 4 q^{84} - 4 q^{85} + 6 q^{86} - 7 q^{87} + 3 q^{88} + 2 q^{90} - 2 q^{91} + 2 q^{92} + 7 q^{93} - 6 q^{94} + 2 q^{95} + q^{96} + 10 q^{97} + 11 q^{98} - 6 q^{99}+O(q^{100}) \) 2 * q - q^2 + q^3 - q^4 - q^5 - 2 * q^6 - q^7 + 2 * q^8 - q^9 - q^10 + 3 * q^11 + q^12 + 4 * q^13 - 4 * q^14 - 2 * q^15 - q^16 + 2 * q^17 - q^18 + 2 * q^19 + 2 * q^20 - 5 * q^21 - 6 * q^22 - q^23 + q^24 + 4 * q^25 - 2 * q^26 - 2 * q^27 + 5 * q^28 - 14 * q^29 + q^30 - 7 * q^31 - q^32 - 3 * q^33 - 4 * q^34 - 4 * q^35 + 2 * q^36 + 2 * q^37 + 2 * q^38 + 2 * q^39 - q^40 - 4 * q^41 + q^42 - 12 * q^43 + 3 * q^44 - q^45 - q^46 - 6 * q^47 - 2 * q^48 - 13 * q^49 - 8 * q^50 - 2 * q^51 - 2 * q^52 + 9 * q^53 + q^54 - 6 * q^55 - q^56 + 4 * q^57 + 7 * q^58 + 9 * q^59 + q^60 - 6 * q^61 + 14 * q^62 - 4 * q^63 + 2 * q^64 - 2 * q^65 - 3 * q^66 - 10 * q^67 + 2 * q^68 - 2 * q^69 + 5 * q^70 - 16 * q^71 - q^72 + 10 * q^73 + 2 * q^74 - 4 * q^75 - 4 * q^76 - 15 * q^77 - 4 * q^78 + 15 * q^79 - q^80 - q^81 + 2 * q^82 + 2 * q^83 + 4 * q^84 - 4 * q^85 + 6 * q^86 - 7 * q^87 + 3 * q^88 + 2 * q^90 - 2 * q^91 + 2 * q^92 + 7 * q^93 - 6 * q^94 + 2 * q^95 + q^96 + 10 * q^97 + 11 * q^98 - 6 * q^99

Introduction

L-functions

Modular forms

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