LMFDB - Embedded newform 546.2.i.b.79.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(79,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("546.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.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:	$4.35983195036$
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			79.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	546.79
Dual form			546.2.i.b.235.1

$q$-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} +(0.500000 + 0.866025i) q^{11} +(-0.500000 + 0.866025i) q^{12} -1.00000 q^{13} +(-2.00000 - 1.73205i) q^{14} -1.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.00000 + 5.19615i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(2.00000 - 3.46410i) q^{19} -1.00000 q^{20} +(2.50000 - 0.866025i) q^{21} -1.00000 q^{22} +(3.00000 - 5.19615i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(2.00000 + 3.46410i) q^{25} +(0.500000 - 0.866025i) q^{26} +1.00000 q^{27} +(2.50000 - 0.866025i) q^{28} +3.00000 q^{29} +(0.500000 - 0.866025i) q^{30} +(5.50000 + 9.52628i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.500000 - 0.866025i) q^{33} -6.00000 q^{34} +(2.00000 + 1.73205i) q^{35} +1.00000 q^{36} +(-2.00000 + 3.46410i) q^{37} +(2.00000 + 3.46410i) q^{38} +(0.500000 + 0.866025i) q^{39} +(0.500000 - 0.866025i) q^{40} +12.0000 q^{41} +(-0.500000 + 2.59808i) q^{42} -8.00000 q^{43} +(0.500000 - 0.866025i) q^{44} +(0.500000 + 0.866025i) q^{45} +(3.00000 + 5.19615i) q^{46} +(4.00000 - 6.92820i) q^{47} +1.00000 q^{48} +(-6.50000 - 2.59808i) q^{49} -4.00000 q^{50} +(3.00000 - 5.19615i) q^{51} +(0.500000 + 0.866025i) q^{52} +(2.50000 + 4.33013i) q^{53} +(-0.500000 + 0.866025i) q^{54} +1.00000 q^{55} +(-0.500000 + 2.59808i) q^{56} -4.00000 q^{57} +(-1.50000 + 2.59808i) q^{58} +(2.50000 + 4.33013i) q^{59} +(0.500000 + 0.866025i) q^{60} +(-6.00000 + 10.3923i) q^{61} -11.0000 q^{62} +(-2.00000 - 1.73205i) q^{63} +1.00000 q^{64} +(-0.500000 + 0.866025i) q^{65} +(0.500000 + 0.866025i) q^{66} +(-8.00000 - 13.8564i) q^{67} +(3.00000 - 5.19615i) q^{68} -6.00000 q^{69} +(-2.50000 + 0.866025i) q^{70} +6.00000 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} -4.00000 q^{76} +(-2.50000 + 0.866025i) q^{77} -1.00000 q^{78} +(-3.50000 + 6.06218i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-6.00000 + 10.3923i) q^{82} -17.0000 q^{83} +(-2.00000 - 1.73205i) q^{84} +6.00000 q^{85} +(4.00000 - 6.92820i) q^{86} +(-1.50000 - 2.59808i) q^{87} +(0.500000 + 0.866025i) q^{88} +(6.00000 - 10.3923i) q^{89} -1.00000 q^{90} +(0.500000 - 2.59808i) q^{91} -6.00000 q^{92} +(5.50000 - 9.52628i) q^{93} +(4.00000 + 6.92820i) q^{94} +(-2.00000 - 3.46410i) q^{95} +(-0.500000 + 0.866025i) q^{96} +13.0000 q^{97} +(5.50000 - 4.33013i) q^{98} -1.00000 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	\( 2 q - q^{2} - q^{3} - q^{4} + q^{5} + 2 q^{6} - q^{7} + 2 q^{8} - q^{9} + q^{10} + q^{11} - q^{12} - 2 q^{13} - 4 q^{14} - 2 q^{15} - q^{16} + 6 q^{17} - q^{18} + 4 q^{19} - 2 q^{20} + 5 q^{21} - 2 q^{22} + 6 q^{23} - q^{24} + 4 q^{25} + q^{26} + 2 q^{27} + 5 q^{28} + 6 q^{29} + q^{30} + 11 q^{31} - q^{32} + q^{33} - 12 q^{34} + 4 q^{35} + 2 q^{36} - 4 q^{37} + 4 q^{38} + q^{39} + q^{40} + 24 q^{41} - q^{42} - 16 q^{43} + q^{44} + q^{45} + 6 q^{46} + 8 q^{47} + 2 q^{48} - 13 q^{49} - 8 q^{50} + 6 q^{51} + q^{52} + 5 q^{53} - q^{54} + 2 q^{55} - q^{56} - 8 q^{57} - 3 q^{58} + 5 q^{59} + q^{60} - 12 q^{61} - 22 q^{62} - 4 q^{63} + 2 q^{64} - q^{65} + q^{66} - 16 q^{67} + 6 q^{68} - 12 q^{69} - 5 q^{70} + 12 q^{71} - q^{72} + 10 q^{73} - 4 q^{74} + 4 q^{75} - 8 q^{76} - 5 q^{77} - 2 q^{78} - 7 q^{79} + q^{80} - q^{81} - 12 q^{82} - 34 q^{83} - 4 q^{84} + 12 q^{85} + 8 q^{86} - 3 q^{87} + q^{88} + 12 q^{89} - 2 q^{90} + q^{91} - 12 q^{92} + 11 q^{93} + 8 q^{94} - 4 q^{95} - q^{96} + 26 q^{97} + 11 q^{98} - 2 q^{99}+O(q^{100}) \) 2 * q - q^2 - q^3 - q^4 + q^5 + 2 * q^6 - q^7 + 2 * q^8 - q^9 + q^10 + q^11 - q^12 - 2 * q^13 - 4 * q^14 - 2 * q^15 - q^16 + 6 * q^17 - q^18 + 4 * q^19 - 2 * q^20 + 5 * q^21 - 2 * q^22 + 6 * q^23 - q^24 + 4 * q^25 + q^26 + 2 * q^27 + 5 * q^28 + 6 * q^29 + q^30 + 11 * q^31 - q^32 + q^33 - 12 * q^34 + 4 * q^35 + 2 * q^36 - 4 * q^37 + 4 * q^38 + q^39 + q^40 + 24 * q^41 - q^42 - 16 * q^43 + q^44 + q^45 + 6 * q^46 + 8 * q^47 + 2 * q^48 - 13 * q^49 - 8 * q^50 + 6 * q^51 + q^52 + 5 * q^53 - q^54 + 2 * q^55 - q^56 - 8 * q^57 - 3 * q^58 + 5 * q^59 + q^60 - 12 * q^61 - 22 * q^62 - 4 * q^63 + 2 * q^64 - q^65 + q^66 - 16 * q^67 + 6 * q^68 - 12 * q^69 - 5 * q^70 + 12 * q^71 - q^72 + 10 * q^73 - 4 * q^74 + 4 * q^75 - 8 * q^76 - 5 * q^77 - 2 * q^78 - 7 * q^79 + q^80 - q^81 - 12 * q^82 - 34 * q^83 - 4 * q^84 + 12 * q^85 + 8 * q^86 - 3 * q^87 + q^88 + 12 * q^89 - 2 * q^90 + q^91 - 12 * q^92 + 11 * q^93 + 8 * q^94 - 4 * q^95 - q^96 + 26 * q^97 + 11 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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	−0.732294	−	0.680989i	$-0.761550\pi$
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i	0.955901	+	0.293691i	$0.0948835\pi$
$6$	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
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i	0.931505	−	0.363727i	$-0.118496\pi$
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i	−0.780750	+	0.624844i	$0.785163\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	−1.00000			−0.277350
$13$	−1.00000			−0.277350
$14$	−2.00000	−	1.73205i	−0.534522	−	0.462910i
$15$	−1.00000			−0.258199
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	3.00000	+	5.19615i	0.727607	+	1.26025i	0.957892	+	0.287129i	$0.0927008\pi$
$17$	3.00000	+	5.19615i	0.727607	+	1.26025i	−0.230285	+	0.973123i	$0.573966\pi$
$18$	−0.500000	−	0.866025i	−0.117851	−	0.204124i
$19$	2.00000	−	3.46410i	0.458831	−	0.794719i	−0.540068	−	0.841621i	$-0.681602\pi$
$19$	2.00000	−	3.46410i	0.458831	−	0.794719i	0.998899	+	0.0469020i	$0.0149348\pi$
$20$	−1.00000			−0.223607
$21$	2.50000	−	0.866025i	0.545545	−	0.188982i
$22$	−1.00000			−0.213201
$23$	3.00000	−	5.19615i	0.625543	−	1.08347i	−0.362892	−	0.931831i	$-0.618211\pi$
$23$	3.00000	−	5.19615i	0.625543	−	1.08347i	0.988436	−	0.151642i	$-0.0484560\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	2.00000	+	3.46410i	0.400000	+	0.692820i
$26$	0.500000	−	0.866025i	0.0980581	−	0.169842i
$27$	1.00000			0.192450
$28$	2.50000	−	0.866025i	0.472456	−	0.163663i
$29$	3.00000			0.557086			0.278543	−	0.960424i	$-0.410149\pi$
$29$	3.00000			0.557086			0.278543	+	0.960424i	$0.410149\pi$
$30$	0.500000	−	0.866025i	0.0912871	−	0.158114i
$31$	5.50000	+	9.52628i	0.987829	+	1.71097i	0.628619	+	0.777714i	$0.283621\pi$
$31$	5.50000	+	9.52628i	0.987829	+	1.71097i	0.359211	+	0.933257i	$0.383046\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	0.500000	−	0.866025i	0.0870388	−	0.150756i
$34$	−6.00000			−1.02899
$35$	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	$-0.939977\pi$
$37$	−2.00000	+	3.46410i	−0.328798	+	0.569495i	0.653476	+	0.756948i	$0.273310\pi$
$38$	2.00000	+	3.46410i	0.324443	+	0.561951i
$39$	0.500000	+	0.866025i	0.0800641	+	0.138675i
$40$	0.500000	−	0.866025i	0.0790569	−	0.136931i
$41$	12.0000			1.87409			0.937043	−	0.349215i	$-0.113552\pi$
$41$	12.0000			1.87409			0.937043	+	0.349215i	$0.113552\pi$
$42$	−0.500000	+	2.59808i	−0.0771517	+	0.400892i
$43$	−8.00000			−1.21999			−0.609994	−	0.792406i	$-0.708828\pi$
$43$	−8.00000			−1.21999			−0.609994	+	0.792406i	$0.708828\pi$
$44$	0.500000	−	0.866025i	0.0753778	−	0.130558i
$45$	0.500000	+	0.866025i	0.0745356	+	0.129099i
$46$	3.00000	+	5.19615i	0.442326	+	0.766131i
$47$	4.00000	−	6.92820i	0.583460	−	1.01058i	−0.411606	−	0.911362i	$-0.635032\pi$
$47$	4.00000	−	6.92820i	0.583460	−	1.01058i	0.995066	−	0.0992202i	$-0.0316348\pi$
$48$	1.00000			0.144338
$49$	−6.50000	−	2.59808i	−0.928571	−	0.371154i
$50$	−4.00000			−0.565685
$51$	3.00000	−	5.19615i	0.420084	−	0.727607i
$52$	0.500000	+	0.866025i	0.0693375	+	0.120096i
$53$	2.50000	+	4.33013i	0.343401	+	0.594789i	0.985062	−	0.172200i	$-0.0550875\pi$
$53$	2.50000	+	4.33013i	0.343401	+	0.594789i	−0.641661	+	0.766989i	$0.721754\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$	1.00000			0.134840
$56$	−0.500000	+	2.59808i	−0.0668153	+	0.347183i
$57$	−4.00000			−0.529813
$58$	−1.50000	+	2.59808i	−0.196960	+	0.341144i
$59$	2.50000	+	4.33013i	0.325472	+	0.563735i	0.981608	−	0.190909i	$-0.0611434\pi$
$59$	2.50000	+	4.33013i	0.325472	+	0.563735i	−0.656136	+	0.754643i	$0.727810\pi$
$60$	0.500000	+	0.866025i	0.0645497	+	0.111803i
$61$	−6.00000	+	10.3923i	−0.768221	+	1.33060i	0.170305	+	0.985391i	$0.445525\pi$
$61$	−6.00000	+	10.3923i	−0.768221	+	1.33060i	−0.938527	+	0.345207i	$0.887809\pi$
$62$	−11.0000			−1.39700
$63$	−2.00000	−	1.73205i	−0.251976	−	0.218218i
$64$	1.00000			0.125000
$65$	−0.500000	+	0.866025i	−0.0620174	+	0.107417i
$66$	0.500000	+	0.866025i	0.0615457	+	0.106600i
$67$	−8.00000	−	13.8564i	−0.977356	−	1.69283i	−0.671932	−	0.740613i	$-0.734535\pi$
$67$	−8.00000	−	13.8564i	−0.977356	−	1.69283i	−0.305424	−	0.952217i	$-0.598798\pi$
$68$	3.00000	−	5.19615i	0.363803	−	0.630126i
$69$	−6.00000			−0.722315
$70$	−2.50000	+	0.866025i	−0.298807	+	0.103510i
$71$	6.00000			0.712069			0.356034	−	0.934473i	$-0.384129\pi$
$71$	6.00000			0.712069			0.356034	+	0.934473i	$0.384129\pi$
$72$	−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	$0.634347\pi$
$74$	−2.00000	−	3.46410i	−0.232495	−	0.402694i
$75$	2.00000	−	3.46410i	0.230940	−	0.400000i
$76$	−4.00000			−0.458831
$77$	−2.50000	+	0.866025i	−0.284901	+	0.0986928i
$78$	−1.00000			−0.113228
$79$	−3.50000	+	6.06218i	−0.393781	+	0.682048i	−0.992945	−	0.118578i	$-0.962166\pi$
$79$	−3.50000	+	6.06218i	−0.393781	+	0.682048i	0.599164	+	0.800626i	$0.295500\pi$
$80$	0.500000	+	0.866025i	0.0559017	+	0.0968246i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−6.00000	+	10.3923i	−0.662589	+	1.14764i
$83$	−17.0000			−1.86599			−0.932996	−	0.359886i	$-0.882816\pi$
$83$	−17.0000			−1.86599			−0.932996	+	0.359886i	$0.882816\pi$
$84$	−2.00000	−	1.73205i	−0.218218	−	0.188982i
$85$	6.00000			0.650791
$86$	4.00000	−	6.92820i	0.431331	−	0.747087i
$87$	−1.50000	−	2.59808i	−0.160817	−	0.278543i
$88$	0.500000	+	0.866025i	0.0533002	+	0.0923186i
$89$	6.00000	−	10.3923i	0.635999	−	1.10158i	−0.350304	−	0.936636i	$-0.613922\pi$
$89$	6.00000	−	10.3923i	0.635999	−	1.10158i	0.986303	−	0.164946i	$-0.0527450\pi$
$90$	−1.00000			−0.105409
$91$	0.500000	−	2.59808i	0.0524142	−	0.272352i
$92$	−6.00000			−0.625543
$93$	5.50000	−	9.52628i	0.570323	−	0.987829i
$94$	4.00000	+	6.92820i	0.412568	+	0.714590i
$95$	−2.00000	−	3.46410i	−0.205196	−	0.355409i
$96$	−0.500000	+	0.866025i	−0.0510310	+	0.0883883i
$97$	13.0000			1.31995			0.659975	−	0.751288i	$-0.270567\pi$
$97$	13.0000			1.31995			0.659975	+	0.751288i	$0.270567\pi$
$98$	5.50000	−	4.33013i	0.555584	−	0.437409i
$99$	−1.00000			−0.100504
$100$	2.00000	−	3.46410i	0.200000	−	0.346410i
$101$	−5.00000	−	8.66025i	−0.497519	−	0.861727i	0.502477	−	0.864590i	$-0.332422\pi$
$101$	−5.00000	−	8.66025i	−0.497519	−	0.861727i	−0.999996	+	0.00286291i	$0.999089\pi$
$102$	3.00000	+	5.19615i	0.297044	+	0.514496i
$103$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$103$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$104$	−1.00000			−0.0980581
$105$	0.500000	−	2.59808i	0.0487950	−	0.253546i
$106$	−5.00000			−0.485643
$107$	−3.50000	+	6.06218i	−0.338358	+	0.586053i	−0.984124	−	0.177482i	$-0.943205\pi$
$107$	−3.50000	+	6.06218i	−0.338358	+	0.586053i	0.645766	+	0.763535i	$0.276538\pi$
$108$	−0.500000	−	0.866025i	−0.0481125	−	0.0833333i
$109$	−6.00000	−	10.3923i	−0.574696	−	0.995402i	−0.996075	−	0.0885176i	$-0.971787\pi$
$109$	−6.00000	−	10.3923i	−0.574696	−	0.995402i	0.421379	−	0.906885i	$-0.361546\pi$
$110$	−0.500000	+	0.866025i	−0.0476731	+	0.0825723i
$111$	4.00000			0.379663
$112$	−2.00000	−	1.73205i	−0.188982	−	0.163663i
$113$	−4.00000			−0.376288			−0.188144	−	0.982141i	$-0.560247\pi$
$113$	−4.00000			−0.376288			−0.188144	+	0.982141i	$0.560247\pi$
$114$	2.00000	−	3.46410i	0.187317	−	0.324443i
$115$	−3.00000	−	5.19615i	−0.279751	−	0.484544i
$116$	−1.50000	−	2.59808i	−0.139272	−	0.241225i
$117$	0.500000	−	0.866025i	0.0462250	−	0.0800641i
$118$	−5.00000			−0.460287
$119$	−15.0000	+	5.19615i	−1.37505	+	0.476331i
$120$	−1.00000			−0.0912871
$121$	5.00000	−	8.66025i	0.454545	−	0.787296i
$122$	−6.00000	−	10.3923i	−0.543214	−	0.940875i
$123$	−6.00000	−	10.3923i	−0.541002	−	0.937043i
$124$	5.50000	−	9.52628i	0.493915	−	0.855485i
$125$	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
$129$	4.00000	+	6.92820i	0.352180	+	0.609994i
$130$	−0.500000	−	0.866025i	−0.0438529	−	0.0759555i
$131$	−0.500000	+	0.866025i	−0.0436852	+	0.0756650i	−0.887041	−	0.461690i	$-0.847243\pi$
$131$	−0.500000	+	0.866025i	−0.0436852	+	0.0756650i	0.843356	+	0.537355i	$0.180577\pi$
$132$	−1.00000			−0.0870388
$133$	8.00000	+	6.92820i	0.693688	+	0.600751i
$134$	16.0000			1.38219
$135$	0.500000	−	0.866025i	0.0430331	−	0.0745356i
$136$	3.00000	+	5.19615i	0.257248	+	0.445566i
$137$	4.00000	+	6.92820i	0.341743	+	0.591916i	0.984757	−	0.173939i	$-0.0556494\pi$
$137$	4.00000	+	6.92820i	0.341743	+	0.591916i	−0.643013	+	0.765855i	$0.722316\pi$
$138$	3.00000	−	5.19615i	0.255377	−	0.442326i
$139$		0			0			−	1.00000i	$-0.5\pi$
$139$		0			0				1.00000i	$0.5\pi$
$140$	0.500000	−	2.59808i	0.0422577	−	0.219578i
$141$	−8.00000			−0.673722
$142$	−3.00000	+	5.19615i	−0.251754	+	0.436051i
$143$	−0.500000	−	0.866025i	−0.0418121	−	0.0724207i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	1.50000	−	2.59808i	0.124568	−	0.215758i
$146$	−10.0000			−0.827606
$147$	1.00000	+	6.92820i	0.0824786	+	0.571429i
$148$	4.00000			0.328798
$149$	5.00000	−	8.66025i	0.409616	−	0.709476i	−0.585231	−	0.810867i	$-0.698996\pi$
$149$	5.00000	−	8.66025i	0.409616	−	0.709476i	0.994847	+	0.101391i	$0.0323294\pi$
$150$	2.00000	+	3.46410i	0.163299	+	0.282843i
$151$	−6.50000	−	11.2583i	−0.528962	−	0.916190i	−0.999430	−	0.0337724i	$-0.989248\pi$
$151$	−6.50000	−	11.2583i	−0.528962	−	0.916190i	0.470467	−	0.882418i	$-0.344085\pi$
$152$	2.00000	−	3.46410i	0.162221	−	0.280976i
$153$	−6.00000			−0.485071
$154$	0.500000	−	2.59808i	0.0402911	−	0.209359i
$155$	11.0000			0.883541
$156$	0.500000	−	0.866025i	0.0400320	−	0.0693375i
$157$	9.00000	+	15.5885i	0.718278	+	1.24409i	0.961681	+	0.274169i	$0.0884028\pi$
$157$	9.00000	+	15.5885i	0.718278	+	1.24409i	−0.243403	+	0.969925i	$0.578264\pi$
$158$	−3.50000	−	6.06218i	−0.278445	−	0.482281i
$159$	2.50000	−	4.33013i	0.198263	−	0.343401i
$160$	−1.00000			−0.0790569
$161$	12.0000	+	10.3923i	0.945732	+	0.819028i
$162$	1.00000			0.0785674
$163$	4.00000	−	6.92820i	0.313304	−	0.542659i	−0.665771	−	0.746156i	$-0.731897\pi$
$163$	4.00000	−	6.92820i	0.313304	−	0.542659i	0.979076	+	0.203497i	$0.0652307\pi$
$164$	−6.00000	−	10.3923i	−0.468521	−	0.811503i
$165$	−0.500000	−	0.866025i	−0.0389249	−	0.0674200i
$166$	8.50000	−	14.7224i	0.659728	−	1.14268i
$167$	−24.0000			−1.85718			−0.928588	−	0.371113i	$-0.878976\pi$
$167$	−24.0000			−1.85718			−0.928588	+	0.371113i	$0.878976\pi$
$168$	2.50000	−	0.866025i	0.192879	−	0.0668153i
$169$	1.00000			0.0769231
$170$	−3.00000	+	5.19615i	−0.230089	+	0.398527i
$171$	2.00000	+	3.46410i	0.152944	+	0.264906i
$172$	4.00000	+	6.92820i	0.304997	+	0.528271i
$173$	−3.00000	+	5.19615i	−0.228086	+	0.395056i	−0.957241	−	0.289292i	$-0.906580\pi$
$173$	−3.00000	+	5.19615i	−0.228086	+	0.395056i	0.729155	+	0.684349i	$0.239913\pi$
$174$	3.00000			0.227429
$175$	−10.0000	+	3.46410i	−0.755929	+	0.261861i
$176$	−1.00000			−0.0753778
$177$	2.50000	−	4.33013i	0.187912	−	0.325472i
$178$	6.00000	+	10.3923i	0.449719	+	0.778936i
$179$	−6.00000	−	10.3923i	−0.448461	−	0.776757i	0.549825	−	0.835280i	$-0.314694\pi$
$179$	−6.00000	−	10.3923i	−0.448461	−	0.776757i	−0.998286	+	0.0585225i	$0.981361\pi$
$180$	0.500000	−	0.866025i	0.0372678	−	0.0645497i
$181$	−16.0000			−1.18927			−0.594635	−	0.803996i	$-0.702704\pi$
$181$	−16.0000			−1.18927			−0.594635	+	0.803996i	$0.702704\pi$
$182$	2.00000	+	1.73205i	0.148250	+	0.128388i
$183$	12.0000			0.887066
$184$	3.00000	−	5.19615i	0.221163	−	0.383065i
$185$	2.00000	+	3.46410i	0.147043	+	0.254686i
$186$	5.50000	+	9.52628i	0.403280	+	0.698501i
$187$	−3.00000	+	5.19615i	−0.219382	+	0.379980i
$188$	−8.00000			−0.583460
$189$	−0.500000	+	2.59808i	−0.0363696	+	0.188982i
$190$	4.00000			0.290191
$191$	3.00000	−	5.19615i	0.217072	−	0.375980i	−0.736839	−	0.676068i	$-0.763683\pi$
$191$	3.00000	−	5.19615i	0.217072	−	0.375980i	0.953912	+	0.300088i	$0.0970159\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	−7.50000	−	12.9904i	−0.539862	−	0.935068i	−0.998911	−	0.0466572i	$-0.985143\pi$
$193$	−7.50000	−	12.9904i	−0.539862	−	0.935068i	0.459049	−	0.888411i	$-0.348190\pi$
$194$	−6.50000	+	11.2583i	−0.466673	+	0.808301i
$195$	1.00000			0.0716115
$196$	1.00000	+	6.92820i	0.0714286	+	0.494872i
$197$	−18.0000			−1.28245			−0.641223	−	0.767354i	$-0.721573\pi$
$197$	−18.0000			−1.28245			−0.641223	+	0.767354i	$0.721573\pi$
$198$	0.500000	−	0.866025i	0.0355335	−	0.0615457i
$199$	−4.00000	−	6.92820i	−0.283552	−	0.491127i	0.688705	−	0.725042i	$-0.258180\pi$
$199$	−4.00000	−	6.92820i	−0.283552	−	0.491127i	−0.972257	+	0.233915i	$0.924846\pi$
$200$	2.00000	+	3.46410i	0.141421	+	0.244949i
$201$	−8.00000	+	13.8564i	−0.564276	+	0.977356i
$202$	10.0000			0.703598
$203$	−1.50000	+	7.79423i	−0.105279	+	0.547048i
$204$	−6.00000			−0.420084
$205$	6.00000	−	10.3923i	0.419058	−	0.725830i
$206$		0			0
$207$	3.00000	+	5.19615i	0.208514	+	0.361158i
$208$	0.500000	−	0.866025i	0.0346688	−	0.0600481i
$209$	4.00000			0.276686
$210$	2.00000	+	1.73205i	0.138013	+	0.119523i
$211$	12.0000			0.826114			0.413057	−	0.910705i	$-0.364461\pi$
$211$	12.0000			0.826114			0.413057	+	0.910705i	$0.364461\pi$
$212$	2.50000	−	4.33013i	0.171701	−	0.297394i
$213$	−3.00000	−	5.19615i	−0.205557	−	0.356034i
$214$	−3.50000	−	6.06218i	−0.239255	−	0.414402i
$215$	−4.00000	+	6.92820i	−0.272798	+	0.472500i
$216$	1.00000			0.0680414
$217$	−27.5000	+	9.52628i	−1.86682	+	0.646686i
$218$	12.0000			0.812743
$219$	5.00000	−	8.66025i	0.337869	−	0.585206i
$220$	−0.500000	−	0.866025i	−0.0337100	−	0.0583874i
$221$	−3.00000	−	5.19615i	−0.201802	−	0.349531i
$222$	−2.00000	+	3.46410i	−0.134231	+	0.232495i
$223$	7.00000			0.468755			0.234377	−	0.972146i	$-0.424695\pi$
$223$	7.00000			0.468755			0.234377	+	0.972146i	$0.424695\pi$
$224$	2.50000	−	0.866025i	0.167038	−	0.0578638i
$225$	−4.00000			−0.266667
$226$	2.00000	−	3.46410i	0.133038	−	0.230429i
$227$	7.50000	+	12.9904i	0.497792	+	0.862202i	0.999997	−	0.00254715i	$-0.000810783\pi$
$227$	7.50000	+	12.9904i	0.497792	+	0.862202i	−0.502204	+	0.864749i	$0.667477\pi$
$228$	2.00000	+	3.46410i	0.132453	+	0.229416i
$229$	−3.00000	+	5.19615i	−0.198246	+	0.343371i	−0.947960	−	0.318390i	$-0.896858\pi$
$229$	−3.00000	+	5.19615i	−0.198246	+	0.343371i	0.749714	+	0.661762i	$0.230191\pi$
$230$	6.00000			0.395628
$231$	2.00000	+	1.73205i	0.131590	+	0.113961i
$232$	3.00000			0.196960
$233$	−3.00000	+	5.19615i	−0.196537	+	0.340411i	−0.947403	−	0.320043i	$-0.896303\pi$
$233$	−3.00000	+	5.19615i	−0.196537	+	0.340411i	0.750867	+	0.660454i	$0.229636\pi$
$234$	0.500000	+	0.866025i	0.0326860	+	0.0566139i
$235$	−4.00000	−	6.92820i	−0.260931	−	0.451946i
$236$	2.50000	−	4.33013i	0.162736	−	0.281867i
$237$	7.00000			0.454699
$238$	3.00000	−	15.5885i	0.194461	−	1.01045i
$239$	−6.00000			−0.388108			−0.194054	−	0.980991i	$-0.562164\pi$
$239$	−6.00000			−0.388108			−0.194054	+	0.980991i	$0.562164\pi$
$240$	0.500000	−	0.866025i	0.0322749	−	0.0559017i
$241$	7.50000	+	12.9904i	0.483117	+	0.836784i	0.999812	−	0.0193858i	$-0.00617107\pi$
$241$	7.50000	+	12.9904i	0.483117	+	0.836784i	−0.516695	+	0.856170i	$0.672838\pi$
$242$	5.00000	+	8.66025i	0.321412	+	0.556702i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	12.0000			0.768221
$245$	−5.50000	+	4.33013i	−0.351382	+	0.276642i
$246$	12.0000			0.765092
$247$	−2.00000	+	3.46410i	−0.127257	+	0.220416i
$248$	5.50000	+	9.52628i	0.349250	+	0.604919i
$249$	8.50000	+	14.7224i	0.538666	+	0.932996i
$250$	−4.50000	+	7.79423i	−0.284605	+	0.492950i
$251$	17.0000			1.07303			0.536515	−	0.843891i	$-0.319740\pi$
$251$	17.0000			1.07303			0.536515	+	0.843891i	$0.319740\pi$
$252$	−0.500000	+	2.59808i	−0.0314970	+	0.163663i
$253$	6.00000			0.377217
$254$	3.50000	−	6.06218i	0.219610	−	0.380375i
$255$	−3.00000	−	5.19615i	−0.187867	−	0.325396i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	3.00000	−	5.19615i	0.187135	−	0.324127i	−0.757159	−	0.653231i	$-0.773413\pi$
$257$	3.00000	−	5.19615i	0.187135	−	0.324127i	0.944294	+	0.329104i	$0.106747\pi$
$258$	−8.00000			−0.498058
$259$	−8.00000	−	6.92820i	−0.497096	−	0.430498i
$260$	1.00000			0.0620174
$261$	−1.50000	+	2.59808i	−0.0928477	+	0.160817i
$262$	−0.500000	−	0.866025i	−0.0308901	−	0.0535032i
$263$	9.00000	+	15.5885i	0.554964	+	0.961225i	0.997906	+	0.0646755i	$0.0206012\pi$
$263$	9.00000	+	15.5885i	0.554964	+	0.961225i	−0.442943	+	0.896550i	$0.646065\pi$
$264$	0.500000	−	0.866025i	0.0307729	−	0.0533002i
$265$	5.00000			0.307148
$266$	−10.0000	+	3.46410i	−0.613139	+	0.212398i
$267$	−12.0000			−0.734388
$268$	−8.00000	+	13.8564i	−0.488678	+	0.846415i
$269$	4.50000	+	7.79423i	0.274370	+	0.475223i	0.969976	−	0.243201i	$-0.0781974\pi$
$269$	4.50000	+	7.79423i	0.274370	+	0.475223i	−0.695606	+	0.718423i	$0.744864\pi$
$270$	0.500000	+	0.866025i	0.0304290	+	0.0527046i
$271$	3.50000	−	6.06218i	0.212610	−	0.368251i	−0.739921	−	0.672694i	$-0.765137\pi$
$271$	3.50000	−	6.06218i	0.212610	−	0.368251i	0.952531	+	0.304443i	$0.0984703\pi$
$272$	−6.00000			−0.363803
$273$	−2.50000	+	0.866025i	−0.151307	+	0.0524142i
$274$	−8.00000			−0.483298
$275$	−2.00000	+	3.46410i	−0.120605	+	0.208893i
$276$	3.00000	+	5.19615i	0.180579	+	0.312772i
$277$	5.00000	+	8.66025i	0.300421	+	0.520344i	0.976231	−	0.216731i	$-0.0695395\pi$
$277$	5.00000	+	8.66025i	0.300421	+	0.520344i	−0.675810	+	0.737075i	$0.736206\pi$
$278$		0			0
$279$	−11.0000			−0.658553
$280$	2.00000	+	1.73205i	0.119523	+	0.103510i
$281$	4.00000			0.238620			0.119310	−	0.992857i	$-0.461932\pi$
$281$	4.00000			0.238620			0.119310	+	0.992857i	$0.461932\pi$
$282$	4.00000	−	6.92820i	0.238197	−	0.412568i
$283$	−5.00000	−	8.66025i	−0.297219	−	0.514799i	0.678280	−	0.734804i	$-0.262726\pi$
$283$	−5.00000	−	8.66025i	−0.297219	−	0.514799i	−0.975499	+	0.220005i	$0.929393\pi$
$284$	−3.00000	−	5.19615i	−0.178017	−	0.308335i
$285$	−2.00000	+	3.46410i	−0.118470	+	0.205196i
$286$	1.00000			0.0591312
$287$	−6.00000	+	31.1769i	−0.354169	+	1.84032i
$288$	1.00000			0.0589256
$289$	−9.50000	+	16.4545i	−0.558824	+	0.967911i
$290$	1.50000	+	2.59808i	0.0880830	+	0.152564i
$291$	−6.50000	−	11.2583i	−0.381037	−	0.659975i
$292$	5.00000	−	8.66025i	0.292603	−	0.506803i
$293$	−7.00000			−0.408944			−0.204472	−	0.978872i	$-0.565548\pi$
$293$	−7.00000			−0.408944			−0.204472	+	0.978872i	$0.565548\pi$
$294$	−6.50000	−	2.59808i	−0.379088	−	0.151523i
$295$	5.00000			0.291111
$296$	−2.00000	+	3.46410i	−0.116248	+	0.201347i
$297$	0.500000	+	0.866025i	0.0290129	+	0.0502519i
$298$	5.00000	+	8.66025i	0.289642	+	0.501675i
$299$	−3.00000	+	5.19615i	−0.173494	+	0.300501i
$300$	−4.00000			−0.230940
$301$	4.00000	−	20.7846i	0.230556	−	1.19800i
$302$	13.0000			0.748066
$303$	−5.00000	+	8.66025i	−0.287242	+	0.497519i
$304$	2.00000	+	3.46410i	0.114708	+	0.198680i
$305$	6.00000	+	10.3923i	0.343559	+	0.595062i
$306$	3.00000	−	5.19615i	0.171499	−	0.297044i
$307$	6.00000			0.342438			0.171219	−	0.985233i	$-0.445229\pi$
$307$	6.00000			0.342438			0.171219	+	0.985233i	$0.445229\pi$
$308$	2.00000	+	1.73205i	0.113961	+	0.0986928i
$309$		0			0
$310$	−5.50000	+	9.52628i	−0.312379	+	0.541056i
$311$	−1.00000	−	1.73205i	−0.0567048	−	0.0982156i	0.836280	−	0.548303i	$-0.184726\pi$
$311$	−1.00000	−	1.73205i	−0.0567048	−	0.0982156i	−0.892984	+	0.450088i	$0.851393\pi$
$312$	0.500000	+	0.866025i	0.0283069	+	0.0490290i
$313$	−6.50000	+	11.2583i	−0.367402	+	0.636358i	−0.989158	−	0.146852i	$-0.953086\pi$
$313$	−6.50000	+	11.2583i	−0.367402	+	0.636358i	0.621757	+	0.783210i	$0.286419\pi$
$314$	−18.0000			−1.01580
$315$	−2.50000	+	0.866025i	−0.140859	+	0.0487950i
$316$	7.00000			0.393781
$317$	1.50000	−	2.59808i	0.0842484	−	0.145922i	−0.820822	−	0.571184i	$-0.806484\pi$
$317$	1.50000	−	2.59808i	0.0842484	−	0.145922i	0.905071	+	0.425261i	$0.139818\pi$
$318$	2.50000	+	4.33013i	0.140193	+	0.242821i
$319$	1.50000	+	2.59808i	0.0839839	+	0.145464i
$320$	0.500000	−	0.866025i	0.0279508	−	0.0484123i
$321$	7.00000			0.390702
$322$	−15.0000	+	5.19615i	−0.835917	+	0.289570i
$323$	24.0000			1.33540
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	−2.00000	−	3.46410i	−0.110940	−	0.192154i
$326$	4.00000	+	6.92820i	0.221540	+	0.383718i
$327$	−6.00000	+	10.3923i	−0.331801	+	0.574696i
$328$	12.0000			0.662589
$329$	16.0000	+	13.8564i	0.882109	+	0.763928i
$330$	1.00000			0.0550482
$331$	4.00000	−	6.92820i	0.219860	−	0.380808i	−0.734905	−	0.678170i	$-0.762773\pi$
$331$	4.00000	−	6.92820i	0.219860	−	0.380808i	0.954765	+	0.297361i	$0.0961066\pi$
$332$	8.50000	+	14.7224i	0.466498	+	0.807998i
$333$	−2.00000	−	3.46410i	−0.109599	−	0.189832i
$334$	12.0000	−	20.7846i	0.656611	−	1.13728i
$335$	−16.0000			−0.874173
$336$	−0.500000	+	2.59808i	−0.0272772	+	0.141737i
$337$	25.0000			1.36184			0.680918	−	0.732359i	$-0.261581\pi$
$337$	25.0000			1.36184			0.680918	+	0.732359i	$0.261581\pi$
$338$	−0.500000	+	0.866025i	−0.0271964	+	0.0471056i
$339$	2.00000	+	3.46410i	0.108625	+	0.188144i
$340$	−3.00000	−	5.19615i	−0.162698	−	0.281801i
$341$	−5.50000	+	9.52628i	−0.297842	+	0.515877i
$342$	−4.00000			−0.216295
$343$	10.0000	−	15.5885i	0.539949	−	0.841698i
$344$	−8.00000			−0.431331
$345$	−3.00000	+	5.19615i	−0.161515	+	0.279751i
$346$	−3.00000	−	5.19615i	−0.161281	−	0.279347i
$347$	−10.0000	−	17.3205i	−0.536828	−	0.929814i	−0.999072	−	0.0430610i	$-0.986289\pi$
$347$	−10.0000	−	17.3205i	−0.536828	−	0.929814i	0.462244	−	0.886753i	$-0.347044\pi$
$348$	−1.50000	+	2.59808i	−0.0804084	+	0.139272i
$349$	14.0000			0.749403			0.374701	−	0.927146i	$-0.377745\pi$
$349$	14.0000			0.749403			0.374701	+	0.927146i	$0.377745\pi$
$350$	2.00000	−	10.3923i	0.106904	−	0.555492i
$351$	−1.00000			−0.0533761
$352$	0.500000	−	0.866025i	0.0266501	−	0.0461593i
$353$	−15.0000	−	25.9808i	−0.798369	−	1.38282i	−0.920677	−	0.390324i	$-0.872363\pi$
$353$	−15.0000	−	25.9808i	−0.798369	−	1.38282i	0.122308	−	0.992492i	$-0.460970\pi$
$354$	2.50000	+	4.33013i	0.132874	+	0.230144i
$355$	3.00000	−	5.19615i	0.159223	−	0.275783i
$356$	−12.0000			−0.635999
$357$	12.0000	+	10.3923i	0.635107	+	0.550019i
$358$	12.0000			0.634220
$359$	11.0000	−	19.0526i	0.580558	−	1.00556i	−0.414855	−	0.909887i	$-0.636168\pi$
$359$	11.0000	−	19.0526i	0.580558	−	1.00556i	0.995413	−	0.0956683i	$-0.0304988\pi$
$360$	0.500000	+	0.866025i	0.0263523	+	0.0456435i
$361$	1.50000	+	2.59808i	0.0789474	+	0.136741i
$362$	8.00000	−	13.8564i	0.420471	−	0.728277i
$363$	−10.0000			−0.524864
$364$	−2.50000	+	0.866025i	−0.131036	+	0.0453921i
$365$	10.0000			0.523424
$366$	−6.00000	+	10.3923i	−0.313625	+	0.543214i
$367$	3.50000	+	6.06218i	0.182699	+	0.316443i	0.942799	−	0.333363i	$-0.108183\pi$
$367$	3.50000	+	6.06218i	0.182699	+	0.316443i	−0.760100	+	0.649806i	$0.774850\pi$
$368$	3.00000	+	5.19615i	0.156386	+	0.270868i
$369$	−6.00000	+	10.3923i	−0.312348	+	0.541002i
$370$	−4.00000			−0.207950
$371$	−12.5000	+	4.33013i	−0.648968	+	0.224809i
$372$	−11.0000			−0.570323
$373$	−13.0000	+	22.5167i	−0.673114	+	1.16587i	0.303902	+	0.952703i	$0.401711\pi$
$373$	−13.0000	+	22.5167i	−0.673114	+	1.16587i	−0.977016	+	0.213165i	$0.931623\pi$
$374$	−3.00000	−	5.19615i	−0.155126	−	0.268687i
$375$	−4.50000	−	7.79423i	−0.232379	−	0.402492i
$376$	4.00000	−	6.92820i	0.206284	−	0.357295i
$377$	−3.00000			−0.154508
$378$	−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	$0.365203\pi$
$380$	−2.00000	+	3.46410i	−0.102598	+	0.177705i
$381$	3.50000	+	6.06218i	0.179310	+	0.310575i
$382$	3.00000	+	5.19615i	0.153493	+	0.265858i
$383$	7.00000	−	12.1244i	0.357683	−	0.619526i	−0.629890	−	0.776684i	$-0.716900\pi$
$383$	7.00000	−	12.1244i	0.357683	−	0.619526i	0.987573	+	0.157159i	$0.0502334\pi$
$384$	1.00000			0.0510310
$385$	−0.500000	+	2.59808i	−0.0254824	+	0.132410i
$386$	15.0000			0.763480
$387$	4.00000	−	6.92820i	0.203331	−	0.352180i
$388$	−6.50000	−	11.2583i	−0.329988	−	0.571555i
$389$	−11.0000	−	19.0526i	−0.557722	−	0.966003i	−0.997686	−	0.0679877i	$-0.978342\pi$
$389$	−11.0000	−	19.0526i	−0.557722	−	0.966003i	0.439964	−	0.898015i	$-0.354991\pi$
$390$	−0.500000	+	0.866025i	−0.0253185	+	0.0438529i
$391$	36.0000			1.82060
$392$	−6.50000	−	2.59808i	−0.328300	−	0.131223i
$393$	1.00000			0.0504433
$394$	9.00000	−	15.5885i	0.453413	−	0.785335i
$395$	3.50000	+	6.06218i	0.176104	+	0.305021i
$396$	0.500000	+	0.866025i	0.0251259	+	0.0435194i
$397$	9.00000	−	15.5885i	0.451697	−	0.782362i	−0.546795	−	0.837267i	$-0.684152\pi$
$397$	9.00000	−	15.5885i	0.451697	−	0.782362i	0.998492	+	0.0549046i	$0.0174855\pi$
$398$	8.00000			0.401004
$399$	2.00000	−	10.3923i	0.100125	−	0.520266i
$400$	−4.00000			−0.200000
$401$	9.00000	−	15.5885i	0.449439	−	0.778450i	−0.548911	−	0.835881i	$-0.684957\pi$
$401$	9.00000	−	15.5885i	0.449439	−	0.778450i	0.998350	+	0.0574304i	$0.0182907\pi$
$402$	−8.00000	−	13.8564i	−0.399004	−	0.691095i
$403$	−5.50000	−	9.52628i	−0.273975	−	0.474538i
$404$	−5.00000	+	8.66025i	−0.248759	+	0.430864i
$405$	−1.00000			−0.0496904
$406$	−6.00000	−	5.19615i	−0.297775	−	0.257881i
$407$	−4.00000			−0.198273
$408$	3.00000	−	5.19615i	0.148522	−	0.257248i
$409$	−12.5000	−	21.6506i	−0.618085	−	1.07056i	−0.989835	−	0.142222i	$-0.954575\pi$
$409$	−12.5000	−	21.6506i	−0.618085	−	1.07056i	0.371750	−	0.928333i	$-0.378758\pi$
$410$	6.00000	+	10.3923i	0.296319	+	0.513239i
$411$	4.00000	−	6.92820i	0.197305	−	0.341743i
$412$		0			0
$413$	−12.5000	+	4.33013i	−0.615085	+	0.213072i
$414$	−6.00000			−0.294884
$415$	−8.50000	+	14.7224i	−0.417249	+	0.722696i
$416$	0.500000	+	0.866025i	0.0245145	+	0.0424604i
$417$		0			0
$418$	−2.00000	+	3.46410i	−0.0978232	+	0.169435i
$419$	16.0000			0.781651			0.390826	−	0.920465i	$-0.372190\pi$
$419$	16.0000			0.781651			0.390826	+	0.920465i	$0.372190\pi$
$420$	−2.50000	+	0.866025i	−0.121988	+	0.0422577i
$421$	−36.0000			−1.75453			−0.877266	−	0.480004i	$-0.840635\pi$
$421$	−36.0000			−1.75453			−0.877266	+	0.480004i	$0.840635\pi$
$422$	−6.00000	+	10.3923i	−0.292075	+	0.505889i
$423$	4.00000	+	6.92820i	0.194487	+	0.336861i
$424$	2.50000	+	4.33013i	0.121411	+	0.210290i
$425$	−12.0000	+	20.7846i	−0.582086	+	1.00820i
$426$	6.00000			0.290701
$427$	−24.0000	−	20.7846i	−1.16144	−	1.00584i
$428$	7.00000			0.338358
$429$	−0.500000	+	0.866025i	−0.0241402	+	0.0418121i
$430$	−4.00000	−	6.92820i	−0.192897	−	0.334108i
$431$	19.0000	+	32.9090i	0.915198	+	1.58517i	0.806611	+	0.591082i	$0.201299\pi$
$431$	19.0000	+	32.9090i	0.915198	+	1.58517i	0.108586	+	0.994087i	$0.465368\pi$
$432$	−0.500000	+	0.866025i	−0.0240563	+	0.0416667i
$433$	−14.0000			−0.672797			−0.336399	−	0.941720i	$-0.609209\pi$
$433$	−14.0000			−0.672797			−0.336399	+	0.941720i	$0.609209\pi$
$434$	5.50000	−	28.5788i	0.264008	−	1.37183i
$435$	−3.00000			−0.143839
$436$	−6.00000	+	10.3923i	−0.287348	+	0.497701i
$437$	−12.0000	−	20.7846i	−0.574038	−	0.994263i
$438$	5.00000	+	8.66025i	0.238909	+	0.413803i
$439$	8.50000	−	14.7224i	0.405683	−	0.702663i	−0.588718	−	0.808339i	$-0.700367\pi$
$439$	8.50000	−	14.7224i	0.405683	−	0.702663i	0.994401	+	0.105675i	$0.0337004\pi$
$440$	1.00000			0.0476731
$441$	5.50000	−	4.33013i	0.261905	−	0.206197i
$442$	6.00000			0.285391
$443$	19.5000	−	33.7750i	0.926473	−	1.60470i	0.137298	−	0.990530i	$-0.456158\pi$
$443$	19.5000	−	33.7750i	0.926473	−	1.60470i	0.789175	−	0.614168i	$-0.210508\pi$
$444$	−2.00000	−	3.46410i	−0.0949158	−	0.164399i
$445$	−6.00000	−	10.3923i	−0.284427	−	0.492642i
$446$	−3.50000	+	6.06218i	−0.165730	+	0.287052i
$447$	−10.0000			−0.472984
$448$	−0.500000	+	2.59808i	−0.0236228	+	0.122748i
$449$	20.0000			0.943858			0.471929	−	0.881636i	$-0.343558\pi$
$449$	20.0000			0.943858			0.471929	+	0.881636i	$0.343558\pi$
$450$	2.00000	−	3.46410i	0.0942809	−	0.163299i
$451$	6.00000	+	10.3923i	0.282529	+	0.489355i
$452$	2.00000	+	3.46410i	0.0940721	+	0.162938i
$453$	−6.50000	+	11.2583i	−0.305397	+	0.528962i
$454$	−15.0000			−0.703985
$455$	−2.00000	−	1.73205i	−0.0937614	−	0.0811998i
$456$	−4.00000			−0.187317
$457$	5.50000	−	9.52628i	0.257279	−	0.445621i	−0.708233	−	0.705979i	$-0.750507\pi$
$457$	5.50000	−	9.52628i	0.257279	−	0.445621i	0.965512	+	0.260358i	$0.0838407\pi$
$458$	−3.00000	−	5.19615i	−0.140181	−	0.242800i
$459$	3.00000	+	5.19615i	0.140028	+	0.242536i
$460$	−3.00000	+	5.19615i	−0.139876	+	0.242272i
$461$	34.0000			1.58354			0.791769	−	0.610821i	$-0.209160\pi$
$461$	34.0000			1.58354			0.791769	+	0.610821i	$0.209160\pi$
$462$	−2.50000	+	0.866025i	−0.116311	+	0.0402911i
$463$	−24.0000			−1.11537			−0.557687	−	0.830051i	$-0.688311\pi$
$463$	−24.0000			−1.11537			−0.557687	+	0.830051i	$0.688311\pi$
$464$	−1.50000	+	2.59808i	−0.0696358	+	0.120613i
$465$	−5.50000	−	9.52628i	−0.255056	−	0.441771i
$466$	−3.00000	−	5.19615i	−0.138972	−	0.240707i
$467$	−6.00000	+	10.3923i	−0.277647	+	0.480899i	−0.970799	−	0.239892i	$-0.922888\pi$
$467$	−6.00000	+	10.3923i	−0.277647	+	0.480899i	0.693153	+	0.720791i	$0.256221\pi$
$468$	−1.00000			−0.0462250
$469$	40.0000	−	13.8564i	1.84703	−	0.639829i
$470$	8.00000			0.369012
$471$	9.00000	−	15.5885i	0.414698	−	0.718278i
$472$	2.50000	+	4.33013i	0.115072	+	0.199310i
$473$	−4.00000	−	6.92820i	−0.183920	−	0.318559i
$474$	−3.50000	+	6.06218i	−0.160760	+	0.278445i
$475$	16.0000			0.734130
$476$	12.0000	+	10.3923i	0.550019	+	0.476331i
$477$	−5.00000			−0.228934
$478$	3.00000	−	5.19615i	0.137217	−	0.237666i
$479$	−7.00000	−	12.1244i	−0.319838	−	0.553976i	0.660616	−	0.750724i	$-0.270295\pi$
$479$	−7.00000	−	12.1244i	−0.319838	−	0.553976i	−0.980454	+	0.196748i	$0.936962\pi$
$480$	0.500000	+	0.866025i	0.0228218	+	0.0395285i
$481$	2.00000	−	3.46410i	0.0911922	−	0.157949i
$482$	−15.0000			−0.683231
$483$	3.00000	−	15.5885i	0.136505	−	0.709299i
$484$	−10.0000			−0.454545
$485$	6.50000	−	11.2583i	0.295150	−	0.511214i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	−11.5000	−	19.9186i	−0.521115	−	0.902597i	−0.999698	−	0.0245553i	$-0.992183\pi$
$487$	−11.5000	−	19.9186i	−0.521115	−	0.902597i	0.478584	−	0.878042i	$-0.341150\pi$
$488$	−6.00000	+	10.3923i	−0.271607	+	0.470438i
$489$	−8.00000			−0.361773
$490$	−1.00000	−	6.92820i	−0.0451754	−	0.312984i
$491$	−35.0000			−1.57953			−0.789764	−	0.613411i	$-0.789797\pi$
$491$	−35.0000			−1.57953			−0.789764	+	0.613411i	$0.789797\pi$
$492$	−6.00000	+	10.3923i	−0.270501	+	0.468521i
$493$	9.00000	+	15.5885i	0.405340	+	0.702069i
$494$	−2.00000	−	3.46410i	−0.0899843	−	0.155857i
$495$	−0.500000	+	0.866025i	−0.0224733	+	0.0389249i
$496$	−11.0000			−0.493915
$497$	−3.00000	+	15.5885i	−0.134568	+	0.699238i
$498$	−17.0000			−0.761788
$499$	14.0000	−	24.2487i	0.626726	−	1.08552i	−0.361478	−	0.932381i	$-0.617728\pi$
$499$	14.0000	−	24.2487i	0.626726	−	1.08552i	0.988204	−	0.153141i	$-0.0489388\pi$
$500$	−4.50000	−	7.79423i	−0.201246	−	0.348569i
$501$	12.0000	+	20.7846i	0.536120	+	0.928588i
$502$	−8.50000	+	14.7224i	−0.379374	+	0.657094i
$503$	−6.00000			−0.267527			−0.133763	−	0.991013i	$-0.542706\pi$
$503$	−6.00000			−0.267527			−0.133763	+	0.991013i	$0.542706\pi$
$504$	−2.00000	−	1.73205i	−0.0890871	−	0.0771517i
$505$	−10.0000			−0.444994
$506$	−3.00000	+	5.19615i	−0.133366	+	0.230997i
$507$	−0.500000	−	0.866025i	−0.0222058	−	0.0384615i
$508$	3.50000	+	6.06218i	0.155287	+	0.268966i
$509$	−6.50000	+	11.2583i	−0.288107	+	0.499017i	−0.973358	−	0.229291i	$-0.926359\pi$
$509$	−6.50000	+	11.2583i	−0.288107	+	0.499017i	0.685251	+	0.728307i	$0.259693\pi$
$510$	6.00000			0.265684
$511$	−25.0000	+	8.66025i	−1.10593	+	0.383107i
$512$	1.00000			0.0441942
$513$	2.00000	−	3.46410i	0.0883022	−	0.152944i
$514$	3.00000	+	5.19615i	0.132324	+	0.229192i
$515$		0			0
$516$	4.00000	−	6.92820i	0.176090	−	0.304997i
$517$	8.00000			0.351840
$518$	10.0000	−	3.46410i	0.439375	−	0.152204i
$519$	6.00000			0.263371
$520$	−0.500000	+	0.866025i	−0.0219265	+	0.0379777i
$521$	−14.0000	−	24.2487i	−0.613351	−	1.06236i	−0.990671	−	0.136272i	$-0.956488\pi$
$521$	−14.0000	−	24.2487i	−0.613351	−	1.06236i	0.377320	−	0.926083i	$-0.376846\pi$
$522$	−1.50000	−	2.59808i	−0.0656532	−	0.113715i
$523$	−8.00000	+	13.8564i	−0.349816	+	0.605898i	−0.986216	−	0.165460i	$-0.947089\pi$
$523$	−8.00000	+	13.8564i	−0.349816	+	0.605898i	0.636401	+	0.771358i	$0.280422\pi$
$524$	1.00000			0.0436852
$525$	8.00000	+	6.92820i	0.349149	+	0.302372i
$526$	−18.0000			−0.784837
$527$	−33.0000	+	57.1577i	−1.43750	+	2.48983i
$528$	0.500000	+	0.866025i	0.0217597	+	0.0376889i
$529$	−6.50000	−	11.2583i	−0.282609	−	0.489493i
$530$	−2.50000	+	4.33013i	−0.108593	+	0.188089i
$531$	−5.00000			−0.216982
$532$	2.00000	−	10.3923i	0.0867110	−	0.450564i
$533$	−12.0000			−0.519778
$534$	6.00000	−	10.3923i	0.259645	−	0.449719i
$535$	3.50000	+	6.06218i	0.151318	+	0.262091i
$536$	−8.00000	−	13.8564i	−0.345547	−	0.598506i
$537$	−6.00000	+	10.3923i	−0.258919	+	0.448461i
$538$	−9.00000			−0.388018
$539$	−1.00000	−	6.92820i	−0.0430730	−	0.298419i
$540$	−1.00000			−0.0430331
$541$	−16.0000	+	27.7128i	−0.687894	+	1.19147i	0.284624	+	0.958639i	$0.408131\pi$
$541$	−16.0000	+	27.7128i	−0.687894	+	1.19147i	−0.972518	+	0.232828i	$0.925202\pi$
$542$	3.50000	+	6.06218i	0.150338	+	0.260393i
$543$	8.00000	+	13.8564i	0.343313	+	0.594635i
$544$	3.00000	−	5.19615i	0.128624	−	0.222783i
$545$	−12.0000			−0.514024
$546$	0.500000	−	2.59808i	0.0213980	−	0.111187i
$547$	36.0000			1.53925			0.769624	−	0.638497i	$-0.220443\pi$
$547$	36.0000			1.53925			0.769624	+	0.638497i	$0.220443\pi$
$548$	4.00000	−	6.92820i	0.170872	−	0.295958i
$549$	−6.00000	−	10.3923i	−0.256074	−	0.443533i
$550$	−2.00000	−	3.46410i	−0.0852803	−	0.147710i
$551$	6.00000	−	10.3923i	0.255609	−	0.442727i
$552$	−6.00000			−0.255377
$553$	−14.0000	−	12.1244i	−0.595341	−	0.515580i
$554$	−10.0000			−0.424859
$555$	2.00000	−	3.46410i	0.0848953	−	0.147043i
$556$		0			0
$557$	8.50000	+	14.7224i	0.360157	+	0.623809i	0.987986	−	0.154541i	$-0.0493899\pi$
$557$	8.50000	+	14.7224i	0.360157	+	0.623809i	−0.627830	+	0.778351i	$0.716057\pi$
$558$	5.50000	−	9.52628i	0.232834	−	0.403280i
$559$	8.00000			0.338364
$560$	−2.50000	+	0.866025i	−0.105644	+	0.0365963i
$561$	6.00000			0.253320
$562$	−2.00000	+	3.46410i	−0.0843649	+	0.146124i
$563$	−10.5000	−	18.1865i	−0.442522	−	0.766471i	0.555354	−	0.831614i	$-0.312583\pi$
$563$	−10.5000	−	18.1865i	−0.442522	−	0.766471i	−0.997876	+	0.0651433i	$0.979250\pi$
$564$	4.00000	+	6.92820i	0.168430	+	0.291730i
$565$	−2.00000	+	3.46410i	−0.0841406	+	0.145736i
$566$	10.0000			0.420331
$567$	2.50000	−	0.866025i	0.104990	−	0.0363696i
$568$	6.00000			0.251754
$569$	2.00000	−	3.46410i	0.0838444	−	0.145223i	−0.821054	−	0.570851i	$-0.806613\pi$
$569$	2.00000	−	3.46410i	0.0838444	−	0.145223i	0.904898	+	0.425628i	$0.139947\pi$
$570$	−2.00000	−	3.46410i	−0.0837708	−	0.145095i
$571$	−14.0000	−	24.2487i	−0.585882	−	1.01478i	−0.994765	−	0.102190i	$-0.967415\pi$
$571$	−14.0000	−	24.2487i	−0.585882	−	1.01478i	0.408883	−	0.912587i	$-0.365918\pi$
$572$	−0.500000	+	0.866025i	−0.0209061	+	0.0362103i
$573$	−6.00000			−0.250654
$574$	−24.0000	−	20.7846i	−1.00174	−	0.867533i
$575$	24.0000			1.00087
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−0.500000	−	0.866025i	−0.0208153	−	0.0360531i	0.855430	−	0.517918i	$-0.173293\pi$
$577$	−0.500000	−	0.866025i	−0.0208153	−	0.0360531i	−0.876245	+	0.481865i	$0.839960\pi$
$578$	−9.50000	−	16.4545i	−0.395148	−	0.684416i
$579$	−7.50000	+	12.9904i	−0.311689	+	0.539862i
$580$	−3.00000			−0.124568
$581$	8.50000	−	44.1673i	0.352639	−	1.83237i
$582$	13.0000			0.538867
$583$	−2.50000	+	4.33013i	−0.103539	+	0.179336i
$584$	5.00000	+	8.66025i	0.206901	+	0.358364i
$585$	−0.500000	−	0.866025i	−0.0206725	−	0.0358057i
$586$	3.50000	−	6.06218i	0.144584	−	0.250426i
$587$	5.00000			0.206372			0.103186	−	0.994662i	$-0.467096\pi$
$587$	5.00000			0.206372			0.103186	+	0.994662i	$0.467096\pi$
$588$	5.50000	−	4.33013i	0.226816	−	0.178571i
$589$	44.0000			1.81299
$590$	−2.50000	+	4.33013i	−0.102923	+	0.178269i
$591$	9.00000	+	15.5885i	0.370211	+	0.641223i
$592$	−2.00000	−	3.46410i	−0.0821995	−	0.142374i
$593$	18.0000	−	31.1769i	0.739171	−	1.28028i	−0.213697	−	0.976900i	$-0.568551\pi$
$593$	18.0000	−	31.1769i	0.739171	−	1.28028i	0.952869	−	0.303383i	$-0.0981160\pi$
$594$	−1.00000			−0.0410305
$595$	−3.00000	+	15.5885i	−0.122988	+	0.639064i
$596$	−10.0000			−0.409616
$597$	−4.00000	+	6.92820i	−0.163709	+	0.283552i
$598$	−3.00000	−	5.19615i	−0.122679	−	0.212486i
$599$	5.00000	+	8.66025i	0.204294	+	0.353848i	0.949908	−	0.312531i	$-0.101177\pi$
$599$	5.00000	+	8.66025i	0.204294	+	0.353848i	−0.745613	+	0.666379i	$0.767843\pi$
$600$	2.00000	−	3.46410i	0.0816497	−	0.141421i
$601$	11.0000			0.448699			0.224350	−	0.974509i	$-0.427974\pi$
$601$	11.0000			0.448699			0.224350	+	0.974509i	$0.427974\pi$
$602$	16.0000	+	13.8564i	0.652111	+	0.564745i
$603$	16.0000			0.651570
$604$	−6.50000	+	11.2583i	−0.264481	+	0.458095i
$605$	−5.00000	−	8.66025i	−0.203279	−	0.352089i
$606$	−5.00000	−	8.66025i	−0.203111	−	0.351799i
$607$	−14.5000	+	25.1147i	−0.588537	+	1.01938i	0.405887	+	0.913923i	$0.366962\pi$
$607$	−14.5000	+	25.1147i	−0.588537	+	1.01938i	−0.994424	+	0.105453i	$0.966371\pi$
$608$	−4.00000			−0.162221
$609$	7.50000	−	2.59808i	0.303915	−	0.105279i
$610$	−12.0000			−0.485866
$611$	−4.00000	+	6.92820i	−0.161823	+	0.280285i
$612$	3.00000	+	5.19615i	0.121268	+	0.210042i
$613$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$613$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$614$	−3.00000	+	5.19615i	−0.121070	+	0.209700i
$615$	−12.0000			−0.483887
$616$	−2.50000	+	0.866025i	−0.100728	+	0.0348932i
$617$	−36.0000			−1.44931			−0.724653	−	0.689114i	$-0.758000\pi$
$617$	−36.0000			−1.44931			−0.724653	+	0.689114i	$0.758000\pi$
$618$		0			0
$619$	4.00000	+	6.92820i	0.160774	+	0.278468i	0.935146	−	0.354262i	$-0.115268\pi$
$619$	4.00000	+	6.92820i	0.160774	+	0.278468i	−0.774373	+	0.632730i	$0.781934\pi$
$620$	−5.50000	−	9.52628i	−0.220885	−	0.382585i
$621$	3.00000	−	5.19615i	0.120386	−	0.208514i
$622$	2.00000			0.0801927
$623$	24.0000	+	20.7846i	0.961540	+	0.832718i
$624$	−1.00000			−0.0400320
$625$	−5.50000	+	9.52628i	−0.220000	+	0.381051i
$626$	−6.50000	−	11.2583i	−0.259792	−	0.449973i
$627$	−2.00000	−	3.46410i	−0.0798723	−	0.138343i
$628$	9.00000	−	15.5885i	0.359139	−	0.622047i
$629$	−24.0000			−0.956943
$630$	0.500000	−	2.59808i	0.0199205	−	0.103510i
$631$	−29.0000			−1.15447			−0.577236	−	0.816577i	$-0.695869\pi$
$631$	−29.0000			−1.15447			−0.577236	+	0.816577i	$0.695869\pi$
$632$	−3.50000	+	6.06218i	−0.139223	+	0.241140i
$633$	−6.00000	−	10.3923i	−0.238479	−	0.413057i
$634$	1.50000	+	2.59808i	0.0595726	+	0.103183i
$635$	−3.50000	+	6.06218i	−0.138893	+	0.240570i
$636$	−5.00000			−0.198263
$637$	6.50000	+	2.59808i	0.257539	+	0.102940i
$638$	−3.00000			−0.118771
$639$	−3.00000	+	5.19615i	−0.118678	+	0.205557i
$640$	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	$0.757174\pi$
$642$	−3.50000	+	6.06218i	−0.138134	+	0.239255i
$643$	20.0000			0.788723			0.394362	−	0.918955i	$-0.370966\pi$
$643$	20.0000			0.788723			0.394362	+	0.918955i	$0.370966\pi$
$644$	3.00000	−	15.5885i	0.118217	−	0.614271i
$645$	8.00000			0.315000
$646$	−12.0000	+	20.7846i	−0.472134	+	0.817760i
$647$	2.00000	+	3.46410i	0.0786281	+	0.136188i	0.902658	−	0.430358i	$-0.141613\pi$
$647$	2.00000	+	3.46410i	0.0786281	+	0.136188i	−0.824030	+	0.566546i	$0.808279\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	−2.50000	+	4.33013i	−0.0981336	+	0.169972i
$650$	4.00000			0.156893
$651$	22.0000	+	19.0526i	0.862248	+	0.746729i
$652$	−8.00000			−0.313304
$653$	5.50000	−	9.52628i	0.215232	−	0.372792i	−0.738113	−	0.674678i	$-0.764283\pi$
$653$	5.50000	−	9.52628i	0.215232	−	0.372792i	0.953344	+	0.301885i	$0.0976160\pi$
$654$	−6.00000	−	10.3923i	−0.234619	−	0.406371i
$655$	0.500000	+	0.866025i	0.0195366	+	0.0338384i
$656$	−6.00000	+	10.3923i	−0.234261	+	0.405751i
$657$	−10.0000			−0.390137
$658$	−20.0000	+	6.92820i	−0.779681	+	0.270089i
$659$	−12.0000			−0.467454			−0.233727	−	0.972302i	$-0.575092\pi$
$659$	−12.0000			−0.467454			−0.233727	+	0.972302i	$0.575092\pi$
$660$	−0.500000	+	0.866025i	−0.0194625	+	0.0337100i
$661$	−11.0000	−	19.0526i	−0.427850	−	0.741059i	0.568831	−	0.822454i	$-0.307396\pi$
$661$	−11.0000	−	19.0526i	−0.427850	−	0.741059i	−0.996682	+	0.0813955i	$0.974062\pi$
$662$	4.00000	+	6.92820i	0.155464	+	0.269272i
$663$	−3.00000	+	5.19615i	−0.116510	+	0.201802i
$664$	−17.0000			−0.659728
$665$	10.0000	−	3.46410i	0.387783	−	0.134332i
$666$	4.00000			0.154997
$667$	9.00000	−	15.5885i	0.348481	−	0.603587i
$668$	12.0000	+	20.7846i	0.464294	+	0.804181i
$669$	−3.50000	−	6.06218i	−0.135318	−	0.234377i
$670$	8.00000	−	13.8564i	0.309067	−	0.535320i
$671$	−12.0000			−0.463255
$672$	−2.00000	−	1.73205i	−0.0771517	−	0.0668153i
$673$	−39.0000			−1.50334			−0.751670	−	0.659540i	$-0.770751\pi$
$673$	−39.0000			−1.50334			−0.751670	+	0.659540i	$0.770751\pi$
$674$	−12.5000	+	21.6506i	−0.481482	+	0.833951i
$675$	2.00000	+	3.46410i	0.0769800	+	0.133333i
$676$	−0.500000	−	0.866025i	−0.0192308	−	0.0333087i
$677$	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	$-0.0681471\pi$
$678$	−4.00000			−0.153619
$679$	−6.50000	+	33.7750i	−0.249447	+	1.29617i
$680$	6.00000			0.230089
$681$	7.50000	−	12.9904i	0.287401	−	0.497792i
$682$	−5.50000	−	9.52628i	−0.210606	−	0.364780i
$683$	13.5000	+	23.3827i	0.516563	+	0.894714i	0.999815	+	0.0192323i	$0.00612219\pi$
$683$	13.5000	+	23.3827i	0.516563	+	0.894714i	−0.483252	+	0.875481i	$0.660544\pi$
$684$	2.00000	−	3.46410i	0.0764719	−	0.132453i
$685$	8.00000			0.305664
$686$	8.50000	+	16.4545i	0.324532	+	0.628235i
$687$	6.00000			0.228914
$688$	4.00000	−	6.92820i	0.152499	−	0.264135i
$689$	−2.50000	−	4.33013i	−0.0952424	−	0.164965i
$690$	−3.00000	−	5.19615i	−0.114208	−	0.197814i
$691$	20.0000	−	34.6410i	0.760836	−	1.31781i	−0.181584	−	0.983375i	$-0.558123\pi$
$691$	20.0000	−	34.6410i	0.760836	−	1.31781i	0.942420	−	0.334431i	$-0.108544\pi$
$692$	6.00000			0.228086
$693$	0.500000	−	2.59808i	0.0189934	−	0.0986928i
$694$	20.0000			0.759190
$695$		0			0
$696$	−1.50000	−	2.59808i	−0.0568574	−	0.0984798i
$697$	36.0000	+	62.3538i	1.36360	+	2.36182i
$698$	−7.00000	+	12.1244i	−0.264954	+	0.458914i
$699$	6.00000			0.226941
$700$	8.00000	+	6.92820i	0.302372	+	0.261861i
$701$	−13.0000			−0.491003			−0.245502	−	0.969396i	$-0.578953\pi$
$701$	−13.0000			−0.491003			−0.245502	+	0.969396i	$0.578953\pi$
$702$	0.500000	−	0.866025i	0.0188713	−	0.0326860i
$703$	8.00000	+	13.8564i	0.301726	+	0.522604i
$704$	0.500000	+	0.866025i	0.0188445	+	0.0326396i
$705$	−4.00000	+	6.92820i	−0.150649	+	0.260931i
$706$	30.0000			1.12906
$707$	25.0000	−	8.66025i	0.940222	−	0.325702i
$708$	−5.00000			−0.187912
$709$	−3.00000	+	5.19615i	−0.112667	+	0.195146i	−0.916845	−	0.399244i	$-0.869273\pi$
$709$	−3.00000	+	5.19615i	−0.112667	+	0.195146i	0.804178	+	0.594389i	$0.202606\pi$
$710$	3.00000	+	5.19615i	0.112588	+	0.195008i
$711$	−3.50000	−	6.06218i	−0.131260	−	0.227349i
$712$	6.00000	−	10.3923i	0.224860	−	0.389468i
$713$	66.0000			2.47172
$714$	−15.0000	+	5.19615i	−0.561361	+	0.194461i
$715$	−1.00000			−0.0373979
$716$	−6.00000	+	10.3923i	−0.224231	+	0.388379i
$717$	3.00000	+	5.19615i	0.112037	+	0.194054i
$718$	11.0000	+	19.0526i	0.410516	+	0.711035i
$719$	−23.0000	+	39.8372i	−0.857755	+	1.48568i	0.0163099	+	0.999867i	$0.494808\pi$
$719$	−23.0000	+	39.8372i	−0.857755	+	1.48568i	−0.874065	+	0.485809i	$0.838525\pi$
$720$	−1.00000			−0.0372678
$721$		0			0
$722$	−3.00000			−0.111648
$723$	7.50000	−	12.9904i	0.278928	−	0.483117i
$724$	8.00000	+	13.8564i	0.297318	+	0.514969i
$725$	6.00000	+	10.3923i	0.222834	+	0.385961i
$726$	5.00000	−	8.66025i	0.185567	−	0.321412i
$727$	19.0000			0.704671			0.352335	−	0.935874i	$-0.385388\pi$
$727$	19.0000			0.704671			0.352335	+	0.935874i	$0.385388\pi$
$728$	0.500000	−	2.59808i	0.0185312	−	0.0962911i
$729$	1.00000			0.0370370
$730$	−5.00000	+	8.66025i	−0.185058	+	0.320530i
$731$	−24.0000	−	41.5692i	−0.887672	−	1.53749i
$732$	−6.00000	−	10.3923i	−0.221766	−	0.384111i
$733$	−1.00000	+	1.73205i	−0.0369358	+	0.0639748i	−0.883902	−	0.467671i	$-0.845093\pi$
$733$	−1.00000	+	1.73205i	−0.0369358	+	0.0639748i	0.846967	+	0.531646i	$0.178426\pi$
$734$	−7.00000			−0.258375
$735$	6.50000	+	2.59808i	0.239756	+	0.0958315i
$736$	−6.00000			−0.221163
$737$	8.00000	−	13.8564i	0.294684	−	0.510407i
$738$	−6.00000	−	10.3923i	−0.220863	−	0.382546i
$739$	13.0000	+	22.5167i	0.478213	+	0.828289i	0.999688	−	0.0249776i	$-0.00795146\pi$
$739$	13.0000	+	22.5167i	0.478213	+	0.828289i	−0.521475	+	0.853266i	$0.674618\pi$
$740$	2.00000	−	3.46410i	0.0735215	−	0.127343i
$741$	4.00000			0.146944
$742$	2.50000	−	12.9904i	0.0917779	−	0.476892i
$743$	−32.0000			−1.17397			−0.586983	−	0.809599i	$-0.699684\pi$
$743$	−32.0000			−1.17397			−0.586983	+	0.809599i	$0.699684\pi$
$744$	5.50000	−	9.52628i	0.201640	−	0.349250i
$745$	−5.00000	−	8.66025i	−0.183186	−	0.317287i
$746$	−13.0000	−	22.5167i	−0.475964	−	0.824394i
$747$	8.50000	−	14.7224i	0.310999	−	0.538666i
$748$	6.00000			0.219382
$749$	−14.0000	−	12.1244i	−0.511549	−	0.443014i
$750$	9.00000			0.328634
$751$	−12.5000	+	21.6506i	−0.456131	+	0.790043i	−0.998752	−	0.0499348i	$-0.984099\pi$
$751$	−12.5000	+	21.6506i	−0.456131	+	0.790043i	0.542621	+	0.839978i	$0.317432\pi$
$752$	4.00000	+	6.92820i	0.145865	+	0.252646i
$753$	−8.50000	−	14.7224i	−0.309757	−	0.536515i
$754$	1.50000	−	2.59808i	0.0546268	−	0.0946164i
$755$	−13.0000			−0.473118
$756$	2.50000	−	0.866025i	0.0909241	−	0.0314970i
$757$	−38.0000			−1.38113			−0.690567	−	0.723269i	$-0.742639\pi$
$757$	−38.0000			−1.38113			−0.690567	+	0.723269i	$0.742639\pi$
$758$	−8.00000	+	13.8564i	−0.290573	+	0.503287i
$759$	−3.00000	−	5.19615i	−0.108893	−	0.188608i
$760$	−2.00000	−	3.46410i	−0.0725476	−	0.125656i
$761$	14.0000	−	24.2487i	0.507500	−	0.879015i	−0.492463	−	0.870334i	$-0.663903\pi$
$761$	14.0000	−	24.2487i	0.507500	−	0.879015i	0.999962	−	0.00868155i	$-0.00276346\pi$
$762$	−7.00000			−0.253583
$763$	30.0000	−	10.3923i	1.08607	−	0.376227i
$764$	−6.00000			−0.217072
$765$	−3.00000	+	5.19615i	−0.108465	+	0.187867i
$766$	7.00000	+	12.1244i	0.252920	+	0.438071i
$767$	−2.50000	−	4.33013i	−0.0902698	−	0.156352i
$768$	−0.500000	+	0.866025i	−0.0180422	+	0.0312500i
$769$	31.0000			1.11789			0.558944	−	0.829205i	$-0.311207\pi$
$769$	31.0000			1.11789			0.558944	+	0.829205i	$0.311207\pi$
$770$	−2.00000	−	1.73205i	−0.0720750	−	0.0624188i

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.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} +(0.500000 + 0.866025i) q^{11} +(-0.500000 + 0.866025i) q^{12} -1.00000 q^{13} +(-2.00000 - 1.73205i) q^{14} -1.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.00000 + 5.19615i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(2.00000 - 3.46410i) q^{19} -1.00000 q^{20} +(2.50000 - 0.866025i) q^{21} -1.00000 q^{22} +(3.00000 - 5.19615i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(2.00000 + 3.46410i) q^{25} +(0.500000 - 0.866025i) q^{26} +1.00000 q^{27} +(2.50000 - 0.866025i) q^{28} +3.00000 q^{29} +(0.500000 - 0.866025i) q^{30} +(5.50000 + 9.52628i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.500000 - 0.866025i) q^{33} -6.00000 q^{34} +(2.00000 + 1.73205i) q^{35} +1.00000 q^{36} +(-2.00000 + 3.46410i) q^{37} +(2.00000 + 3.46410i) q^{38} +(0.500000 + 0.866025i) q^{39} +(0.500000 - 0.866025i) q^{40} +12.0000 q^{41} +(-0.500000 + 2.59808i) q^{42} -8.00000 q^{43} +(0.500000 - 0.866025i) q^{44} +(0.500000 + 0.866025i) q^{45} +(3.00000 + 5.19615i) q^{46} +(4.00000 - 6.92820i) q^{47} +1.00000 q^{48} +(-6.50000 - 2.59808i) q^{49} -4.00000 q^{50} +(3.00000 - 5.19615i) q^{51} +(0.500000 + 0.866025i) q^{52} +(2.50000 + 4.33013i) q^{53} +(-0.500000 + 0.866025i) q^{54} +1.00000 q^{55} +(-0.500000 + 2.59808i) q^{56} -4.00000 q^{57} +(-1.50000 + 2.59808i) q^{58} +(2.50000 + 4.33013i) q^{59} +(0.500000 + 0.866025i) q^{60} +(-6.00000 + 10.3923i) q^{61} -11.0000 q^{62} +(-2.00000 - 1.73205i) q^{63} +1.00000 q^{64} +(-0.500000 + 0.866025i) q^{65} +(0.500000 + 0.866025i) q^{66} +(-8.00000 - 13.8564i) q^{67} +(3.00000 - 5.19615i) q^{68} -6.00000 q^{69} +(-2.50000 + 0.866025i) q^{70} +6.00000 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} -4.00000 q^{76} +(-2.50000 + 0.866025i) q^{77} -1.00000 q^{78} +(-3.50000 + 6.06218i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-6.00000 + 10.3923i) q^{82} -17.0000 q^{83} +(-2.00000 - 1.73205i) q^{84} +6.00000 q^{85} +(4.00000 - 6.92820i) q^{86} +(-1.50000 - 2.59808i) q^{87} +(0.500000 + 0.866025i) q^{88} +(6.00000 - 10.3923i) q^{89} -1.00000 q^{90} +(0.500000 - 2.59808i) q^{91} -6.00000 q^{92} +(5.50000 - 9.52628i) q^{93} +(4.00000 + 6.92820i) q^{94} +(-2.00000 - 3.46410i) q^{95} +(-0.500000 + 0.866025i) q^{96} +13.0000 q^{97} +(5.50000 - 4.33013i) q^{98} -1.00000 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	\( 2 q - q^{2} - q^{3} - q^{4} + q^{5} + 2 q^{6} - q^{7} + 2 q^{8} - q^{9} + q^{10} + q^{11} - q^{12} - 2 q^{13} - 4 q^{14} - 2 q^{15} - q^{16} + 6 q^{17} - q^{18} + 4 q^{19} - 2 q^{20} + 5 q^{21} - 2 q^{22} + 6 q^{23} - q^{24} + 4 q^{25} + q^{26} + 2 q^{27} + 5 q^{28} + 6 q^{29} + q^{30} + 11 q^{31} - q^{32} + q^{33} - 12 q^{34} + 4 q^{35} + 2 q^{36} - 4 q^{37} + 4 q^{38} + q^{39} + q^{40} + 24 q^{41} - q^{42} - 16 q^{43} + q^{44} + q^{45} + 6 q^{46} + 8 q^{47} + 2 q^{48} - 13 q^{49} - 8 q^{50} + 6 q^{51} + q^{52} + 5 q^{53} - q^{54} + 2 q^{55} - q^{56} - 8 q^{57} - 3 q^{58} + 5 q^{59} + q^{60} - 12 q^{61} - 22 q^{62} - 4 q^{63} + 2 q^{64} - q^{65} + q^{66} - 16 q^{67} + 6 q^{68} - 12 q^{69} - 5 q^{70} + 12 q^{71} - q^{72} + 10 q^{73} - 4 q^{74} + 4 q^{75} - 8 q^{76} - 5 q^{77} - 2 q^{78} - 7 q^{79} + q^{80} - q^{81} - 12 q^{82} - 34 q^{83} - 4 q^{84} + 12 q^{85} + 8 q^{86} - 3 q^{87} + q^{88} + 12 q^{89} - 2 q^{90} + q^{91} - 12 q^{92} + 11 q^{93} + 8 q^{94} - 4 q^{95} - q^{96} + 26 q^{97} + 11 q^{98} - 2 q^{99}+O(q^{100}) \) 2 * q - q^2 - q^3 - q^4 + q^5 + 2 * q^6 - q^7 + 2 * q^8 - q^9 + q^10 + q^11 - q^12 - 2 * q^13 - 4 * q^14 - 2 * q^15 - q^16 + 6 * q^17 - q^18 + 4 * q^19 - 2 * q^20 + 5 * q^21 - 2 * q^22 + 6 * q^23 - q^24 + 4 * q^25 + q^26 + 2 * q^27 + 5 * q^28 + 6 * q^29 + q^30 + 11 * q^31 - q^32 + q^33 - 12 * q^34 + 4 * q^35 + 2 * q^36 - 4 * q^37 + 4 * q^38 + q^39 + q^40 + 24 * q^41 - q^42 - 16 * q^43 + q^44 + q^45 + 6 * q^46 + 8 * q^47 + 2 * q^48 - 13 * q^49 - 8 * q^50 + 6 * q^51 + q^52 + 5 * q^53 - q^54 + 2 * q^55 - q^56 - 8 * q^57 - 3 * q^58 + 5 * q^59 + q^60 - 12 * q^61 - 22 * q^62 - 4 * q^63 + 2 * q^64 - q^65 + q^66 - 16 * q^67 + 6 * q^68 - 12 * q^69 - 5 * q^70 + 12 * q^71 - q^72 + 10 * q^73 - 4 * q^74 + 4 * q^75 - 8 * q^76 - 5 * q^77 - 2 * q^78 - 7 * q^79 + q^80 - q^81 - 12 * q^82 - 34 * q^83 - 4 * q^84 + 12 * q^85 + 8 * q^86 - 3 * q^87 + q^88 + 12 * q^89 - 2 * q^90 + q^91 - 12 * q^92 + 11 * q^93 + 8 * q^94 - 4 * q^95 - q^96 + 26 * q^97 + 11 * q^98 - 2 * q^99

Introduction

L-functions

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