LMFDB - Embedded newform 546.2.bn.d.101.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(101,546)]

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([3, 1, 5]))

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

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

chi := DirichletCharacter("546.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bn (of order $6$, 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:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	546.101
Dual form			546.2.bn.d.173.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(1.50000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.50000 - 0.866025i) q^{5} -1.73205i q^{6} +(0.500000 - 2.59808i) q^{7} -1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(1.50000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.50000 - 0.866025i) q^{5} -1.73205i q^{6} +(0.500000 - 2.59808i) q^{7} -1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} -1.73205i q^{10} -3.00000 q^{11} +(-1.50000 - 0.866025i) q^{12} +(1.00000 + 3.46410i) q^{13} +(-2.00000 - 1.73205i) q^{14} +(1.50000 - 2.59808i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.00000 + 5.19615i) q^{17} +(-1.50000 - 2.59808i) q^{18} -7.00000 q^{19} +(-1.50000 - 0.866025i) q^{20} +(-1.50000 - 4.33013i) q^{21} +(-1.50000 + 2.59808i) q^{22} +(3.00000 + 1.73205i) q^{23} +(-1.50000 + 0.866025i) q^{24} +(-1.00000 + 1.73205i) q^{25} +(3.50000 + 0.866025i) q^{26} -5.19615i q^{27} +(-2.50000 + 0.866025i) q^{28} +(7.50000 - 4.33013i) q^{29} +(-1.50000 - 2.59808i) q^{30} +(-0.500000 + 0.866025i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-4.50000 + 2.59808i) q^{33} +6.00000 q^{34} +(-1.50000 - 4.33013i) q^{35} -3.00000 q^{36} +(-3.50000 + 6.06218i) q^{38} +(4.50000 + 4.33013i) q^{39} +(-1.50000 + 0.866025i) q^{40} +(4.50000 - 2.59808i) q^{41} +(-4.50000 - 0.866025i) q^{42} +(-0.500000 + 0.866025i) q^{43} +(1.50000 + 2.59808i) q^{44} -5.19615i q^{45} +(3.00000 - 1.73205i) q^{46} +(-1.50000 + 0.866025i) q^{47} +1.73205i q^{48} +(-6.50000 - 2.59808i) q^{49} +(1.00000 + 1.73205i) q^{50} +(9.00000 + 5.19615i) q^{51} +(2.50000 - 2.59808i) q^{52} +(-1.50000 - 0.866025i) q^{53} +(-4.50000 - 2.59808i) q^{54} +(-4.50000 + 2.59808i) q^{55} +(-0.500000 + 2.59808i) q^{56} +(-10.5000 + 6.06218i) q^{57} -8.66025i q^{58} +(9.00000 - 5.19615i) q^{59} -3.00000 q^{60} -1.73205i q^{61} +(0.500000 + 0.866025i) q^{62} +(-6.00000 - 5.19615i) q^{63} +1.00000 q^{64} +(4.50000 + 4.33013i) q^{65} +5.19615i q^{66} +1.73205i q^{67} +(3.00000 - 5.19615i) q^{68} +6.00000 q^{69} +(-4.50000 - 0.866025i) q^{70} +(-4.50000 + 7.79423i) q^{71} +(-1.50000 + 2.59808i) q^{72} +(-6.50000 + 11.2583i) q^{73} +3.46410i q^{75} +(3.50000 + 6.06218i) q^{76} +(-1.50000 + 7.79423i) q^{77} +(6.00000 - 1.73205i) q^{78} +(-0.500000 - 0.866025i) q^{79} +1.73205i q^{80} +(-4.50000 - 7.79423i) q^{81} -5.19615i q^{82} +3.46410i q^{83} +(-3.00000 + 3.46410i) q^{84} +(9.00000 + 5.19615i) q^{85} +(0.500000 + 0.866025i) q^{86} +(7.50000 - 12.9904i) q^{87} +3.00000 q^{88} +(6.00000 + 3.46410i) q^{89} +(-4.50000 - 2.59808i) q^{90} +(9.50000 - 0.866025i) q^{91} -3.46410i q^{92} +1.73205i q^{93} +1.73205i q^{94} +(-10.5000 + 6.06218i) q^{95} +(1.50000 + 0.866025i) q^{96} +(9.50000 - 16.4545i) q^{97} +(-5.50000 + 4.33013i) q^{98} +(-4.50000 + 7.79423i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + 3 q^{3} - q^{4} + 3 q^{5} + q^{7} - 2 q^{8} + 3 q^{9}+O(q^{10}) $ 2 * q + q^2 + 3 * q^3 - q^4 + 3 * q^5 + q^7 - 2 * q^8 + 3 * q^9	$ 2 q + q^{2} + 3 q^{3} - q^{4} + 3 q^{5} + q^{7} - 2 q^{8} + 3 q^{9} - 6 q^{11} - 3 q^{12} + 2 q^{13} - 4 q^{14} + 3 q^{15} - q^{16} + 6 q^{17} - 3 q^{18} - 14 q^{19} - 3 q^{20} - 3 q^{21} - 3 q^{22} + 6 q^{23} - 3 q^{24} - 2 q^{25} + 7 q^{26} - 5 q^{28} + 15 q^{29} - 3 q^{30} - q^{31} + q^{32} - 9 q^{33} + 12 q^{34} - 3 q^{35} - 6 q^{36} - 7 q^{38} + 9 q^{39} - 3 q^{40} + 9 q^{41} - 9 q^{42} - q^{43} + 3 q^{44} + 6 q^{46} - 3 q^{47} - 13 q^{49} + 2 q^{50} + 18 q^{51} + 5 q^{52} - 3 q^{53} - 9 q^{54} - 9 q^{55} - q^{56} - 21 q^{57} + 18 q^{59} - 6 q^{60} + q^{62} - 12 q^{63} + 2 q^{64} + 9 q^{65} + 6 q^{68} + 12 q^{69} - 9 q^{70} - 9 q^{71} - 3 q^{72} - 13 q^{73} + 7 q^{76} - 3 q^{77} + 12 q^{78} - q^{79} - 9 q^{81} - 6 q^{84} + 18 q^{85} + q^{86} + 15 q^{87} + 6 q^{88} + 12 q^{89} - 9 q^{90} + 19 q^{91} - 21 q^{95} + 3 q^{96} + 19 q^{97} - 11 q^{98} - 9 q^{99}+O(q^{100}) $ 2 * q + q^2 + 3 * q^3 - q^4 + 3 * q^5 + q^7 - 2 * q^8 + 3 * q^9 - 6 * q^11 - 3 * q^12 + 2 * q^13 - 4 * q^14 + 3 * q^15 - q^16 + 6 * q^17 - 3 * q^18 - 14 * q^19 - 3 * q^20 - 3 * q^21 - 3 * q^22 + 6 * q^23 - 3 * q^24 - 2 * q^25 + 7 * q^26 - 5 * q^28 + 15 * q^29 - 3 * q^30 - q^31 + q^32 - 9 * q^33 + 12 * q^34 - 3 * q^35 - 6 * q^36 - 7 * q^38 + 9 * q^39 - 3 * q^40 + 9 * q^41 - 9 * q^42 - q^43 + 3 * q^44 + 6 * q^46 - 3 * q^47 - 13 * q^49 + 2 * q^50 + 18 * q^51 + 5 * q^52 - 3 * q^53 - 9 * q^54 - 9 * q^55 - q^56 - 21 * q^57 + 18 * q^59 - 6 * q^60 + q^62 - 12 * q^63 + 2 * q^64 + 9 * q^65 + 6 * q^68 + 12 * q^69 - 9 * q^70 - 9 * q^71 - 3 * q^72 - 13 * q^73 + 7 * q^76 - 3 * q^77 + 12 * q^78 - q^79 - 9 * q^81 - 6 * q^84 + 18 * q^85 + q^86 + 15 * q^87 + 6 * q^88 + 12 * q^89 - 9 * q^90 + 19 * q^91 - 21 * q^95 + 3 * q^96 + 19 * q^97 - 11 * q^98 - 9 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	1.50000	−	0.866025i	0.866025	−	0.500000i
$3$	1.50000	−	0.866025i	0.866025	−	0.500000i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	1.50000	−	0.866025i	0.670820	−	0.387298i	−0.125567	−	0.992085i	$-0.540075\pi$
$5$	1.50000	−	0.866025i	0.670820	−	0.387298i	0.796387	+	0.604787i	$0.206742\pi$
$6$		−	1.73205i		−	0.707107i
$7$	0.500000	−	2.59808i	0.188982	−	0.981981i
$7$	0.500000	−	2.59808i	0.188982	−	0.981981i
$8$	−1.00000			−0.353553
$9$	1.50000	−	2.59808i	0.500000	−	0.866025i
$10$		−	1.73205i		−	0.547723i
$11$	−3.00000			−0.904534			−0.452267	−	0.891883i	$-0.649385\pi$
$11$	−3.00000			−0.904534			−0.452267	+	0.891883i	$0.649385\pi$
$12$	−1.50000	−	0.866025i	−0.433013	−	0.250000i
$13$	1.00000	+	3.46410i	0.277350	+	0.960769i
$13$	1.00000	+	3.46410i	0.277350	+	0.960769i
$14$	−2.00000	−	1.73205i	−0.534522	−	0.462910i
$15$	1.50000	−	2.59808i	0.387298	−	0.670820i
$16$	−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	$0.573966\pi$
$18$	−1.50000	−	2.59808i	−0.353553	−	0.612372i
$19$	−7.00000			−1.60591			−0.802955	−	0.596040i	$-0.796740\pi$
$19$	−7.00000			−1.60591			−0.802955	+	0.596040i	$0.796740\pi$
$20$	−1.50000	−	0.866025i	−0.335410	−	0.193649i
$21$	−1.50000	−	4.33013i	−0.327327	−	0.944911i
$22$	−1.50000	+	2.59808i	−0.319801	+	0.553912i
$23$	3.00000	+	1.73205i	0.625543	+	0.361158i	0.779024	−	0.626994i	$-0.215715\pi$
$23$	3.00000	+	1.73205i	0.625543	+	0.361158i	−0.153481	+	0.988152i	$0.549048\pi$
$24$	−1.50000	+	0.866025i	−0.306186	+	0.176777i
$25$	−1.00000	+	1.73205i	−0.200000	+	0.346410i
$26$	3.50000	+	0.866025i	0.686406	+	0.169842i
$27$		−	5.19615i		−	1.00000i
$28$	−2.50000	+	0.866025i	−0.472456	+	0.163663i
$29$	7.50000	−	4.33013i	1.39272	−	0.804084i	0.399100	−	0.916907i	$-0.369323\pi$
$29$	7.50000	−	4.33013i	1.39272	−	0.804084i	0.993615	+	0.112823i	$0.0359893\pi$
$30$	−1.50000	−	2.59808i	−0.273861	−	0.474342i
$31$	−0.500000	+	0.866025i	−0.0898027	+	0.155543i	−0.907428	−	0.420208i	$-0.861957\pi$
$31$	−0.500000	+	0.866025i	−0.0898027	+	0.155543i	0.817625	+	0.575751i	$0.195290\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−4.50000	+	2.59808i	−0.783349	+	0.452267i
$34$	6.00000			1.02899
$35$	−1.50000	−	4.33013i	−0.253546	−	0.731925i
$36$	−3.00000			−0.500000
$37$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$37$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$38$	−3.50000	+	6.06218i	−0.567775	+	0.983415i
$39$	4.50000	+	4.33013i	0.720577	+	0.693375i
$40$	−1.50000	+	0.866025i	−0.237171	+	0.136931i
$41$	4.50000	−	2.59808i	0.702782	−	0.405751i	−0.105601	−	0.994409i	$-0.533677\pi$
$41$	4.50000	−	2.59808i	0.702782	−	0.405751i	0.808383	+	0.588657i	$0.200343\pi$
$42$	−4.50000	−	0.866025i	−0.694365	−	0.133631i
$43$	−0.500000	+	0.866025i	−0.0762493	+	0.132068i	−0.901629	−	0.432511i	$-0.857628\pi$
$43$	−0.500000	+	0.866025i	−0.0762493	+	0.132068i	0.825380	+	0.564578i	$0.190961\pi$
$44$	1.50000	+	2.59808i	0.226134	+	0.391675i
$45$		−	5.19615i		−	0.774597i
$46$	3.00000	−	1.73205i	0.442326	−	0.255377i
$47$	−1.50000	+	0.866025i	−0.218797	+	0.126323i	−0.605393	−	0.795926i	$-0.706984\pi$
$47$	−1.50000	+	0.866025i	−0.218797	+	0.126323i	0.386596	+	0.922249i	$0.373651\pi$
$48$			1.73205i			0.250000i
$49$	−6.50000	−	2.59808i	−0.928571	−	0.371154i
$50$	1.00000	+	1.73205i	0.141421	+	0.244949i
$51$	9.00000	+	5.19615i	1.26025	+	0.727607i
$52$	2.50000	−	2.59808i	0.346688	−	0.360288i
$53$	−1.50000	−	0.866025i	−0.206041	−	0.118958i	0.393429	−	0.919355i	$-0.371289\pi$
$53$	−1.50000	−	0.866025i	−0.206041	−	0.118958i	−0.599470	+	0.800397i	$0.704622\pi$
$54$	−4.50000	−	2.59808i	−0.612372	−	0.353553i
$55$	−4.50000	+	2.59808i	−0.606780	+	0.350325i
$56$	−0.500000	+	2.59808i	−0.0668153	+	0.347183i
$57$	−10.5000	+	6.06218i	−1.39076	+	0.802955i
$58$		−	8.66025i		−	1.13715i
$59$	9.00000	−	5.19615i	1.17170	−	0.676481i	0.217620	−	0.976034i	$-0.430171\pi$
$59$	9.00000	−	5.19615i	1.17170	−	0.676481i	0.954080	+	0.299552i	$0.0968372\pi$
$60$	−3.00000			−0.387298
$61$		−	1.73205i		−	0.221766i	−0.993833	−	0.110883i	$-0.964632\pi$
$61$		−	1.73205i		−	0.221766i	0.993833	−	0.110883i	$-0.0353679\pi$
$62$	0.500000	+	0.866025i	0.0635001	+	0.109985i
$63$	−6.00000	−	5.19615i	−0.755929	−	0.654654i
$64$	1.00000			0.125000
$65$	4.50000	+	4.33013i	0.558156	+	0.537086i
$66$			5.19615i			0.639602i
$67$			1.73205i			0.211604i	0.994387	+	0.105802i	$0.0337409\pi$
$67$			1.73205i			0.211604i	−0.994387	+	0.105802i	$0.966259\pi$
$68$	3.00000	−	5.19615i	0.363803	−	0.630126i
$69$	6.00000			0.722315
$70$	−4.50000	−	0.866025i	−0.537853	−	0.103510i
$71$	−4.50000	+	7.79423i	−0.534052	+	0.925005i	0.465157	+	0.885228i	$0.345998\pi$
$71$	−4.50000	+	7.79423i	−0.534052	+	0.925005i	−0.999209	+	0.0397765i	$0.987335\pi$
$72$	−1.50000	+	2.59808i	−0.176777	+	0.306186i
$73$	−6.50000	+	11.2583i	−0.760767	+	1.31769i	0.181688	+	0.983356i	$0.441844\pi$
$73$	−6.50000	+	11.2583i	−0.760767	+	1.31769i	−0.942455	+	0.334332i	$0.891489\pi$
$74$		0			0
$75$			3.46410i			0.400000i
$76$	3.50000	+	6.06218i	0.401478	+	0.695379i
$77$	−1.50000	+	7.79423i	−0.170941	+	0.888235i
$78$	6.00000	−	1.73205i	0.679366	−	0.196116i
$79$	−0.500000	−	0.866025i	−0.0562544	−	0.0974355i	0.836527	−	0.547926i	$-0.184582\pi$
$79$	−0.500000	−	0.866025i	−0.0562544	−	0.0974355i	−0.892781	+	0.450490i	$0.851249\pi$
$80$			1.73205i			0.193649i
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$		−	5.19615i		−	0.573819i
$83$			3.46410i			0.380235i	0.981761	+	0.190117i	$0.0608868\pi$
$83$			3.46410i			0.380235i	−0.981761	+	0.190117i	$0.939113\pi$
$84$	−3.00000	+	3.46410i	−0.327327	+	0.377964i
$85$	9.00000	+	5.19615i	0.976187	+	0.563602i
$86$	0.500000	+	0.866025i	0.0539164	+	0.0933859i
$87$	7.50000	−	12.9904i	0.804084	−	1.39272i
$88$	3.00000			0.319801
$89$	6.00000	+	3.46410i	0.635999	+	0.367194i	0.783072	−	0.621932i	$-0.213652\pi$
$89$	6.00000	+	3.46410i	0.635999	+	0.367194i	−0.147073	+	0.989126i	$0.546985\pi$
$90$	−4.50000	−	2.59808i	−0.474342	−	0.273861i
$91$	9.50000	−	0.866025i	0.995871	−	0.0907841i
$92$		−	3.46410i		−	0.361158i
$93$			1.73205i			0.179605i
$94$			1.73205i			0.178647i
$95$	−10.5000	+	6.06218i	−1.07728	+	0.621966i
$96$	1.50000	+	0.866025i	0.153093	+	0.0883883i
$97$	9.50000	−	16.4545i	0.964579	−	1.67070i	0.253837	−	0.967247i	$-0.418307\pi$
$97$	9.50000	−	16.4545i	0.964579	−	1.67070i	0.710742	−	0.703452i	$-0.248359\pi$
$98$	−5.50000	+	4.33013i	−0.555584	+	0.437409i
$99$	−4.50000	+	7.79423i	−0.452267	+	0.783349i
$100$	2.00000			0.200000
$101$	9.00000			0.895533			0.447767	−	0.894150i	$-0.352219\pi$
$101$	9.00000			0.895533			0.447767	+	0.894150i	$0.352219\pi$
$102$	9.00000	−	5.19615i	0.891133	−	0.514496i
$103$	−7.50000	+	4.33013i	−0.738997	+	0.426660i	−0.821705	−	0.569914i	$-0.806977\pi$
$103$	−7.50000	+	4.33013i	−0.738997	+	0.426660i	0.0827075	+	0.996574i	$0.473643\pi$
$104$	−1.00000	−	3.46410i	−0.0980581	−	0.339683i
$105$	−6.00000	−	5.19615i	−0.585540	−	0.507093i
$106$	−1.50000	+	0.866025i	−0.145693	+	0.0841158i
$107$	−9.00000	−	5.19615i	−0.870063	−	0.502331i	−0.00269372	−	0.999996i	$-0.500857\pi$
$107$	−9.00000	−	5.19615i	−0.870063	−	0.502331i	−0.867369	+	0.497665i	$0.834191\pi$
$108$	−4.50000	+	2.59808i	−0.433013	+	0.250000i
$109$	−7.50000	−	4.33013i	−0.718370	−	0.414751i	0.0957826	−	0.995402i	$-0.469465\pi$
$109$	−7.50000	−	4.33013i	−0.718370	−	0.414751i	−0.814152	+	0.580651i	$0.802798\pi$
$110$			5.19615i			0.495434i
$111$		0			0
$112$	2.00000	+	1.73205i	0.188982	+	0.163663i
$113$	1.50000	+	0.866025i	0.141108	+	0.0814688i	0.568892	−	0.822412i	$-0.307372\pi$
$113$	1.50000	+	0.866025i	0.141108	+	0.0814688i	−0.427784	+	0.903881i	$0.640706\pi$
$114$			12.1244i			1.13555i
$115$	6.00000			0.559503
$116$	−7.50000	−	4.33013i	−0.696358	−	0.402042i
$117$	10.5000	+	2.59808i	0.970725	+	0.240192i
$118$		−	10.3923i		−	0.956689i
$119$	15.0000	−	5.19615i	1.37505	−	0.476331i
$120$	−1.50000	+	2.59808i	−0.136931	+	0.237171i
$121$	−2.00000			−0.181818
$122$	−1.50000	−	0.866025i	−0.135804	−	0.0784063i
$123$	4.50000	−	7.79423i	0.405751	−	0.702782i
$124$	1.00000			0.0898027
$125$			12.1244i			1.08444i
$126$	−7.50000	+	2.59808i	−0.668153	+	0.231455i
$127$	8.50000	+	14.7224i	0.754253	+	1.30640i	0.945745	+	0.324910i	$0.105334\pi$
$127$	8.50000	+	14.7224i	0.754253	+	1.30640i	−0.191492	+	0.981494i	$0.561333\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$			1.73205i			0.152499i
$130$	6.00000	−	1.73205i	0.526235	−	0.151911i
$131$	−1.50000	−	2.59808i	−0.131056	−	0.226995i	0.793028	−	0.609185i	$-0.208503\pi$
$131$	−1.50000	−	2.59808i	−0.131056	−	0.226995i	−0.924084	+	0.382190i	$0.875170\pi$
$132$	4.50000	+	2.59808i	0.391675	+	0.226134i
$133$	−3.50000	+	18.1865i	−0.303488	+	1.57697i
$134$	1.50000	+	0.866025i	0.129580	+	0.0748132i
$135$	−4.50000	−	7.79423i	−0.387298	−	0.670820i
$136$	−3.00000	−	5.19615i	−0.257248	−	0.445566i
$137$	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	$0.750827\pi$
$138$	3.00000	−	5.19615i	0.255377	−	0.442326i
$139$	19.5000	+	11.2583i	1.65397	+	0.954919i	0.975417	+	0.220366i	$0.0707252\pi$
$139$	19.5000	+	11.2583i	1.65397	+	0.954919i	0.678551	+	0.734553i	$0.262608\pi$
$140$	−3.00000	+	3.46410i	−0.253546	+	0.292770i
$141$	−1.50000	+	2.59808i	−0.126323	+	0.218797i
$142$	4.50000	+	7.79423i	0.377632	+	0.654077i
$143$	−3.00000	−	10.3923i	−0.250873	−	0.869048i
$144$	1.50000	+	2.59808i	0.125000	+	0.216506i
$145$	7.50000	−	12.9904i	0.622841	−	1.07879i
$146$	6.50000	+	11.2583i	0.537944	+	0.931746i
$147$	−12.0000	+	1.73205i	−0.989743	+	0.142857i
$148$		0			0
$149$	−21.0000			−1.72039			−0.860194	−	0.509968i	$-0.829657\pi$
$149$	−21.0000			−1.72039			−0.860194	+	0.509968i	$0.829657\pi$
$150$	3.00000	+	1.73205i	0.244949	+	0.141421i
$151$	−19.5000	−	11.2583i	−1.58689	−	0.916190i	−0.993816	−	0.111040i	$-0.964582\pi$
$151$	−19.5000	−	11.2583i	−1.58689	−	0.916190i	−0.593072	−	0.805150i	$-0.702085\pi$
$152$	7.00000			0.567775
$153$	18.0000			1.45521
$154$	6.00000	+	5.19615i	0.483494	+	0.418718i
$155$			1.73205i			0.139122i
$156$	1.50000	−	6.06218i	0.120096	−	0.485363i
$157$	1.50000	+	0.866025i	0.119713	+	0.0691164i	0.558661	−	0.829396i	$-0.311315\pi$
$157$	1.50000	+	0.866025i	0.119713	+	0.0691164i	−0.438948	+	0.898513i	$0.644649\pi$
$158$	−1.00000			−0.0795557
$159$	−3.00000			−0.237915
$160$	1.50000	+	0.866025i	0.118585	+	0.0684653i
$161$	6.00000	−	6.92820i	0.472866	−	0.546019i
$162$	−9.00000			−0.707107
$163$		−	5.19615i		−	0.406994i	−0.979076	−	0.203497i	$-0.934769\pi$
$163$		−	5.19615i		−	0.406994i	0.979076	−	0.203497i	$-0.0652307\pi$
$164$	−4.50000	−	2.59808i	−0.351391	−	0.202876i
$165$	−4.50000	+	7.79423i	−0.350325	+	0.606780i
$166$	3.00000	+	1.73205i	0.232845	+	0.134433i
$167$	−7.50000	+	4.33013i	−0.580367	+	0.335075i	−0.761279	−	0.648424i	$-0.775428\pi$
$167$	−7.50000	+	4.33013i	−0.580367	+	0.335075i	0.180912	+	0.983499i	$0.442095\pi$
$168$	1.50000	+	4.33013i	0.115728	+	0.334077i
$169$	−11.0000	+	6.92820i	−0.846154	+	0.532939i
$170$	9.00000	−	5.19615i	0.690268	−	0.398527i
$171$	−10.5000	+	18.1865i	−0.802955	+	1.39076i
$172$	1.00000			0.0762493
$173$	9.00000			0.684257			0.342129	−	0.939653i	$-0.388852\pi$
$173$	9.00000			0.684257			0.342129	+	0.939653i	$0.388852\pi$
$174$	−7.50000	−	12.9904i	−0.568574	−	0.984798i
$175$	4.00000	+	3.46410i	0.302372	+	0.261861i
$176$	1.50000	−	2.59808i	0.113067	−	0.195837i
$177$	9.00000	−	15.5885i	0.676481	−	1.17170i
$178$	6.00000	−	3.46410i	0.449719	−	0.259645i
$179$		−	19.0526i		−	1.42406i	−0.702152	−	0.712028i	$-0.747777\pi$
$179$		−	19.0526i		−	1.42406i	0.702152	−	0.712028i	$-0.252223\pi$
$180$	−4.50000	+	2.59808i	−0.335410	+	0.193649i
$181$			13.8564i			1.02994i	0.857209	+	0.514969i	$0.172197\pi$
$181$			13.8564i			1.02994i	−0.857209	+	0.514969i	$0.827803\pi$
$182$	4.00000	−	8.66025i	0.296500	−	0.641941i
$183$	−1.50000	−	2.59808i	−0.110883	−	0.192055i
$184$	−3.00000	−	1.73205i	−0.221163	−	0.127688i
$185$		0			0
$186$	1.50000	+	0.866025i	0.109985	+	0.0635001i
$187$	−9.00000	−	15.5885i	−0.658145	−	1.13994i
$188$	1.50000	+	0.866025i	0.109399	+	0.0631614i
$189$	−13.5000	−	2.59808i	−0.981981	−	0.188982i
$190$			12.1244i			0.879593i
$191$			15.5885i			1.12794i	0.825795	+	0.563971i	$0.190727\pi$
$191$			15.5885i			1.12794i	−0.825795	+	0.563971i	$0.809273\pi$
$192$	1.50000	−	0.866025i	0.108253	−	0.0625000i
$193$			12.1244i			0.872730i	0.899770	+	0.436365i	$0.143734\pi$
$193$			12.1244i			0.872730i	−0.899770	+	0.436365i	$0.856266\pi$
$194$	−9.50000	−	16.4545i	−0.682060	−	1.18136i
$195$	10.5000	+	2.59808i	0.751921	+	0.186052i
$196$	1.00000	+	6.92820i	0.0714286	+	0.494872i
$197$	10.5000	+	18.1865i	0.748094	+	1.29574i	0.948735	+	0.316072i	$0.102364\pi$
$197$	10.5000	+	18.1865i	0.748094	+	1.29574i	−0.200641	+	0.979665i	$0.564303\pi$
$198$	4.50000	+	7.79423i	0.319801	+	0.553912i
$199$	−3.00000	+	1.73205i	−0.212664	+	0.122782i	−0.602549	−	0.798082i	$-0.705848\pi$
$199$	−3.00000	+	1.73205i	−0.212664	+	0.122782i	0.389885	+	0.920864i	$0.372515\pi$
$200$	1.00000	−	1.73205i	0.0707107	−	0.122474i
$201$	1.50000	+	2.59808i	0.105802	+	0.183254i
$202$	4.50000	−	7.79423i	0.316619	−	0.548400i
$203$	−7.50000	−	21.6506i	−0.526397	−	1.51958i
$204$		−	10.3923i		−	0.727607i
$205$	4.50000	−	7.79423i	0.314294	−	0.544373i
$206$			8.66025i			0.603388i
$207$	9.00000	−	5.19615i	0.625543	−	0.361158i
$208$	−3.50000	−	0.866025i	−0.242681	−	0.0600481i
$209$	21.0000			1.45260
$210$	−7.50000	+	2.59808i	−0.517549	+	0.179284i
$211$	0.500000	+	0.866025i	0.0344214	+	0.0596196i	0.882723	−	0.469894i	$-0.155708\pi$
$211$	0.500000	+	0.866025i	0.0344214	+	0.0596196i	−0.848301	+	0.529514i	$0.822374\pi$
$212$			1.73205i			0.118958i
$213$			15.5885i			1.06810i
$214$	−9.00000	+	5.19615i	−0.615227	+	0.355202i
$215$			1.73205i			0.118125i
$216$			5.19615i			0.353553i
$217$	2.00000	+	1.73205i	0.135769	+	0.117579i
$218$	−7.50000	+	4.33013i	−0.507964	+	0.293273i
$219$			22.5167i			1.52153i
$220$	4.50000	+	2.59808i	0.303390	+	0.175162i
$221$	−15.0000	+	15.5885i	−1.00901	+	1.04859i
$222$		0			0
$223$	−14.5000	−	25.1147i	−0.970992	−	1.68181i	−0.692574	−	0.721347i	$-0.743523\pi$
$223$	−14.5000	−	25.1147i	−0.970992	−	1.68181i	−0.278418	−	0.960460i	$-0.589810\pi$
$224$	2.50000	−	0.866025i	0.167038	−	0.0578638i
$225$	3.00000	+	5.19615i	0.200000	+	0.346410i
$226$	1.50000	−	0.866025i	0.0997785	−	0.0576072i
$227$	9.00000	−	5.19615i	0.597351	−	0.344881i	−0.170648	−	0.985332i	$-0.554586\pi$
$227$	9.00000	−	5.19615i	0.597351	−	0.344881i	0.767999	+	0.640451i	$0.221253\pi$
$228$	10.5000	+	6.06218i	0.695379	+	0.401478i
$229$	−12.5000	−	21.6506i	−0.826023	−	1.43071i	−0.901135	−	0.433539i	$-0.857265\pi$
$229$	−12.5000	−	21.6506i	−0.826023	−	1.43071i	0.0751115	−	0.997175i	$-0.476069\pi$
$230$	3.00000	−	5.19615i	0.197814	−	0.342624i
$231$	4.50000	+	12.9904i	0.296078	+	0.854704i
$232$	−7.50000	+	4.33013i	−0.492399	+	0.284287i
$233$	−19.5000	+	11.2583i	−1.27749	+	0.737558i	−0.976386	−	0.216034i	$-0.930688\pi$
$233$	−19.5000	+	11.2583i	−1.27749	+	0.737558i	−0.301102	+	0.953592i	$0.597354\pi$
$234$	7.50000	−	7.79423i	0.490290	−	0.509525i
$235$	−1.50000	+	2.59808i	−0.0978492	+	0.169480i
$236$	−9.00000	−	5.19615i	−0.585850	−	0.338241i
$237$	−1.50000	−	0.866025i	−0.0974355	−	0.0562544i
$238$	3.00000	−	15.5885i	0.194461	−	1.01045i
$239$	−12.0000			−0.776215			−0.388108	−	0.921614i	$-0.626871\pi$
$239$	−12.0000			−0.776215			−0.388108	+	0.921614i	$0.626871\pi$
$240$	1.50000	+	2.59808i	0.0968246	+	0.167705i
$241$	−5.00000	−	8.66025i	−0.322078	−	0.557856i	0.658838	−	0.752285i	$-0.271048\pi$
$241$	−5.00000	−	8.66025i	−0.322078	−	0.557856i	−0.980917	+	0.194429i	$0.937715\pi$
$242$	−1.00000	+	1.73205i	−0.0642824	+	0.111340i
$243$	−13.5000	−	7.79423i	−0.866025	−	0.500000i
$244$	−1.50000	+	0.866025i	−0.0960277	+	0.0554416i
$245$	−12.0000	+	1.73205i	−0.766652	+	0.110657i
$246$	−4.50000	−	7.79423i	−0.286910	−	0.496942i
$247$	−7.00000	−	24.2487i	−0.445399	−	1.54291i
$248$	0.500000	−	0.866025i	0.0317500	−	0.0549927i
$249$	3.00000	+	5.19615i	0.190117	+	0.329293i
$250$	10.5000	+	6.06218i	0.664078	+	0.383406i
$251$	−7.50000	+	12.9904i	−0.473396	+	0.819946i	−0.999536	−	0.0304521i	$-0.990305\pi$
$251$	−7.50000	+	12.9904i	−0.473396	+	0.819946i	0.526140	+	0.850398i	$0.323639\pi$
$252$	−1.50000	+	7.79423i	−0.0944911	+	0.490990i
$253$	−9.00000	−	5.19615i	−0.565825	−	0.326679i
$254$	17.0000			1.06667
$255$	18.0000			1.12720
$256$	−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	$0.106747\pi$
$258$	1.50000	+	0.866025i	0.0933859	+	0.0539164i
$259$		0			0
$260$	1.50000	−	6.06218i	0.0930261	−	0.375960i
$261$		−	25.9808i		−	1.60817i
$262$	−3.00000			−0.185341
$263$			8.66025i			0.534014i	0.963695	+	0.267007i	$0.0860347\pi$
$263$			8.66025i			0.534014i	−0.963695	+	0.267007i	$0.913965\pi$
$264$	4.50000	−	2.59808i	0.276956	−	0.159901i
$265$	−3.00000			−0.184289
$266$	14.0000	+	12.1244i	0.858395	+	0.743392i
$267$	12.0000			0.734388
$268$	1.50000	−	0.866025i	0.0916271	−	0.0529009i
$269$	−15.0000	−	25.9808i	−0.914566	−	1.58408i	−0.807535	−	0.589819i	$-0.799199\pi$
$269$	−15.0000	−	25.9808i	−0.914566	−	1.58408i	−0.107031	−	0.994256i	$-0.534134\pi$
$270$	−9.00000			−0.547723
$271$	8.00000	−	13.8564i	0.485965	−	0.841717i	−0.513905	−	0.857847i	$-0.671801\pi$
$271$	8.00000	−	13.8564i	0.485965	−	0.841717i	0.999870	+	0.0161307i	$0.00513477\pi$
$272$	−6.00000			−0.363803
$273$	13.5000	−	9.52628i	0.817057	−	0.576557i
$274$	6.00000			0.362473
$275$	3.00000	−	5.19615i	0.180907	−	0.313340i
$276$	−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	$0.736206\pi$
$278$	19.5000	−	11.2583i	1.16953	−	0.675230i
$279$	1.50000	+	2.59808i	0.0898027	+	0.155543i
$280$	1.50000	+	4.33013i	0.0896421	+	0.258775i
$281$	6.00000			0.357930			0.178965	−	0.983855i	$-0.442725\pi$
$281$	6.00000			0.357930			0.178965	+	0.983855i	$0.442725\pi$
$282$	1.50000	+	2.59808i	0.0893237	+	0.154713i
$283$		−	22.5167i		−	1.33848i	−0.743048	−	0.669238i	$-0.766621\pi$
$283$		−	22.5167i		−	1.33848i	0.743048	−	0.669238i	$-0.233379\pi$
$284$	9.00000			0.534052
$285$	−10.5000	+	18.1865i	−0.621966	+	1.07728i
$286$	−10.5000	−	2.59808i	−0.620878	−	0.153627i
$287$	−4.50000	−	12.9904i	−0.265627	−	0.766798i
$288$	3.00000			0.176777
$289$	−9.50000	+	16.4545i	−0.558824	+	0.967911i
$290$	−7.50000	−	12.9904i	−0.440415	−	0.762821i
$291$		−	32.9090i		−	1.92916i
$292$	13.0000			0.760767
$293$	−25.5000	−	14.7224i	−1.48973	−	0.860094i	−0.489795	−	0.871838i	$-0.662928\pi$
$293$	−25.5000	−	14.7224i	−1.48973	−	0.860094i	−0.999931	+	0.0117441i	$0.996262\pi$
$294$	−4.50000	+	11.2583i	−0.262445	+	0.656599i
$295$	9.00000	−	15.5885i	0.524000	−	0.907595i
$296$		0			0
$297$			15.5885i			0.904534i
$298$	−10.5000	+	18.1865i	−0.608249	+	1.05352i
$299$	−3.00000	+	12.1244i	−0.173494	+	0.701170i
$300$	3.00000	−	1.73205i	0.173205	−	0.100000i
$301$	2.00000	+	1.73205i	0.115278	+	0.0998337i
$302$	−19.5000	+	11.2583i	−1.12210	+	0.647844i
$303$	13.5000	−	7.79423i	0.775555	−	0.447767i
$304$	3.50000	−	6.06218i	0.200739	−	0.347690i
$305$	−1.50000	−	2.59808i	−0.0858898	−	0.148765i
$306$	9.00000	−	15.5885i	0.514496	−	0.891133i
$307$	4.00000			0.228292			0.114146	−	0.993464i	$-0.463587\pi$
$307$	4.00000			0.228292			0.114146	+	0.993464i	$0.463587\pi$
$308$	7.50000	−	2.59808i	0.427352	−	0.148039i
$309$	−7.50000	+	12.9904i	−0.426660	+	0.738997i
$310$	1.50000	+	0.866025i	0.0851943	+	0.0491869i
$311$	1.50000	−	2.59808i	0.0850572	−	0.147323i	−0.820358	−	0.571850i	$-0.806226\pi$
$311$	1.50000	−	2.59808i	0.0850572	−	0.147323i	0.905416	+	0.424526i	$0.139559\pi$
$312$	−4.50000	−	4.33013i	−0.254762	−	0.245145i
$313$	−4.50000	+	2.59808i	−0.254355	+	0.146852i	−0.621757	−	0.783210i	$-0.713581\pi$
$313$	−4.50000	+	2.59808i	−0.254355	+	0.146852i	0.367402	+	0.930062i	$0.380247\pi$
$314$	1.50000	−	0.866025i	0.0846499	−	0.0488726i
$315$	−13.5000	−	2.59808i	−0.760639	−	0.146385i
$316$	−0.500000	+	0.866025i	−0.0281272	+	0.0487177i
$317$	−1.50000	−	2.59808i	−0.0842484	−	0.145922i	0.820822	−	0.571184i	$-0.193516\pi$
$317$	−1.50000	−	2.59808i	−0.0842484	−	0.145922i	−0.905071	+	0.425261i	$0.860182\pi$
$318$	−1.50000	+	2.59808i	−0.0841158	+	0.145693i
$319$	−22.5000	+	12.9904i	−1.25976	+	0.727322i
$320$	1.50000	−	0.866025i	0.0838525	−	0.0484123i
$321$	−18.0000			−1.00466
$322$	−3.00000	−	8.66025i	−0.167183	−	0.482617i
$323$	−21.0000	−	36.3731i	−1.16847	−	2.02385i
$324$	−4.50000	+	7.79423i	−0.250000	+	0.433013i
$325$	−7.00000	−	1.73205i	−0.388290	−	0.0960769i
$326$	−4.50000	−	2.59808i	−0.249232	−	0.143894i
$327$	−15.0000			−0.829502
$328$	−4.50000	+	2.59808i	−0.248471	+	0.143455i
$329$	1.50000	+	4.33013i	0.0826977	+	0.238728i
$330$	4.50000	+	7.79423i	0.247717	+	0.429058i
$331$		−	25.9808i		−	1.42803i	−0.700129	−	0.714016i	$-0.746874\pi$
$331$		−	25.9808i		−	1.42803i	0.700129	−	0.714016i	$-0.253126\pi$
$332$	3.00000	−	1.73205i	0.164646	−	0.0950586i
$333$		0			0
$334$			8.66025i			0.473868i
$335$	1.50000	+	2.59808i	0.0819538	+	0.141948i
$336$	4.50000	+	0.866025i	0.245495	+	0.0472456i
$337$	−10.0000			−0.544735			−0.272367	−	0.962193i	$-0.587807\pi$
$337$	−10.0000			−0.544735			−0.272367	+	0.962193i	$0.587807\pi$
$338$	0.500000	+	12.9904i	0.0271964	+	0.706584i
$339$	3.00000			0.162938
$340$		−	10.3923i		−	0.563602i
$341$	1.50000	−	2.59808i	0.0812296	−	0.140694i
$342$	10.5000	+	18.1865i	0.567775	+	0.983415i
$343$	−10.0000	+	15.5885i	−0.539949	+	0.841698i
$344$	0.500000	−	0.866025i	0.0269582	−	0.0466930i
$345$	9.00000	−	5.19615i	0.484544	−	0.279751i
$346$	4.50000	−	7.79423i	0.241921	−	0.419020i
$347$	9.00000	−	5.19615i	0.483145	−	0.278944i	−0.238581	−	0.971123i	$-0.576682\pi$
$347$	9.00000	−	5.19615i	0.483145	−	0.278944i	0.721726	+	0.692179i	$0.243349\pi$
$348$	−15.0000			−0.804084
$349$	17.5000	+	30.3109i	0.936754	+	1.62250i	0.771477	+	0.636257i	$0.219518\pi$
$349$	17.5000	+	30.3109i	0.936754	+	1.62250i	0.165277	+	0.986247i	$0.447148\pi$
$350$	5.00000	−	1.73205i	0.267261	−	0.0925820i
$351$	18.0000	−	5.19615i	0.960769	−	0.277350i
$352$	−1.50000	−	2.59808i	−0.0799503	−	0.138478i
$353$		−	25.9808i		−	1.38282i	−0.722464	−	0.691408i	$-0.756991\pi$
$353$		−	25.9808i		−	1.38282i	0.722464	−	0.691408i	$-0.243009\pi$
$354$	−9.00000	−	15.5885i	−0.478345	−	0.828517i
$355$			15.5885i			0.827349i
$356$		−	6.92820i		−	0.367194i
$357$	18.0000	−	20.7846i	0.952661	−	1.10004i
$358$	−16.5000	−	9.52628i	−0.872052	−	0.503480i
$359$	1.50000	+	2.59808i	0.0791670	+	0.137121i	0.902891	−	0.429870i	$-0.141441\pi$
$359$	1.50000	+	2.59808i	0.0791670	+	0.137121i	−0.823724	+	0.566991i	$0.808107\pi$
$360$			5.19615i			0.273861i
$361$	30.0000			1.57895
$362$	12.0000	+	6.92820i	0.630706	+	0.364138i
$363$	−3.00000	+	1.73205i	−0.157459	+	0.0909091i
$364$	−5.50000	−	7.79423i	−0.288278	−	0.408529i
$365$			22.5167i			1.17858i
$366$	−3.00000			−0.156813
$367$		−	15.5885i		−	0.813711i	−0.913493	−	0.406855i	$-0.866625\pi$
$367$		−	15.5885i		−	0.813711i	0.913493	−	0.406855i	$-0.133375\pi$
$368$	−3.00000	+	1.73205i	−0.156386	+	0.0902894i
$369$		−	15.5885i		−	0.811503i
$370$		0			0
$371$	−3.00000	+	3.46410i	−0.155752	+	0.179847i
$372$	1.50000	−	0.866025i	0.0777714	−	0.0449013i
$373$	−29.0000			−1.50156			−0.750782	−	0.660551i	$-0.770323\pi$
$373$	−29.0000			−1.50156			−0.750782	+	0.660551i	$0.770323\pi$
$374$	−18.0000			−0.930758
$375$	10.5000	+	18.1865i	0.542218	+	0.939149i
$376$	1.50000	−	0.866025i	0.0773566	−	0.0446619i
$377$	22.5000	+	21.6506i	1.15881	+	1.11506i
$378$	−9.00000	+	10.3923i	−0.462910	+	0.534522i
$379$	−16.5000	+	9.52628i	−0.847548	+	0.489332i	−0.859823	−	0.510593i	$-0.829426\pi$
$379$	−16.5000	+	9.52628i	−0.847548	+	0.489332i	0.0122747	+	0.999925i	$0.496093\pi$
$380$	10.5000	+	6.06218i	0.538639	+	0.310983i
$381$	25.5000	+	14.7224i	1.30640	+	0.754253i
$382$	13.5000	+	7.79423i	0.690720	+	0.398787i
$383$			5.19615i			0.265511i	0.991149	+	0.132755i	$0.0423825\pi$
$383$			5.19615i			0.265511i	−0.991149	+	0.132755i	$0.957617\pi$
$384$		−	1.73205i		−	0.0883883i
$385$	4.50000	+	12.9904i	0.229341	+	0.662051i
$386$	10.5000	+	6.06218i	0.534436	+	0.308557i
$387$	1.50000	+	2.59808i	0.0762493	+	0.132068i
$388$	−19.0000			−0.964579
$389$	4.50000	+	2.59808i	0.228159	+	0.131728i	0.609722	−	0.792615i	$-0.291281\pi$
$389$	4.50000	+	2.59808i	0.228159	+	0.131728i	−0.381563	+	0.924343i	$0.624614\pi$
$390$	7.50000	−	7.79423i	0.379777	−	0.394676i
$391$			20.7846i			1.05112i
$392$	6.50000	+	2.59808i	0.328300	+	0.131223i
$393$	−4.50000	−	2.59808i	−0.226995	−	0.131056i
$394$	21.0000			1.05796
$395$	−1.50000	−	0.866025i	−0.0754732	−	0.0435745i
$396$	9.00000			0.452267
$397$	29.0000			1.45547			0.727734	−	0.685859i	$-0.240573\pi$
$397$	29.0000			1.45547			0.727734	+	0.685859i	$0.240573\pi$
$398$			3.46410i			0.173640i
$399$	10.5000	+	30.3109i	0.525657	+	1.51744i
$400$	−1.00000	−	1.73205i	−0.0500000	−	0.0866025i
$401$	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	$0.0182907\pi$
$402$	3.00000			0.149626
$403$	−3.50000	−	0.866025i	−0.174347	−	0.0431398i
$404$	−4.50000	−	7.79423i	−0.223883	−	0.387777i
$405$	−13.5000	−	7.79423i	−0.670820	−	0.387298i
$406$	−22.5000	−	4.33013i	−1.11666	−	0.214901i
$407$		0			0
$408$	−9.00000	−	5.19615i	−0.445566	−	0.257248i
$409$	11.0000	+	19.0526i	0.543915	+	0.942088i	0.998674	+	0.0514740i	$0.0163919\pi$
$409$	11.0000	+	19.0526i	0.543915	+	0.942088i	−0.454759	+	0.890614i	$0.650275\pi$
$410$	−4.50000	−	7.79423i	−0.222239	−	0.384930i
$411$	9.00000	+	5.19615i	0.443937	+	0.256307i
$412$	7.50000	+	4.33013i	0.369498	+	0.213330i
$413$	−9.00000	−	25.9808i	−0.442861	−	1.27843i
$414$		−	10.3923i		−	0.510754i
$415$	3.00000	+	5.19615i	0.147264	+	0.255069i
$416$	−2.50000	+	2.59808i	−0.122573	+	0.127381i
$417$	39.0000			1.90984
$418$	10.5000	−	18.1865i	0.513572	−	0.889532i
$419$	−16.5000	−	28.5788i	−0.806078	−	1.39617i	−0.915561	−	0.402179i	$-0.868253\pi$
$419$	−16.5000	−	28.5788i	−0.806078	−	1.39617i	0.109483	−	0.993989i	$-0.465080\pi$
$420$	−1.50000	+	7.79423i	−0.0731925	+	0.380319i
$421$			13.8564i			0.675320i	0.941268	+	0.337660i	$0.109635\pi$
$421$			13.8564i			0.675320i	−0.941268	+	0.337660i	$0.890365\pi$
$422$	1.00000			0.0486792
$423$			5.19615i			0.252646i
$424$	1.50000	+	0.866025i	0.0728464	+	0.0420579i
$425$	−12.0000			−0.582086
$426$	13.5000	+	7.79423i	0.654077	+	0.377632i
$427$	−4.50000	−	0.866025i	−0.217770	−	0.0419099i
$428$			10.3923i			0.502331i
$429$	−13.5000	−	12.9904i	−0.651786	−	0.627182i
$430$	1.50000	+	0.866025i	0.0723364	+	0.0417635i
$431$	21.0000			1.01153			0.505767	−	0.862670i	$-0.331209\pi$
$431$	21.0000			1.01153			0.505767	+	0.862670i	$0.331209\pi$
$432$	4.50000	+	2.59808i	0.216506	+	0.125000i
$433$	4.50000	+	2.59808i	0.216256	+	0.124856i	0.604216	−	0.796821i	$-0.293487\pi$
$433$	4.50000	+	2.59808i	0.216256	+	0.124856i	−0.387959	+	0.921676i	$0.626820\pi$
$434$	2.50000	−	0.866025i	0.120004	−	0.0415705i
$435$		−	25.9808i		−	1.24568i
$436$			8.66025i			0.414751i
$437$	−21.0000	−	12.1244i	−1.00457	−	0.579987i
$438$	19.5000	+	11.2583i	0.931746	+	0.537944i
$439$	−3.00000	−	1.73205i	−0.143182	−	0.0826663i	0.426698	−	0.904394i	$-0.359677\pi$
$439$	−3.00000	−	1.73205i	−0.143182	−	0.0826663i	−0.569880	+	0.821728i	$0.693010\pi$
$440$	4.50000	−	2.59808i	0.214529	−	0.123858i
$441$	−16.5000	+	12.9904i	−0.785714	+	0.618590i
$442$	6.00000	+	20.7846i	0.285391	+	0.988623i
$443$	−10.5000	+	6.06218i	−0.498870	+	0.288023i	−0.728247	−	0.685315i	$-0.759665\pi$
$443$	−10.5000	+	6.06218i	−0.498870	+	0.288023i	0.229377	+	0.973338i	$0.426331\pi$
$444$		0			0
$445$	12.0000			0.568855
$446$	−29.0000			−1.37319
$447$	−31.5000	+	18.1865i	−1.48990	+	0.860194i
$448$	0.500000	−	2.59808i	0.0236228	−	0.122748i
$449$	−7.50000	+	12.9904i	−0.353947	+	0.613054i	−0.986937	−	0.161106i	$-0.948494\pi$
$449$	−7.50000	+	12.9904i	−0.353947	+	0.613054i	0.632990	+	0.774160i	$0.281827\pi$
$450$	6.00000			0.282843
$451$	−13.5000	+	7.79423i	−0.635690	+	0.367016i
$452$		−	1.73205i		−	0.0814688i
$453$	−39.0000			−1.83238
$454$		−	10.3923i		−	0.487735i
$455$	13.5000	−	9.52628i	0.632890	−	0.446599i
$456$	10.5000	−	6.06218i	0.491708	−	0.283887i
$457$	18.0000	+	10.3923i	0.842004	+	0.486132i	0.857945	−	0.513741i	$-0.171741\pi$
$457$	18.0000	+	10.3923i	0.842004	+	0.486132i	−0.0159406	+	0.999873i	$0.505074\pi$
$458$	−25.0000			−1.16817
$459$	27.0000	−	15.5885i	1.26025	−	0.727607i
$460$	−3.00000	−	5.19615i	−0.139876	−	0.242272i
$461$	22.5000	+	12.9904i	1.04793	+	0.605022i	0.922069	−	0.387026i	$-0.126497\pi$
$461$	22.5000	+	12.9904i	1.04793	+	0.605022i	0.125860	+	0.992048i	$0.459831\pi$
$462$	13.5000	+	2.59808i	0.628077	+	0.120873i
$463$		−	31.1769i		−	1.44891i	−0.689320	−	0.724457i	$-0.742091\pi$
$463$		−	31.1769i		−	1.44891i	0.689320	−	0.724457i	$-0.257909\pi$
$464$			8.66025i			0.402042i
$465$	1.50000	+	2.59808i	0.0695608	+	0.120483i
$466$			22.5167i			1.04306i
$467$	4.50000	+	7.79423i	0.208235	+	0.360674i	0.951159	−	0.308702i	$-0.0998947\pi$
$467$	4.50000	+	7.79423i	0.208235	+	0.360674i	−0.742923	+	0.669376i	$0.766561\pi$
$468$	−3.00000	−	10.3923i	−0.138675	−	0.480384i
$469$	4.50000	+	0.866025i	0.207791	+	0.0399893i
$470$	1.50000	+	2.59808i	0.0691898	+	0.119840i
$471$	3.00000			0.138233
$472$	−9.00000	+	5.19615i	−0.414259	+	0.239172i
$473$	1.50000	−	2.59808i	0.0689701	−	0.119460i
$474$	−1.50000	+	0.866025i	−0.0688973	+	0.0397779i
$475$	7.00000	−	12.1244i	0.321182	−	0.556304i
$476$	−12.0000	−	10.3923i	−0.550019	−	0.476331i
$477$	−4.50000	+	2.59808i	−0.206041	+	0.118958i
$478$	−6.00000	+	10.3923i	−0.274434	+	0.475333i
$479$			19.0526i			0.870534i	0.900302	+	0.435267i	$0.143346\pi$
$479$			19.0526i			0.870534i	−0.900302	+	0.435267i	$0.856654\pi$
$480$	3.00000			0.136931
$481$		0			0
$482$	−10.0000			−0.455488
$483$	3.00000	−	15.5885i	0.136505	−	0.709299i
$484$	1.00000	+	1.73205i	0.0454545	+	0.0787296i
$485$		−	32.9090i		−	1.49432i
$486$	−13.5000	+	7.79423i	−0.612372	+	0.353553i
$487$	−3.00000	+	1.73205i	−0.135943	+	0.0784867i	−0.566429	−	0.824110i	$-0.691675\pi$
$487$	−3.00000	+	1.73205i	−0.135943	+	0.0784867i	0.430486	+	0.902597i	$0.358342\pi$
$488$			1.73205i			0.0784063i
$489$	−4.50000	−	7.79423i	−0.203497	−	0.352467i
$490$	−4.50000	+	11.2583i	−0.203289	+	0.508600i
$491$	31.5000	−	18.1865i	1.42158	−	0.820747i	0.425141	−	0.905127i	$-0.360224\pi$
$491$	31.5000	−	18.1865i	1.42158	−	0.820747i	0.996434	+	0.0843802i	$0.0268910\pi$
$492$	−9.00000			−0.405751
$493$	45.0000	+	25.9808i	2.02670	+	1.17011i
$494$	−24.5000	−	6.06218i	−1.10231	−	0.272750i
$495$			15.5885i			0.700649i
$496$	−0.500000	−	0.866025i	−0.0224507	−	0.0388857i
$497$	18.0000	+	15.5885i	0.807410	+	0.699238i
$498$	6.00000			0.268866
$499$	−28.5000	+	16.4545i	−1.27584	+	0.736604i	−0.976080	−	0.217412i	$-0.930238\pi$
$499$	−28.5000	+	16.4545i	−1.27584	+	0.736604i	−0.299755	+	0.954016i	$0.596905\pi$
$500$	10.5000	−	6.06218i	0.469574	−	0.271109i
$501$	−7.50000	+	12.9904i	−0.335075	+	0.580367i
$502$	7.50000	+	12.9904i	0.334741	+	0.579789i
$503$	−13.5000	+	23.3827i	−0.601935	+	1.04258i	0.390593	+	0.920564i	$0.372270\pi$
$503$	−13.5000	+	23.3827i	−0.601935	+	1.04258i	−0.992528	+	0.122019i	$0.961063\pi$
$504$	6.00000	+	5.19615i	0.267261	+	0.231455i
$505$	13.5000	−	7.79423i	0.600742	−	0.346839i
$506$	−9.00000	+	5.19615i	−0.400099	+	0.230997i
$507$	−10.5000	+	19.9186i	−0.466321	+	0.884615i
$508$	8.50000	−	14.7224i	0.377127	−	0.653202i
$509$	6.00000	+	3.46410i	0.265945	+	0.153544i	0.627044	−	0.778984i	$-0.284265\pi$
$509$	6.00000	+	3.46410i	0.265945	+	0.153544i	−0.361098	+	0.932528i	$0.617598\pi$
$510$	9.00000	−	15.5885i	0.398527	−	0.690268i
$511$	26.0000	+	22.5167i	1.15017	+	0.996078i
$512$	−1.00000			−0.0441942
$513$			36.3731i			1.60591i
$514$	−3.00000	−	5.19615i	−0.132324	−	0.229192i
$515$	−7.50000	+	12.9904i	−0.330489	+	0.572425i
$516$	1.50000	−	0.866025i	0.0660338	−	0.0381246i
$517$	4.50000	−	2.59808i	0.197910	−	0.114263i
$518$		0			0
$519$	13.5000	−	7.79423i	0.592584	−	0.342129i
$520$	−4.50000	−	4.33013i	−0.197338	−	0.189889i
$521$	7.50000	−	12.9904i	0.328581	−	0.569119i	−0.653650	−	0.756797i	$-0.726763\pi$
$521$	7.50000	−	12.9904i	0.328581	−	0.569119i	0.982231	+	0.187678i	$0.0600963\pi$
$522$	−22.5000	−	12.9904i	−0.984798	−	0.568574i
$523$	27.0000	+	15.5885i	1.18063	+	0.681636i	0.956160	−	0.292846i	$-0.0946023\pi$
$523$	27.0000	+	15.5885i	1.18063	+	0.681636i	0.224468	+	0.974481i	$0.427936\pi$
$524$	−1.50000	+	2.59808i	−0.0655278	+	0.113497i
$525$	9.00000	+	1.73205i	0.392792	+	0.0755929i
$526$	7.50000	+	4.33013i	0.327016	+	0.188803i
$527$	−6.00000			−0.261364
$528$		−	5.19615i		−	0.226134i
$529$	−5.50000	−	9.52628i	−0.239130	−	0.414186i
$530$	−1.50000	+	2.59808i	−0.0651558	+	0.112853i
$531$		−	31.1769i		−	1.35296i
$532$	17.5000	−	6.06218i	0.758721	−	0.262829i
$533$	13.5000	+	12.9904i	0.584750	+	0.562676i
$534$	6.00000	−	10.3923i	0.259645	−	0.449719i
$535$	−18.0000			−0.778208
$536$		−	1.73205i		−	0.0748132i
$537$	−16.5000	−	28.5788i	−0.712028	−	1.23327i
$538$	−30.0000			−1.29339
$539$	19.5000	+	7.79423i	0.839924	+	0.335721i
$540$	−4.50000	+	7.79423i	−0.193649	+	0.335410i
$541$	−13.5000	+	7.79423i	−0.580410	+	0.335100i	−0.761296	−	0.648404i	$-0.775437\pi$
$541$	−13.5000	+	7.79423i	−0.580410	+	0.335100i	0.180886	+	0.983504i	$0.442103\pi$
$542$	−8.00000	−	13.8564i	−0.343629	−	0.595184i
$543$	12.0000	+	20.7846i	0.514969	+	0.891953i
$544$	−3.00000	+	5.19615i	−0.128624	+	0.222783i
$545$	−15.0000			−0.642529
$546$	−1.50000	−	16.4545i	−0.0641941	−	0.704187i
$547$	44.0000			1.88130			0.940652	−	0.339372i	$-0.110215\pi$
$547$	44.0000			1.88130			0.940652	+	0.339372i	$0.110215\pi$
$548$	3.00000	−	5.19615i	0.128154	−	0.221969i
$549$	−4.50000	−	2.59808i	−0.192055	−	0.110883i
$550$	−3.00000	−	5.19615i	−0.127920	−	0.221565i
$551$	−52.5000	+	30.3109i	−2.23658	+	1.29129i
$552$	−6.00000			−0.255377
$553$	−2.50000	+	0.866025i	−0.106311	+	0.0368271i
$554$	10.0000			0.424859
$555$		0			0
$556$		−	22.5167i		−	0.954919i
$557$	−33.0000			−1.39825			−0.699127	−	0.714997i	$-0.746428\pi$
$557$	−33.0000			−1.39825			−0.699127	+	0.714997i	$0.746428\pi$
$558$	3.00000			0.127000
$559$	−3.50000	−	0.866025i	−0.148034	−	0.0366290i
$560$	4.50000	+	0.866025i	0.190160	+	0.0365963i
$561$	−27.0000	−	15.5885i	−1.13994	−	0.658145i
$562$	3.00000	−	5.19615i	0.126547	−	0.219186i
$563$	6.00000	+	10.3923i	0.252870	+	0.437983i	0.964315	−	0.264758i	$-0.0852922\pi$
$563$	6.00000	+	10.3923i	0.252870	+	0.437983i	−0.711445	+	0.702742i	$0.751959\pi$
$564$	3.00000			0.126323
$565$	3.00000			0.126211
$566$	−19.5000	−	11.2583i	−0.819646	−	0.473223i
$567$	−22.5000	+	7.79423i	−0.944911	+	0.327327i
$568$	4.50000	−	7.79423i	0.188816	−	0.327039i
$569$	−12.0000	−	6.92820i	−0.503066	−	0.290445i	0.226913	−	0.973915i	$-0.427137\pi$
$569$	−12.0000	−	6.92820i	−0.503066	−	0.290445i	−0.729979	+	0.683470i	$0.760470\pi$
$570$	10.5000	+	18.1865i	0.439797	+	0.761750i
$571$	2.50000	−	4.33013i	0.104622	−	0.181210i	−0.808962	−	0.587861i	$-0.799970\pi$
$571$	2.50000	−	4.33013i	0.104622	−	0.181210i	0.913584	+	0.406651i	$0.133303\pi$
$572$	−7.50000	+	7.79423i	−0.313591	+	0.325893i
$573$	13.5000	+	23.3827i	0.563971	+	0.976826i
$574$	−13.5000	−	2.59808i	−0.563479	−	0.108442i
$575$	−6.00000	+	3.46410i	−0.250217	+	0.144463i
$576$	1.50000	−	2.59808i	0.0625000	−	0.108253i
$577$	3.50000	−	6.06218i	0.145707	−	0.252372i	−0.783930	−	0.620850i	$-0.786788\pi$
$577$	3.50000	−	6.06218i	0.145707	−	0.252372i	0.929636	+	0.368478i	$0.120121\pi$
$578$	9.50000	+	16.4545i	0.395148	+	0.684416i
$579$	10.5000	+	18.1865i	0.436365	+	0.755807i
$580$	−15.0000			−0.622841
$581$	9.00000	+	1.73205i	0.373383	+	0.0718576i
$582$	−28.5000	−	16.4545i	−1.18136	−	0.682060i
$583$	4.50000	+	2.59808i	0.186371	+	0.107601i
$584$	6.50000	−	11.2583i	0.268972	−	0.465873i
$585$	18.0000	−	5.19615i	0.744208	−	0.214834i
$586$	−25.5000	+	14.7224i	−1.05340	+	0.608178i
$587$	28.5000	−	16.4545i	1.17632	−	0.679149i	0.221160	−	0.975237i	$-0.429016\pi$
$587$	28.5000	−	16.4545i	1.17632	−	0.679149i	0.955161	+	0.296088i	$0.0956823\pi$
$588$	7.50000	+	9.52628i	0.309295	+	0.392857i
$589$	3.50000	−	6.06218i	0.144215	−	0.249788i
$590$	−9.00000	−	15.5885i	−0.370524	−	0.641767i
$591$	31.5000	+	18.1865i	1.29574	+	0.748094i
$592$		0			0
$593$	7.50000	−	4.33013i	0.307988	−	0.177817i	−0.338038	−	0.941133i	$-0.609763\pi$
$593$	7.50000	−	4.33013i	0.307988	−	0.177817i	0.646026	+	0.763316i	$0.276430\pi$
$594$	13.5000	+	7.79423i	0.553912	+	0.319801i
$595$	18.0000	−	20.7846i	0.737928	−	0.852086i
$596$	10.5000	+	18.1865i	0.430097	+	0.744949i
$597$	−3.00000	+	5.19615i	−0.122782	+	0.212664i
$598$	9.00000	+	8.66025i	0.368037	+	0.354144i
$599$	−25.5000	−	14.7224i	−1.04190	−	0.601542i	−0.121530	−	0.992588i	$-0.538780\pi$
$599$	−25.5000	−	14.7224i	−1.04190	−	0.601542i	−0.920371	+	0.391045i	$0.872114\pi$
$600$		−	3.46410i		−	0.141421i
$601$	−19.5000	+	11.2583i	−0.795422	+	0.459237i	−0.841868	−	0.539684i	$-0.818544\pi$
$601$	−19.5000	+	11.2583i	−0.795422	+	0.459237i	0.0464461	+	0.998921i	$0.485210\pi$
$602$	2.50000	−	0.866025i	0.101892	−	0.0352966i
$603$	4.50000	+	2.59808i	0.183254	+	0.105802i
$604$			22.5167i			0.916190i
$605$	−3.00000	+	1.73205i	−0.121967	+	0.0704179i
$606$		−	15.5885i		−	0.633238i
$607$			19.0526i			0.773320i	0.922222	+	0.386660i	$0.126371\pi$
$607$			19.0526i			0.773320i	−0.922222	+	0.386660i	$0.873629\pi$
$608$	−3.50000	−	6.06218i	−0.141944	−	0.245854i
$609$	−30.0000	−	25.9808i	−1.21566	−	1.05279i
$610$	−3.00000			−0.121466
$611$	−4.50000	−	4.33013i	−0.182051	−	0.175178i
$612$	−9.00000	−	15.5885i	−0.363803	−	0.630126i
$613$		−	22.5167i		−	0.909439i	−0.890635	−	0.454720i	$-0.849739\pi$
$613$		−	22.5167i		−	0.909439i	0.890635	−	0.454720i	$-0.150261\pi$
$614$	2.00000	−	3.46410i	0.0807134	−	0.139800i
$615$		−	15.5885i		−	0.628587i
$616$	1.50000	−	7.79423i	0.0604367	−	0.314038i
$617$	4.50000	−	7.79423i	0.181163	−	0.313784i	−0.761114	−	0.648618i	$-0.775347\pi$
$617$	4.50000	−	7.79423i	0.181163	−	0.313784i	0.942277	+	0.334835i	$0.108680\pi$
$618$	7.50000	+	12.9904i	0.301694	+	0.522550i
$619$	−2.50000	+	4.33013i	−0.100483	+	0.174042i	−0.911884	−	0.410448i	$-0.865372\pi$
$619$	−2.50000	+	4.33013i	−0.100483	+	0.174042i	0.811400	+	0.584491i	$0.198706\pi$
$620$	1.50000	−	0.866025i	0.0602414	−	0.0347804i
$621$	9.00000	−	15.5885i	0.361158	−	0.625543i
$622$	−1.50000	−	2.59808i	−0.0601445	−	0.104173i
$623$	12.0000	−	13.8564i	0.480770	−	0.555145i
$624$	−6.00000	+	1.73205i	−0.240192	+	0.0693375i
$625$	5.50000	+	9.52628i	0.220000	+	0.381051i
$626$			5.19615i			0.207680i
$627$	31.5000	−	18.1865i	1.25799	−	0.726300i
$628$		−	1.73205i		−	0.0691164i
$629$		0			0
$630$	−9.00000	+	10.3923i	−0.358569	+	0.414039i
$631$	−1.50000	−	0.866025i	−0.0597141	−	0.0344759i	0.469846	−	0.882749i	$-0.344310\pi$
$631$	−1.50000	−	0.866025i	−0.0597141	−	0.0344759i	−0.529560	+	0.848273i	$0.677643\pi$
$632$	0.500000	+	0.866025i	0.0198889	+	0.0344486i
$633$	1.50000	+	0.866025i	0.0596196	+	0.0344214i
$634$	−3.00000			−0.119145
$635$	25.5000	+	14.7224i	1.01194	+	0.584242i
$636$	1.50000	+	2.59808i	0.0594789	+	0.103020i
$637$	2.50000	−	25.1147i	0.0990536	−	0.995082i
$638$			25.9808i			1.02859i
$639$	13.5000	+	23.3827i	0.534052	+	0.925005i
$640$		−	1.73205i		−	0.0684653i
$641$	−30.0000	+	17.3205i	−1.18493	+	0.684119i	−0.957150	−	0.289594i	$-0.906480\pi$
$641$	−30.0000	+	17.3205i	−1.18493	+	0.684119i	−0.227779	+	0.973713i	$0.573146\pi$
$642$	−9.00000	+	15.5885i	−0.355202	+	0.615227i
$643$	14.5000	−	25.1147i	0.571824	−	0.990429i	−0.424555	−	0.905402i	$-0.639569\pi$
$643$	14.5000	−	25.1147i	0.571824	−	0.990429i	0.996379	−	0.0850262i	$-0.0270974\pi$
$644$	−9.00000	−	1.73205i	−0.354650	−	0.0682524i
$645$	1.50000	+	2.59808i	0.0590624	+	0.102299i
$646$	−42.0000			−1.65247
$647$	3.00000			0.117942			0.0589711	−	0.998260i	$-0.481218\pi$
$647$	3.00000			0.117942			0.0589711	+	0.998260i	$0.481218\pi$
$648$	4.50000	+	7.79423i	0.176777	+	0.306186i
$649$	−27.0000	+	15.5885i	−1.05984	+	0.611900i
$650$	−5.00000	+	5.19615i	−0.196116	+	0.203810i
$651$	4.50000	+	0.866025i	0.176369	+	0.0339422i
$652$	−4.50000	+	2.59808i	−0.176234	+	0.101749i
$653$	36.0000	+	20.7846i	1.40879	+	0.813365i	0.995272	−	0.0971316i	$-0.0309668\pi$
$653$	36.0000	+	20.7846i	1.40879	+	0.813365i	0.413517	+	0.910496i	$0.364300\pi$
$654$	−7.50000	+	12.9904i	−0.293273	+	0.507964i
$655$	−4.50000	−	2.59808i	−0.175830	−	0.101515i
$656$			5.19615i			0.202876i
$657$	19.5000	+	33.7750i	0.760767	+	1.31769i
$658$	4.50000	+	0.866025i	0.175428	+	0.0337612i
$659$	34.5000	+	19.9186i	1.34393	+	0.775918i	0.987382	−	0.158359i	$-0.0506204\pi$
$659$	34.5000	+	19.9186i	1.34393	+	0.775918i	0.356548	+	0.934277i	$0.383954\pi$
$660$	9.00000			0.350325
$661$	13.0000			0.505641			0.252821	−	0.967513i	$-0.418642\pi$
$661$	13.0000			0.505641			0.252821	+	0.967513i	$0.418642\pi$
$662$	−22.5000	−	12.9904i	−0.874487	−	0.504885i
$663$	−9.00000	+	36.3731i	−0.349531	+	1.41261i
$664$		−	3.46410i		−	0.134433i
$665$	10.5000	+	30.3109i	0.407173	+	1.17541i
$666$		0			0
$667$	30.0000			1.16160
$668$	7.50000	+	4.33013i	0.290184	+	0.167538i
$669$	−43.5000	−	25.1147i	−1.68181	−	0.970992i
$670$	3.00000			0.115900
$671$			5.19615i			0.200595i
$672$	3.00000	−	3.46410i	0.115728	−	0.133631i
$673$	−3.50000	−	6.06218i	−0.134915	−	0.233680i	0.790650	−	0.612268i	$-0.209743\pi$
$673$	−3.50000	−	6.06218i	−0.134915	−	0.233680i	−0.925565	+	0.378589i	$0.876409\pi$
$674$	−5.00000	+	8.66025i	−0.192593	+	0.333581i
$675$	9.00000	+	5.19615i	0.346410	+	0.200000i
$676$	11.5000	+	6.06218i	0.442308	+	0.233161i
$677$	13.5000	+	23.3827i	0.518847	+	0.898670i	0.999760	+	0.0219013i	$0.00697196\pi$
$677$	13.5000	+	23.3827i	0.518847	+	0.898670i	−0.480913	+	0.876768i	$0.659695\pi$
$678$	1.50000	−	2.59808i	0.0576072	−	0.0997785i
$679$	−38.0000	−	32.9090i	−1.45831	−	1.26293i
$680$	−9.00000	−	5.19615i	−0.345134	−	0.199263i
$681$	9.00000	−	15.5885i	0.344881	−	0.597351i
$682$	−1.50000	−	2.59808i	−0.0574380	−	0.0994855i
$683$	6.00000	+	10.3923i	0.229584	+	0.397650i	0.957685	−	0.287819i	$-0.0929302\pi$
$683$	6.00000	+	10.3923i	0.229584	+	0.397650i	−0.728101	+	0.685470i	$0.759597\pi$
$684$	21.0000			0.802955
$685$	9.00000	+	5.19615i	0.343872	+	0.198535i
$686$	8.50000	+	16.4545i	0.324532	+	0.628235i
$687$	−37.5000	−	21.6506i	−1.43071	−	0.826023i
$688$	−0.500000	−	0.866025i	−0.0190623	−	0.0330169i
$689$	1.50000	−	6.06218i	0.0571454	−	0.230951i
$690$		−	10.3923i		−	0.395628i
$691$	−22.0000	+	38.1051i	−0.836919	+	1.44959i	0.0555386	+	0.998457i	$0.482312\pi$
$691$	−22.0000	+	38.1051i	−0.836919	+	1.44959i	−0.892458	+	0.451130i	$0.851021\pi$
$692$	−4.50000	−	7.79423i	−0.171064	−	0.296292i
$693$	18.0000	+	15.5885i	0.683763	+	0.592157i
$694$		−	10.3923i		−	0.394486i
$695$	39.0000			1.47935
$696$	−7.50000	+	12.9904i	−0.284287	+	0.492399i
$697$	27.0000	+	15.5885i	1.02270	+	0.590455i
$698$	35.0000			1.32477
$699$	−19.5000	+	33.7750i	−0.737558	+	1.27749i
$700$	1.00000	−	5.19615i	0.0377964	−	0.196396i
$701$		−	27.7128i		−	1.04670i	−0.852118	−	0.523349i	$-0.824682\pi$
$701$		−	27.7128i		−	1.04670i	0.852118	−	0.523349i	$-0.175318\pi$
$702$	4.50000	−	18.1865i	0.169842	−	0.686406i
$703$		0			0
$704$	−3.00000			−0.113067
$705$			5.19615i			0.195698i
$706$	−22.5000	−	12.9904i	−0.846799	−	0.488899i
$707$	4.50000	−	23.3827i	0.169240	−	0.879396i
$708$	−18.0000			−0.676481
$709$		−	25.9808i		−	0.975728i	−0.872920	−	0.487864i	$-0.837776\pi$
$709$		−	25.9808i		−	0.975728i	0.872920	−	0.487864i	$-0.162224\pi$
$710$	13.5000	+	7.79423i	0.506646	+	0.292512i
$711$	−3.00000			−0.112509
$712$	−6.00000	−	3.46410i	−0.224860	−	0.129823i
$713$	−3.00000	+	1.73205i	−0.112351	+	0.0648658i
$714$	−9.00000	−	25.9808i	−0.336817	−	0.972306i
$715$	−13.5000	−	12.9904i	−0.504871	−	0.485813i
$716$	−16.5000	+	9.52628i	−0.616634	+	0.356014i
$717$	−18.0000	+	10.3923i	−0.672222	+	0.388108i
$718$	3.00000			0.111959
$719$	−3.00000			−0.111881			−0.0559406	−	0.998434i	$-0.517816\pi$
$719$	−3.00000			−0.111881			−0.0559406	+	0.998434i	$0.517816\pi$
$720$	4.50000	+	2.59808i	0.167705	+	0.0968246i
$721$	7.50000	+	21.6506i	0.279315	+	0.806312i
$722$	15.0000	−	25.9808i	0.558242	−	0.966904i
$723$	−15.0000	−	8.66025i	−0.557856	−	0.322078i
$724$	12.0000	−	6.92820i	0.445976	−	0.257485i
$725$			17.3205i			0.643268i
$726$			3.46410i			0.128565i
$727$		−	10.3923i		−	0.385429i	−0.981255	−	0.192715i	$-0.938271\pi$
$727$		−	10.3923i		−	0.385429i	0.981255	−	0.192715i	$-0.0617292\pi$
$728$	−9.50000	+	0.866025i	−0.352093	+	0.0320970i
$729$	−27.0000			−1.00000
$730$	19.5000	+	11.2583i	0.721727	+	0.416689i
$731$	−6.00000			−0.221918
$732$	−1.50000	+	2.59808i	−0.0554416	+	0.0960277i
$733$	−18.5000	−	32.0429i	−0.683313	−	1.18353i	−0.973964	−	0.226704i	$-0.927205\pi$
$733$	−18.5000	−	32.0429i	−0.683313	−	1.18353i	0.290651	−	0.956829i	$-0.406128\pi$
$734$	−13.5000	−	7.79423i	−0.498294	−	0.287690i
$735$	−16.5000	+	12.9904i	−0.608612	+	0.479157i
$736$			3.46410i			0.127688i
$737$		−	5.19615i		−	0.191403i
$738$	−13.5000	−	7.79423i	−0.496942	−	0.286910i
$739$		−	19.0526i		−	0.700860i	−0.936589	−	0.350430i	$-0.886036\pi$
$739$		−	19.0526i		−	0.700860i	0.936589	−	0.350430i	$-0.113964\pi$
$740$		0			0
$741$	−31.5000	−	30.3109i	−1.15718	−	1.11350i
$742$	1.50000	+	4.33013i	0.0550667	+	0.158964i
$743$	4.50000	+	7.79423i	0.165089	+	0.285943i	0.936687	−	0.350168i	$-0.113876\pi$
$743$	4.50000	+	7.79423i	0.165089	+	0.285943i	−0.771598	+	0.636111i	$0.780542\pi$
$744$		−	1.73205i		−	0.0635001i
$745$	−31.5000	+	18.1865i	−1.15407	+	0.666303i
$746$	−14.5000	+	25.1147i	−0.530883	+	0.919516i
$747$	9.00000	+	5.19615i	0.329293	+	0.190117i
$748$	−9.00000	+	15.5885i	−0.329073	+	0.569970i
$749$	−18.0000	+	20.7846i	−0.657706	+	0.759453i
$750$	21.0000			0.766812
$751$	−2.00000	+	3.46410i	−0.0729810	+	0.126407i	−0.900207	−	0.435463i	$-0.856585\pi$
$751$	−2.00000	+	3.46410i	−0.0729810	+	0.126407i	0.827225	+	0.561870i	$0.189918\pi$
$752$		−	1.73205i		−	0.0631614i
$753$			25.9808i			0.946792i
$754$	30.0000	−	8.66025i	1.09254	−	0.315388i
$755$	−39.0000			−1.41936
$756$	4.50000	+	12.9904i	0.163663	+	0.472456i
$757$	−23.5000	−	40.7032i	−0.854122	−	1.47938i	−0.877457	−	0.479655i	$-0.840762\pi$
$757$	−23.5000	−	40.7032i	−0.854122	−	1.47938i	0.0233351	−	0.999728i	$-0.492572\pi$
$758$			19.0526i			0.692020i
$759$	−18.0000			−0.653359
$760$	10.5000	−	6.06218i	0.380875	−	0.219898i
$761$		−	29.4449i		−	1.06738i	−0.845682	−	0.533688i	$-0.820806\pi$
$761$		−	29.4449i		−	1.06738i	0.845682	−	0.533688i	$-0.179194\pi$
$762$	25.5000	−	14.7224i	0.923768	−	0.533337i
$763$	−15.0000	+	17.3205i	−0.543036	+	0.627044i
$764$	13.5000	−	7.79423i	0.488413	−	0.281985i
$765$	27.0000	−	15.5885i	0.976187	−	0.563602i
$766$	4.50000	+	2.59808i	0.162592	+	0.0938723i
$767$	27.0000	+	25.9808i	0.974913	+	0.938111i
$768$	−1.50000	−	0.866025i	−0.0541266	−	0.0312500i
$769$	−6.50000	−	11.2583i	−0.234396	−	0.405986i	0.724701	−	0.689063i	$-0.241978\pi$
$769$	−6.50000	−	11.2583i	−0.234396	−	0.405986i	−0.959097	+	0.283078i	$0.908645\pi$
$770$	13.5000	+	2.59808i	0.486506	+	0.0936282i
$771$		−	10.3923i		−	0.374270i
$772$	10.5000	−	6.06218i	0.377903	−	0.218183i
$773$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$773$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$774$	3.00000			0.107833
$775$	−1.00000	−	1.73205i	−0.0359211	−	0.0622171i
$776$	−9.50000	+	16.4545i	−0.341030	+	0.590682i
$777$		0			0
$778$	4.50000	−	2.59808i	0.161333	−	0.0931455i
$779$	−31.5000	+	18.1865i	−1.12860	+	0.651600i
$780$	−3.00000	−	10.3923i	−0.107417	−	0.372104i
$781$	13.5000	−	23.3827i	0.483068	−	0.836698i
$782$	18.0000	+	10.3923i	0.643679	+	0.371628i
$783$	−22.5000	−	38.9711i	−0.804084	−	1.39272i
$784$	5.50000	−	4.33013i	0.196429	−	0.154647i
$785$	3.00000			0.107075
$786$	−4.50000	+	2.59808i	−0.160510	+	0.0926703i
$787$	2.00000	+	3.46410i	0.0712923	+	0.123482i	0.899468	−	0.436987i	$-0.143954\pi$
$787$	2.00000	+	3.46410i	0.0712923	+	0.123482i	−0.828176	+	0.560469i	$0.810621\pi$
$788$	10.5000	−	18.1865i	0.374047	−	0.647868i
$789$	7.50000	+	12.9904i	0.267007	+	0.462470i
$790$	−1.50000	+	0.866025i	−0.0533676	+	0.0308118i
$791$	3.00000	−	3.46410i	0.106668	−	0.123169i
$792$	4.50000	−	7.79423i	0.159901	−	0.276956i
$793$	6.00000	−	1.73205i	0.213066	−	0.0615069i
$794$	14.5000	−	25.1147i	0.514586	−	0.891289i
$795$	−4.50000	+	2.59808i	−0.159599	+	0.0921443i
$796$	3.00000	+	1.73205i	0.106332	+	0.0613909i
$797$	19.5000	−	33.7750i	0.690725	−	1.19637i	−0.280875	−	0.959744i	$-0.590625\pi$
$797$	19.5000	−	33.7750i	0.690725	−	1.19637i	0.971601	−	0.236627i	$-0.0760420\pi$
$798$	31.5000	+	6.06218i	1.11509	+	0.214599i
$799$	−9.00000	−	5.19615i	−0.318397	−	0.183827i
$800$	−2.00000			−0.0707107
$801$	18.0000	−	10.3923i	0.635999	−	0.367194i
$802$	−9.00000	−	15.5885i	−0.317801	−	0.550448i
$803$	19.5000	−	33.7750i	0.688140	−	1.19189i
$804$	1.50000	−	2.59808i	0.0529009	−	0.0916271i
$805$	3.00000	−	15.5885i	0.105736	−	0.549421i
$806$	−2.50000	+	2.59808i	−0.0880587	+	0.0915133i
$807$	−45.0000	−	25.9808i	−1.58408	−	0.914566i
$808$	−9.00000			−0.316619
$809$		−	50.2295i		−	1.76597i	−0.469397	−	0.882987i	$-0.655529\pi$
$809$		−	50.2295i		−	1.76597i	0.469397	−	0.882987i	$-0.344471\pi$
$810$	−13.5000	+	7.79423i	−0.474342	+	0.273861i
$811$	28.0000			0.983213			0.491606	−	0.870817i	$-0.336410\pi$
$811$	28.0000			0.983213			0.491606	+	0.870817i	$0.336410\pi$
$812$	−15.0000	+	17.3205i	−0.526397	+	0.607831i
$813$		−	27.7128i		−	0.971931i
$814$		0			0
$815$	−4.50000	−	7.79423i	−0.157628	−	0.273020i
$816$	−9.00000	+	5.19615i	−0.315063	+	0.181902i
$817$	3.50000	−	6.06218i	0.122449	−	0.212089i
$818$	22.0000			0.769212
$819$	12.0000	−	25.9808i	0.419314	−	0.907841i
$820$	−9.00000			−0.314294
$821$	3.00000	−	5.19615i	0.104701	−	0.181347i	−0.808915	−	0.587925i	$-0.799945\pi$
$821$	3.00000	−	5.19615i	0.104701	−	0.181347i	0.913616	+	0.406578i	$0.133278\pi$
$822$	9.00000	−	5.19615i	0.313911	−	0.181237i
$823$	8.00000	+	13.8564i	0.278862	+	0.483004i	0.971102	−	0.238664i	$-0.0767093\pi$
$823$	8.00000	+	13.8564i	0.278862	+	0.483004i	−0.692240	+	0.721668i	$0.743376\pi$
$824$	7.50000	−	4.33013i	0.261275	−	0.150847i
$825$		−	10.3923i		−	0.361814i
$826$	−27.0000	−	5.19615i	−0.939450	−	0.180797i
$827$	36.0000			1.25184			0.625921	−	0.779886i	$-0.284723\pi$
$827$	36.0000			1.25184			0.625921	+	0.779886i	$0.284723\pi$
$828$	−9.00000	−	5.19615i	−0.312772	−	0.180579i
$829$			15.5885i			0.541409i	0.962662	+	0.270705i	$0.0872567\pi$
$829$			15.5885i			0.541409i	−0.962662	+	0.270705i	$0.912743\pi$
$830$	6.00000			0.208263
$831$	15.0000	+	8.66025i	0.520344	+	0.300421i
$832$	1.00000	+	3.46410i	0.0346688	+	0.120096i
$833$	−6.00000	−	41.5692i	−0.207888	−	1.44029i
$834$	19.5000	−	33.7750i	0.675230	−	1.16953i
$835$	−7.50000	+	12.9904i	−0.259548	+	0.449551i
$836$	−10.5000	−	18.1865i	−0.363150	−	0.628994i
$837$	4.50000	+	2.59808i	0.155543	+	0.0898027i
$838$	−33.0000			−1.13997
$839$	−4.50000	−	2.59808i	−0.155357	−	0.0896956i	0.420306	−	0.907382i	$-0.361923\pi$
$839$	−4.50000	−	2.59808i	−0.155357	−	0.0896956i	−0.575663	+	0.817687i	$0.695256\pi$
$840$	6.00000	+	5.19615i	0.207020	+	0.179284i
$841$	23.0000	−	39.8372i	0.793103	−	1.37370i
$842$	12.0000	+	6.92820i	0.413547	+	0.238762i
$843$	9.00000	−	5.19615i	0.309976	−	0.178965i
$844$	0.500000	−	0.866025i	0.0172107	−	0.0298098i
$845$	−10.5000	+	19.9186i	−0.361211	+	0.685220i
$846$	4.50000	+	2.59808i	0.154713	+	0.0893237i
$847$	−1.00000	+	5.19615i	−0.0343604	+	0.178542i
$848$	1.50000	−	0.866025i	0.0515102	−	0.0297394i
$849$	−19.5000	−	33.7750i	−0.669238	−	1.15915i
$850$	−6.00000	+	10.3923i	−0.205798	+	0.356453i
$851$		0			0
$852$	13.5000	−	7.79423i	0.462502	−	0.267026i
$853$	−10.0000			−0.342393			−0.171197	−	0.985237i	$-0.554763\pi$
$853$	−10.0000			−0.342393			−0.171197	+	0.985237i	$0.554763\pi$
$854$	−3.00000	+	3.46410i	−0.102658	+	0.118539i
$855$			36.3731i			1.24393i
$856$	9.00000	+	5.19615i	0.307614	+	0.177601i
$857$	19.5000	−	33.7750i	0.666107	−	1.15373i	−0.312877	−	0.949794i	$-0.601293\pi$
$857$	19.5000	−	33.7750i	0.666107	−	1.15373i	0.978984	−	0.203938i	$-0.0653741\pi$
$858$	−18.0000	+	5.19615i	−0.614510	+	0.177394i
$859$	4.50000	−	2.59808i	0.153538	−	0.0886452i	−0.421263	−	0.906939i	$-0.638413\pi$
$859$	4.50000	−	2.59808i	0.153538	−	0.0886452i	0.574801	+	0.818293i	$0.305080\pi$
$860$	1.50000	−	0.866025i	0.0511496	−	0.0295312i
$861$	−18.0000	−	15.5885i	−0.613438	−	0.531253i
$862$	10.5000	−	18.1865i	0.357631	−	0.619436i
$863$	19.5000	+	33.7750i	0.663788	+	1.14971i	0.979612	+	0.200897i	$0.0643855\pi$
$863$	19.5000	+	33.7750i	0.663788	+	1.14971i	−0.315825	+	0.948818i	$0.602281\pi$
$864$	4.50000	−	2.59808i	0.153093	−	0.0883883i
$865$	13.5000	−	7.79423i	0.459014	−	0.265012i
$866$	4.50000	−	2.59808i	0.152916	−	0.0882862i
$867$			32.9090i			1.11765i
$868$	0.500000	−	2.59808i	0.0169711	−	0.0881845i
$869$	1.50000	+	2.59808i	0.0508840	+	0.0881337i
$870$	−22.5000	−	12.9904i	−0.762821	−	0.440415i
$871$	−6.00000	+	1.73205i	−0.203302	+	0.0586883i
$872$	7.50000	+	4.33013i	0.253982	+	0.146637i
$873$	−28.5000	−	49.3634i	−0.964579	−	1.67070i
$874$	−21.0000	+	12.1244i	−0.710336	+	0.410112i
$875$	31.5000	+	6.06218i	1.06489	+	0.204939i
$876$	19.5000	−	11.2583i	0.658844	−	0.380384i
$877$		−	12.1244i		−	0.409410i	−0.978824	−	0.204705i	$-0.934376\pi$
$877$		−	12.1244i		−	0.409410i	0.978824	−	0.204705i	$-0.0656236\pi$
$878$	−3.00000	+	1.73205i	−0.101245	+	0.0584539i
$879$	−51.0000			−1.72019
$880$		−	5.19615i		−	0.175162i
$881$	−28.5000	−	49.3634i	−0.960189	−	1.66310i	−0.722019	−	0.691873i	$-0.756786\pi$
$881$	−28.5000	−	49.3634i	−0.960189	−	1.66310i	−0.238171	−	0.971223i	$-0.576548\pi$
$882$	3.00000	+	20.7846i	0.101015	+	0.699854i
$883$	−52.0000			−1.74994			−0.874970	−	0.484178i	$-0.839119\pi$
$883$	−52.0000			−1.74994			−0.874970	+	0.484178i	$0.839119\pi$
$884$	21.0000	+	5.19615i	0.706306	+	0.174766i
$885$		−	31.1769i		−	1.04800i
$886$			12.1244i			0.407326i
$887$	−12.0000	+	20.7846i	−0.402921	+	0.697879i	−0.994077	−	0.108678i	$-0.965338\pi$
$887$	−12.0000	+	20.7846i	−0.402921	+	0.697879i	0.591156	+	0.806557i	$0.298672\pi$
$888$		0			0
$889$	42.5000	−	14.7224i	1.42540	−	0.493775i
$890$	6.00000	−	10.3923i	0.201120	−	0.348351i
$891$	13.5000	+	23.3827i	0.452267	+	0.783349i
$892$	−14.5000	+	25.1147i	−0.485496	+	0.840904i
$893$	10.5000	−	6.06218i	0.351369	−	0.202863i
$894$			36.3731i			1.21650i
$895$	−16.5000	−	28.5788i	−0.551534	−	0.955285i
$896$	−2.00000	−	1.73205i	−0.0668153	−	0.0578638i
$897$	6.00000	+	20.7846i	0.200334	+	0.693978i
$898$	7.50000	+	12.9904i	0.250278	+	0.433495i
$899$			8.66025i			0.288836i
$900$	3.00000	−	5.19615i	0.100000	−	0.173205i
$901$		−	10.3923i		−	0.346218i
$902$			15.5885i			0.519039i
$903$	4.50000	+	0.866025i	0.149751	+	0.0288195i
$904$	−1.50000	−	0.866025i	−0.0498893	−	0.0288036i
$905$	12.0000	+	20.7846i	0.398893	+	0.690904i
$906$	−19.5000	+	33.7750i	−0.647844	+	1.12210i
$907$	−7.00000			−0.232431			−0.116216	−	0.993224i	$-0.537076\pi$
$907$	−7.00000			−0.232431			−0.116216	+	0.993224i	$0.537076\pi$
$908$	−9.00000	−	5.19615i	−0.298675	−	0.172440i
$909$	13.5000	−	23.3827i	0.447767	−	0.775555i
$910$	−1.50000	−	16.4545i	−0.0497245	−	0.545461i
$911$			24.2487i			0.803396i	0.915772	+	0.401698i	$0.131580\pi$
$911$			24.2487i			0.803396i	−0.915772	+	0.401698i	$0.868420\pi$
$912$		−	12.1244i		−	0.401478i
$913$		−	10.3923i		−	0.343935i
$914$	18.0000	−	10.3923i	0.595387	−	0.343747i
$915$	−4.50000	−	2.59808i	−0.148765	−	0.0858898i
$916$	−12.5000	+	21.6506i	−0.413012	+	0.715357i
$917$	−7.50000	+	2.59808i	−0.247672	+	0.0857960i
$918$		−	31.1769i		−	1.02899i
$919$	−37.0000			−1.22052			−0.610259	−	0.792202i	$-0.708935\pi$
$919$	−37.0000			−1.22052			−0.610259	+	0.792202i	$0.708935\pi$
$920$	−6.00000			−0.197814
$921$	6.00000	−	3.46410i	0.197707	−	0.114146i
$922$	22.5000	−	12.9904i	0.740998	−	0.427815i
$923$	−31.5000	−	7.79423i	−1.03684	−	0.256550i
$924$	9.00000	−	10.3923i	0.296078	−	0.341882i
$925$		0			0
$926$	−27.0000	−	15.5885i	−0.887275	−	0.512268i
$927$			25.9808i			0.853320i
$928$	7.50000	+	4.33013i	0.246200	+	0.142143i
$929$		−	8.66025i		−	0.284134i	−0.989857	−	0.142067i	$-0.954625\pi$
$929$		−	8.66025i		−	0.284134i	0.989857	−	0.142067i	$-0.0453748\pi$
$930$	3.00000			0.0983739
$931$	45.5000	+	18.1865i	1.49120	+	0.596040i
$932$	19.5000	+	11.2583i	0.638744	+	0.368779i
$933$		−	5.19615i		−	0.170114i
$934$	9.00000			0.294489
$935$	−27.0000	−	15.5885i	−0.882994	−	0.509797i
$936$	−10.5000	−	2.59808i	−0.343203	−	0.0849208i
$937$			20.7846i			0.679004i	0.940605	+	0.339502i	$0.110258\pi$
$937$			20.7846i			0.679004i	−0.940605	+	0.339502i	$0.889742\pi$
$938$	3.00000	−	3.46410i	0.0979535	−	0.113107i
$939$	−4.50000	+	7.79423i	−0.146852	+	0.254355i
$940$	3.00000			0.0978492
$941$	−16.5000	−	9.52628i	−0.537885	−	0.310548i	0.206337	−	0.978481i	$-0.433846\pi$
$941$	−16.5000	−	9.52628i	−0.537885	−	0.310548i	−0.744221	+	0.667933i	$0.767179\pi$
$942$	1.50000	−	2.59808i	0.0488726	−	0.0846499i
$943$	18.0000			0.586161
$944$			10.3923i			0.338241i
$945$	−22.5000	+	7.79423i	−0.731925	+	0.253546i
$946$	−1.50000	−	2.59808i	−0.0487692	−	0.0844707i
$947$	−6.00000	+	10.3923i	−0.194974	+	0.337705i	−0.946892	−	0.321552i	$-0.895796\pi$
$947$	−6.00000	+	10.3923i	−0.194974	+	0.337705i	0.751918	+	0.659256i	$0.229129\pi$
$948$			1.73205i			0.0562544i
$949$	−45.5000	−	11.2583i	−1.47699	−	0.365461i
$950$	−7.00000	−	12.1244i	−0.227110	−	0.393366i
$951$	−4.50000	−	2.59808i	−0.145922	−	0.0842484i
$952$	−15.0000	+	5.19615i	−0.486153	+	0.168408i
$953$	25.5000	+	14.7224i	0.826026	+	0.476906i	0.852490	−	0.522743i	$-0.175091\pi$
$953$	25.5000	+	14.7224i	0.826026	+	0.476906i	−0.0264640	+	0.999650i	$0.508425\pi$
$954$			5.19615i			0.168232i
$955$	13.5000	+	23.3827i	0.436850	+	0.756646i
$956$	6.00000	+	10.3923i	0.194054	+	0.336111i
$957$	−22.5000	+	38.9711i	−0.727322	+	1.25976i
$958$	16.5000	+	9.52628i	0.533091	+	0.307780i
$959$	15.0000	−	5.19615i	0.484375	−	0.167793i
$960$	1.50000	−	2.59808i	0.0484123	−	0.0838525i
$961$	15.0000	+	25.9808i	0.483871	+	0.838089i
$962$		0			0
$963$	−27.0000	+	15.5885i	−0.870063	+	0.502331i
$964$	−5.00000	+	8.66025i	−0.161039	+	0.278928i
$965$	10.5000	+	18.1865i	0.338007	+	0.585445i
$966$	−12.0000	−	10.3923i	−0.386094	−	0.334367i
$967$			10.3923i			0.334194i	0.985940	+	0.167097i	$0.0534393\pi$
$967$			10.3923i			0.334194i	−0.985940	+	0.167097i	$0.946561\pi$
$968$	2.00000			0.0642824
$969$	−63.0000	−	36.3731i	−2.02385	−	1.16847i
$970$	−28.5000	−	16.4545i	−0.915080	−	0.528322i
$971$	33.0000			1.05902			0.529510	−	0.848304i	$-0.322376\pi$
$971$	33.0000			1.05902			0.529510	+	0.848304i	$0.322376\pi$
$972$			15.5885i			0.500000i
$973$	39.0000	−	45.0333i	1.25028	−	1.44370i
$974$			3.46410i			0.110997i
$975$	−12.0000	+	3.46410i	−0.384308	+	0.110940i
$976$	1.50000	+	0.866025i	0.0480138	+	0.0277208i
$977$	3.00000			0.0959785			0.0479893	−	0.998848i	$-0.484719\pi$
$977$	3.00000			0.0959785			0.0479893	+	0.998848i	$0.484719\pi$
$978$	−9.00000			−0.287788
$979$	−18.0000	−	10.3923i	−0.575282	−	0.332140i
$980$	7.50000	+	9.52628i	0.239579	+	0.304306i
$981$	−22.5000	+	12.9904i	−0.718370	+	0.414751i
$982$		−	36.3731i		−	1.16071i
$983$	25.5000	+	14.7224i	0.813324	+	0.469573i	0.848109	−	0.529822i	$-0.177741\pi$
$983$	25.5000	+	14.7224i	0.813324	+	0.469573i	−0.0347851	+	0.999395i	$0.511075\pi$
$984$	−4.50000	+	7.79423i	−0.143455	+	0.248471i
$985$	31.5000	+	18.1865i	1.00367	+	0.579471i
$986$	45.0000	−	25.9808i	1.43309	−	0.827396i
$987$	6.00000	+	5.19615i	0.190982	+	0.165395i
$988$	−17.5000	+	18.1865i	−0.556749	+	0.578591i
$989$	−3.00000	+	1.73205i	−0.0953945	+	0.0550760i
$990$	13.5000	+	7.79423i	0.429058	+	0.247717i
$991$	25.0000			0.794151			0.397076	−	0.917786i	$-0.370025\pi$
$991$	25.0000			0.794151			0.397076	+	0.917786i	$0.370025\pi$
$992$	−1.00000			−0.0317500
$993$	−22.5000	−	38.9711i	−0.714016	−	1.23671i
$994$	22.5000	−	7.79423i	0.713657	−	0.247218i
$995$	−3.00000	+	5.19615i	−0.0951064	+	0.164729i
$996$	3.00000	−	5.19615i	0.0950586	−	0.164646i
$997$	24.0000	−	13.8564i	0.760088	−	0.438837i	−0.0692396	−	0.997600i	$-0.522057\pi$
$997$	24.0000	−	13.8564i	0.760088	−	0.438837i	0.829327	+	0.558763i	$0.188724\pi$
$998$			32.9090i			1.04172i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bn.d.101.1	yes	2
3.2	odd	2		546.2.bn.a.101.1	yes	2
7.5	odd	6		546.2.bi.b.257.1	yes	2
13.4	even	6		546.2.bi.d.17.1	yes	2
21.5	even	6		546.2.bi.d.257.1	yes	2
39.17	odd	6		546.2.bi.b.17.1	✓	2
91.82	odd	6		546.2.bn.a.173.1	yes	2
273.173	even	6	inner	546.2.bn.d.173.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bi.b.17.1	✓	2	39.17	odd	6
546.2.bi.b.257.1	yes	2	7.5	odd	6
546.2.bi.d.17.1	yes	2	13.4	even	6
546.2.bi.d.257.1	yes	2	21.5	even	6
546.2.bn.a.101.1	yes	2	3.2	odd	2
546.2.bn.a.173.1	yes	2	91.82	odd	6
546.2.bn.d.101.1	yes	2	1.1	even	1	trivial
546.2.bn.d.173.1	yes	2	273.173	even	6	inner

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.bn (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(1.50000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.50000 - 0.866025i) q^{5} -1.73205i q^{6} +(0.500000 - 2.59808i) q^{7} -1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(1.50000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.50000 - 0.866025i) q^{5} -1.73205i q^{6} +(0.500000 - 2.59808i) q^{7} -1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} -1.73205i q^{10} -3.00000 q^{11} +(-1.50000 - 0.866025i) q^{12} +(1.00000 + 3.46410i) q^{13} +(-2.00000 - 1.73205i) q^{14} +(1.50000 - 2.59808i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.00000 + 5.19615i) q^{17} +(-1.50000 - 2.59808i) q^{18} -7.00000 q^{19} +(-1.50000 - 0.866025i) q^{20} +(-1.50000 - 4.33013i) q^{21} +(-1.50000 + 2.59808i) q^{22} +(3.00000 + 1.73205i) q^{23} +(-1.50000 + 0.866025i) q^{24} +(-1.00000 + 1.73205i) q^{25} +(3.50000 + 0.866025i) q^{26} -5.19615i q^{27} +(-2.50000 + 0.866025i) q^{28} +(7.50000 - 4.33013i) q^{29} +(-1.50000 - 2.59808i) q^{30} +(-0.500000 + 0.866025i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-4.50000 + 2.59808i) q^{33} +6.00000 q^{34} +(-1.50000 - 4.33013i) q^{35} -3.00000 q^{36} +(-3.50000 + 6.06218i) q^{38} +(4.50000 + 4.33013i) q^{39} +(-1.50000 + 0.866025i) q^{40} +(4.50000 - 2.59808i) q^{41} +(-4.50000 - 0.866025i) q^{42} +(-0.500000 + 0.866025i) q^{43} +(1.50000 + 2.59808i) q^{44} -5.19615i q^{45} +(3.00000 - 1.73205i) q^{46} +(-1.50000 + 0.866025i) q^{47} +1.73205i q^{48} +(-6.50000 - 2.59808i) q^{49} +(1.00000 + 1.73205i) q^{50} +(9.00000 + 5.19615i) q^{51} +(2.50000 - 2.59808i) q^{52} +(-1.50000 - 0.866025i) q^{53} +(-4.50000 - 2.59808i) q^{54} +(-4.50000 + 2.59808i) q^{55} +(-0.500000 + 2.59808i) q^{56} +(-10.5000 + 6.06218i) q^{57} -8.66025i q^{58} +(9.00000 - 5.19615i) q^{59} -3.00000 q^{60} -1.73205i q^{61} +(0.500000 + 0.866025i) q^{62} +(-6.00000 - 5.19615i) q^{63} +1.00000 q^{64} +(4.50000 + 4.33013i) q^{65} +5.19615i q^{66} +1.73205i q^{67} +(3.00000 - 5.19615i) q^{68} +6.00000 q^{69} +(-4.50000 - 0.866025i) q^{70} +(-4.50000 + 7.79423i) q^{71} +(-1.50000 + 2.59808i) q^{72} +(-6.50000 + 11.2583i) q^{73} +3.46410i q^{75} +(3.50000 + 6.06218i) q^{76} +(-1.50000 + 7.79423i) q^{77} +(6.00000 - 1.73205i) q^{78} +(-0.500000 - 0.866025i) q^{79} +1.73205i q^{80} +(-4.50000 - 7.79423i) q^{81} -5.19615i q^{82} +3.46410i q^{83} +(-3.00000 + 3.46410i) q^{84} +(9.00000 + 5.19615i) q^{85} +(0.500000 + 0.866025i) q^{86} +(7.50000 - 12.9904i) q^{87} +3.00000 q^{88} +(6.00000 + 3.46410i) q^{89} +(-4.50000 - 2.59808i) q^{90} +(9.50000 - 0.866025i) q^{91} -3.46410i q^{92} +1.73205i q^{93} +1.73205i q^{94} +(-10.5000 + 6.06218i) q^{95} +(1.50000 + 0.866025i) q^{96} +(9.50000 - 16.4545i) q^{97} +(-5.50000 + 4.33013i) q^{98} +(-4.50000 + 7.79423i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + 3 q^{3} - q^{4} + 3 q^{5} + q^{7} - 2 q^{8} + 3 q^{9}+O(q^{10}) \) 2 * q + q^2 + 3 * q^3 - q^4 + 3 * q^5 + q^7 - 2 * q^8 + 3 * q^9	\( 2 q + q^{2} + 3 q^{3} - q^{4} + 3 q^{5} + q^{7} - 2 q^{8} + 3 q^{9} - 6 q^{11} - 3 q^{12} + 2 q^{13} - 4 q^{14} + 3 q^{15} - q^{16} + 6 q^{17} - 3 q^{18} - 14 q^{19} - 3 q^{20} - 3 q^{21} - 3 q^{22} + 6 q^{23} - 3 q^{24} - 2 q^{25} + 7 q^{26} - 5 q^{28} + 15 q^{29} - 3 q^{30} - q^{31} + q^{32} - 9 q^{33} + 12 q^{34} - 3 q^{35} - 6 q^{36} - 7 q^{38} + 9 q^{39} - 3 q^{40} + 9 q^{41} - 9 q^{42} - q^{43} + 3 q^{44} + 6 q^{46} - 3 q^{47} - 13 q^{49} + 2 q^{50} + 18 q^{51} + 5 q^{52} - 3 q^{53} - 9 q^{54} - 9 q^{55} - q^{56} - 21 q^{57} + 18 q^{59} - 6 q^{60} + q^{62} - 12 q^{63} + 2 q^{64} + 9 q^{65} + 6 q^{68} + 12 q^{69} - 9 q^{70} - 9 q^{71} - 3 q^{72} - 13 q^{73} + 7 q^{76} - 3 q^{77} + 12 q^{78} - q^{79} - 9 q^{81} - 6 q^{84} + 18 q^{85} + q^{86} + 15 q^{87} + 6 q^{88} + 12 q^{89} - 9 q^{90} + 19 q^{91} - 21 q^{95} + 3 q^{96} + 19 q^{97} - 11 q^{98} - 9 q^{99}+O(q^{100}) \) 2 * q + q^2 + 3 * q^3 - q^4 + 3 * q^5 + q^7 - 2 * q^8 + 3 * q^9 - 6 * q^11 - 3 * q^12 + 2 * q^13 - 4 * q^14 + 3 * q^15 - q^16 + 6 * q^17 - 3 * q^18 - 14 * q^19 - 3 * q^20 - 3 * q^21 - 3 * q^22 + 6 * q^23 - 3 * q^24 - 2 * q^25 + 7 * q^26 - 5 * q^28 + 15 * q^29 - 3 * q^30 - q^31 + q^32 - 9 * q^33 + 12 * q^34 - 3 * q^35 - 6 * q^36 - 7 * q^38 + 9 * q^39 - 3 * q^40 + 9 * q^41 - 9 * q^42 - q^43 + 3 * q^44 + 6 * q^46 - 3 * q^47 - 13 * q^49 + 2 * q^50 + 18 * q^51 + 5 * q^52 - 3 * q^53 - 9 * q^54 - 9 * q^55 - q^56 - 21 * q^57 + 18 * q^59 - 6 * q^60 + q^62 - 12 * q^63 + 2 * q^64 + 9 * q^65 + 6 * q^68 + 12 * q^69 - 9 * q^70 - 9 * q^71 - 3 * q^72 - 13 * q^73 + 7 * q^76 - 3 * q^77 + 12 * q^78 - q^79 - 9 * q^81 - 6 * q^84 + 18 * q^85 + q^86 + 15 * q^87 + 6 * q^88 + 12 * q^89 - 9 * q^90 + 19 * q^91 - 21 * q^95 + 3 * q^96 + 19 * q^97 - 11 * q^98 - 9 * q^99

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