LMFDB - Embedded newform 546.2.bi.d.257.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(17,546)]

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, 1]))

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

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

chi := DirichletCharacter("546.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bi (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:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			257.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	546.257
Dual form			546.2.bi.d.17.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(-1.50000 + 0.866025i) q^{3} +1.00000 q^{4} +(-1.50000 - 0.866025i) q^{5} +(-1.50000 + 0.866025i) q^{6} +(-2.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(-1.50000 + 0.866025i) q^{3} +1.00000 q^{4} +(-1.50000 - 0.866025i) q^{5} +(-1.50000 + 0.866025i) q^{6} +(-2.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +(-1.50000 - 0.866025i) q^{10} +(-1.50000 + 2.59808i) q^{11} +(-1.50000 + 0.866025i) q^{12} +(-1.00000 - 3.46410i) q^{13} +(-2.00000 + 1.73205i) q^{14} +3.00000 q^{15} +1.00000 q^{16} -6.00000 q^{17} +(1.50000 - 2.59808i) q^{18} +(-3.50000 - 6.06218i) q^{19} +(-1.50000 - 0.866025i) q^{20} +(1.50000 - 4.33013i) q^{21} +(-1.50000 + 2.59808i) q^{22} +3.46410i q^{23} +(-1.50000 + 0.866025i) q^{24} +(-1.00000 - 1.73205i) q^{25} +(-1.00000 - 3.46410i) q^{26} +5.19615i q^{27} +(-2.00000 + 1.73205i) q^{28} +(-7.50000 + 4.33013i) q^{29} +3.00000 q^{30} +(0.500000 + 0.866025i) q^{31} +1.00000 q^{32} -5.19615i q^{33} -6.00000 q^{34} +(4.50000 - 0.866025i) q^{35} +(1.50000 - 2.59808i) 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} +(1.50000 - 4.33013i) q^{42} +(-0.500000 + 0.866025i) q^{43} +(-1.50000 + 2.59808i) q^{44} +(-4.50000 + 2.59808i) q^{45} +3.46410i q^{46} +(1.50000 + 0.866025i) q^{47} +(-1.50000 + 0.866025i) q^{48} +(1.00000 - 6.92820i) q^{49} +(-1.00000 - 1.73205i) q^{50} +(9.00000 - 5.19615i) q^{51} +(-1.00000 - 3.46410i) q^{52} +(-1.50000 + 0.866025i) q^{53} +5.19615i q^{54} +(4.50000 - 2.59808i) q^{55} +(-2.00000 + 1.73205i) q^{56} +(10.5000 + 6.06218i) q^{57} +(-7.50000 + 4.33013i) q^{58} +10.3923i q^{59} +3.00000 q^{60} +(1.50000 - 0.866025i) q^{61} +(0.500000 + 0.866025i) q^{62} +(1.50000 + 7.79423i) q^{63} +1.00000 q^{64} +(-1.50000 + 6.06218i) q^{65} -5.19615i q^{66} +(-1.50000 - 0.866025i) q^{67} -6.00000 q^{68} +(-3.00000 - 5.19615i) 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} +(3.00000 + 1.73205i) q^{75} +(-3.50000 - 6.06218i) q^{76} +(-1.50000 - 7.79423i) q^{77} +(4.50000 + 4.33013i) q^{78} +(-0.500000 + 0.866025i) q^{79} +(-1.50000 - 0.866025i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(4.50000 - 2.59808i) q^{82} +3.46410i q^{83} +(1.50000 - 4.33013i) q^{84} +(9.00000 + 5.19615i) q^{85} +(-0.500000 + 0.866025i) q^{86} +(7.50000 - 12.9904i) q^{87} +(-1.50000 + 2.59808i) q^{88} -6.92820i q^{89} +(-4.50000 + 2.59808i) q^{90} +(8.00000 + 5.19615i) q^{91} +3.46410i q^{92} +(-1.50000 - 0.866025i) q^{93} +(1.50000 + 0.866025i) q^{94} +12.1244i q^{95} +(-1.50000 + 0.866025i) q^{96} +(-9.50000 + 16.4545i) q^{97} +(1.00000 - 6.92820i) q^{98} +(4.50000 + 7.79423i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 3 q^{3} + 2 q^{4} - 3 q^{5} - 3 q^{6} - 4 q^{7} + 2 q^{8} + 3 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - 3 * q^3 + 2 * q^4 - 3 * q^5 - 3 * q^6 - 4 * q^7 + 2 * q^8 + 3 * q^9	$ 2 q + 2 q^{2} - 3 q^{3} + 2 q^{4} - 3 q^{5} - 3 q^{6} - 4 q^{7} + 2 q^{8} + 3 q^{9} - 3 q^{10} - 3 q^{11} - 3 q^{12} - 2 q^{13} - 4 q^{14} + 6 q^{15} + 2 q^{16} - 12 q^{17} + 3 q^{18} - 7 q^{19} - 3 q^{20} + 3 q^{21} - 3 q^{22} - 3 q^{24} - 2 q^{25} - 2 q^{26} - 4 q^{28} - 15 q^{29} + 6 q^{30} + q^{31} + 2 q^{32} - 12 q^{34} + 9 q^{35} + 3 q^{36} - 7 q^{38} + 9 q^{39} - 3 q^{40} + 9 q^{41} + 3 q^{42} - q^{43} - 3 q^{44} - 9 q^{45} + 3 q^{47} - 3 q^{48} + 2 q^{49} - 2 q^{50} + 18 q^{51} - 2 q^{52} - 3 q^{53} + 9 q^{55} - 4 q^{56} + 21 q^{57} - 15 q^{58} + 6 q^{60} + 3 q^{61} + q^{62} + 3 q^{63} + 2 q^{64} - 3 q^{65} - 3 q^{67} - 12 q^{68} - 6 q^{69} + 9 q^{70} + 9 q^{71} + 3 q^{72} + 13 q^{73} + 6 q^{75} - 7 q^{76} - 3 q^{77} + 9 q^{78} - q^{79} - 3 q^{80} - 9 q^{81} + 9 q^{82} + 3 q^{84} + 18 q^{85} - q^{86} + 15 q^{87} - 3 q^{88} - 9 q^{90} + 16 q^{91} - 3 q^{93} + 3 q^{94} - 3 q^{96} - 19 q^{97} + 2 q^{98} + 9 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 - 3 * q^3 + 2 * q^4 - 3 * q^5 - 3 * q^6 - 4 * q^7 + 2 * q^8 + 3 * q^9 - 3 * q^10 - 3 * q^11 - 3 * q^12 - 2 * q^13 - 4 * q^14 + 6 * q^15 + 2 * q^16 - 12 * q^17 + 3 * q^18 - 7 * q^19 - 3 * q^20 + 3 * q^21 - 3 * q^22 - 3 * q^24 - 2 * q^25 - 2 * q^26 - 4 * q^28 - 15 * q^29 + 6 * q^30 + q^31 + 2 * q^32 - 12 * q^34 + 9 * q^35 + 3 * q^36 - 7 * q^38 + 9 * q^39 - 3 * q^40 + 9 * q^41 + 3 * q^42 - q^43 - 3 * q^44 - 9 * q^45 + 3 * q^47 - 3 * q^48 + 2 * q^49 - 2 * q^50 + 18 * q^51 - 2 * q^52 - 3 * q^53 + 9 * q^55 - 4 * q^56 + 21 * q^57 - 15 * q^58 + 6 * q^60 + 3 * q^61 + q^62 + 3 * q^63 + 2 * q^64 - 3 * q^65 - 3 * q^67 - 12 * q^68 - 6 * q^69 + 9 * q^70 + 9 * q^71 + 3 * q^72 + 13 * q^73 + 6 * q^75 - 7 * q^76 - 3 * q^77 + 9 * q^78 - q^79 - 3 * q^80 - 9 * q^81 + 9 * q^82 + 3 * q^84 + 18 * q^85 - q^86 + 15 * q^87 - 3 * q^88 - 9 * q^90 + 16 * q^91 - 3 * q^93 + 3 * q^94 - 3 * q^96 - 19 * q^97 + 2 * q^98 + 9 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	−1.50000	+	0.866025i	−0.866025	+	0.500000i
$3$	−1.50000	+	0.866025i	−0.866025	+	0.500000i
$4$	1.00000			0.500000
$5$	−1.50000	−	0.866025i	−0.670820	−	0.387298i	0.125567	−	0.992085i	$-0.459925\pi$
$5$	−1.50000	−	0.866025i	−0.670820	−	0.387298i	−0.796387	+	0.604787i	$0.793258\pi$
$6$	−1.50000	+	0.866025i	−0.612372	+	0.353553i
$7$	−2.00000	+	1.73205i	−0.755929	+	0.654654i
$7$	−2.00000	+	1.73205i	−0.755929	+	0.654654i
$8$	1.00000			0.353553
$9$	1.50000	−	2.59808i	0.500000	−	0.866025i
$10$	−1.50000	−	0.866025i	−0.474342	−	0.273861i
$11$	−1.50000	+	2.59808i	−0.452267	+	0.783349i	−0.998526	−	0.0542666i	$-0.982718\pi$
$11$	−1.50000	+	2.59808i	−0.452267	+	0.783349i	0.546259	+	0.837616i	$0.316051\pi$
$12$	−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
$15$	3.00000			0.774597
$16$	1.00000			0.250000
$17$	−6.00000			−1.45521			−0.727607	−	0.685994i	$-0.759367\pi$
$17$	−6.00000			−1.45521			−0.727607	+	0.685994i	$0.759367\pi$
$18$	1.50000	−	2.59808i	0.353553	−	0.612372i
$19$	−3.50000	−	6.06218i	−0.802955	−	1.39076i	−0.917663	−	0.397360i	$-0.869927\pi$
$19$	−3.50000	−	6.06218i	−0.802955	−	1.39076i	0.114708	−	0.993399i	$-0.463407\pi$
$20$	−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
$23$			3.46410i			0.722315i	0.932505	+	0.361158i	$0.117618\pi$
$23$			3.46410i			0.722315i	−0.932505	+	0.361158i	$0.882382\pi$
$24$	−1.50000	+	0.866025i	−0.306186	+	0.176777i
$25$	−1.00000	−	1.73205i	−0.200000	−	0.346410i
$26$	−1.00000	−	3.46410i	−0.196116	−	0.679366i
$27$			5.19615i			1.00000i
$28$	−2.00000	+	1.73205i	−0.377964	+	0.327327i
$29$	−7.50000	+	4.33013i	−1.39272	+	0.804084i	−0.993615	−	0.112823i	$-0.964011\pi$
$29$	−7.50000	+	4.33013i	−1.39272	+	0.804084i	−0.399100	+	0.916907i	$0.630677\pi$
$30$	3.00000			0.547723
$31$	0.500000	+	0.866025i	0.0898027	+	0.155543i	0.907428	−	0.420208i	$-0.138043\pi$
$31$	0.500000	+	0.866025i	0.0898027	+	0.155543i	−0.817625	+	0.575751i	$0.804710\pi$
$32$	1.00000			0.176777
$33$		−	5.19615i		−	0.904534i
$34$	−6.00000			−1.02899
$35$	4.50000	−	0.866025i	0.760639	−	0.146385i
$36$	1.50000	−	2.59808i	0.250000	−	0.433013i
$37$		0			0		1.00000			$0$
$37$		0			0		−1.00000			$\pi$
$38$	−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	$0.200343\pi$
$42$	1.50000	−	4.33013i	0.231455	−	0.668153i
$43$	−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
$45$	−4.50000	+	2.59808i	−0.670820	+	0.387298i
$46$			3.46410i			0.510754i
$47$	1.50000	+	0.866025i	0.218797	+	0.126323i	0.605393	−	0.795926i	$-0.293016\pi$
$47$	1.50000	+	0.866025i	0.218797	+	0.126323i	−0.386596	+	0.922249i	$0.626349\pi$
$48$	−1.50000	+	0.866025i	−0.216506	+	0.125000i
$49$	1.00000	−	6.92820i	0.142857	−	0.989743i
$50$	−1.00000	−	1.73205i	−0.141421	−	0.244949i
$51$	9.00000	−	5.19615i	1.26025	−	0.727607i
$52$	−1.00000	−	3.46410i	−0.138675	−	0.480384i
$53$	−1.50000	+	0.866025i	−0.206041	+	0.118958i	−0.599470	−	0.800397i	$-0.704622\pi$
$53$	−1.50000	+	0.866025i	−0.206041	+	0.118958i	0.393429	+	0.919355i	$0.371289\pi$
$54$			5.19615i			0.707107i
$55$	4.50000	−	2.59808i	0.606780	−	0.350325i
$56$	−2.00000	+	1.73205i	−0.267261	+	0.231455i
$57$	10.5000	+	6.06218i	1.39076	+	0.802955i
$58$	−7.50000	+	4.33013i	−0.984798	+	0.568574i
$59$			10.3923i			1.35296i	0.736460	+	0.676481i	$0.236496\pi$
$59$			10.3923i			1.35296i	−0.736460	+	0.676481i	$0.763504\pi$
$60$	3.00000			0.387298
$61$	1.50000	−	0.866025i	0.192055	−	0.110883i	−0.400889	−	0.916127i	$-0.631299\pi$
$61$	1.50000	−	0.866025i	0.192055	−	0.110883i	0.592944	+	0.805243i	$0.297965\pi$
$62$	0.500000	+	0.866025i	0.0635001	+	0.109985i
$63$	1.50000	+	7.79423i	0.188982	+	0.981981i
$64$	1.00000			0.125000
$65$	−1.50000	+	6.06218i	−0.186052	+	0.751921i
$66$		−	5.19615i		−	0.639602i
$67$	−1.50000	−	0.866025i	−0.183254	−	0.105802i	0.405567	−	0.914066i	$-0.367074\pi$
$67$	−1.50000	−	0.866025i	−0.183254	−	0.105802i	−0.588821	+	0.808264i	$0.700408\pi$
$68$	−6.00000			−0.727607
$69$	−3.00000	−	5.19615i	−0.361158	−	0.625543i
$70$	4.50000	−	0.866025i	0.537853	−	0.103510i
$71$	4.50000	−	7.79423i	0.534052	−	0.925005i	−0.465157	−	0.885228i	$-0.654002\pi$
$71$	4.50000	−	7.79423i	0.534052	−	0.925005i	0.999209	−	0.0397765i	$-0.0126646\pi$
$72$	1.50000	−	2.59808i	0.176777	−	0.306186i
$73$	6.50000	+	11.2583i	0.760767	+	1.31769i	0.942455	+	0.334332i	$0.108511\pi$
$73$	6.50000	+	11.2583i	0.760767	+	1.31769i	−0.181688	+	0.983356i	$0.558156\pi$
$74$		0			0
$75$	3.00000	+	1.73205i	0.346410	+	0.200000i
$76$	−3.50000	−	6.06218i	−0.401478	−	0.695379i
$77$	−1.50000	−	7.79423i	−0.170941	−	0.888235i
$78$	4.50000	+	4.33013i	0.509525	+	0.490290i
$79$	−0.500000	+	0.866025i	−0.0562544	+	0.0974355i	−0.892781	−	0.450490i	$-0.851249\pi$
$79$	−0.500000	+	0.866025i	−0.0562544	+	0.0974355i	0.836527	+	0.547926i	$0.184582\pi$
$80$	−1.50000	−	0.866025i	−0.167705	−	0.0968246i
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$	4.50000	−	2.59808i	0.496942	−	0.286910i
$83$			3.46410i			0.380235i	0.981761	+	0.190117i	$0.0608868\pi$
$83$			3.46410i			0.380235i	−0.981761	+	0.190117i	$0.939113\pi$
$84$	1.50000	−	4.33013i	0.163663	−	0.472456i
$85$	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
$88$	−1.50000	+	2.59808i	−0.159901	+	0.276956i
$89$		−	6.92820i		−	0.734388i	−0.930144	−	0.367194i	$-0.880318\pi$
$89$		−	6.92820i		−	0.734388i	0.930144	−	0.367194i	$-0.119682\pi$
$90$	−4.50000	+	2.59808i	−0.474342	+	0.273861i
$91$	8.00000	+	5.19615i	0.838628	+	0.544705i
$92$			3.46410i			0.361158i
$93$	−1.50000	−	0.866025i	−0.155543	−	0.0898027i
$94$	1.50000	+	0.866025i	0.154713	+	0.0893237i
$95$			12.1244i			1.24393i
$96$	−1.50000	+	0.866025i	−0.153093	+	0.0883883i
$97$	−9.50000	+	16.4545i	−0.964579	+	1.67070i	−0.253837	+	0.967247i	$0.581693\pi$
$97$	−9.50000	+	16.4545i	−0.964579	+	1.67070i	−0.710742	+	0.703452i	$0.751641\pi$
$98$	1.00000	−	6.92820i	0.101015	−	0.699854i
$99$	4.50000	+	7.79423i	0.452267	+	0.783349i
$100$	−1.00000	−	1.73205i	−0.100000	−	0.173205i
$101$	−4.50000	+	7.79423i	−0.447767	+	0.775555i	−0.998240	−	0.0592978i	$-0.981114\pi$
$101$	−4.50000	+	7.79423i	−0.447767	+	0.775555i	0.550474	+	0.834853i	$0.314447\pi$
$102$	9.00000	−	5.19615i	0.891133	−	0.514496i
$103$	−7.50000	−	4.33013i	−0.738997	−	0.426660i	0.0827075	−	0.996574i	$-0.473643\pi$
$103$	−7.50000	−	4.33013i	−0.738997	−	0.426660i	−0.821705	+	0.569914i	$0.806977\pi$
$104$	−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
$107$		−	10.3923i		−	1.00466i	−0.864675	−	0.502331i	$-0.832476\pi$
$107$		−	10.3923i		−	1.00466i	0.864675	−	0.502331i	$-0.167524\pi$
$108$			5.19615i			0.500000i
$109$	7.50000	−	4.33013i	0.718370	−	0.414751i	−0.0957826	−	0.995402i	$-0.530535\pi$
$109$	7.50000	−	4.33013i	0.718370	−	0.414751i	0.814152	+	0.580651i	$0.197202\pi$
$110$	4.50000	−	2.59808i	0.429058	−	0.247717i
$111$		0			0
$112$	−2.00000	+	1.73205i	−0.188982	+	0.163663i
$113$	−1.50000	−	0.866025i	−0.141108	−	0.0814688i	0.427784	−	0.903881i	$-0.359294\pi$
$113$	−1.50000	−	0.866025i	−0.141108	−	0.0814688i	−0.568892	+	0.822412i	$0.692628\pi$
$114$	10.5000	+	6.06218i	0.983415	+	0.567775i
$115$	3.00000	−	5.19615i	0.279751	−	0.484544i
$116$	−7.50000	+	4.33013i	−0.696358	+	0.402042i
$117$	−10.5000	−	2.59808i	−0.970725	−	0.240192i
$118$			10.3923i			0.956689i
$119$	12.0000	−	10.3923i	1.10004	−	0.952661i
$120$	3.00000			0.273861
$121$	1.00000	+	1.73205i	0.0909091	+	0.157459i
$122$	1.50000	−	0.866025i	0.135804	−	0.0784063i
$123$	−4.50000	+	7.79423i	−0.405751	+	0.702782i
$124$	0.500000	+	0.866025i	0.0449013	+	0.0777714i
$125$			12.1244i			1.08444i
$126$	1.50000	+	7.79423i	0.133631	+	0.694365i
$127$	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	$0.561333\pi$
$128$	1.00000			0.0883883
$129$		−	1.73205i		−	0.152499i
$130$	−1.50000	+	6.06218i	−0.131559	+	0.531688i
$131$	−1.50000	+	2.59808i	−0.131056	+	0.226995i	−0.924084	−	0.382190i	$-0.875170\pi$
$131$	−1.50000	+	2.59808i	−0.131056	+	0.226995i	0.793028	+	0.609185i	$0.208503\pi$
$132$		−	5.19615i		−	0.452267i
$133$	17.5000	+	6.06218i	1.51744	+	0.525657i
$134$	−1.50000	−	0.866025i	−0.129580	−	0.0748132i
$135$	4.50000	−	7.79423i	0.387298	−	0.670820i
$136$	−6.00000			−0.514496
$137$	6.00000			0.512615			0.256307	−	0.966595i	$-0.417494\pi$
$137$	6.00000			0.512615			0.256307	+	0.966595i	$0.417494\pi$
$138$	−3.00000	−	5.19615i	−0.255377	−	0.442326i
$139$	−19.5000	−	11.2583i	−1.65397	−	0.954919i	−0.975417	−	0.220366i	$-0.929275\pi$
$139$	−19.5000	−	11.2583i	−1.65397	−	0.954919i	−0.678551	−	0.734553i	$-0.737392\pi$
$140$	4.50000	−	0.866025i	0.380319	−	0.0731925i
$141$	−3.00000			−0.252646
$142$	4.50000	−	7.79423i	0.377632	−	0.654077i
$143$	10.5000	+	2.59808i	0.878054	+	0.217262i
$144$	1.50000	−	2.59808i	0.125000	−	0.216506i
$145$	15.0000			1.24568
$146$	6.50000	+	11.2583i	0.537944	+	0.931746i
$147$	4.50000	+	11.2583i	0.371154	+	0.928571i
$148$		0			0
$149$	−10.5000	−	18.1865i	−0.860194	−	1.48990i	−0.871742	−	0.489966i	$-0.837009\pi$
$149$	−10.5000	−	18.1865i	−0.860194	−	1.48990i	0.0115483	−	0.999933i	$-0.496324\pi$
$150$	3.00000	+	1.73205i	0.244949	+	0.141421i
$151$	19.5000	−	11.2583i	1.58689	−	0.916190i	0.593072	−	0.805150i	$-0.297915\pi$
$151$	19.5000	−	11.2583i	1.58689	−	0.916190i	0.993816	−	0.111040i	$-0.0354182\pi$
$152$	−3.50000	−	6.06218i	−0.283887	−	0.491708i
$153$	−9.00000	+	15.5885i	−0.727607	+	1.26025i
$154$	−1.50000	−	7.79423i	−0.120873	−	0.628077i
$155$		−	1.73205i		−	0.139122i
$156$	4.50000	+	4.33013i	0.360288	+	0.346688i
$157$	1.50000	−	0.866025i	0.119713	−	0.0691164i	−0.438948	−	0.898513i	$-0.644649\pi$
$157$	1.50000	−	0.866025i	0.119713	−	0.0691164i	0.558661	+	0.829396i	$0.311315\pi$
$158$	−0.500000	+	0.866025i	−0.0397779	+	0.0688973i
$159$	1.50000	−	2.59808i	0.118958	−	0.206041i
$160$	−1.50000	−	0.866025i	−0.118585	−	0.0684653i
$161$	−6.00000	−	6.92820i	−0.472866	−	0.546019i
$162$	−4.50000	−	7.79423i	−0.353553	−	0.612372i
$163$	−4.50000	+	2.59808i	−0.352467	+	0.203497i	−0.665771	−	0.746156i	$-0.731897\pi$
$163$	−4.50000	+	2.59808i	−0.352467	+	0.203497i	0.313304	+	0.949653i	$0.398564\pi$
$164$	4.50000	−	2.59808i	0.351391	−	0.202876i
$165$	−4.50000	+	7.79423i	−0.350325	+	0.606780i
$166$			3.46410i			0.268866i
$167$	−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
$171$	−21.0000			−1.60591
$172$	−0.500000	+	0.866025i	−0.0381246	+	0.0660338i
$173$	−4.50000	−	7.79423i	−0.342129	−	0.592584i	0.642699	−	0.766119i	$-0.277815\pi$
$173$	−4.50000	−	7.79423i	−0.342129	−	0.592584i	−0.984828	+	0.173534i	$0.944481\pi$
$174$	7.50000	−	12.9904i	0.568574	−	0.984798i
$175$	5.00000	+	1.73205i	0.377964	+	0.130931i
$176$	−1.50000	+	2.59808i	−0.113067	+	0.195837i
$177$	−9.00000	−	15.5885i	−0.676481	−	1.17170i
$178$		−	6.92820i		−	0.519291i
$179$	−16.5000	−	9.52628i	−1.23327	−	0.712028i	−0.265558	−	0.964095i	$-0.585556\pi$
$179$	−16.5000	−	9.52628i	−1.23327	−	0.712028i	−0.967710	+	0.252067i	$0.918890\pi$
$180$	−4.50000	+	2.59808i	−0.335410	+	0.193649i
$181$		−	13.8564i		−	1.02994i	−0.857209	−	0.514969i	$-0.827803\pi$
$181$		−	13.8564i		−	1.02994i	0.857209	−	0.514969i	$-0.172197\pi$
$182$	8.00000	+	5.19615i	0.592999	+	0.385164i
$183$	−1.50000	+	2.59808i	−0.110883	+	0.192055i
$184$			3.46410i			0.255377i
$185$		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
$189$	−9.00000	−	10.3923i	−0.654654	−	0.755929i
$190$			12.1244i			0.879593i
$191$	−13.5000	+	7.79423i	−0.976826	+	0.563971i	−0.901310	−	0.433174i	$-0.857394\pi$
$191$	−13.5000	+	7.79423i	−0.976826	+	0.563971i	−0.0755154	+	0.997145i	$0.524060\pi$
$192$	−1.50000	+	0.866025i	−0.108253	+	0.0625000i
$193$	−10.5000	−	6.06218i	−0.755807	−	0.436365i	0.0719816	−	0.997406i	$-0.477068\pi$
$193$	−10.5000	−	6.06218i	−0.755807	−	0.436365i	−0.827788	+	0.561041i	$0.810401\pi$
$194$	−9.50000	+	16.4545i	−0.682060	+	1.18136i
$195$	−3.00000	−	10.3923i	−0.214834	−	0.744208i
$196$	1.00000	−	6.92820i	0.0714286	−	0.494872i
$197$	−10.5000	−	18.1865i	−0.748094	−	1.29574i	−0.948735	−	0.316072i	$-0.897636\pi$
$197$	−10.5000	−	18.1865i	−0.748094	−	1.29574i	0.200641	−	0.979665i	$-0.435697\pi$
$198$	4.50000	+	7.79423i	0.319801	+	0.553912i
$199$			3.46410i			0.245564i	0.992434	+	0.122782i	$0.0391815\pi$
$199$			3.46410i			0.245564i	−0.992434	+	0.122782i	$0.960818\pi$
$200$	−1.00000	−	1.73205i	−0.0707107	−	0.122474i
$201$	3.00000			0.211604
$202$	−4.50000	+	7.79423i	−0.316619	+	0.548400i
$203$	7.50000	−	21.6506i	0.526397	−	1.51958i
$204$	9.00000	−	5.19615i	0.630126	−	0.363803i
$205$	−9.00000			−0.628587
$206$	−7.50000	−	4.33013i	−0.522550	−	0.301694i
$207$	9.00000	+	5.19615i	0.625543	+	0.361158i
$208$	−1.00000	−	3.46410i	−0.0693375	−	0.240192i
$209$	21.0000			1.45260
$210$	−6.00000	+	5.19615i	−0.414039	+	0.358569i
$211$	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	$0.822374\pi$
$212$	−1.50000	+	0.866025i	−0.103020	+	0.0594789i
$213$			15.5885i			1.06810i
$214$		−	10.3923i		−	0.710403i
$215$	1.50000	−	0.866025i	0.102299	−	0.0590624i
$216$			5.19615i			0.353553i
$217$	−2.50000	−	0.866025i	−0.169711	−	0.0587896i
$218$	7.50000	−	4.33013i	0.507964	−	0.293273i
$219$	−19.5000	−	11.2583i	−1.31769	−	0.760767i
$220$	4.50000	−	2.59808i	0.303390	−	0.175162i
$221$	6.00000	+	20.7846i	0.403604	+	1.39812i
$222$		0			0
$223$	14.5000	+	25.1147i	0.970992	+	1.68181i	0.692574	+	0.721347i	$0.256477\pi$
$223$	14.5000	+	25.1147i	0.970992	+	1.68181i	0.278418	+	0.960460i	$0.410190\pi$
$224$	−2.00000	+	1.73205i	−0.133631	+	0.115728i
$225$	−6.00000			−0.400000
$226$	−1.50000	−	0.866025i	−0.0997785	−	0.0576072i
$227$			10.3923i			0.689761i	0.938647	+	0.344881i	$0.112081\pi$
$227$			10.3923i			0.689761i	−0.938647	+	0.344881i	$0.887919\pi$
$228$	10.5000	+	6.06218i	0.695379	+	0.401478i
$229$	12.5000	−	21.6506i	0.826023	−	1.43071i	−0.0751115	−	0.997175i	$-0.523931\pi$
$229$	12.5000	−	21.6506i	0.826023	−	1.43071i	0.901135	−	0.433539i	$-0.142735\pi$
$230$	3.00000	−	5.19615i	0.197814	−	0.342624i
$231$	9.00000	+	10.3923i	0.592157	+	0.683763i
$232$	−7.50000	+	4.33013i	−0.492399	+	0.284287i
$233$	−19.5000	−	11.2583i	−1.27749	−	0.737558i	−0.301102	−	0.953592i	$-0.597354\pi$
$233$	−19.5000	−	11.2583i	−1.27749	−	0.737558i	−0.976386	+	0.216034i	$0.930688\pi$
$234$	−10.5000	−	2.59808i	−0.686406	−	0.169842i
$235$	−1.50000	−	2.59808i	−0.0978492	−	0.169480i
$236$			10.3923i			0.676481i
$237$		−	1.73205i		−	0.112509i
$238$	12.0000	−	10.3923i	0.777844	−	0.673633i
$239$	12.0000			0.776215			0.388108	−	0.921614i	$-0.373129\pi$
$239$	12.0000			0.776215			0.388108	+	0.921614i	$0.373129\pi$
$240$	3.00000			0.193649
$241$	−10.0000			−0.644157			−0.322078	−	0.946713i	$-0.604381\pi$
$241$	−10.0000			−0.644157			−0.322078	+	0.946713i	$0.604381\pi$
$242$	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
$245$	−7.50000	+	9.52628i	−0.479157	+	0.608612i
$246$	−4.50000	+	7.79423i	−0.286910	+	0.496942i
$247$	−17.5000	+	18.1865i	−1.11350	+	1.15718i
$248$	0.500000	+	0.866025i	0.0317500	+	0.0549927i
$249$	−3.00000	−	5.19615i	−0.190117	−	0.329293i
$250$			12.1244i			0.766812i
$251$	−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
$254$	8.50000	+	14.7224i	0.533337	+	0.923768i
$255$	−18.0000			−1.12720
$256$	1.00000			0.0625000
$257$	−6.00000			−0.374270			−0.187135	−	0.982334i	$-0.559920\pi$
$257$	−6.00000			−0.374270			−0.187135	+	0.982334i	$0.559920\pi$
$258$		−	1.73205i		−	0.107833i
$259$		0			0
$260$	−1.50000	+	6.06218i	−0.0930261	+	0.375960i
$261$			25.9808i			1.60817i
$262$	−1.50000	+	2.59808i	−0.0926703	+	0.160510i
$263$	7.50000	+	4.33013i	0.462470	+	0.267007i	0.713082	−	0.701080i	$-0.247299\pi$
$263$	7.50000	+	4.33013i	0.462470	+	0.267007i	−0.250612	+	0.968088i	$0.580632\pi$
$264$		−	5.19615i		−	0.319801i
$265$	3.00000			0.184289
$266$	17.5000	+	6.06218i	1.07299	+	0.371696i
$267$	6.00000	+	10.3923i	0.367194	+	0.635999i
$268$	−1.50000	−	0.866025i	−0.0916271	−	0.0529009i
$269$	30.0000			1.82913			0.914566	−	0.404436i	$-0.132532\pi$
$269$	30.0000			1.82913			0.914566	+	0.404436i	$0.132532\pi$
$270$	4.50000	−	7.79423i	0.273861	−	0.474342i
$271$	16.0000			0.971931			0.485965	−	0.873978i	$-0.338468\pi$
$271$	16.0000			0.971931			0.485965	+	0.873978i	$0.338468\pi$
$272$	−6.00000			−0.363803
$273$	−16.5000	−	0.866025i	−0.998625	−	0.0524142i
$274$	6.00000			0.362473
$275$	6.00000			0.361814
$276$	−3.00000	−	5.19615i	−0.180579	−	0.312772i
$277$	−10.0000			−0.600842			−0.300421	−	0.953807i	$-0.597127\pi$
$277$	−10.0000			−0.600842			−0.300421	+	0.953807i	$0.597127\pi$
$278$	−19.5000	−	11.2583i	−1.16953	−	0.675230i
$279$	3.00000			0.179605
$280$	4.50000	−	0.866025i	0.268926	−	0.0517549i
$281$	−6.00000			−0.357930			−0.178965	−	0.983855i	$-0.557275\pi$
$281$	−6.00000			−0.357930			−0.178965	+	0.983855i	$0.557275\pi$
$282$	−3.00000			−0.178647
$283$	−19.5000	−	11.2583i	−1.15915	−	0.669238i	−0.208053	−	0.978117i	$-0.566713\pi$
$283$	−19.5000	−	11.2583i	−1.15915	−	0.669238i	−0.951101	+	0.308879i	$0.900046\pi$
$284$	4.50000	−	7.79423i	0.267026	−	0.462502i
$285$	−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
$288$	1.50000	−	2.59808i	0.0883883	−	0.153093i
$289$	19.0000			1.11765
$290$	15.0000			0.880830
$291$		−	32.9090i		−	1.92916i
$292$	6.50000	+	11.2583i	0.380384	+	0.658844i
$293$	−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
$297$	−13.5000	−	7.79423i	−0.783349	−	0.452267i
$298$	−10.5000	−	18.1865i	−0.608249	−	1.05352i
$299$	12.0000	−	3.46410i	0.693978	−	0.200334i
$300$	3.00000	+	1.73205i	0.173205	+	0.100000i
$301$	−0.500000	−	2.59808i	−0.0288195	−	0.149751i
$302$	19.5000	−	11.2583i	1.12210	−	0.647844i
$303$		−	15.5885i		−	0.895533i
$304$	−3.50000	−	6.06218i	−0.200739	−	0.347690i
$305$	−3.00000			−0.171780
$306$	−9.00000	+	15.5885i	−0.514496	+	0.891133i
$307$	−4.00000			−0.228292			−0.114146	−	0.993464i	$-0.536413\pi$
$307$	−4.00000			−0.228292			−0.114146	+	0.993464i	$0.536413\pi$
$308$	−1.50000	−	7.79423i	−0.0854704	−	0.444117i
$309$	15.0000			0.853320
$310$		−	1.73205i		−	0.0983739i
$311$	1.50000	+	2.59808i	0.0850572	+	0.147323i	0.905416	−	0.424526i	$-0.139559\pi$
$311$	1.50000	+	2.59808i	0.0850572	+	0.147323i	−0.820358	+	0.571850i	$0.806226\pi$
$312$	4.50000	+	4.33013i	0.254762	+	0.245145i
$313$	−4.50000	−	2.59808i	−0.254355	−	0.146852i	0.367402	−	0.930062i	$-0.380247\pi$
$313$	−4.50000	−	2.59808i	−0.254355	−	0.146852i	−0.621757	+	0.783210i	$0.713581\pi$
$314$	1.50000	−	0.866025i	0.0846499	−	0.0488726i
$315$	4.50000	−	12.9904i	0.253546	−	0.731925i
$316$	−0.500000	+	0.866025i	−0.0281272	+	0.0487177i
$317$	1.50000	−	2.59808i	0.0842484	−	0.145922i	−0.820822	−	0.571184i	$-0.806484\pi$
$317$	1.50000	−	2.59808i	0.0842484	−	0.145922i	0.905071	+	0.425261i	$0.139818\pi$
$318$	1.50000	−	2.59808i	0.0841158	−	0.145693i
$319$		−	25.9808i		−	1.45464i
$320$	−1.50000	−	0.866025i	−0.0838525	−	0.0484123i
$321$	9.00000	+	15.5885i	0.502331	+	0.870063i
$322$	−6.00000	−	6.92820i	−0.334367	−	0.386094i
$323$	21.0000	+	36.3731i	1.16847	+	2.02385i
$324$	−4.50000	−	7.79423i	−0.250000	−	0.433013i
$325$	−5.00000	+	5.19615i	−0.277350	+	0.288231i
$326$	−4.50000	+	2.59808i	−0.249232	+	0.143894i
$327$	−7.50000	+	12.9904i	−0.414751	+	0.718370i
$328$	4.50000	−	2.59808i	0.248471	−	0.143455i
$329$	−4.50000	+	0.866025i	−0.248093	+	0.0477455i
$330$	−4.50000	+	7.79423i	−0.247717	+	0.429058i
$331$	−22.5000	+	12.9904i	−1.23671	+	0.714016i	−0.968421	−	0.249322i	$-0.919792\pi$
$331$	−22.5000	+	12.9904i	−1.23671	+	0.714016i	−0.268291	+	0.963338i	$0.586459\pi$
$332$			3.46410i			0.190117i
$333$		0			0
$334$	−7.50000	+	4.33013i	−0.410382	+	0.236934i
$335$	1.50000	+	2.59808i	0.0819538	+	0.141948i
$336$	1.50000	−	4.33013i	0.0818317	−	0.236228i
$337$	−10.0000			−0.544735			−0.272367	−	0.962193i	$-0.587807\pi$
$337$	−10.0000			−0.544735			−0.272367	+	0.962193i	$0.587807\pi$
$338$	−11.0000	+	6.92820i	−0.598321	+	0.376845i
$339$	3.00000			0.162938
$340$	9.00000	+	5.19615i	0.488094	+	0.281801i
$341$	−3.00000			−0.162459
$342$	−21.0000			−1.13555
$343$	10.0000	+	15.5885i	0.539949	+	0.841698i
$344$	−0.500000	+	0.866025i	−0.0269582	+	0.0466930i
$345$			10.3923i			0.559503i
$346$	−4.50000	−	7.79423i	−0.241921	−	0.419020i
$347$		−	10.3923i		−	0.557888i	−0.960307	−	0.278944i	$-0.910016\pi$
$347$		−	10.3923i		−	0.557888i	0.960307	−	0.278944i	$-0.0899844\pi$
$348$	7.50000	−	12.9904i	0.402042	−	0.696358i
$349$	−17.5000	−	30.3109i	−0.936754	−	1.62250i	−0.771477	−	0.636257i	$-0.780482\pi$
$349$	−17.5000	−	30.3109i	−0.936754	−	1.62250i	−0.165277	−	0.986247i	$-0.552852\pi$
$350$	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
$353$	22.5000	+	12.9904i	1.19755	+	0.691408i	0.960009	−	0.279968i	$-0.0903240\pi$
$353$	22.5000	+	12.9904i	1.19755	+	0.691408i	0.237545	+	0.971377i	$0.423657\pi$
$354$	−9.00000	−	15.5885i	−0.478345	−	0.828517i
$355$	−13.5000	+	7.79423i	−0.716506	+	0.413675i
$356$		−	6.92820i		−	0.367194i
$357$	−9.00000	+	25.9808i	−0.476331	+	1.37505i
$358$	−16.5000	−	9.52628i	−0.872052	−	0.503480i
$359$	−1.50000	+	2.59808i	−0.0791670	+	0.137121i	−0.902891	−	0.429870i	$-0.858559\pi$
$359$	−1.50000	+	2.59808i	−0.0791670	+	0.137121i	0.823724	+	0.566991i	$0.191893\pi$
$360$	−4.50000	+	2.59808i	−0.237171	+	0.136931i
$361$	−15.0000	+	25.9808i	−0.789474	+	1.36741i
$362$		−	13.8564i		−	0.728277i
$363$	−3.00000	−	1.73205i	−0.157459	−	0.0909091i
$364$	8.00000	+	5.19615i	0.419314	+	0.272352i
$365$		−	22.5167i		−	1.17858i
$366$	−1.50000	+	2.59808i	−0.0784063	+	0.135804i
$367$	−13.5000	−	7.79423i	−0.704694	−	0.406855i	0.104399	−	0.994535i	$-0.466708\pi$
$367$	−13.5000	−	7.79423i	−0.704694	−	0.406855i	−0.809093	+	0.587680i	$0.800041\pi$
$368$			3.46410i			0.180579i
$369$		−	15.5885i		−	0.811503i
$370$		0			0
$371$	1.50000	−	4.33013i	0.0778761	−	0.224809i
$372$	−1.50000	−	0.866025i	−0.0777714	−	0.0449013i
$373$	14.5000	+	25.1147i	0.750782	+	1.30039i	0.947444	+	0.319921i	$0.103656\pi$
$373$	14.5000	+	25.1147i	0.750782	+	1.30039i	−0.196663	+	0.980471i	$0.563010\pi$
$374$	9.00000	−	15.5885i	0.465379	−	0.806060i
$375$	−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	$0.496093\pi$
$380$			12.1244i			0.621966i
$381$	−25.5000	−	14.7224i	−1.30640	−	0.754253i
$382$	−13.5000	+	7.79423i	−0.690720	+	0.398787i
$383$	4.50000	−	2.59808i	0.229939	−	0.132755i	−0.380605	−	0.924738i	$-0.624284\pi$
$383$	4.50000	−	2.59808i	0.229939	−	0.132755i	0.610544	+	0.791982i	$0.290951\pi$
$384$	−1.50000	+	0.866025i	−0.0765466	+	0.0441942i
$385$	−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
$388$	−9.50000	+	16.4545i	−0.482289	+	0.835350i
$389$	4.50000	−	2.59808i	0.228159	−	0.131728i	−0.381563	−	0.924343i	$-0.624614\pi$
$389$	4.50000	−	2.59808i	0.228159	−	0.131728i	0.609722	+	0.792615i	$0.291281\pi$
$390$	−3.00000	−	10.3923i	−0.151911	−	0.526235i
$391$		−	20.7846i		−	1.05112i
$392$	1.00000	−	6.92820i	0.0505076	−	0.349927i
$393$		−	5.19615i		−	0.262111i
$394$	−10.5000	−	18.1865i	−0.528982	−	0.916224i
$395$	1.50000	−	0.866025i	0.0754732	−	0.0435745i
$396$	4.50000	+	7.79423i	0.226134	+	0.391675i
$397$	14.5000	+	25.1147i	0.727734	+	1.26047i	0.957839	+	0.287307i	$0.0927599\pi$
$397$	14.5000	+	25.1147i	0.727734	+	1.26047i	−0.230105	+	0.973166i	$0.573907\pi$
$398$			3.46410i			0.173640i
$399$	−31.5000	+	6.06218i	−1.57697	+	0.303488i
$400$	−1.00000	−	1.73205i	−0.0500000	−	0.0866025i
$401$	18.0000			0.898877			0.449439	−	0.893311i	$-0.351624\pi$
$401$	18.0000			0.898877			0.449439	+	0.893311i	$0.351624\pi$
$402$	3.00000			0.149626
$403$	2.50000	−	2.59808i	0.124534	−	0.129419i
$404$	−4.50000	+	7.79423i	−0.223883	+	0.387777i
$405$			15.5885i			0.774597i
$406$	7.50000	−	21.6506i	0.372219	−	1.07450i
$407$		0			0
$408$	9.00000	−	5.19615i	0.445566	−	0.257248i
$409$	22.0000			1.08783			0.543915	−	0.839140i	$-0.316941\pi$
$409$	22.0000			1.08783			0.543915	+	0.839140i	$0.316941\pi$
$410$	−9.00000			−0.444478
$411$	−9.00000	+	5.19615i	−0.443937	+	0.256307i
$412$	−7.50000	−	4.33013i	−0.369498	−	0.213330i
$413$	−18.0000	−	20.7846i	−0.885722	−	1.02274i
$414$	9.00000	+	5.19615i	0.442326	+	0.255377i
$415$	3.00000	−	5.19615i	0.147264	−	0.255069i
$416$	−1.00000	−	3.46410i	−0.0490290	−	0.169842i
$417$	39.0000			1.90984
$418$	21.0000			1.02714
$419$	−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	$-0.465080\pi$
$420$	−6.00000	+	5.19615i	−0.292770	+	0.253546i
$421$			13.8564i			0.675320i	0.941268	+	0.337660i	$0.109635\pi$
$421$			13.8564i			0.675320i	−0.941268	+	0.337660i	$0.890365\pi$
$422$	0.500000	+	0.866025i	0.0243396	+	0.0421575i
$423$	4.50000	−	2.59808i	0.218797	−	0.126323i
$424$	−1.50000	+	0.866025i	−0.0728464	+	0.0420579i
$425$	6.00000	+	10.3923i	0.291043	+	0.504101i
$426$			15.5885i			0.755263i
$427$	−1.50000	+	4.33013i	−0.0725901	+	0.209550i
$428$		−	10.3923i		−	0.502331i
$429$	−18.0000	+	5.19615i	−0.869048	+	0.250873i
$430$	1.50000	−	0.866025i	0.0723364	−	0.0417635i
$431$	10.5000	−	18.1865i	0.505767	−	0.876014i	−0.494211	−	0.869342i	$-0.664543\pi$
$431$	10.5000	−	18.1865i	0.505767	−	0.876014i	0.999978	−	0.00667224i	$-0.00212386\pi$
$432$			5.19615i			0.250000i
$433$	−4.50000	−	2.59808i	−0.216256	−	0.124856i	0.387959	−	0.921676i	$-0.373180\pi$
$433$	−4.50000	−	2.59808i	−0.216256	−	0.124856i	−0.604216	+	0.796821i	$0.706513\pi$
$434$	−2.50000	−	0.866025i	−0.120004	−	0.0415705i
$435$	−22.5000	+	12.9904i	−1.07879	+	0.622841i
$436$	7.50000	−	4.33013i	0.359185	−	0.207375i
$437$	21.0000	−	12.1244i	1.00457	−	0.579987i
$438$	−19.5000	−	11.2583i	−0.931746	−	0.537944i
$439$		−	3.46410i		−	0.165333i	−0.996577	−	0.0826663i	$-0.973656\pi$
$439$		−	3.46410i		−	0.165333i	0.996577	−	0.0826663i	$-0.0263436\pi$
$440$	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	0.229377	−	0.973338i	$-0.426331\pi$
$443$	−10.5000	−	6.06218i	−0.498870	−	0.288023i	−0.728247	+	0.685315i	$0.759665\pi$
$444$		0			0
$445$	−6.00000	+	10.3923i	−0.284427	+	0.492642i
$446$	14.5000	+	25.1147i	0.686595	+	1.18922i
$447$	31.5000	+	18.1865i	1.48990	+	0.860194i
$448$	−2.00000	+	1.73205i	−0.0944911	+	0.0818317i
$449$	7.50000	−	12.9904i	0.353947	−	0.613054i	−0.632990	−	0.774160i	$-0.718173\pi$
$449$	7.50000	−	12.9904i	0.353947	−	0.613054i	0.986937	+	0.161106i	$0.0515060\pi$
$450$	−6.00000			−0.282843
$451$			15.5885i			0.734032i
$452$	−1.50000	−	0.866025i	−0.0705541	−	0.0407344i
$453$	−19.5000	+	33.7750i	−0.916190	+	1.58689i
$454$			10.3923i			0.487735i
$455$	−7.50000	−	14.7224i	−0.351605	−	0.690198i
$456$	10.5000	+	6.06218i	0.491708	+	0.283887i
$457$		−	20.7846i		−	0.972263i	−0.873886	−	0.486132i	$-0.838408\pi$
$457$		−	20.7846i		−	0.972263i	0.873886	−	0.486132i	$-0.161592\pi$
$458$	12.5000	−	21.6506i	0.584087	−	1.01167i
$459$		−	31.1769i		−	1.45521i
$460$	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	$0.459831\pi$
$462$	9.00000	+	10.3923i	0.418718	+	0.483494i
$463$		−	31.1769i		−	1.44891i	−0.689320	−	0.724457i	$-0.742091\pi$
$463$		−	31.1769i		−	1.44891i	0.689320	−	0.724457i	$-0.257909\pi$
$464$	−7.50000	+	4.33013i	−0.348179	+	0.201021i
$465$	1.50000	+	2.59808i	0.0695608	+	0.120483i
$466$	−19.5000	−	11.2583i	−0.903320	−	0.521532i
$467$	4.50000	−	7.79423i	0.208235	−	0.360674i	−0.742923	−	0.669376i	$-0.766561\pi$
$467$	4.50000	−	7.79423i	0.208235	−	0.360674i	0.951159	+	0.308702i	$0.0998947\pi$
$468$	−10.5000	−	2.59808i	−0.485363	−	0.120096i
$469$	4.50000	−	0.866025i	0.207791	−	0.0399893i
$470$	−1.50000	−	2.59808i	−0.0691898	−	0.119840i
$471$	−1.50000	+	2.59808i	−0.0691164	+	0.119713i
$472$			10.3923i			0.478345i
$473$	−1.50000	−	2.59808i	−0.0689701	−	0.119460i
$474$		−	1.73205i		−	0.0795557i
$475$	−7.00000	+	12.1244i	−0.321182	+	0.556304i
$476$	12.0000	−	10.3923i	0.550019	−	0.476331i
$477$			5.19615i			0.237915i
$478$	12.0000			0.548867
$479$	−16.5000	−	9.52628i	−0.753904	−	0.435267i	0.0731986	−	0.997317i	$-0.476679\pi$
$479$	−16.5000	−	9.52628i	−0.753904	−	0.435267i	−0.827103	+	0.562051i	$0.810013\pi$
$480$	3.00000			0.136931
$481$		0			0
$482$	−10.0000			−0.455488
$483$	15.0000	+	5.19615i	0.682524	+	0.236433i
$484$	1.00000	+	1.73205i	0.0454545	+	0.0787296i
$485$	28.5000	−	16.4545i	1.29412	−	0.747160i
$486$	13.5000	+	7.79423i	0.612372	+	0.353553i
$487$		−	3.46410i		−	0.156973i	−0.996915	−	0.0784867i	$-0.974991\pi$
$487$		−	3.46410i		−	0.156973i	0.996915	−	0.0784867i	$-0.0250088\pi$
$488$	1.50000	−	0.866025i	0.0679018	−	0.0392031i
$489$	4.50000	−	7.79423i	0.203497	−	0.352467i
$490$	−7.50000	+	9.52628i	−0.338815	+	0.430353i
$491$	−31.5000	+	18.1865i	−1.42158	+	0.820747i	−0.996434	−	0.0843802i	$-0.973109\pi$
$491$	−31.5000	+	18.1865i	−1.42158	+	0.820747i	−0.425141	+	0.905127i	$0.639776\pi$
$492$	−4.50000	+	7.79423i	−0.202876	+	0.351391i
$493$	45.0000	−	25.9808i	2.02670	−	1.17011i
$494$	−17.5000	+	18.1865i	−0.787362	+	0.818251i
$495$		−	15.5885i		−	0.700649i
$496$	0.500000	+	0.866025i	0.0224507	+	0.0388857i
$497$	4.50000	+	23.3827i	0.201853	+	1.04886i
$498$	−3.00000	−	5.19615i	−0.134433	−	0.232845i
$499$	28.5000	+	16.4545i	1.27584	+	0.736604i	0.976080	−	0.217412i	$-0.0697616\pi$
$499$	28.5000	+	16.4545i	1.27584	+	0.736604i	0.299755	+	0.954016i	$0.403095\pi$
$500$			12.1244i			0.542218i
$501$	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	$0.961063\pi$
$504$	1.50000	+	7.79423i	0.0668153	+	0.347183i
$505$	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
$509$		−	6.92820i		−	0.307087i	−0.988142	−	0.153544i	$-0.950931\pi$
$509$		−	6.92820i		−	0.307087i	0.988142	−	0.153544i	$-0.0490686\pi$
$510$	−18.0000			−0.797053
$511$	−32.5000	−	11.2583i	−1.43772	−	0.498039i
$512$	1.00000			0.0441942
$513$	31.5000	−	18.1865i	1.39076	−	0.802955i
$514$	−6.00000			−0.264649
$515$	7.50000	+	12.9904i	0.330489	+	0.572425i
$516$		−	1.73205i		−	0.0762493i
$517$	−4.50000	+	2.59808i	−0.197910	+	0.114263i
$518$		0			0
$519$	13.5000	+	7.79423i	0.592584	+	0.342129i
$520$	−1.50000	+	6.06218i	−0.0657794	+	0.265844i
$521$	7.50000	+	12.9904i	0.328581	+	0.569119i	0.982231	−	0.187678i	$-0.0600963\pi$
$521$	7.50000	+	12.9904i	0.328581	+	0.569119i	−0.653650	+	0.756797i	$0.726763\pi$
$522$			25.9808i			1.13715i
$523$			31.1769i			1.36327i	0.731692	+	0.681636i	$0.238731\pi$
$523$			31.1769i			1.36327i	−0.731692	+	0.681636i	$0.761269\pi$
$524$	−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
$527$	−3.00000	−	5.19615i	−0.130682	−	0.226348i
$528$		−	5.19615i		−	0.226134i
$529$	11.0000			0.478261
$530$	3.00000			0.130312
$531$	27.0000	+	15.5885i	1.17170	+	0.676481i
$532$	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
$535$	−9.00000	+	15.5885i	−0.389104	+	0.673948i
$536$	−1.50000	−	0.866025i	−0.0647901	−	0.0374066i
$537$	33.0000			1.42406
$538$	30.0000			1.29339
$539$	16.5000	+	12.9904i	0.710705	+	0.559535i
$540$	4.50000	−	7.79423i	0.193649	−	0.335410i
$541$	13.5000	+	7.79423i	0.580410	+	0.335100i	0.761296	−	0.648404i	$-0.224563\pi$
$541$	13.5000	+	7.79423i	0.580410	+	0.335100i	−0.180886	+	0.983504i	$0.557897\pi$
$542$	16.0000			0.687259
$543$	12.0000	+	20.7846i	0.514969	+	0.891953i
$544$	−6.00000			−0.257248
$545$	−15.0000			−0.642529
$546$	−16.5000	−	0.866025i	−0.706135	−	0.0370625i
$547$	44.0000			1.88130			0.940652	−	0.339372i	$-0.110215\pi$
$547$	44.0000			1.88130			0.940652	+	0.339372i	$0.110215\pi$
$548$	6.00000			0.256307
$549$		−	5.19615i		−	0.221766i
$550$	6.00000			0.255841
$551$	52.5000	+	30.3109i	2.23658	+	1.29129i
$552$	−3.00000	−	5.19615i	−0.127688	−	0.221163i
$553$	−0.500000	−	2.59808i	−0.0212622	−	0.110481i
$554$	−10.0000			−0.424859
$555$		0			0
$556$	−19.5000	−	11.2583i	−0.826984	−	0.477460i
$557$	−16.5000	+	28.5788i	−0.699127	+	1.21092i	0.269642	+	0.962961i	$0.413095\pi$
$557$	−16.5000	+	28.5788i	−0.699127	+	1.21092i	−0.968769	+	0.247964i	$0.920239\pi$
$558$	3.00000			0.127000
$559$	3.50000	+	0.866025i	0.148034	+	0.0366290i
$560$	4.50000	−	0.866025i	0.190160	−	0.0365963i
$561$			31.1769i			1.31629i
$562$	−6.00000			−0.253095
$563$	−12.0000			−0.505740			−0.252870	−	0.967500i	$-0.581374\pi$
$563$	−12.0000			−0.505740			−0.252870	+	0.967500i	$0.581374\pi$
$564$	−3.00000			−0.126323
$565$	1.50000	+	2.59808i	0.0631055	+	0.109302i
$566$	−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
$569$		−	13.8564i		−	0.580891i	−0.956892	−	0.290445i	$-0.906197\pi$
$569$		−	13.8564i		−	0.580891i	0.956892	−	0.290445i	$-0.0938035\pi$
$570$	−10.5000	−	18.1865i	−0.439797	−	0.761750i
$571$	2.50000	+	4.33013i	0.104622	+	0.181210i	0.913584	−	0.406651i	$-0.133303\pi$
$571$	2.50000	+	4.33013i	0.104622	+	0.181210i	−0.808962	+	0.587861i	$0.799970\pi$
$572$	10.5000	+	2.59808i	0.439027	+	0.108631i
$573$	13.5000	−	23.3827i	0.563971	−	0.976826i
$574$	−4.50000	+	12.9904i	−0.187826	+	0.542208i
$575$	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	$-0.213212\pi$
$577$	−3.50000	−	6.06218i	−0.145707	−	0.252372i	−0.929636	+	0.368478i	$0.879879\pi$
$578$	19.0000			0.790296
$579$	21.0000			0.872730
$580$	15.0000			0.622841
$581$	−6.00000	−	6.92820i	−0.248922	−	0.287430i
$582$		−	32.9090i		−	1.36412i
$583$		−	5.19615i		−	0.215203i
$584$	6.50000	+	11.2583i	0.268972	+	0.465873i
$585$	13.5000	+	12.9904i	0.558156	+	0.537086i
$586$	−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	$0.0956823\pi$
$588$	4.50000	+	11.2583i	0.185577	+	0.464286i
$589$	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	$-0.390237\pi$
$593$	−7.50000	−	4.33013i	−0.307988	−	0.177817i	−0.646026	+	0.763316i	$0.723570\pi$
$594$	−13.5000	−	7.79423i	−0.553912	−	0.319801i
$595$	−27.0000	+	5.19615i	−1.10689	+	0.213021i
$596$	−10.5000	−	18.1865i	−0.430097	−	0.744949i
$597$	−3.00000	−	5.19615i	−0.122782	−	0.212664i
$598$	12.0000	−	3.46410i	0.490716	−	0.141658i
$599$	−25.5000	+	14.7224i	−1.04190	+	0.601542i	−0.920371	−	0.391045i	$-0.872114\pi$
$599$	−25.5000	+	14.7224i	−1.04190	+	0.601542i	−0.121530	+	0.992588i	$0.538780\pi$
$600$	3.00000	+	1.73205i	0.122474	+	0.0707107i
$601$	19.5000	−	11.2583i	0.795422	−	0.459237i	−0.0464461	−	0.998921i	$-0.514790\pi$
$601$	19.5000	−	11.2583i	0.795422	−	0.459237i	0.841868	+	0.539684i	$0.181456\pi$
$602$	−0.500000	−	2.59808i	−0.0203785	−	0.105890i
$603$	−4.50000	+	2.59808i	−0.183254	+	0.105802i
$604$	19.5000	−	11.2583i	0.793444	−	0.458095i
$605$		−	3.46410i		−	0.140836i
$606$		−	15.5885i		−	0.633238i
$607$	−16.5000	+	9.52628i	−0.669714	+	0.386660i	−0.795968	−	0.605338i	$-0.793038\pi$
$607$	−16.5000	+	9.52628i	−0.669714	+	0.386660i	0.126254	+	0.991998i	$0.459705\pi$
$608$	−3.50000	−	6.06218i	−0.141944	−	0.245854i
$609$	7.50000	+	38.9711i	0.303915	+	1.57919i
$610$	−3.00000			−0.121466
$611$	1.50000	−	6.06218i	0.0606835	−	0.245249i
$612$	−9.00000	+	15.5885i	−0.363803	+	0.630126i
$613$	19.5000	+	11.2583i	0.787598	+	0.454720i	0.839116	−	0.543952i	$-0.183073\pi$
$613$	19.5000	+	11.2583i	0.787598	+	0.454720i	−0.0515185	+	0.998672i	$0.516406\pi$
$614$	−4.00000			−0.161427
$615$	13.5000	−	7.79423i	0.544373	−	0.314294i
$616$	−1.50000	−	7.79423i	−0.0604367	−	0.314038i
$617$	−4.50000	+	7.79423i	−0.181163	+	0.313784i	−0.942277	−	0.334835i	$-0.891320\pi$
$617$	−4.50000	+	7.79423i	−0.181163	+	0.313784i	0.761114	+	0.648618i	$0.224653\pi$
$618$	15.0000			0.603388
$619$	2.50000	+	4.33013i	0.100483	+	0.174042i	0.911884	−	0.410448i	$-0.134628\pi$
$619$	2.50000	+	4.33013i	0.100483	+	0.174042i	−0.811400	+	0.584491i	$0.801294\pi$
$620$		−	1.73205i		−	0.0695608i
$621$	−18.0000			−0.722315
$622$	1.50000	+	2.59808i	0.0601445	+	0.104173i
$623$	12.0000	+	13.8564i	0.480770	+	0.555145i
$624$	4.50000	+	4.33013i	0.180144	+	0.173344i
$625$	5.50000	−	9.52628i	0.220000	−	0.381051i
$626$	−4.50000	−	2.59808i	−0.179856	−	0.103840i
$627$	−31.5000	+	18.1865i	−1.25799	+	0.726300i
$628$	1.50000	−	0.866025i	0.0598565	−	0.0345582i
$629$		0			0
$630$	4.50000	−	12.9904i	0.179284	−	0.517549i
$631$	−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
$634$	1.50000	−	2.59808i	0.0595726	−	0.103183i
$635$		−	29.4449i		−	1.16848i
$636$	1.50000	−	2.59808i	0.0594789	−	0.103020i
$637$	−25.0000	+	3.46410i	−0.990536	+	0.137253i
$638$		−	25.9808i		−	1.02859i
$639$	−13.5000	−	23.3827i	−0.534052	−	0.925005i
$640$	−1.50000	−	0.866025i	−0.0592927	−	0.0342327i
$641$			34.6410i			1.36824i	0.729370	+	0.684119i	$0.239813\pi$
$641$			34.6410i			1.36824i	−0.729370	+	0.684119i	$0.760187\pi$
$642$	9.00000	+	15.5885i	0.355202	+	0.615227i
$643$	−14.5000	+	25.1147i	−0.571824	+	0.990429i	0.424555	+	0.905402i	$0.360431\pi$
$643$	−14.5000	+	25.1147i	−0.571824	+	0.990429i	−0.996379	+	0.0850262i	$0.972903\pi$
$644$	−6.00000	−	6.92820i	−0.236433	−	0.273009i
$645$	−1.50000	+	2.59808i	−0.0590624	+	0.102299i
$646$	21.0000	+	36.3731i	0.826234	+	1.43108i
$647$	−1.50000	+	2.59808i	−0.0589711	+	0.102141i	−0.894004	−	0.448059i	$-0.852115\pi$
$647$	−1.50000	+	2.59808i	−0.0589711	+	0.102141i	0.835033	+	0.550200i	$0.185449\pi$
$648$	−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
$653$			41.5692i			1.62673i	0.581754	+	0.813365i	$0.302367\pi$
$653$			41.5692i			1.62673i	−0.581754	+	0.813365i	$0.697633\pi$
$654$	−7.50000	+	12.9904i	−0.293273	+	0.507964i
$655$	4.50000	−	2.59808i	0.175830	−	0.101515i
$656$	4.50000	−	2.59808i	0.175695	−	0.101438i
$657$	39.0000			1.52153
$658$	−4.50000	+	0.866025i	−0.175428	+	0.0337612i
$659$	−34.5000	−	19.9186i	−1.34393	−	0.775918i	−0.356548	−	0.934277i	$-0.616046\pi$
$659$	−34.5000	−	19.9186i	−1.34393	−	0.775918i	−0.987382	+	0.158359i	$0.949380\pi$
$660$	−4.50000	+	7.79423i	−0.175162	+	0.303390i
$661$	6.50000	−	11.2583i	0.252821	−	0.437898i	−0.711481	−	0.702706i	$-0.751975\pi$
$661$	6.50000	−	11.2583i	0.252821	−	0.437898i	0.964301	+	0.264807i	$0.0853084\pi$
$662$	−22.5000	+	12.9904i	−0.874487	+	0.504885i
$663$	−27.0000	−	25.9808i	−1.04859	−	1.00901i
$664$			3.46410i			0.134433i
$665$	−21.0000	−	24.2487i	−0.814345	−	0.940325i
$666$		0			0
$667$	−15.0000	−	25.9808i	−0.580802	−	1.00598i
$668$	−7.50000	+	4.33013i	−0.290184	+	0.167538i
$669$	−43.5000	−	25.1147i	−1.68181	−	0.970992i
$670$	1.50000	+	2.59808i	0.0579501	+	0.100372i
$671$			5.19615i			0.200595i
$672$	1.50000	−	4.33013i	0.0578638	−	0.167038i
$673$	−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	$0.876409\pi$
$674$	−10.0000			−0.385186
$675$	9.00000	−	5.19615i	0.346410	−	0.200000i
$676$	−11.0000	+	6.92820i	−0.423077	+	0.266469i
$677$	13.5000	−	23.3827i	0.518847	−	0.898670i	−0.480913	−	0.876768i	$-0.659695\pi$
$677$	13.5000	−	23.3827i	0.518847	−	0.898670i	0.999760	−	0.0219013i	$-0.00697196\pi$
$678$	3.00000			0.115214
$679$	−9.50000	−	49.3634i	−0.364577	−	1.89440i
$680$	9.00000	+	5.19615i	0.345134	+	0.199263i
$681$	−9.00000	−	15.5885i	−0.344881	−	0.597351i
$682$	−3.00000			−0.114876
$683$	12.0000			0.459167			0.229584	−	0.973289i	$-0.426264\pi$
$683$	12.0000			0.459167			0.229584	+	0.973289i	$0.426264\pi$
$684$	−21.0000			−0.802955
$685$	−9.00000	−	5.19615i	−0.343872	−	0.198535i
$686$	10.0000	+	15.5885i	0.381802	+	0.595170i
$687$			43.3013i			1.65205i
$688$	−0.500000	+	0.866025i	−0.0190623	+	0.0330169i
$689$	4.50000	+	4.33013i	0.171436	+	0.164965i
$690$			10.3923i			0.395628i
$691$	−44.0000			−1.67384			−0.836919	−	0.547326i	$-0.815646\pi$
$691$	−44.0000			−1.67384			−0.836919	+	0.547326i	$0.815646\pi$
$692$	−4.50000	−	7.79423i	−0.171064	−	0.296292i
$693$	−22.5000	−	7.79423i	−0.854704	−	0.296078i
$694$		−	10.3923i		−	0.394486i
$695$	19.5000	+	33.7750i	0.739677	+	1.28116i
$696$	7.50000	−	12.9904i	0.284287	−	0.492399i
$697$	−27.0000	+	15.5885i	−1.02270	+	0.590455i
$698$	−17.5000	−	30.3109i	−0.662385	−	1.14728i
$699$	39.0000			1.47512
$700$	5.00000	+	1.73205i	0.188982	+	0.0654654i
$701$			27.7128i			1.04670i	0.852118	+	0.523349i	$0.175318\pi$
$701$			27.7128i			1.04670i	−0.852118	+	0.523349i	$0.824682\pi$
$702$	18.0000	−	5.19615i	0.679366	−	0.196116i
$703$		0			0
$704$	−1.50000	+	2.59808i	−0.0565334	+	0.0979187i
$705$	4.50000	+	2.59808i	0.169480	+	0.0978492i
$706$	22.5000	+	12.9904i	0.846799	+	0.488899i
$707$	−4.50000	−	23.3827i	−0.169240	−	0.879396i
$708$	−9.00000	−	15.5885i	−0.338241	−	0.585850i
$709$	−22.5000	+	12.9904i	−0.845005	+	0.487864i	−0.858962	−	0.512039i	$-0.828890\pi$
$709$	−22.5000	+	12.9904i	−0.845005	+	0.487864i	0.0139572	+	0.999903i	$0.495557\pi$
$710$	−13.5000	+	7.79423i	−0.506646	+	0.292512i
$711$	1.50000	+	2.59808i	0.0562544	+	0.0974355i
$712$		−	6.92820i		−	0.259645i
$713$	−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
$718$	−1.50000	+	2.59808i	−0.0559795	+	0.0969593i
$719$	1.50000	+	2.59808i	0.0559406	+	0.0968919i	0.892640	−	0.450771i	$-0.148851\pi$
$719$	1.50000	+	2.59808i	0.0559406	+	0.0968919i	−0.836699	+	0.547663i	$0.815518\pi$
$720$	−4.50000	+	2.59808i	−0.167705	+	0.0968246i
$721$	22.5000	−	4.33013i	0.837944	−	0.161262i
$722$	−15.0000	+	25.9808i	−0.558242	+	0.966904i
$723$	15.0000	−	8.66025i	0.557856	−	0.322078i
$724$		−	13.8564i		−	0.514969i
$725$	15.0000	+	8.66025i	0.557086	+	0.321634i
$726$	−3.00000	−	1.73205i	−0.111340	−	0.0642824i
$727$			10.3923i			0.385429i	0.981255	+	0.192715i	$0.0617292\pi$
$727$			10.3923i			0.385429i	−0.981255	+	0.192715i	$0.938271\pi$
$728$	8.00000	+	5.19615i	0.296500	+	0.192582i
$729$	−27.0000			−1.00000
$730$		−	22.5167i		−	0.833379i
$731$	3.00000	−	5.19615i	0.110959	−	0.192187i
$732$	−1.50000	+	2.59808i	−0.0554416	+	0.0960277i
$733$	18.5000	−	32.0429i	0.683313	−	1.18353i	−0.290651	−	0.956829i	$-0.593872\pi$
$733$	18.5000	−	32.0429i	0.683313	−	1.18353i	0.973964	−	0.226704i	$-0.0727949\pi$
$734$	−13.5000	−	7.79423i	−0.498294	−	0.287690i
$735$	3.00000	−	20.7846i	0.110657	−	0.766652i
$736$			3.46410i			0.127688i
$737$	4.50000	−	2.59808i	0.165760	−	0.0957014i
$738$		−	15.5885i		−	0.573819i
$739$	16.5000	+	9.52628i	0.606962	+	0.350430i	0.771776	−	0.635895i	$-0.219369\pi$
$739$	16.5000	+	9.52628i	0.606962	+	0.350430i	−0.164813	+	0.986325i	$0.552702\pi$
$740$		0			0
$741$	10.5000	−	42.4352i	0.385727	−	1.55890i
$742$	1.50000	−	4.33013i	0.0550667	−	0.158964i
$743$	−4.50000	−	7.79423i	−0.165089	−	0.285943i	0.771598	−	0.636111i	$-0.219458\pi$
$743$	−4.50000	−	7.79423i	−0.165089	−	0.285943i	−0.936687	+	0.350168i	$0.886124\pi$
$744$	−1.50000	−	0.866025i	−0.0549927	−	0.0317500i
$745$			36.3731i			1.33261i
$746$	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
$750$	−10.5000	−	18.1865i	−0.383406	−	0.664078i
$751$	4.00000			0.145962			0.0729810	−	0.997333i	$-0.476749\pi$
$751$	4.00000			0.145962			0.0729810	+	0.997333i	$0.476749\pi$
$752$	1.50000	+	0.866025i	0.0546994	+	0.0315807i
$753$		−	25.9808i		−	0.946792i
$754$	22.5000	+	21.6506i	0.819402	+	0.788470i
$755$	−39.0000			−1.41936
$756$	−9.00000	−	10.3923i	−0.327327	−	0.377964i
$757$	−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	$-0.492572\pi$
$758$	−16.5000	+	9.52628i	−0.599307	+	0.346010i
$759$	18.0000			0.653359
$760$			12.1244i			0.439797i
$761$	−25.5000	+	14.7224i	−0.924374	+	0.533688i	−0.885028	−	0.465538i	$-0.845861\pi$
$761$	−25.5000	+	14.7224i	−0.924374	+	0.533688i	−0.0393463	+	0.999226i	$0.512528\pi$
$762$	−25.5000	−	14.7224i	−0.923768	−	0.533337i
$763$	−7.50000	+	21.6506i	−0.271518	+	0.783806i
$764$	−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
$767$	36.0000	−	10.3923i	1.29988	−	0.375244i
$768$	−1.50000	+	0.866025i	−0.0541266	+	0.0312500i
$769$	6.50000	+	11.2583i	0.234396	+	0.405986i	0.959097	−	0.283078i	$-0.0913554\pi$
$769$	6.50000	+	11.2583i	0.234396	+	0.405986i	−0.724701	+	0.689063i	$0.758022\pi$
$770$	−4.50000	+	12.9904i	−0.162169	+	0.468141i
$771$	9.00000	−	5.19615i	0.324127	−	0.187135i
$772$	−10.5000	−	6.06218i	−0.377903	−	0.218183i
$773$		0			0		1.00000			$0$
$773$		0			0		−1.00000			$\pi$
$774$	1.50000	+	2.59808i	0.0539164	+	0.0933859i
$775$	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
$782$		−	20.7846i		−	0.743256i
$783$	−22.5000	−	38.9711i	−0.804084	−	1.39272i
$784$	1.00000	−	6.92820i	0.0357143	−	0.247436i
$785$	−3.00000			−0.107075
$786$		−	5.19615i		−	0.185341i
$787$	4.00000			0.142585			0.0712923	−	0.997455i	$-0.477288\pi$
$787$	4.00000			0.142585			0.0712923	+	0.997455i	$0.477288\pi$
$788$	−10.5000	−	18.1865i	−0.374047	−	0.647868i
$789$	−15.0000			−0.534014
$790$	1.50000	−	0.866025i	0.0533676	−	0.0308118i
$791$	4.50000	−	0.866025i	0.160002	−	0.0307923i
$792$	4.50000	+	7.79423i	0.159901	+	0.276956i
$793$	−4.50000	−	4.33013i	−0.159800	−	0.153767i
$794$	14.5000	+	25.1147i	0.514586	+	0.891289i
$795$	−4.50000	+	2.59808i	−0.159599	+	0.0921443i
$796$			3.46410i			0.122782i
$797$	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
$800$	−1.00000	−	1.73205i	−0.0353553	−	0.0612372i
$801$	−18.0000	−	10.3923i	−0.635999	−	0.367194i
$802$	18.0000			0.635602
$803$	−39.0000			−1.37628
$804$	3.00000			0.105802
$805$	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
$808$	−4.50000	+	7.79423i	−0.158309	+	0.274200i
$809$	−43.5000	−	25.1147i	−1.52938	−	0.882987i	−0.999388	−	0.0349836i	$-0.988862\pi$
$809$	−43.5000	−	25.1147i	−1.52938	−	0.882987i	−0.529991	−	0.848003i	$-0.677805\pi$
$810$			15.5885i			0.547723i
$811$	−28.0000			−0.983213			−0.491606	−	0.870817i	$-0.663590\pi$
$811$	−28.0000			−0.983213			−0.491606	+	0.870817i	$0.663590\pi$
$812$	7.50000	−	21.6506i	0.263198	−	0.759788i
$813$	−24.0000	+	13.8564i	−0.841717	+	0.485965i
$814$		0			0
$815$	9.00000			0.315256
$816$	9.00000	−	5.19615i	0.315063	−	0.181902i
$817$	7.00000			0.244899
$818$	22.0000			0.769212
$819$	25.5000	−	12.9904i	0.891042	−	0.453921i
$820$	−9.00000			−0.314294
$821$	6.00000			0.209401			0.104701	−	0.994504i	$-0.466612\pi$
$821$	6.00000			0.209401			0.104701	+	0.994504i	$0.466612\pi$
$822$	−9.00000	+	5.19615i	−0.313911	+	0.181237i
$823$	−16.0000			−0.557725			−0.278862	−	0.960331i	$-0.589957\pi$
$823$	−16.0000			−0.557725			−0.278862	+	0.960331i	$0.589957\pi$
$824$	−7.50000	−	4.33013i	−0.261275	−	0.150847i
$825$	−9.00000	+	5.19615i	−0.313340	+	0.180907i
$826$	−18.0000	−	20.7846i	−0.626300	−	0.723189i
$827$	−36.0000			−1.25184			−0.625921	−	0.779886i	$-0.715277\pi$
$827$	−36.0000			−1.25184			−0.625921	+	0.779886i	$0.715277\pi$
$828$	9.00000	+	5.19615i	0.312772	+	0.180579i
$829$	13.5000	+	7.79423i	0.468874	+	0.270705i	0.715768	−	0.698338i	$-0.246077\pi$
$829$	13.5000	+	7.79423i	0.468874	+	0.270705i	−0.246894	+	0.969042i	$0.579410\pi$
$830$	3.00000	−	5.19615i	0.104132	−	0.180361i
$831$	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
$834$	39.0000			1.35046
$835$	15.0000			0.519096
$836$	21.0000			0.726300
$837$	−4.50000	+	2.59808i	−0.155543	+	0.0898027i
$838$	−16.5000	−	28.5788i	−0.569983	−	0.987240i
$839$	−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
$842$			13.8564i			0.477523i
$843$	9.00000	−	5.19615i	0.309976	−	0.178965i
$844$	0.500000	+	0.866025i	0.0172107	+	0.0298098i
$845$	22.5000	−	0.866025i	0.774024	−	0.0297922i
$846$	4.50000	−	2.59808i	0.154713	−	0.0893237i
$847$	−5.00000	−	1.73205i	−0.171802	−	0.0595140i
$848$	−1.50000	+	0.866025i	−0.0515102	+	0.0297394i
$849$	39.0000			1.33848
$850$	6.00000	+	10.3923i	0.205798	+	0.356453i
$851$		0			0
$852$			15.5885i			0.534052i
$853$	10.0000			0.342393			0.171197	−	0.985237i	$-0.445237\pi$
$853$	10.0000			0.342393			0.171197	+	0.985237i	$0.445237\pi$
$854$	−1.50000	+	4.33013i	−0.0513289	+	0.148174i
$855$	31.5000	+	18.1865i	1.07728	+	0.621966i
$856$		−	10.3923i		−	0.355202i
$857$	19.5000	+	33.7750i	0.666107	+	1.15373i	0.978984	+	0.203938i	$0.0653741\pi$
$857$	19.5000	+	33.7750i	0.666107	+	1.15373i	−0.312877	+	0.949794i	$0.601293\pi$
$858$	−18.0000	+	5.19615i	−0.614510	+	0.177394i
$859$	4.50000	+	2.59808i	0.153538	+	0.0886452i	0.574801	−	0.818293i	$-0.305080\pi$
$859$	4.50000	+	2.59808i	0.153538	+	0.0886452i	−0.421263	+	0.906939i	$0.638413\pi$
$860$	1.50000	−	0.866025i	0.0511496	−	0.0295312i
$861$	−4.50000	−	23.3827i	−0.153360	−	0.796880i
$862$	10.5000	−	18.1865i	0.357631	−	0.619436i
$863$	−19.5000	+	33.7750i	−0.663788	+	1.14971i	0.315825	+	0.948818i	$0.397719\pi$
$863$	−19.5000	+	33.7750i	−0.663788	+	1.14971i	−0.979612	+	0.200897i	$0.935615\pi$
$864$			5.19615i			0.176777i
$865$			15.5885i			0.530023i
$866$	−4.50000	−	2.59808i	−0.152916	−	0.0882862i
$867$	−28.5000	+	16.4545i	−0.967911	+	0.558824i
$868$	−2.50000	−	0.866025i	−0.0848555	−	0.0293948i
$869$	−1.50000	−	2.59808i	−0.0508840	−	0.0881337i
$870$	−22.5000	+	12.9904i	−0.762821	+	0.440415i
$871$	−1.50000	+	6.06218i	−0.0508256	+	0.205409i
$872$	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
$875$	−21.0000	−	24.2487i	−0.709930	−	0.819756i
$876$	−19.5000	−	11.2583i	−0.658844	−	0.380384i
$877$	−10.5000	+	6.06218i	−0.354560	+	0.204705i	−0.666692	−	0.745334i	$-0.732290\pi$
$877$	−10.5000	+	6.06218i	−0.354560	+	0.204705i	0.312132	+	0.950039i	$0.398957\pi$
$878$		−	3.46410i		−	0.116908i
$879$	51.0000			1.72019
$880$	4.50000	−	2.59808i	0.151695	−	0.0875811i
$881$	−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	$-0.576548\pi$
$882$	−16.5000	−	12.9904i	−0.555584	−	0.437409i
$883$	−52.0000			−1.74994			−0.874970	−	0.484178i	$-0.839119\pi$
$883$	−52.0000			−1.74994			−0.874970	+	0.484178i	$0.839119\pi$
$884$	6.00000	+	20.7846i	0.201802	+	0.699062i
$885$			31.1769i			1.04800i
$886$	−10.5000	−	6.06218i	−0.352754	−	0.203663i
$887$	24.0000			0.805841			0.402921	−	0.915235i	$-0.367995\pi$
$887$	24.0000			0.805841			0.402921	+	0.915235i	$0.367995\pi$
$888$		0			0
$889$	−42.5000	−	14.7224i	−1.42540	−	0.493775i
$890$	−6.00000	+	10.3923i	−0.201120	+	0.348351i
$891$	27.0000			0.904534
$892$	14.5000	+	25.1147i	0.485496	+	0.840904i
$893$		−	12.1244i		−	0.405726i
$894$	31.5000	+	18.1865i	1.05352	+	0.608249i
$895$	16.5000	+	28.5788i	0.551534	+	0.955285i
$896$	−2.00000	+	1.73205i	−0.0668153	+	0.0578638i
$897$	−15.0000	+	15.5885i	−0.500835	+	0.520483i
$898$	7.50000	−	12.9904i	0.250278	−	0.433495i
$899$	−7.50000	−	4.33013i	−0.250139	−	0.144418i
$900$	−6.00000			−0.200000
$901$	9.00000	−	5.19615i	0.299833	−	0.173109i
$902$			15.5885i			0.519039i
$903$	3.00000	+	3.46410i	0.0998337	+	0.115278i
$904$	−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
$907$	3.50000	−	6.06218i	0.116216	−	0.201291i	−0.802049	−	0.597258i	$-0.796257\pi$
$907$	3.50000	−	6.06218i	0.116216	−	0.201291i	0.918265	+	0.395966i	$0.129590\pi$
$908$			10.3923i			0.344881i
$909$	13.5000	+	23.3827i	0.447767	+	0.775555i
$910$	−7.50000	−	14.7224i	−0.248623	−	0.488044i
$911$		−	24.2487i		−	0.803396i	−0.915772	−	0.401698i	$-0.868420\pi$
$911$		−	24.2487i		−	0.803396i	0.915772	−	0.401698i	$-0.131580\pi$
$912$	10.5000	+	6.06218i	0.347690	+	0.200739i
$913$	−9.00000	−	5.19615i	−0.297857	−	0.171968i
$914$		−	20.7846i		−	0.687494i
$915$	4.50000	−	2.59808i	0.148765	−	0.0858898i
$916$	12.5000	−	21.6506i	0.413012	−	0.715357i
$917$	−1.50000	−	7.79423i	−0.0495344	−	0.257388i
$918$		−	31.1769i		−	1.02899i
$919$	18.5000	+	32.0429i	0.610259	+	1.05700i	0.991197	+	0.132398i	$0.0422678\pi$
$919$	18.5000	+	32.0429i	0.610259	+	1.05700i	−0.380938	+	0.924601i	$0.624399\pi$
$920$	3.00000	−	5.19615i	0.0989071	−	0.171312i
$921$	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
$926$		−	31.1769i		−	1.02454i
$927$	−22.5000	+	12.9904i	−0.738997	+	0.426660i
$928$	−7.50000	+	4.33013i	−0.246200	+	0.142143i
$929$	−7.50000	+	4.33013i	−0.246067	+	0.142067i	−0.617962	−	0.786208i	$-0.712041\pi$
$929$	−7.50000	+	4.33013i	−0.246067	+	0.142067i	0.371895	+	0.928275i	$0.378708\pi$
$930$	1.50000	+	2.59808i	0.0491869	+	0.0851943i
$931$	−45.5000	+	18.1865i	−1.49120	+	0.596040i
$932$	−19.5000	−	11.2583i	−0.638744	−	0.368779i
$933$	−4.50000	−	2.59808i	−0.147323	−	0.0850572i
$934$	4.50000	−	7.79423i	0.147244	−	0.255035i
$935$	−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	$-0.889742\pi$
$937$		−	20.7846i		−	0.679004i	0.940605	−	0.339502i	$-0.110258\pi$
$938$	4.50000	−	0.866025i	0.146930	−	0.0282767i
$939$	9.00000			0.293704
$940$	−1.50000	−	2.59808i	−0.0489246	−	0.0847399i
$941$	16.5000	−	9.52628i	0.537885	−	0.310548i	−0.206337	−	0.978481i	$-0.566154\pi$
$941$	16.5000	−	9.52628i	0.537885	−	0.310548i	0.744221	+	0.667933i	$0.232821\pi$
$942$	−1.50000	+	2.59808i	−0.0488726	+	0.0846499i
$943$	9.00000	+	15.5885i	0.293080	+	0.507630i
$944$			10.3923i			0.338241i
$945$	4.50000	+	23.3827i	0.146385	+	0.760639i
$946$	−1.50000	−	2.59808i	−0.0487692	−	0.0844707i
$947$	−12.0000			−0.389948			−0.194974	−	0.980808i	$-0.562462\pi$
$947$	−12.0000			−0.389948			−0.194974	+	0.980808i	$0.562462\pi$
$948$		−	1.73205i		−	0.0562544i
$949$	32.5000	−	33.7750i	1.05499	−	1.09638i
$950$	−7.00000	+	12.1244i	−0.227110	+	0.393366i
$951$			5.19615i			0.168497i
$952$	12.0000	−	10.3923i	0.388922	−	0.336817i
$953$	−25.5000	−	14.7224i	−0.826026	−	0.476906i	0.0264640	−	0.999650i	$-0.491575\pi$
$953$	−25.5000	−	14.7224i	−0.826026	−	0.476906i	−0.852490	+	0.522743i	$0.824909\pi$
$954$			5.19615i			0.168232i
$955$	27.0000			0.873699
$956$	12.0000			0.388108
$957$	22.5000	+	38.9711i	0.727322	+	1.25976i
$958$	−16.5000	−	9.52628i	−0.533091	−	0.307780i
$959$	−12.0000	+	10.3923i	−0.387500	+	0.335585i
$960$	3.00000			0.0968246
$961$	15.0000	−	25.9808i	0.483871	−	0.838089i
$962$		0			0
$963$	−27.0000	−	15.5885i	−0.870063	−	0.502331i
$964$	−10.0000			−0.322078
$965$	10.5000	+	18.1865i	0.338007	+	0.585445i
$966$	15.0000	+	5.19615i	0.482617	+	0.167183i
$967$			10.3923i			0.334194i	0.985940	+	0.167097i	$0.0534393\pi$
$967$			10.3923i			0.334194i	−0.985940	+	0.167097i	$0.946561\pi$
$968$	1.00000	+	1.73205i	0.0321412	+	0.0556702i
$969$	−63.0000	−	36.3731i	−2.02385	−	1.16847i
$970$	28.5000	−	16.4545i	0.915080	−	0.528322i
$971$	−16.5000	−	28.5788i	−0.529510	−	0.917139i	−0.999408	−	0.0344175i	$-0.989042\pi$
$971$	−16.5000	−	28.5788i	−0.529510	−	0.917139i	0.469897	−	0.882721i	$-0.344291\pi$
$972$	13.5000	+	7.79423i	0.433013	+	0.250000i
$973$	58.5000	−	11.2583i	1.87542	−	0.360925i
$974$		−	3.46410i		−	0.110997i
$975$	3.00000	−	12.1244i	0.0960769	−	0.388290i
$976$	1.50000	−	0.866025i	0.0480138	−	0.0277208i
$977$	1.50000	−	2.59808i	0.0479893	−	0.0831198i	−0.841033	−	0.540984i	$-0.818052\pi$
$977$	1.50000	−	2.59808i	0.0479893	−	0.0831198i	0.889022	+	0.457864i	$0.151385\pi$
$978$	4.50000	−	7.79423i	0.143894	−	0.249232i
$979$	18.0000	+	10.3923i	0.575282	+	0.332140i
$980$	−7.50000	+	9.52628i	−0.239579	+	0.304306i
$981$		−	25.9808i		−	0.829502i
$982$	−31.5000	+	18.1865i	−1.00521	+	0.580356i
$983$	−25.5000	+	14.7224i	−0.813324	+	0.469573i	−0.848109	−	0.529822i	$-0.822259\pi$
$983$	−25.5000	+	14.7224i	−0.813324	+	0.469573i	0.0347851	+	0.999395i	$0.488925\pi$
$984$	−4.50000	+	7.79423i	−0.143455	+	0.248471i
$985$			36.3731i			1.15894i
$986$	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
$990$		−	15.5885i		−	0.495434i
$991$	−12.5000	+	21.6506i	−0.397076	+	0.687755i	−0.993364	−	0.115015i	$-0.963308\pi$
$991$	−12.5000	+	21.6506i	−0.397076	+	0.687755i	0.596288	+	0.802771i	$0.296642\pi$
$992$	0.500000	+	0.866025i	0.0158750	+	0.0274963i
$993$	22.5000	−	38.9711i	0.714016	−	1.23671i
$994$	4.50000	+	23.3827i	0.142731	+	0.741654i
$995$	3.00000	−	5.19615i	0.0951064	−	0.164729i
$996$	−3.00000	−	5.19615i	−0.0950586	−	0.164646i
$997$		−	27.7128i		−	0.877674i	−0.898567	−	0.438837i	$-0.855391\pi$
$997$		−	27.7128i		−	0.877674i	0.898567	−	0.438837i	$-0.144609\pi$
$998$	28.5000	+	16.4545i	0.902152	+	0.520858i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bi.b.17.1	✓	2	91.17	odd	6
546.2.bi.b.257.1	yes	2	3.2	odd	2
546.2.bi.d.17.1	yes	2	273.17	even	6	inner
546.2.bi.d.257.1	yes	2	1.1	even	1	trivial
546.2.bn.a.101.1	yes	2	7.3	odd	6
546.2.bn.a.173.1	yes	2	39.17	odd	6
546.2.bn.d.101.1	yes	2	21.17	even	6
546.2.bn.d.173.1	yes	2	13.4	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bi (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(-1.50000 + 0.866025i) q^{3} +1.00000 q^{4} +(-1.50000 - 0.866025i) q^{5} +(-1.50000 + 0.866025i) q^{6} +(-2.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(-1.50000 + 0.866025i) q^{3} +1.00000 q^{4} +(-1.50000 - 0.866025i) q^{5} +(-1.50000 + 0.866025i) q^{6} +(-2.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +(-1.50000 - 0.866025i) q^{10} +(-1.50000 + 2.59808i) q^{11} +(-1.50000 + 0.866025i) q^{12} +(-1.00000 - 3.46410i) q^{13} +(-2.00000 + 1.73205i) q^{14} +3.00000 q^{15} +1.00000 q^{16} -6.00000 q^{17} +(1.50000 - 2.59808i) q^{18} +(-3.50000 - 6.06218i) q^{19} +(-1.50000 - 0.866025i) q^{20} +(1.50000 - 4.33013i) q^{21} +(-1.50000 + 2.59808i) q^{22} +3.46410i q^{23} +(-1.50000 + 0.866025i) q^{24} +(-1.00000 - 1.73205i) q^{25} +(-1.00000 - 3.46410i) q^{26} +5.19615i q^{27} +(-2.00000 + 1.73205i) q^{28} +(-7.50000 + 4.33013i) q^{29} +3.00000 q^{30} +(0.500000 + 0.866025i) q^{31} +1.00000 q^{32} -5.19615i q^{33} -6.00000 q^{34} +(4.50000 - 0.866025i) q^{35} +(1.50000 - 2.59808i) 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} +(1.50000 - 4.33013i) q^{42} +(-0.500000 + 0.866025i) q^{43} +(-1.50000 + 2.59808i) q^{44} +(-4.50000 + 2.59808i) q^{45} +3.46410i q^{46} +(1.50000 + 0.866025i) q^{47} +(-1.50000 + 0.866025i) q^{48} +(1.00000 - 6.92820i) q^{49} +(-1.00000 - 1.73205i) q^{50} +(9.00000 - 5.19615i) q^{51} +(-1.00000 - 3.46410i) q^{52} +(-1.50000 + 0.866025i) q^{53} +5.19615i q^{54} +(4.50000 - 2.59808i) q^{55} +(-2.00000 + 1.73205i) q^{56} +(10.5000 + 6.06218i) q^{57} +(-7.50000 + 4.33013i) q^{58} +10.3923i q^{59} +3.00000 q^{60} +(1.50000 - 0.866025i) q^{61} +(0.500000 + 0.866025i) q^{62} +(1.50000 + 7.79423i) q^{63} +1.00000 q^{64} +(-1.50000 + 6.06218i) q^{65} -5.19615i q^{66} +(-1.50000 - 0.866025i) q^{67} -6.00000 q^{68} +(-3.00000 - 5.19615i) 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} +(3.00000 + 1.73205i) q^{75} +(-3.50000 - 6.06218i) q^{76} +(-1.50000 - 7.79423i) q^{77} +(4.50000 + 4.33013i) q^{78} +(-0.500000 + 0.866025i) q^{79} +(-1.50000 - 0.866025i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(4.50000 - 2.59808i) q^{82} +3.46410i q^{83} +(1.50000 - 4.33013i) q^{84} +(9.00000 + 5.19615i) q^{85} +(-0.500000 + 0.866025i) q^{86} +(7.50000 - 12.9904i) q^{87} +(-1.50000 + 2.59808i) q^{88} -6.92820i q^{89} +(-4.50000 + 2.59808i) q^{90} +(8.00000 + 5.19615i) q^{91} +3.46410i q^{92} +(-1.50000 - 0.866025i) q^{93} +(1.50000 + 0.866025i) q^{94} +12.1244i q^{95} +(-1.50000 + 0.866025i) q^{96} +(-9.50000 + 16.4545i) q^{97} +(1.00000 - 6.92820i) q^{98} +(4.50000 + 7.79423i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 3 q^{3} + 2 q^{4} - 3 q^{5} - 3 q^{6} - 4 q^{7} + 2 q^{8} + 3 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - 3 * q^3 + 2 * q^4 - 3 * q^5 - 3 * q^6 - 4 * q^7 + 2 * q^8 + 3 * q^9	\( 2 q + 2 q^{2} - 3 q^{3} + 2 q^{4} - 3 q^{5} - 3 q^{6} - 4 q^{7} + 2 q^{8} + 3 q^{9} - 3 q^{10} - 3 q^{11} - 3 q^{12} - 2 q^{13} - 4 q^{14} + 6 q^{15} + 2 q^{16} - 12 q^{17} + 3 q^{18} - 7 q^{19} - 3 q^{20} + 3 q^{21} - 3 q^{22} - 3 q^{24} - 2 q^{25} - 2 q^{26} - 4 q^{28} - 15 q^{29} + 6 q^{30} + q^{31} + 2 q^{32} - 12 q^{34} + 9 q^{35} + 3 q^{36} - 7 q^{38} + 9 q^{39} - 3 q^{40} + 9 q^{41} + 3 q^{42} - q^{43} - 3 q^{44} - 9 q^{45} + 3 q^{47} - 3 q^{48} + 2 q^{49} - 2 q^{50} + 18 q^{51} - 2 q^{52} - 3 q^{53} + 9 q^{55} - 4 q^{56} + 21 q^{57} - 15 q^{58} + 6 q^{60} + 3 q^{61} + q^{62} + 3 q^{63} + 2 q^{64} - 3 q^{65} - 3 q^{67} - 12 q^{68} - 6 q^{69} + 9 q^{70} + 9 q^{71} + 3 q^{72} + 13 q^{73} + 6 q^{75} - 7 q^{76} - 3 q^{77} + 9 q^{78} - q^{79} - 3 q^{80} - 9 q^{81} + 9 q^{82} + 3 q^{84} + 18 q^{85} - q^{86} + 15 q^{87} - 3 q^{88} - 9 q^{90} + 16 q^{91} - 3 q^{93} + 3 q^{94} - 3 q^{96} - 19 q^{97} + 2 q^{98} + 9 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - 3 * q^3 + 2 * q^4 - 3 * q^5 - 3 * q^6 - 4 * q^7 + 2 * q^8 + 3 * q^9 - 3 * q^10 - 3 * q^11 - 3 * q^12 - 2 * q^13 - 4 * q^14 + 6 * q^15 + 2 * q^16 - 12 * q^17 + 3 * q^18 - 7 * q^19 - 3 * q^20 + 3 * q^21 - 3 * q^22 - 3 * q^24 - 2 * q^25 - 2 * q^26 - 4 * q^28 - 15 * q^29 + 6 * q^30 + q^31 + 2 * q^32 - 12 * q^34 + 9 * q^35 + 3 * q^36 - 7 * q^38 + 9 * q^39 - 3 * q^40 + 9 * q^41 + 3 * q^42 - q^43 - 3 * q^44 - 9 * q^45 + 3 * q^47 - 3 * q^48 + 2 * q^49 - 2 * q^50 + 18 * q^51 - 2 * q^52 - 3 * q^53 + 9 * q^55 - 4 * q^56 + 21 * q^57 - 15 * q^58 + 6 * q^60 + 3 * q^61 + q^62 + 3 * q^63 + 2 * q^64 - 3 * q^65 - 3 * q^67 - 12 * q^68 - 6 * q^69 + 9 * q^70 + 9 * q^71 + 3 * q^72 + 13 * q^73 + 6 * q^75 - 7 * q^76 - 3 * q^77 + 9 * q^78 - q^79 - 3 * q^80 - 9 * q^81 + 9 * q^82 + 3 * q^84 + 18 * q^85 - q^86 + 15 * q^87 - 3 * q^88 - 9 * q^90 + 16 * q^91 - 3 * q^93 + 3 * q^94 - 3 * q^96 - 19 * q^97 + 2 * q^98 + 9 * q^99

Introduction

L-functions

Modular forms

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