LMFDB - Embedded newform 546.2.i.j.235.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("546.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{7})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 7x^{2} + 49 $ x^4 + 7*x^2 + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			235.1
Root			$-1.32288 - 2.29129i$ of defining polynomial
Character	$\chi$	$=$	546.235
Dual form			546.2.i.j.79.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.822876 - 1.42526i) q^{5} -1.00000 q^{6} +(-1.32288 - 2.29129i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.822876 - 1.42526i) q^{5} -1.00000 q^{6} +(-1.32288 - 2.29129i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.822876 - 1.42526i) q^{10} +(2.32288 - 4.02334i) q^{11} +(-0.500000 - 0.866025i) q^{12} +1.00000 q^{13} +(1.32288 - 2.29129i) q^{14} +1.64575 q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.677124 - 1.17281i) q^{17} +(0.500000 - 0.866025i) q^{18} +(-2.50000 - 4.33013i) q^{19} +1.64575 q^{20} +2.64575 q^{21} +4.64575 q^{22} +(3.82288 + 6.62141i) q^{23} +(0.500000 - 0.866025i) q^{24} +(1.14575 - 1.98450i) q^{25} +(0.500000 + 0.866025i) q^{26} +1.00000 q^{27} +2.64575 q^{28} -6.29150 q^{29} +(0.822876 + 1.42526i) q^{30} +(3.64575 - 6.31463i) q^{31} +(0.500000 - 0.866025i) q^{32} +(2.32288 + 4.02334i) q^{33} +1.35425 q^{34} +(-2.17712 + 3.77089i) q^{35} +1.00000 q^{36} +(-0.177124 - 0.306788i) q^{37} +(2.50000 - 4.33013i) q^{38} +(-0.500000 + 0.866025i) q^{39} +(0.822876 + 1.42526i) q^{40} -7.64575 q^{41} +(1.32288 + 2.29129i) q^{42} +5.29150 q^{43} +(2.32288 + 4.02334i) q^{44} +(-0.822876 + 1.42526i) q^{45} +(-3.82288 + 6.62141i) q^{46} +(-1.50000 - 2.59808i) q^{47} +1.00000 q^{48} +(-3.50000 + 6.06218i) q^{49} +2.29150 q^{50} +(0.677124 + 1.17281i) q^{51} +(-0.500000 + 0.866025i) q^{52} +(1.50000 - 2.59808i) q^{53} +(0.500000 + 0.866025i) q^{54} -7.64575 q^{55} +(1.32288 + 2.29129i) q^{56} +5.00000 q^{57} +(-3.14575 - 5.44860i) q^{58} +(-3.96863 + 6.87386i) q^{59} +(-0.822876 + 1.42526i) q^{60} +(-1.96863 - 3.40976i) q^{61} +7.29150 q^{62} +(-1.32288 + 2.29129i) q^{63} +1.00000 q^{64} +(-0.822876 - 1.42526i) q^{65} +(-2.32288 + 4.02334i) q^{66} +(6.79150 - 11.7632i) q^{67} +(0.677124 + 1.17281i) q^{68} -7.64575 q^{69} -4.35425 q^{70} +5.70850 q^{71} +(0.500000 + 0.866025i) q^{72} +(4.17712 - 7.23499i) q^{73} +(0.177124 - 0.306788i) q^{74} +(1.14575 + 1.98450i) q^{75} +5.00000 q^{76} -12.2915 q^{77} -1.00000 q^{78} +(5.00000 + 8.66025i) q^{79} +(-0.822876 + 1.42526i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.82288 - 6.62141i) q^{82} -2.70850 q^{83} +(-1.32288 + 2.29129i) q^{84} -2.22876 q^{85} +(2.64575 + 4.58258i) q^{86} +(3.14575 - 5.44860i) q^{87} +(-2.32288 + 4.02334i) q^{88} +(-0.531373 - 0.920365i) q^{89} -1.64575 q^{90} +(-1.32288 - 2.29129i) q^{91} -7.64575 q^{92} +(3.64575 + 6.31463i) q^{93} +(1.50000 - 2.59808i) q^{94} +(-4.11438 + 7.12631i) q^{95} +(0.500000 + 0.866025i) q^{96} -14.9373 q^{97} -7.00000 q^{98} -4.64575 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{5} - 4 q^{6} - 4 q^{8} - 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^5 - 4 * q^6 - 4 * q^8 - 2 * q^9	$ 4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{5} - 4 q^{6} - 4 q^{8} - 2 q^{9} - 2 q^{10} + 4 q^{11} - 2 q^{12} + 4 q^{13} - 4 q^{15} - 2 q^{16} + 8 q^{17} + 2 q^{18} - 10 q^{19} - 4 q^{20} + 8 q^{22} + 10 q^{23} + 2 q^{24} - 6 q^{25} + 2 q^{26} + 4 q^{27} - 4 q^{29} - 2 q^{30} + 4 q^{31} + 2 q^{32} + 4 q^{33} + 16 q^{34} - 14 q^{35} + 4 q^{36} - 6 q^{37} + 10 q^{38} - 2 q^{39} - 2 q^{40} - 20 q^{41} + 4 q^{44} + 2 q^{45} - 10 q^{46} - 6 q^{47} + 4 q^{48} - 14 q^{49} - 12 q^{50} + 8 q^{51} - 2 q^{52} + 6 q^{53} + 2 q^{54} - 20 q^{55} + 20 q^{57} - 2 q^{58} + 2 q^{60} + 8 q^{61} + 8 q^{62} + 4 q^{64} + 2 q^{65} - 4 q^{66} + 6 q^{67} + 8 q^{68} - 20 q^{69} - 28 q^{70} + 44 q^{71} + 2 q^{72} + 22 q^{73} + 6 q^{74} - 6 q^{75} + 20 q^{76} - 28 q^{77} - 4 q^{78} + 20 q^{79} + 2 q^{80} - 2 q^{81} - 10 q^{82} - 32 q^{83} + 44 q^{85} + 2 q^{87} - 4 q^{88} - 18 q^{89} + 4 q^{90} - 20 q^{92} + 4 q^{93} + 6 q^{94} + 10 q^{95} + 2 q^{96} - 28 q^{97} - 28 q^{98} - 8 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^5 - 4 * q^6 - 4 * q^8 - 2 * q^9 - 2 * q^10 + 4 * q^11 - 2 * q^12 + 4 * q^13 - 4 * q^15 - 2 * q^16 + 8 * q^17 + 2 * q^18 - 10 * q^19 - 4 * q^20 + 8 * q^22 + 10 * q^23 + 2 * q^24 - 6 * q^25 + 2 * q^26 + 4 * q^27 - 4 * q^29 - 2 * q^30 + 4 * q^31 + 2 * q^32 + 4 * q^33 + 16 * q^34 - 14 * q^35 + 4 * q^36 - 6 * q^37 + 10 * q^38 - 2 * q^39 - 2 * q^40 - 20 * q^41 + 4 * q^44 + 2 * q^45 - 10 * q^46 - 6 * q^47 + 4 * q^48 - 14 * q^49 - 12 * q^50 + 8 * q^51 - 2 * q^52 + 6 * q^53 + 2 * q^54 - 20 * q^55 + 20 * q^57 - 2 * q^58 + 2 * q^60 + 8 * q^61 + 8 * q^62 + 4 * q^64 + 2 * q^65 - 4 * q^66 + 6 * q^67 + 8 * q^68 - 20 * q^69 - 28 * q^70 + 44 * q^71 + 2 * q^72 + 22 * q^73 + 6 * q^74 - 6 * q^75 + 20 * q^76 - 28 * q^77 - 4 * q^78 + 20 * q^79 + 2 * q^80 - 2 * q^81 - 10 * q^82 - 32 * q^83 + 44 * q^85 + 2 * q^87 - 4 * q^88 - 18 * q^89 + 4 * q^90 - 20 * q^92 + 4 * q^93 + 6 * q^94 + 10 * q^95 + 2 * q^96 - 28 * q^97 - 28 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.822876	−	1.42526i	−0.368001	−	0.637397i	0.621252	−	0.783611i	$-0.286624\pi$
$5$	−0.822876	−	1.42526i	−0.368001	−	0.637397i	−0.989253	+	0.146214i	$0.953291\pi$
$6$	−1.00000			−0.408248
$7$	−1.32288	−	2.29129i	−0.500000	−	0.866025i
$7$	−1.32288	−	2.29129i	−0.500000	−	0.866025i
$8$	−1.00000			−0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	0.822876	−	1.42526i	0.260216	−	0.450708i
$11$	2.32288	−	4.02334i	0.700373	−	1.21308i	−0.267962	−	0.963429i	$-0.586350\pi$
$11$	2.32288	−	4.02334i	0.700373	−	1.21308i	0.968335	−	0.249653i	$-0.0803165\pi$
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	1.00000			0.277350
$13$	1.00000			0.277350
$14$	1.32288	−	2.29129i	0.353553	−	0.612372i
$15$	1.64575			0.424931
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	0.677124	−	1.17281i	0.164227	−	0.284449i	−0.772154	−	0.635436i	$-0.780820\pi$
$17$	0.677124	−	1.17281i	0.164227	−	0.284449i	0.936380	+	0.350987i	$0.114154\pi$
$18$	0.500000	−	0.866025i	0.117851	−	0.204124i
$19$	−2.50000	−	4.33013i	−0.573539	−	0.993399i	−0.996199	−	0.0871106i	$-0.972237\pi$
$19$	−2.50000	−	4.33013i	−0.573539	−	0.993399i	0.422659	−	0.906289i	$-0.361097\pi$
$20$	1.64575			0.368001
$21$	2.64575			0.577350
$22$	4.64575			0.990478
$23$	3.82288	+	6.62141i	0.797125	+	1.38066i	0.921481	+	0.388423i	$0.126980\pi$
$23$	3.82288	+	6.62141i	0.797125	+	1.38066i	−0.124357	+	0.992238i	$0.539687\pi$
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$	1.14575	−	1.98450i	0.229150	−	0.396900i
$26$	0.500000	+	0.866025i	0.0980581	+	0.169842i
$27$	1.00000			0.192450
$28$	2.64575			0.500000
$29$	−6.29150			−1.16830			−0.584151	−	0.811645i	$-0.698573\pi$
$29$	−6.29150			−1.16830			−0.584151	+	0.811645i	$0.698573\pi$
$30$	0.822876	+	1.42526i	0.150236	+	0.260216i
$31$	3.64575	−	6.31463i	0.654796	−	1.13414i	−0.327149	−	0.944973i	$-0.606088\pi$
$31$	3.64575	−	6.31463i	0.654796	−	1.13414i	0.981945	−	0.189167i	$-0.0605789\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	2.32288	+	4.02334i	0.404361	+	0.700373i
$34$	1.35425			0.232252
$35$	−2.17712	+	3.77089i	−0.368001	+	0.637397i
$36$	1.00000			0.166667
$37$	−0.177124	−	0.306788i	−0.0291191	−	0.0504357i	0.851099	−	0.525006i	$-0.175937\pi$
$37$	−0.177124	−	0.306788i	−0.0291191	−	0.0504357i	−0.880218	+	0.474570i	$0.842604\pi$
$38$	2.50000	−	4.33013i	0.405554	−	0.702439i
$39$	−0.500000	+	0.866025i	−0.0800641	+	0.138675i
$40$	0.822876	+	1.42526i	0.130108	+	0.225354i
$41$	−7.64575			−1.19407			−0.597033	−	0.802217i	$-0.703654\pi$
$41$	−7.64575			−1.19407			−0.597033	+	0.802217i	$0.703654\pi$
$42$	1.32288	+	2.29129i	0.204124	+	0.353553i
$43$	5.29150			0.806947			0.403473	−	0.914991i	$-0.367803\pi$
$43$	5.29150			0.806947			0.403473	+	0.914991i	$0.367803\pi$
$44$	2.32288	+	4.02334i	0.350187	+	0.606541i
$45$	−0.822876	+	1.42526i	−0.122667	+	0.212466i
$46$	−3.82288	+	6.62141i	−0.563652	+	0.976274i
$47$	−1.50000	−	2.59808i	−0.218797	−	0.378968i	0.735643	−	0.677369i	$-0.236880\pi$
$47$	−1.50000	−	2.59808i	−0.218797	−	0.378968i	−0.954441	+	0.298401i	$0.903547\pi$
$48$	1.00000			0.144338
$49$	−3.50000	+	6.06218i	−0.500000	+	0.866025i
$50$	2.29150			0.324067
$51$	0.677124	+	1.17281i	0.0948164	+	0.164227i
$52$	−0.500000	+	0.866025i	−0.0693375	+	0.120096i
$53$	1.50000	−	2.59808i	0.206041	−	0.356873i	−0.744423	−	0.667708i	$-0.767275\pi$
$53$	1.50000	−	2.59808i	0.206041	−	0.356873i	0.950464	+	0.310835i	$0.100609\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$	−7.64575			−1.03095
$56$	1.32288	+	2.29129i	0.176777	+	0.306186i
$57$	5.00000			0.662266
$58$	−3.14575	−	5.44860i	−0.413057	−	0.715436i
$59$	−3.96863	+	6.87386i	−0.516671	+	0.894901i	0.483141	+	0.875542i	$0.339496\pi$
$59$	−3.96863	+	6.87386i	−0.516671	+	0.894901i	−0.999813	+	0.0193585i	$0.993838\pi$
$60$	−0.822876	+	1.42526i	−0.106233	+	0.184001i
$61$	−1.96863	−	3.40976i	−0.252057	−	0.436575i	0.712035	−	0.702144i	$-0.247774\pi$
$61$	−1.96863	−	3.40976i	−0.252057	−	0.436575i	−0.964092	+	0.265569i	$0.914440\pi$
$62$	7.29150			0.926022
$63$	−1.32288	+	2.29129i	−0.166667	+	0.288675i
$64$	1.00000			0.125000
$65$	−0.822876	−	1.42526i	−0.102065	−	0.176782i
$66$	−2.32288	+	4.02334i	−0.285926	+	0.495239i
$67$	6.79150	−	11.7632i	0.829714	−	1.43711i	−0.0685485	−	0.997648i	$-0.521837\pi$
$67$	6.79150	−	11.7632i	0.829714	−	1.43711i	0.898263	−	0.439459i	$-0.144830\pi$
$68$	0.677124	+	1.17281i	0.0821134	+	0.142225i
$69$	−7.64575			−0.920440
$70$	−4.35425			−0.520432
$71$	5.70850			0.677474			0.338737	−	0.940881i	$-0.390000\pi$
$71$	5.70850			0.677474			0.338737	+	0.940881i	$0.390000\pi$
$72$	0.500000	+	0.866025i	0.0589256	+	0.102062i
$73$	4.17712	−	7.23499i	0.488895	−	0.846792i	−0.511023	−	0.859567i	$-0.670733\pi$
$73$	4.17712	−	7.23499i	0.488895	−	0.846792i	0.999918	+	0.0127753i	$0.00406663\pi$
$74$	0.177124	−	0.306788i	0.0205903	−	0.0356634i
$75$	1.14575	+	1.98450i	0.132300	+	0.229150i
$76$	5.00000			0.573539
$77$	−12.2915			−1.40075
$78$	−1.00000			−0.113228
$79$	5.00000	+	8.66025i	0.562544	+	0.974355i	0.997274	+	0.0737937i	$0.0235106\pi$
$79$	5.00000	+	8.66025i	0.562544	+	0.974355i	−0.434730	+	0.900561i	$0.643156\pi$
$80$	−0.822876	+	1.42526i	−0.0920003	+	0.159349i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−3.82288	−	6.62141i	−0.422166	−	0.731213i
$83$	−2.70850			−0.297296			−0.148648	−	0.988890i	$-0.547492\pi$
$83$	−2.70850			−0.297296			−0.148648	+	0.988890i	$0.547492\pi$
$84$	−1.32288	+	2.29129i	−0.144338	+	0.250000i
$85$	−2.22876			−0.241743
$86$	2.64575	+	4.58258i	0.285299	+	0.494152i
$87$	3.14575	−	5.44860i	0.337260	−	0.584151i
$88$	−2.32288	+	4.02334i	−0.247619	+	0.428889i
$89$	−0.531373	−	0.920365i	−0.0563254	−	0.0975585i	0.836488	−	0.547985i	$-0.184605\pi$
$89$	−0.531373	−	0.920365i	−0.0563254	−	0.0975585i	−0.892813	+	0.450427i	$0.851272\pi$
$90$	−1.64575			−0.173477
$91$	−1.32288	−	2.29129i	−0.138675	−	0.240192i
$92$	−7.64575			−0.797125
$93$	3.64575	+	6.31463i	0.378047	+	0.654796i
$94$	1.50000	−	2.59808i	0.154713	−	0.267971i
$95$	−4.11438	+	7.12631i	−0.422126	+	0.731144i
$96$	0.500000	+	0.866025i	0.0510310	+	0.0883883i
$97$	−14.9373			−1.51665			−0.758324	−	0.651878i	$-0.773982\pi$
$97$	−14.9373			−1.51665			−0.758324	+	0.651878i	$0.773982\pi$
$98$	−7.00000			−0.707107
$99$	−4.64575			−0.466916
$100$	1.14575	+	1.98450i	0.114575	+	0.198450i
$101$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$101$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$102$	−0.677124	+	1.17281i	−0.0670453	+	0.116126i
$103$	−2.64575	−	4.58258i	−0.260694	−	0.451535i	0.705733	−	0.708478i	$-0.250618\pi$
$103$	−2.64575	−	4.58258i	−0.260694	−	0.451535i	−0.966426	+	0.256943i	$0.917285\pi$
$104$	−1.00000			−0.0980581
$105$	−2.17712	−	3.77089i	−0.212466	−	0.368001i
$106$	3.00000			0.291386
$107$	6.00000	+	10.3923i	0.580042	+	1.00466i	0.995474	+	0.0950377i	$0.0302972\pi$
$107$	6.00000	+	10.3923i	0.580042	+	1.00466i	−0.415432	+	0.909624i	$0.636370\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	2.00000	−	3.46410i	0.191565	−	0.331801i	−0.754204	−	0.656640i	$-0.771977\pi$
$109$	2.00000	−	3.46410i	0.191565	−	0.331801i	0.945769	+	0.324840i	$0.105310\pi$
$110$	−3.82288	−	6.62141i	−0.364497	−	0.631327i
$111$	0.354249			0.0336238
$112$	−1.32288	+	2.29129i	−0.125000	+	0.216506i
$113$	−11.2288			−1.05631			−0.528156	−	0.849147i	$-0.677116\pi$
$113$	−11.2288			−1.05631			−0.528156	+	0.849147i	$0.677116\pi$
$114$	2.50000	+	4.33013i	0.234146	+	0.405554i
$115$	6.29150	−	10.8972i	0.586686	−	1.01617i
$116$	3.14575	−	5.44860i	0.292076	−	0.505890i
$117$	−0.500000	−	0.866025i	−0.0462250	−	0.0800641i
$118$	−7.93725			−0.730683
$119$	−3.58301			−0.328454
$120$	−1.64575			−0.150236
$121$	−5.29150	−	9.16515i	−0.481046	−	0.833196i
$122$	1.96863	−	3.40976i	0.178231	−	0.308705i
$123$	3.82288	−	6.62141i	0.344697	−	0.597033i
$124$	3.64575	+	6.31463i	0.327398	+	0.567070i
$125$	−12.0000			−1.07331
$126$	−2.64575			−0.235702
$127$	16.2288			1.44007			0.720035	−	0.693938i	$-0.244126\pi$
$127$	16.2288			1.44007			0.720035	+	0.693938i	$0.244126\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−2.64575	+	4.58258i	−0.232945	+	0.403473i
$130$	0.822876	−	1.42526i	0.0721710	−	0.125004i
$131$	2.46863	+	4.27579i	0.215685	+	0.373577i	0.953484	−	0.301443i	$-0.0974683\pi$
$131$	2.46863	+	4.27579i	0.215685	+	0.373577i	−0.737799	+	0.675020i	$0.764135\pi$
$132$	−4.64575			−0.404361
$133$	−6.61438	+	11.4564i	−0.573539	+	0.993399i
$134$	13.5830			1.17339
$135$	−0.822876	−	1.42526i	−0.0708219	−	0.122667i
$136$	−0.677124	+	1.17281i	−0.0580629	+	0.100568i
$137$	−8.76013	+	15.1730i	−0.748428	+	1.29632i	0.200147	+	0.979766i	$0.435858\pi$
$137$	−8.76013	+	15.1730i	−0.748428	+	1.29632i	−0.948576	+	0.316550i	$0.897475\pi$
$138$	−3.82288	−	6.62141i	−0.325425	−	0.563652i
$139$	4.22876			0.358678			0.179339	−	0.983787i	$-0.442604\pi$
$139$	4.22876			0.358678			0.179339	+	0.983787i	$0.442604\pi$
$140$	−2.17712	−	3.77089i	−0.184001	−	0.318698i
$141$	3.00000			0.252646
$142$	2.85425	+	4.94370i	0.239523	+	0.414866i
$143$	2.32288	−	4.02334i	0.194249	−	0.336448i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	5.17712	+	8.96704i	0.429937	+	0.744672i
$146$	8.35425			0.691403
$147$	−3.50000	−	6.06218i	−0.288675	−	0.500000i
$148$	0.354249			0.0291191
$149$	11.4686	+	19.8642i	0.939547	+	1.62734i	0.766319	+	0.642461i	$0.222086\pi$
$149$	11.4686	+	19.8642i	0.939547	+	1.62734i	0.173228	+	0.984882i	$0.444580\pi$
$150$	−1.14575	+	1.98450i	−0.0935502	+	0.162034i
$151$	−10.9686	+	18.9982i	−0.892614	+	1.54605i	−0.0558844	+	0.998437i	$0.517798\pi$
$151$	−10.9686	+	18.9982i	−0.892614	+	1.54605i	−0.836730	+	0.547616i	$0.815536\pi$
$152$	2.50000	+	4.33013i	0.202777	+	0.351220i
$153$	−1.35425			−0.109485
$154$	−6.14575	−	10.6448i	−0.495239	−	0.857779i
$155$	−12.0000			−0.963863
$156$	−0.500000	−	0.866025i	−0.0400320	−	0.0693375i
$157$	1.32288	−	2.29129i	0.105577	−	0.182865i	−0.808397	−	0.588638i	$-0.799664\pi$
$157$	1.32288	−	2.29129i	0.105577	−	0.182865i	0.913974	+	0.405773i	$0.132998\pi$
$158$	−5.00000	+	8.66025i	−0.397779	+	0.688973i
$159$	1.50000	+	2.59808i	0.118958	+	0.206041i
$160$	−1.64575			−0.130108
$161$	10.1144	−	17.5186i	0.797125	−	1.38066i
$162$	−1.00000			−0.0785674
$163$	−11.7915	−	20.4235i	−0.923582	−	1.59969i	−0.793826	−	0.608145i	$-0.791914\pi$
$163$	−11.7915	−	20.4235i	−0.923582	−	1.59969i	−0.129755	−	0.991546i	$-0.541419\pi$
$164$	3.82288	−	6.62141i	0.298516	−	0.517046i
$165$	3.82288	−	6.62141i	0.297610	−	0.515476i
$166$	−1.35425	−	2.34563i	−0.105110	−	0.182056i
$167$	24.8745			1.92485			0.962424	−	0.271553i	$-0.0875371\pi$
$167$	24.8745			1.92485			0.962424	+	0.271553i	$0.0875371\pi$
$168$	−2.64575			−0.204124
$169$	1.00000			0.0769231
$170$	−1.11438	−	1.93016i	−0.0854689	−	0.148036i
$171$	−2.50000	+	4.33013i	−0.191180	+	0.331133i
$172$	−2.64575	+	4.58258i	−0.201737	+	0.349418i
$173$	5.85425	+	10.1399i	0.445090	+	0.770919i	0.998059	−	0.0622834i	$-0.0198382\pi$
$173$	5.85425	+	10.1399i	0.445090	+	0.770919i	−0.552968	+	0.833202i	$0.686505\pi$
$174$	6.29150			0.476958
$175$	−6.06275			−0.458301
$176$	−4.64575			−0.350187
$177$	−3.96863	−	6.87386i	−0.298300	−	0.516671i
$178$	0.531373	−	0.920365i	0.0398281	−	0.0689843i
$179$	3.00000	−	5.19615i	0.224231	−	0.388379i	−0.731858	−	0.681457i	$-0.761346\pi$
$179$	3.00000	−	5.19615i	0.224231	−	0.388379i	0.956088	+	0.293079i	$0.0946798\pi$
$180$	−0.822876	−	1.42526i	−0.0613335	−	0.106233i
$181$	9.35425			0.695296			0.347648	−	0.937625i	$-0.386980\pi$
$181$	9.35425			0.695296			0.347648	+	0.937625i	$0.386980\pi$
$182$	1.32288	−	2.29129i	0.0980581	−	0.169842i
$183$	3.93725			0.291050
$184$	−3.82288	−	6.62141i	−0.281826	−	0.488137i
$185$	−0.291503	+	0.504897i	−0.0214317	+	0.0371208i
$186$	−3.64575	+	6.31463i	−0.267319	+	0.463011i
$187$	−3.14575	−	5.44860i	−0.230040	−	0.398441i
$188$	3.00000			0.218797
$189$	−1.32288	−	2.29129i	−0.0962250	−	0.166667i
$190$	−8.22876			−0.596977
$191$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$191$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	−1.53137	+	2.65242i	−0.110231	+	0.190925i	−0.915863	−	0.401490i	$-0.868492\pi$
$193$	−1.53137	+	2.65242i	−0.110231	+	0.190925i	0.805633	+	0.592416i	$0.201826\pi$
$194$	−7.46863	−	12.9360i	−0.536216	−	0.928754i
$195$	1.64575			0.117855
$196$	−3.50000	−	6.06218i	−0.250000	−	0.433013i
$197$	20.8118			1.48278			0.741388	−	0.671076i	$-0.234168\pi$
$197$	20.8118			1.48278			0.741388	+	0.671076i	$0.234168\pi$
$198$	−2.32288	−	4.02334i	−0.165080	−	0.285926i
$199$	−2.11438	+	3.66221i	−0.149884	+	0.259607i	−0.931185	−	0.364548i	$-0.881223\pi$
$199$	−2.11438	+	3.66221i	−0.149884	+	0.259607i	0.781300	+	0.624155i	$0.214557\pi$
$200$	−1.14575	+	1.98450i	−0.0810169	+	0.140325i
$201$	6.79150	+	11.7632i	0.479036	+	0.829714i
$202$		0			0
$203$	8.32288	+	14.4156i	0.584151	+	1.01178i
$204$	−1.35425			−0.0948164
$205$	6.29150	+	10.8972i	0.439418	+	0.761094i
$206$	2.64575	−	4.58258i	0.184338	−	0.319283i
$207$	3.82288	−	6.62141i	0.265708	−	0.460220i
$208$	−0.500000	−	0.866025i	−0.0346688	−	0.0600481i
$209$	−23.2288			−1.60677
$210$	2.17712	−	3.77089i	0.150236	−	0.260216i
$211$	−11.6458			−0.801727			−0.400863	−	0.916138i	$-0.631290\pi$
$211$	−11.6458			−0.801727			−0.400863	+	0.916138i	$0.631290\pi$
$212$	1.50000	+	2.59808i	0.103020	+	0.178437i
$213$	−2.85425	+	4.94370i	−0.195570	+	0.338737i
$214$	−6.00000	+	10.3923i	−0.410152	+	0.710403i
$215$	−4.35425	−	7.54178i	−0.296957	−	0.514345i
$216$	−1.00000			−0.0680414
$217$	−19.2915			−1.30959
$218$	4.00000			0.270914
$219$	4.17712	+	7.23499i	0.282264	+	0.488895i
$220$	3.82288	−	6.62141i	0.257738	−	0.446416i
$221$	0.677124	−	1.17281i	0.0455483	−	0.0788920i
$222$	0.177124	+	0.306788i	0.0118878	+	0.0205903i
$223$	16.5203			1.10628			0.553139	−	0.833089i	$-0.313430\pi$
$223$	16.5203			1.10628			0.553139	+	0.833089i	$0.313430\pi$
$224$	−2.64575			−0.176777
$225$	−2.29150			−0.152767
$226$	−5.61438	−	9.72439i	−0.373463	−	0.646857i
$227$	7.64575	−	13.2428i	0.507466	−	0.878957i	−0.492496	−	0.870315i	$-0.663915\pi$
$227$	7.64575	−	13.2428i	0.507466	−	0.878957i	0.999963	−	0.00864295i	$-0.00275117\pi$
$228$	−2.50000	+	4.33013i	−0.165567	+	0.286770i
$229$	13.2288	+	22.9129i	0.874181	+	1.51413i	0.857633	+	0.514263i	$0.171934\pi$
$229$	13.2288	+	22.9129i	0.874181	+	1.51413i	0.0165480	+	0.999863i	$0.494732\pi$
$230$	12.5830			0.829699
$231$	6.14575	−	10.6448i	0.404361	−	0.700373i
$232$	6.29150			0.413057
$233$	2.32288	+	4.02334i	0.152177	+	0.263578i	0.932027	−	0.362388i	$-0.118038\pi$
$233$	2.32288	+	4.02334i	0.152177	+	0.263578i	−0.779851	+	0.625965i	$0.784705\pi$
$234$	0.500000	−	0.866025i	0.0326860	−	0.0566139i
$235$	−2.46863	+	4.27579i	−0.161035	+	0.278922i
$236$	−3.96863	−	6.87386i	−0.258336	−	0.447450i
$237$	−10.0000			−0.649570
$238$	−1.79150	−	3.10297i	−0.116126	−	0.201136i
$239$	3.00000			0.194054			0.0970269	−	0.995282i	$-0.469067\pi$
$239$	3.00000			0.194054			0.0970269	+	0.995282i	$0.469067\pi$
$240$	−0.822876	−	1.42526i	−0.0531164	−	0.0920003i
$241$	−8.93725	+	15.4798i	−0.575699	+	0.997140i	0.420266	+	0.907401i	$0.361937\pi$
$241$	−8.93725	+	15.4798i	−0.575699	+	0.997140i	−0.995965	+	0.0897393i	$0.971397\pi$
$242$	5.29150	−	9.16515i	0.340151	−	0.589158i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	3.93725			0.252057
$245$	11.5203			0.736002
$246$	7.64575			0.487475
$247$	−2.50000	−	4.33013i	−0.159071	−	0.275519i
$248$	−3.64575	+	6.31463i	−0.231505	+	0.400979i
$249$	1.35425	−	2.34563i	0.0858220	−	0.148648i
$250$	−6.00000	−	10.3923i	−0.379473	−	0.657267i
$251$	−2.70850			−0.170959			−0.0854794	−	0.996340i	$-0.527242\pi$
$251$	−2.70850			−0.170959			−0.0854794	+	0.996340i	$0.527242\pi$
$252$	−1.32288	−	2.29129i	−0.0833333	−	0.144338i
$253$	35.5203			2.23314
$254$	8.11438	+	14.0545i	0.509141	+	0.881859i
$255$	1.11438	−	1.93016i	0.0697851	−	0.120871i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−7.93725	−	13.7477i	−0.495112	−	0.857560i	0.504872	−	0.863194i	$-0.331540\pi$
$257$	−7.93725	−	13.7477i	−0.495112	−	0.857560i	−0.999984	+	0.00563467i	$0.998206\pi$
$258$	−5.29150			−0.329435
$259$	−0.468627	+	0.811686i	−0.0291191	+	0.0504357i
$260$	1.64575			0.102065
$261$	3.14575	+	5.44860i	0.194717	+	0.337260i
$262$	−2.46863	+	4.27579i	−0.152512	+	0.264159i
$263$	−0.822876	+	1.42526i	−0.0507407	+	0.0878854i	−0.890280	−	0.455413i	$-0.849492\pi$
$263$	−0.822876	+	1.42526i	−0.0507407	+	0.0878854i	0.839539	+	0.543299i	$0.182825\pi$
$264$	−2.32288	−	4.02334i	−0.142963	−	0.247619i
$265$	−4.93725			−0.303293
$266$	−13.2288			−0.811107
$267$	1.06275			0.0650390
$268$	6.79150	+	11.7632i	0.414857	+	0.718553i
$269$	12.4373	−	21.5420i	0.758313	−	1.31344i	−0.185398	−	0.982664i	$-0.559357\pi$
$269$	12.4373	−	21.5420i	0.758313	−	1.31344i	0.943710	−	0.330773i	$-0.107309\pi$
$270$	0.822876	−	1.42526i	0.0500786	−	0.0867387i
$271$	8.67712	+	15.0292i	0.527098	+	0.912960i	0.999501	+	0.0315777i	$0.0100532\pi$
$271$	8.67712	+	15.0292i	0.527098	+	0.912960i	−0.472404	+	0.881382i	$0.656613\pi$
$272$	−1.35425			−0.0821134
$273$	2.64575			0.160128
$274$	−17.5203			−1.05844
$275$	−5.32288	−	9.21949i	−0.320981	−	0.555956i
$276$	3.82288	−	6.62141i	0.230110	−	0.398562i
$277$	9.26013	−	16.0390i	0.556387	−	0.963691i	−0.441407	−	0.897307i	$-0.645520\pi$
$277$	9.26013	−	16.0390i	0.556387	−	0.963691i	0.997794	−	0.0663840i	$-0.0211462\pi$
$278$	2.11438	+	3.66221i	0.126812	+	0.219645i
$279$	−7.29150			−0.436531
$280$	2.17712	−	3.77089i	0.130108	−	0.225354i
$281$	18.5830			1.10857			0.554285	−	0.832327i	$-0.312992\pi$
$281$	18.5830			1.10857			0.554285	+	0.832327i	$0.312992\pi$
$282$	1.50000	+	2.59808i	0.0893237	+	0.154713i
$283$	13.4686	−	23.3283i	0.800627	−	1.38673i	−0.118577	−	0.992945i	$-0.537833\pi$
$283$	13.4686	−	23.3283i	0.800627	−	1.38673i	0.919204	−	0.393781i	$-0.128833\pi$
$284$	−2.85425	+	4.94370i	−0.169368	+	0.293355i
$285$	−4.11438	−	7.12631i	−0.243715	−	0.422126i
$286$	4.64575			0.274709
$287$	10.1144	+	17.5186i	0.597033	+	1.03409i
$288$	−1.00000			−0.0589256
$289$	7.58301	+	13.1342i	0.446059	+	0.772597i
$290$	−5.17712	+	8.96704i	−0.304011	+	0.526563i
$291$	7.46863	−	12.9360i	0.437819	−	0.758324i
$292$	4.17712	+	7.23499i	0.244448	+	0.423396i
$293$	−29.5203			−1.72459			−0.862296	−	0.506405i	$-0.830974\pi$
$293$	−29.5203			−1.72459			−0.862296	+	0.506405i	$0.830974\pi$
$294$	3.50000	−	6.06218i	0.204124	−	0.353553i
$295$	13.0627			0.760542
$296$	0.177124	+	0.306788i	0.0102951	+	0.0178317i
$297$	2.32288	−	4.02334i	0.134787	−	0.233458i
$298$	−11.4686	+	19.8642i	−0.664360	+	1.15070i
$299$	3.82288	+	6.62141i	0.221083	+	0.382926i
$300$	−2.29150			−0.132300
$301$	−7.00000	−	12.1244i	−0.403473	−	0.698836i
$302$	−21.9373			−1.26235
$303$		0			0
$304$	−2.50000	+	4.33013i	−0.143385	+	0.248350i
$305$	−3.23987	+	5.61162i	−0.185514	+	0.321320i
$306$	−0.677124	−	1.17281i	−0.0387086	−	0.0670453i
$307$	11.5830			0.661077			0.330539	−	0.943793i	$-0.392770\pi$
$307$	11.5830			0.661077			0.330539	+	0.943793i	$0.392770\pi$
$308$	6.14575	−	10.6448i	0.350187	−	0.606541i
$309$	5.29150			0.301023
$310$	−6.00000	−	10.3923i	−0.340777	−	0.590243i
$311$	8.46863	−	14.6681i	0.480212	−	0.831751i	−0.519531	−	0.854452i	$-0.673893\pi$
$311$	8.46863	−	14.6681i	0.480212	−	0.831751i	0.999742	+	0.0227007i	$0.00722647\pi$
$312$	0.500000	−	0.866025i	0.0283069	−	0.0490290i
$313$	14.5830	+	25.2585i	0.824280	+	1.42770i	0.902468	+	0.430757i	$0.141753\pi$
$313$	14.5830	+	25.2585i	0.824280	+	1.42770i	−0.0781880	+	0.996939i	$0.524913\pi$
$314$	2.64575			0.149308
$315$	4.35425			0.245334
$316$	−10.0000			−0.562544
$317$	1.35425	+	2.34563i	0.0760622	+	0.131744i	0.901548	−	0.432680i	$-0.142432\pi$
$317$	1.35425	+	2.34563i	0.0760622	+	0.131744i	−0.825486	+	0.564423i	$0.809099\pi$
$318$	−1.50000	+	2.59808i	−0.0841158	+	0.145693i
$319$	−14.6144	+	25.3128i	−0.818248	+	1.41725i
$320$	−0.822876	−	1.42526i	−0.0460001	−	0.0796746i
$321$	−12.0000			−0.669775
$322$	20.2288			1.12730
$323$	−6.77124			−0.376762
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	1.14575	−	1.98450i	0.0635548	−	0.110080i
$326$	11.7915	−	20.4235i	0.653071	−	1.13115i
$327$	2.00000	+	3.46410i	0.110600	+	0.191565i
$328$	7.64575			0.422166
$329$	−3.96863	+	6.87386i	−0.218797	+	0.378968i
$330$	7.64575			0.420885
$331$	−16.2915	−	28.2177i	−0.895462	−	1.55099i	−0.833232	−	0.552924i	$-0.813512\pi$
$331$	−16.2915	−	28.2177i	−0.895462	−	1.55099i	−0.0622301	−	0.998062i	$-0.519821\pi$
$332$	1.35425	−	2.34563i	0.0743241	−	0.128733i
$333$	−0.177124	+	0.306788i	−0.00970635	+	0.0168119i
$334$	12.4373	+	21.5420i	0.680536	+	1.17872i
$335$	−22.3542			−1.22134
$336$	−1.32288	−	2.29129i	−0.0721688	−	0.125000i
$337$	5.58301			0.304126			0.152063	−	0.988371i	$-0.451408\pi$
$337$	5.58301			0.304126			0.152063	+	0.988371i	$0.451408\pi$
$338$	0.500000	+	0.866025i	0.0271964	+	0.0471056i
$339$	5.61438	−	9.72439i	0.304931	−	0.528156i
$340$	1.11438	−	1.93016i	0.0604356	−	0.104678i
$341$	−16.9373	−	29.3362i	−0.917204	−	1.58864i
$342$	−5.00000			−0.270369
$343$	18.5203			1.00000
$344$	−5.29150			−0.285299
$345$	6.29150	+	10.8972i	0.338723	+	0.586686i
$346$	−5.85425	+	10.1399i	−0.314726	+	0.545122i
$347$	13.1144	−	22.7148i	0.704017	−	1.21939i	−0.263029	−	0.964788i	$-0.584721\pi$
$347$	13.1144	−	22.7148i	0.704017	−	1.21939i	0.967045	−	0.254605i	$-0.0819453\pi$
$348$	3.14575	+	5.44860i	0.168630	+	0.292076i
$349$	3.06275			0.163945			0.0819725	−	0.996635i	$-0.473878\pi$
$349$	3.06275			0.163945			0.0819725	+	0.996635i	$0.473878\pi$
$350$	−3.03137	−	5.25049i	−0.162034	−	0.280651i
$351$	1.00000			0.0533761
$352$	−2.32288	−	4.02334i	−0.123810	−	0.214445i
$353$	−0.291503	+	0.504897i	−0.0155151	+	0.0268730i	−0.873679	−	0.486503i	$-0.838272\pi$
$353$	−0.291503	+	0.504897i	−0.0155151	+	0.0268730i	0.858164	+	0.513376i	$0.171605\pi$
$354$	3.96863	−	6.87386i	0.210930	−	0.365342i
$355$	−4.69738	−	8.13611i	−0.249311	−	0.431820i
$356$	1.06275			0.0563254
$357$	1.79150	−	3.10297i	0.0948164	−	0.164227i
$358$	6.00000			0.317110
$359$	3.00000	+	5.19615i	0.158334	+	0.274242i	0.934268	−	0.356572i	$-0.116054\pi$
$359$	3.00000	+	5.19615i	0.158334	+	0.274242i	−0.775934	+	0.630814i	$0.782721\pi$
$360$	0.822876	−	1.42526i	0.0433694	−	0.0751179i
$361$	−3.00000	+	5.19615i	−0.157895	+	0.273482i
$362$	4.67712	+	8.10102i	0.245824	+	0.425780i
$363$	10.5830			0.555464
$364$	2.64575			0.138675
$365$	−13.7490			−0.719656
$366$	1.96863	+	3.40976i	0.102902	+	0.178231i
$367$	−10.2915	+	17.8254i	−0.537212	+	0.930479i	0.461841	+	0.886963i	$0.347189\pi$
$367$	−10.2915	+	17.8254i	−0.537212	+	0.930479i	−0.999053	+	0.0435157i	$0.986144\pi$
$368$	3.82288	−	6.62141i	0.199281	−	0.345165i
$369$	3.82288	+	6.62141i	0.199011	+	0.344697i
$370$	−0.583005			−0.0303090
$371$	−7.93725			−0.412082
$372$	−7.29150			−0.378047
$373$	−4.67712	−	8.10102i	−0.242172	−	0.419455i	0.719160	−	0.694844i	$-0.244527\pi$
$373$	−4.67712	−	8.10102i	−0.242172	−	0.419455i	−0.961333	+	0.275389i	$0.911193\pi$
$374$	3.14575	−	5.44860i	0.162663	−	0.281740i
$375$	6.00000	−	10.3923i	0.309839	−	0.536656i
$376$	1.50000	+	2.59808i	0.0773566	+	0.133986i
$377$	−6.29150			−0.324029
$378$	1.32288	−	2.29129i	0.0680414	−	0.117851i
$379$	33.1660			1.70362			0.851812	−	0.523848i	$-0.175504\pi$
$379$	33.1660			1.70362			0.851812	+	0.523848i	$0.175504\pi$
$380$	−4.11438	−	7.12631i	−0.211063	−	0.365572i
$381$	−8.11438	+	14.0545i	−0.415712	+	0.720035i
$382$		0			0
$383$	18.8745	+	32.6916i	0.964442	+	1.67046i	0.711106	+	0.703085i	$0.248195\pi$
$383$	18.8745	+	32.6916i	0.964442	+	1.67046i	0.253336	+	0.967378i	$0.418472\pi$
$384$	−1.00000			−0.0510310
$385$	10.1144	+	17.5186i	0.515476	+	0.892831i
$386$	−3.06275			−0.155890
$387$	−2.64575	−	4.58258i	−0.134491	−	0.232945i
$388$	7.46863	−	12.9360i	0.379162	−	0.656728i
$389$	−9.14575	+	15.8409i	−0.463708	+	0.803166i	−0.999142	−	0.0414111i	$-0.986815\pi$
$389$	−9.14575	+	15.8409i	−0.463708	+	0.803166i	0.535434	+	0.844577i	$0.320148\pi$
$390$	0.822876	+	1.42526i	0.0416679	+	0.0721710i
$391$	10.3542			0.523637
$392$	3.50000	−	6.06218i	0.176777	−	0.306186i
$393$	−4.93725			−0.249052
$394$	10.4059	+	18.0235i	0.524241	+	0.908012i
$395$	8.22876	−	14.2526i	0.414034	−	0.717127i
$396$	2.32288	−	4.02334i	0.116729	−	0.202180i
$397$	−0.468627	−	0.811686i	−0.0235197	−	0.0407373i	0.854026	−	0.520230i	$-0.174154\pi$
$397$	−0.468627	−	0.811686i	−0.0235197	−	0.0407373i	−0.877546	+	0.479493i	$0.840821\pi$
$398$	−4.22876			−0.211968
$399$	−6.61438	−	11.4564i	−0.331133	−	0.573539i
$400$	−2.29150			−0.114575
$401$	−4.11438	−	7.12631i	−0.205462	−	0.355871i	0.744818	−	0.667268i	$-0.232536\pi$
$401$	−4.11438	−	7.12631i	−0.205462	−	0.355871i	−0.950280	+	0.311397i	$0.899203\pi$
$402$	−6.79150	+	11.7632i	−0.338729	+	0.586696i
$403$	3.64575	−	6.31463i	0.181608	−	0.314554i
$404$		0			0
$405$	1.64575			0.0817780
$406$	−8.32288	+	14.4156i	−0.413057	+	0.715436i
$407$	−1.64575			−0.0815769
$408$	−0.677124	−	1.17281i	−0.0335227	−	0.0580629i
$409$	5.53137	−	9.58062i	0.273509	−	0.473731i	−0.696249	−	0.717800i	$-0.745149\pi$
$409$	5.53137	−	9.58062i	0.273509	−	0.473731i	0.969758	+	0.244069i	$0.0784824\pi$
$410$	−6.29150	+	10.8972i	−0.310715	+	0.538174i
$411$	−8.76013	−	15.1730i	−0.432105	−	0.748428i
$412$	5.29150			0.260694
$413$	21.0000			1.03334
$414$	7.64575			0.375768
$415$	2.22876	+	3.86032i	0.109405	+	0.189496i
$416$	0.500000	−	0.866025i	0.0245145	−	0.0424604i
$417$	−2.11438	+	3.66221i	−0.103542	+	0.179339i
$418$	−11.6144	−	20.1167i	−0.568078	−	0.983940i
$419$	−22.4575			−1.09712			−0.548561	−	0.836111i	$-0.684824\pi$
$419$	−22.4575			−1.09712			−0.548561	+	0.836111i	$0.684824\pi$
$420$	4.35425			0.212466
$421$	−29.6458			−1.44485			−0.722423	−	0.691452i	$-0.756972\pi$
$421$	−29.6458			−1.44485			−0.722423	+	0.691452i	$0.756972\pi$
$422$	−5.82288	−	10.0855i	−0.283453	−	0.490955i
$423$	−1.50000	+	2.59808i	−0.0729325	+	0.126323i
$424$	−1.50000	+	2.59808i	−0.0728464	+	0.126174i
$425$	−1.55163	−	2.68751i	−0.0752652	−	0.130363i
$426$	−5.70850			−0.276578
$427$	−5.20850	+	9.02138i	−0.252057	+	0.436575i
$428$	−12.0000			−0.580042
$429$	2.32288	+	4.02334i	0.112149	+	0.194249i
$430$	4.35425	−	7.54178i	0.209981	−	0.363697i
$431$	0.291503	−	0.504897i	0.0140412	−	0.0243200i	−0.858919	−	0.512111i	$-0.828864\pi$
$431$	0.291503	−	0.504897i	0.0140412	−	0.0243200i	0.872961	+	0.487791i	$0.162197\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	−12.4170			−0.596723			−0.298361	−	0.954453i	$-0.596440\pi$
$433$	−12.4170			−0.596723			−0.298361	+	0.954453i	$0.596440\pi$
$434$	−9.64575	−	16.7069i	−0.463011	−	0.801958i
$435$	−10.3542			−0.496448
$436$	2.00000	+	3.46410i	0.0957826	+	0.165900i
$437$	19.1144	−	33.1071i	0.914365	−	1.58373i
$438$	−4.17712	+	7.23499i	−0.199591	+	0.345701i
$439$	−9.17712	−	15.8952i	−0.438000	−	0.758639i	0.559535	−	0.828807i	$-0.310980\pi$
$439$	−9.17712	−	15.8952i	−0.438000	−	0.758639i	−0.997535	+	0.0701681i	$0.977646\pi$
$440$	7.64575			0.364497
$441$	7.00000			0.333333
$442$	1.35425			0.0644150
$443$	−17.4686	−	30.2565i	−0.829960	−	1.43753i	−0.898069	−	0.439854i	$-0.855030\pi$
$443$	−17.4686	−	30.2565i	−0.829960	−	1.43753i	0.0681097	−	0.997678i	$-0.478303\pi$
$444$	−0.177124	+	0.306788i	−0.00840595	+	0.0145595i
$445$	−0.874508	+	1.51469i	−0.0414556	+	0.0718033i
$446$	8.26013	+	14.3070i	0.391128	+	0.677454i
$447$	−22.9373			−1.08489
$448$	−1.32288	−	2.29129i	−0.0625000	−	0.108253i
$449$	12.0000			0.566315			0.283158	−	0.959073i	$-0.408618\pi$
$449$	12.0000			0.566315			0.283158	+	0.959073i	$0.408618\pi$
$450$	−1.14575	−	1.98450i	−0.0540112	−	0.0935502i
$451$	−17.7601	+	30.7614i	−0.836292	+	1.44850i
$452$	5.61438	−	9.72439i	0.264078	−	0.457397i
$453$	−10.9686	−	18.9982i	−0.515351	−	0.892614i
$454$	15.2915			0.717666
$455$	−2.17712	+	3.77089i	−0.102065	+	0.176782i
$456$	−5.00000			−0.234146
$457$	−2.88562	−	4.99804i	−0.134984	−	0.233799i	0.790608	−	0.612323i	$-0.209765\pi$
$457$	−2.88562	−	4.99804i	−0.134984	−	0.233799i	−0.925591	+	0.378525i	$0.876432\pi$
$458$	−13.2288	+	22.9129i	−0.618139	+	1.07065i
$459$	0.677124	−	1.17281i	0.0316055	−	0.0547423i
$460$	6.29150	+	10.8972i	0.293343	+	0.508085i
$461$	16.4575			0.766503			0.383251	−	0.923644i	$-0.374804\pi$
$461$	16.4575			0.766503			0.383251	+	0.923644i	$0.374804\pi$
$462$	12.2915			0.571852
$463$	−17.1660			−0.797772			−0.398886	−	0.917000i	$-0.630603\pi$
$463$	−17.1660			−0.797772			−0.398886	+	0.917000i	$0.630603\pi$
$464$	3.14575	+	5.44860i	0.146038	+	0.252945i
$465$	6.00000	−	10.3923i	0.278243	−	0.481932i
$466$	−2.32288	+	4.02334i	−0.107605	+	0.186378i
$467$	0.239870	+	0.415468i	0.0110999	+	0.0192256i	0.871522	−	0.490356i	$-0.163133\pi$
$467$	0.239870	+	0.415468i	0.0110999	+	0.0192256i	−0.860422	+	0.509582i	$0.829800\pi$
$468$	1.00000			0.0462250
$469$	−35.9373			−1.65943
$470$	−4.93725			−0.227739
$471$	1.32288	+	2.29129i	0.0609549	+	0.105577i
$472$	3.96863	−	6.87386i	0.182671	−	0.316395i
$473$	12.2915	−	21.2895i	0.565164	−	0.978893i
$474$	−5.00000	−	8.66025i	−0.229658	−	0.397779i
$475$	−11.4575			−0.525707
$476$	1.79150	−	3.10297i	0.0821134	−	0.142225i
$477$	−3.00000			−0.137361
$478$	1.50000	+	2.59808i	0.0686084	+	0.118833i
$479$	−14.3745	+	24.8974i	−0.656788	+	1.13759i	0.324654	+	0.945833i	$0.394752\pi$
$479$	−14.3745	+	24.8974i	−0.656788	+	1.13759i	−0.981442	+	0.191757i	$0.938581\pi$
$480$	0.822876	−	1.42526i	0.0375590	−	0.0650540i
$481$	−0.177124	−	0.306788i	−0.00807617	−	0.0139883i
$482$	−17.8745			−0.814162
$483$	10.1144	+	17.5186i	0.460220	+	0.797125i
$484$	10.5830			0.481046
$485$	12.2915	+	21.2895i	0.558128	+	0.966707i
$486$	0.500000	−	0.866025i	0.0226805	−	0.0392837i
$487$	4.03137	−	6.98254i	0.182679	−	0.316409i	−0.760113	−	0.649791i	$-0.774856\pi$
$487$	4.03137	−	6.98254i	0.182679	−	0.316409i	0.942792	+	0.333382i	$0.108190\pi$
$488$	1.96863	+	3.40976i	0.0891156	+	0.154353i
$489$	23.5830			1.06646
$490$	5.76013	+	9.97684i	0.260216	+	0.450708i
$491$	−31.1660			−1.40650			−0.703251	−	0.710941i	$-0.748269\pi$
$491$	−31.1660			−1.40650			−0.703251	+	0.710941i	$0.748269\pi$
$492$	3.82288	+	6.62141i	0.172349	+	0.298516i
$493$	−4.26013	+	7.37876i	−0.191867	+	0.332323i
$494$	2.50000	−	4.33013i	0.112480	−	0.194822i
$495$	3.82288	+	6.62141i	0.171825	+	0.297610i
$496$	−7.29150			−0.327398
$497$	−7.55163	−	13.0798i	−0.338737	−	0.586710i
$498$	2.70850			0.121371
$499$	9.35425	+	16.2020i	0.418754	+	0.725303i	0.995814	−	0.0913986i	$-0.0291337\pi$
$499$	9.35425	+	16.2020i	0.418754	+	0.725303i	−0.577061	+	0.816701i	$0.695800\pi$
$500$	6.00000	−	10.3923i	0.268328	−	0.464758i
$501$	−12.4373	+	21.5420i	−0.555656	+	0.962424i
$502$	−1.35425	−	2.34563i	−0.0604431	−	0.104690i
$503$	−16.4575			−0.733804			−0.366902	−	0.930260i	$-0.619582\pi$
$503$	−16.4575			−0.733804			−0.366902	+	0.930260i	$0.619582\pi$
$504$	1.32288	−	2.29129i	0.0589256	−	0.102062i
$505$		0			0
$506$	17.7601	+	30.7614i	0.789534	+	1.36751i
$507$	−0.500000	+	0.866025i	−0.0222058	+	0.0384615i
$508$	−8.11438	+	14.0545i	−0.360017	+	0.623568i
$509$	−12.0000	−	20.7846i	−0.531891	−	0.921262i	−0.999307	−	0.0372243i	$-0.988148\pi$
$509$	−12.0000	−	20.7846i	−0.531891	−	0.921262i	0.467416	−	0.884037i	$-0.345185\pi$
$510$	2.22876			0.0986910
$511$	−22.1033			−0.977791
$512$	−1.00000			−0.0441942
$513$	−2.50000	−	4.33013i	−0.110378	−	0.191180i
$514$	7.93725	−	13.7477i	0.350097	−	0.606386i
$515$	−4.35425	+	7.54178i	−0.191871	+	0.332331i
$516$	−2.64575	−	4.58258i	−0.116473	−	0.201737i
$517$	−13.9373			−0.612960
$518$	−0.937254			−0.0411806
$519$	−11.7085			−0.513946
$520$	0.822876	+	1.42526i	0.0360855	+	0.0625019i
$521$	−9.00000	+	15.5885i	−0.394297	+	0.682943i	−0.993011	−	0.118020i	$-0.962345\pi$
$521$	−9.00000	+	15.5885i	−0.394297	+	0.682943i	0.598714	+	0.800963i	$0.295679\pi$
$522$	−3.14575	+	5.44860i	−0.137686	+	0.238479i
$523$	18.6458	+	32.2954i	0.815322	+	1.41218i	0.909097	+	0.416585i	$0.136773\pi$
$523$	18.6458	+	32.2954i	0.815322	+	1.41218i	−0.0937748	+	0.995593i	$0.529893\pi$
$524$	−4.93725			−0.215685
$525$	3.03137	−	5.25049i	0.132300	−	0.229150i
$526$	−1.64575			−0.0717582
$527$	−4.93725	−	8.55157i	−0.215070	−	0.372512i
$528$	2.32288	−	4.02334i	0.101090	−	0.175093i
$529$	−17.7288	+	30.7071i	−0.770816	+	1.33509i
$530$	−2.46863	−	4.27579i	−0.107230	−	0.185728i
$531$	7.93725			0.344447
$532$	−6.61438	−	11.4564i	−0.286770	−	0.496700i
$533$	−7.64575			−0.331174
$534$	0.531373	+	0.920365i	0.0229948	+	0.0398281i
$535$	9.87451	−	17.1031i	0.426912	−	0.739434i
$536$	−6.79150	+	11.7632i	−0.293348	+	0.508094i
$537$	3.00000	+	5.19615i	0.129460	+	0.224231i
$538$	24.8745			1.07242
$539$	16.2601	+	28.1634i	0.700373	+	1.21308i
$540$	1.64575			0.0708219
$541$	−18.1771	−	31.4837i	−0.781496	−	1.35359i	−0.931070	−	0.364840i	$-0.881124\pi$
$541$	−18.1771	−	31.4837i	−0.781496	−	1.35359i	0.149575	−	0.988750i	$-0.452210\pi$
$542$	−8.67712	+	15.0292i	−0.372714	+	0.645560i
$543$	−4.67712	+	8.10102i	−0.200715	+	0.347648i
$544$	−0.677124	−	1.17281i	−0.0290315	−	0.0502840i
$545$	−6.58301			−0.281985
$546$	1.32288	+	2.29129i	0.0566139	+	0.0980581i
$547$	−5.06275			−0.216467			−0.108234	−	0.994125i	$-0.534519\pi$
$547$	−5.06275			−0.216467			−0.108234	+	0.994125i	$0.534519\pi$
$548$	−8.76013	−	15.1730i	−0.374214	−	0.648158i
$549$	−1.96863	+	3.40976i	−0.0840190	+	0.145525i
$550$	5.32288	−	9.21949i	0.226968	−	0.393120i
$551$	15.7288	+	27.2430i	0.670068	+	1.16059i
$552$	7.64575			0.325425
$553$	13.2288	−	22.9129i	0.562544	−	0.974355i
$554$	18.5203			0.786850
$555$	−0.291503	−	0.504897i	−0.0123736	−	0.0214317i
$556$	−2.11438	+	3.66221i	−0.0896696	+	0.155312i
$557$	15.5830	−	26.9906i	0.660273	−	1.14363i	−0.320271	−	0.947326i	$-0.603774\pi$
$557$	15.5830	−	26.9906i	0.660273	−	1.14363i	0.980544	−	0.196301i	$-0.0628928\pi$
$558$	−3.64575	−	6.31463i	−0.154337	−	0.267319i
$559$	5.29150			0.223807
$560$	4.35425			0.184001
$561$	6.29150			0.265627
$562$	9.29150	+	16.0934i	0.391938	+	0.678857i
$563$	−23.5203	+	40.7383i	−0.991261	+	1.71691i	−0.381387	+	0.924416i	$0.624553\pi$
$563$	−23.5203	+	40.7383i	−0.991261	+	1.71691i	−0.609874	+	0.792498i	$0.708780\pi$
$564$	−1.50000	+	2.59808i	−0.0631614	+	0.109399i
$565$	9.23987	+	16.0039i	0.388724	+	0.673290i
$566$	26.9373			1.13226
$567$	2.64575			0.111111
$568$	−5.70850			−0.239523
$569$	3.38562	+	5.86407i	0.141933	+	0.245835i	0.928224	−	0.372021i	$-0.121335\pi$
$569$	3.38562	+	5.86407i	0.141933	+	0.245835i	−0.786292	+	0.617855i	$0.788002\pi$
$570$	4.11438	−	7.12631i	0.172332	−	0.298488i
$571$	8.00000	−	13.8564i	0.334790	−	0.579873i	−0.648655	−	0.761083i	$-0.724668\pi$
$571$	8.00000	−	13.8564i	0.334790	−	0.579873i	0.983444	+	0.181210i	$0.0580014\pi$
$572$	2.32288	+	4.02334i	0.0971243	+	0.168224i
$573$		0			0
$574$	−10.1144	+	17.5186i	−0.422166	+	0.731213i
$575$	17.5203			0.730645
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−4.29150	+	7.43310i	−0.178658	+	0.309444i	−0.941421	−	0.337234i	$-0.890509\pi$
$577$	−4.29150	+	7.43310i	−0.178658	+	0.309444i	0.762763	+	0.646678i	$0.223842\pi$
$578$	−7.58301	+	13.1342i	−0.315411	+	0.546309i
$579$	−1.53137	−	2.65242i	−0.0636417	−	0.110231i
$580$	−10.3542			−0.429937
$581$	3.58301	+	6.20595i	0.148648	+	0.257466i
$582$	14.9373			0.619169
$583$	−6.96863	−	12.0700i	−0.288611	−	0.499889i
$584$	−4.17712	+	7.23499i	−0.172851	+	0.299386i
$585$	−0.822876	+	1.42526i	−0.0340217	+	0.0589273i
$586$	−14.7601	−	25.5653i	−0.609735	−	1.05609i
$587$	16.0627			0.662980			0.331490	−	0.943459i	$-0.392449\pi$
$587$	16.0627			0.662980			0.331490	+	0.943459i	$0.392449\pi$
$588$	7.00000			0.288675
$589$	−36.4575			−1.50221
$590$	6.53137	+	11.3127i	0.268892	+	0.465735i
$591$	−10.4059	+	18.0235i	−0.428041	+	0.741388i
$592$	−0.177124	+	0.306788i	−0.00727977	+	0.0126089i
$593$	−3.23987	−	5.61162i	−0.133046	−	0.230442i	0.791804	−	0.610776i	$-0.209142\pi$
$593$	−3.23987	−	5.61162i	−0.133046	−	0.230442i	−0.924849	+	0.380334i	$0.875809\pi$
$594$	4.64575			0.190617
$595$	2.94837	+	5.10672i	0.120871	+	0.209355i
$596$	−22.9373			−0.939547
$597$	−2.11438	−	3.66221i	−0.0865357	−	0.149884i
$598$	−3.82288	+	6.62141i	−0.156329	+	0.270770i
$599$	−7.40588	+	12.8274i	−0.302596	+	0.524112i	−0.976723	−	0.214504i	$-0.931187\pi$
$599$	−7.40588	+	12.8274i	−0.302596	+	0.524112i	0.674127	+	0.738615i	$0.264520\pi$
$600$	−1.14575	−	1.98450i	−0.0467751	−	0.0810169i
$601$	−16.8745			−0.688326			−0.344163	−	0.938910i	$-0.611837\pi$
$601$	−16.8745			−0.688326			−0.344163	+	0.938910i	$0.611837\pi$
$602$	7.00000	−	12.1244i	0.285299	−	0.494152i
$603$	−13.5830			−0.553143
$604$	−10.9686	−	18.9982i	−0.446307	−	0.773027i
$605$	−8.70850	+	15.0836i	−0.354051	+	0.613234i
$606$		0			0
$607$	15.4059	+	26.6838i	0.625305	+	1.08306i	0.988482	+	0.151340i	$0.0483589\pi$
$607$	15.4059	+	26.6838i	0.625305	+	1.08306i	−0.363176	+	0.931720i	$0.618308\pi$
$608$	−5.00000			−0.202777
$609$	−16.6458			−0.674520
$610$	−6.47974			−0.262357
$611$	−1.50000	−	2.59808i	−0.0606835	−	0.105107i
$612$	0.677124	−	1.17281i	0.0273711	−	0.0474082i
$613$	−5.06275	+	8.76893i	−0.204482	+	0.354174i	−0.949968	−	0.312348i	$-0.898884\pi$
$613$	−5.06275	+	8.76893i	−0.204482	+	0.354174i	0.745485	+	0.666522i	$0.232218\pi$
$614$	5.79150	+	10.0312i	0.233726	+	0.404825i
$615$	−12.5830			−0.507396
$616$	12.2915			0.495239
$617$	−21.2915			−0.857164			−0.428582	−	0.903503i	$-0.640987\pi$
$617$	−21.2915			−0.857164			−0.428582	+	0.903503i	$0.640987\pi$
$618$	2.64575	+	4.58258i	0.106428	+	0.184338i
$619$	−10.8745	+	18.8352i	−0.437083	+	0.757051i	−0.997463	−	0.0711852i	$-0.977322\pi$
$619$	−10.8745	+	18.8352i	−0.437083	+	0.757051i	0.560380	+	0.828236i	$0.310655\pi$
$620$	6.00000	−	10.3923i	0.240966	−	0.417365i
$621$	3.82288	+	6.62141i	0.153407	+	0.265708i
$622$	16.9373			0.679122
$623$	−1.40588	+	2.43506i	−0.0563254	+	0.0975585i
$624$	1.00000			0.0400320
$625$	4.14575	+	7.18065i	0.165830	+	0.287226i
$626$	−14.5830	+	25.2585i	−0.582854	+	1.00953i
$627$	11.6144	−	20.1167i	0.463834	−	0.803383i
$628$	1.32288	+	2.29129i	0.0527885	+	0.0914323i
$629$	−0.479741			−0.0191285
$630$	2.17712	+	3.77089i	0.0867387	+	0.150236i
$631$	−38.4575			−1.53097			−0.765485	−	0.643454i	$-0.777501\pi$
$631$	−38.4575			−1.53097			−0.765485	+	0.643454i	$0.777501\pi$
$632$	−5.00000	−	8.66025i	−0.198889	−	0.344486i
$633$	5.82288	−	10.0855i	0.231439	−	0.400863i
$634$	−1.35425	+	2.34563i	−0.0537841	+	0.0931568i
$635$	−13.3542	−	23.1302i	−0.529947	−	0.917895i
$636$	−3.00000			−0.118958
$637$	−3.50000	+	6.06218i	−0.138675	+	0.240192i
$638$	−29.2288			−1.15718
$639$	−2.85425	−	4.94370i	−0.112912	−	0.195570i
$640$	0.822876	−	1.42526i	0.0325270	−	0.0563384i
$641$	21.2915	−	36.8780i	0.840964	−	1.45659i	−0.0481170	−	0.998842i	$-0.515322\pi$
$641$	21.2915	−	36.8780i	0.840964	−	1.45659i	0.889081	−	0.457750i	$-0.151345\pi$
$642$	−6.00000	−	10.3923i	−0.236801	−	0.410152i
$643$	20.8745			0.823210			0.411605	−	0.911362i	$-0.364968\pi$
$643$	20.8745			0.823210			0.411605	+	0.911362i	$0.364968\pi$
$644$	10.1144	+	17.5186i	0.398562	+	0.690330i
$645$	8.70850			0.342897
$646$	−3.38562	−	5.86407i	−0.133206	−	0.230719i
$647$	18.8745	−	32.6916i	0.742033	−	1.28524i	−0.209535	−	0.977801i	$-0.567195\pi$
$647$	18.8745	−	32.6916i	0.742033	−	1.28524i	0.951568	−	0.307438i	$-0.0994718\pi$
$648$	0.500000	−	0.866025i	0.0196419	−	0.0340207i
$649$	18.4373	+	31.9343i	0.723726	+	1.25353i
$650$	2.29150			0.0898801
$651$	9.64575	−	16.7069i	0.378047	−	0.654796i
$652$	23.5830			0.923582
$653$	−6.00000	−	10.3923i	−0.234798	−	0.406682i	0.724416	−	0.689363i	$-0.242110\pi$
$653$	−6.00000	−	10.3923i	−0.234798	−	0.406682i	−0.959214	+	0.282681i	$0.908776\pi$
$654$	−2.00000	+	3.46410i	−0.0782062	+	0.135457i
$655$	4.06275	−	7.03688i	0.158745	−	0.274954i
$656$	3.82288	+	6.62141i	0.149258	+	0.258523i
$657$	−8.35425			−0.325930
$658$	−7.93725			−0.309426
$659$	−1.06275			−0.0413987			−0.0206994	−	0.999786i	$-0.506589\pi$
$659$	−1.06275			−0.0413987			−0.0206994	+	0.999786i	$0.506589\pi$
$660$	3.82288	+	6.62141i	0.148805	+	0.257738i
$661$	10.7601	−	18.6371i	0.418521	−	0.724899i	−0.577270	−	0.816553i	$-0.695882\pi$
$661$	10.7601	−	18.6371i	0.418521	−	0.724899i	0.995791	+	0.0916543i	$0.0292155\pi$
$662$	16.2915	−	28.2177i	0.633187	−	1.09671i
$663$	0.677124	+	1.17281i	0.0262973	+	0.0455483i
$664$	2.70850			0.105110
$665$	21.7712			0.844253
$666$	−0.354249			−0.0137269
$667$	−24.0516	−	41.6586i	−0.931283	−	1.61303i
$668$	−12.4373	+	21.5420i	−0.481212	+	0.833483i
$669$	−8.26013	+	14.3070i	−0.319355	+	0.553139i
$670$	−11.1771	−	19.3593i	−0.431810	−	0.747917i
$671$	−18.2915			−0.706136
$672$	1.32288	−	2.29129i	0.0510310	−	0.0883883i
$673$	14.5830			0.562134			0.281067	−	0.959688i	$-0.409312\pi$
$673$	14.5830			0.562134			0.281067	+	0.959688i	$0.409312\pi$
$674$	2.79150	+	4.83502i	0.107525	+	0.186238i
$675$	1.14575	−	1.98450i	0.0441000	−	0.0763834i
$676$	−0.500000	+	0.866025i	−0.0192308	+	0.0333087i
$677$	11.0830	+	19.1963i	0.425954	+	0.737775i	0.996509	−	0.0834849i	$-0.0266050\pi$
$677$	11.0830	+	19.1963i	0.425954	+	0.737775i	−0.570555	+	0.821260i	$0.693272\pi$
$678$	11.2288			0.431238
$679$	19.7601	+	34.2255i	0.758324	+	1.31346i
$680$	2.22876			0.0854689
$681$	7.64575	+	13.2428i	0.292986	+	0.507466i
$682$	16.9373	−	29.3362i	0.648561	−	1.12334i
$683$	−4.35425	+	7.54178i	−0.166611	+	0.288578i	−0.937226	−	0.348722i	$-0.886616\pi$
$683$	−4.35425	+	7.54178i	−0.166611	+	0.288578i	0.770615	+	0.637300i	$0.219949\pi$
$684$	−2.50000	−	4.33013i	−0.0955899	−	0.165567i
$685$	28.8340			1.10169
$686$	9.26013	+	16.0390i	0.353553	+	0.612372i
$687$	−26.4575			−1.00942
$688$	−2.64575	−	4.58258i	−0.100868	−	0.174709i
$689$	1.50000	−	2.59808i	0.0571454	−	0.0989788i
$690$	−6.29150	+	10.8972i	−0.239513	+	0.414849i
$691$	−17.0203	−	29.4800i	−0.647481	−	1.12147i	−0.983722	−	0.179694i	$-0.942489\pi$
$691$	−17.0203	−	29.4800i	−0.647481	−	1.12147i	0.336241	−	0.941776i	$-0.390844\pi$
$692$	−11.7085			−0.445090
$693$	6.14575	+	10.6448i	0.233458	+	0.404361i
$694$	26.2288			0.995630
$695$	−3.47974	−	6.02709i	−0.131994	−	0.228620i
$696$	−3.14575	+	5.44860i	−0.119239	+	0.206529i
$697$	−5.17712	+	8.96704i	−0.196098	+	0.339651i
$698$	1.53137	+	2.65242i	0.0579633	+	0.100395i
$699$	−4.64575			−0.175718
$700$	3.03137	−	5.25049i	0.114575	−	0.198450i
$701$	12.0000			0.453234			0.226617	−	0.973984i	$-0.427233\pi$
$701$	12.0000			0.453234			0.226617	+	0.973984i	$0.427233\pi$
$702$	0.500000	+	0.866025i	0.0188713	+	0.0326860i
$703$	−0.885622	+	1.53394i	−0.0334019	+	0.0578537i
$704$	2.32288	−	4.02334i	0.0875467	−	0.151635i
$705$	−2.46863	−	4.27579i	−0.0929739	−	0.161035i
$706$	−0.583005			−0.0219417
$707$		0			0
$708$	7.93725			0.298300
$709$	−21.7601	−	37.6897i	−0.817219	−	1.41546i	−0.907724	−	0.419569i	$-0.862181\pi$
$709$	−21.7601	−	37.6897i	−0.817219	−	1.41546i	0.0905049	−	0.995896i	$-0.471152\pi$
$710$	4.69738	−	8.13611i	0.176290	−	0.305343i
$711$	5.00000	−	8.66025i	0.187515	−	0.324785i
$712$	0.531373	+	0.920365i	0.0199140	+	0.0344921i
$713$	55.7490			2.08782
$714$	3.58301			0.134091
$715$	−7.64575			−0.285935
$716$	3.00000	+	5.19615i	0.112115	+	0.194189i
$717$	−1.50000	+	2.59808i	−0.0560185	+	0.0970269i
$718$	−3.00000	+	5.19615i	−0.111959	+	0.193919i
$719$	−11.7085	−	20.2797i	−0.436653	−	0.756306i	0.560776	−	0.827968i	$-0.310503\pi$
$719$	−11.7085	−	20.2797i	−0.436653	−	0.756306i	−0.997429	+	0.0716621i	$0.977170\pi$
$720$	1.64575			0.0613335
$721$	−7.00000	+	12.1244i	−0.260694	+	0.451535i
$722$	−6.00000			−0.223297
$723$	−8.93725	−	15.4798i	−0.332380	−	0.575699i
$724$	−4.67712	+	8.10102i	−0.173824	+	0.301072i
$725$	−7.20850	+	12.4855i	−0.267717	+	0.463699i
$726$	5.29150	+	9.16515i	0.196386	+	0.340151i
$727$	36.4575			1.35213			0.676067	−	0.736840i	$-0.263683\pi$
$727$	36.4575			1.35213			0.676067	+	0.736840i	$0.263683\pi$
$728$	1.32288	+	2.29129i	0.0490290	+	0.0849208i
$729$	1.00000			0.0370370
$730$	−6.87451	−	11.9070i	−0.254437	−	0.440698i
$731$	3.58301	−	6.20595i	0.132522	−	0.229535i
$732$	−1.96863	+	3.40976i	−0.0727625	+	0.126028i
$733$	6.11438	+	10.5904i	0.225840	+	0.391166i	0.956571	−	0.291499i	$-0.0941541\pi$
$733$	6.11438	+	10.5904i	0.225840	+	0.391166i	−0.730731	+	0.682665i	$0.760821\pi$
$734$	−20.5830			−0.759733
$735$	−5.76013	+	9.97684i	−0.212466	+	0.368001i
$736$	7.64575			0.281826
$737$	−31.5516	−	54.6490i	−1.16222	−	2.01302i
$738$	−3.82288	+	6.62141i	−0.140722	+	0.243738i
$739$	3.35425	−	5.80973i	0.123388	−	0.213714i	−0.797714	−	0.603036i	$-0.793957\pi$
$739$	3.35425	−	5.80973i	0.123388	−	0.213714i	0.921102	+	0.389322i	$0.127291\pi$
$740$	−0.291503	−	0.504897i	−0.0107158	−	0.0185604i
$741$	5.00000			0.183680
$742$	−3.96863	−	6.87386i	−0.145693	−	0.252347i
$743$	1.45751			0.0534710			0.0267355	−	0.999643i	$-0.491489\pi$
$743$	1.45751			0.0534710			0.0267355	+	0.999643i	$0.491489\pi$
$744$	−3.64575	−	6.31463i	−0.133660	−	0.231505i
$745$	18.8745	−	32.6916i	0.691508	−	1.19773i
$746$	4.67712	−	8.10102i	0.171242	−	0.296599i
$747$	1.35425	+	2.34563i	0.0495494	+	0.0858220i
$748$	6.29150			0.230040
$749$	15.8745	−	27.4955i	0.580042	−	1.00466i
$750$	12.0000			0.438178
$751$	−4.58301	−	7.93800i	−0.167236	−	0.289662i	0.770211	−	0.637789i	$-0.220151\pi$
$751$	−4.58301	−	7.93800i	−0.167236	−	0.289662i	−0.937447	+	0.348128i	$0.886818\pi$
$752$	−1.50000	+	2.59808i	−0.0546994	+	0.0947421i
$753$	1.35425	−	2.34563i	0.0493516	−	0.0854794i
$754$	−3.14575	−	5.44860i	−0.114562	−	0.198426i
$755$	36.1033			1.31393
$756$	2.64575			0.0962250
$757$	21.3542			0.776133			0.388067	−	0.921631i	$-0.373143\pi$
$757$	21.3542			0.776133			0.388067	+	0.921631i	$0.373143\pi$
$758$	16.5830	+	28.7226i	0.602322	+	1.04325i
$759$	−17.7601	+	30.7614i	−0.644652	+	1.11657i
$760$	4.11438	−	7.12631i	0.149244	−	0.258499i
$761$	1.64575	+	2.85052i	0.0596584	+	0.103331i	0.894312	−	0.447444i	$-0.147666\pi$
$761$	1.64575	+	2.85052i	0.0596584	+	0.103331i	−0.834654	+	0.550775i	$0.814332\pi$
$762$	−16.2288			−0.587906
$763$	−10.5830			−0.383131
$764$		0			0
$765$	1.11438	+	1.93016i	0.0402904	+	0.0697851i
$766$	−18.8745	+	32.6916i	−0.681964	+	1.18120i
$767$	−3.96863	+	6.87386i	−0.143299	+	0.248201i
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$	0.354249			0.0127745			0.00638727	−	0.999980i	$-0.497967\pi$
$769$	0.354249			0.0127745			0.00638727	+	0.999980i	$0.497967\pi$
$770$	−10.1144	+	17.5186i	−0.364497	+	0.631327i
$771$	15.8745			0.571706
$772$	−1.53137	−	2.65242i	−0.0551153	−	0.0954625i
$773$	22.1660

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.822876 - 1.42526i) q^{5} -1.00000 q^{6} +(-1.32288 - 2.29129i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.822876 - 1.42526i) q^{5} -1.00000 q^{6} +(-1.32288 - 2.29129i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.822876 - 1.42526i) q^{10} +(2.32288 - 4.02334i) q^{11} +(-0.500000 - 0.866025i) q^{12} +1.00000 q^{13} +(1.32288 - 2.29129i) q^{14} +1.64575 q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.677124 - 1.17281i) q^{17} +(0.500000 - 0.866025i) q^{18} +(-2.50000 - 4.33013i) q^{19} +1.64575 q^{20} +2.64575 q^{21} +4.64575 q^{22} +(3.82288 + 6.62141i) q^{23} +(0.500000 - 0.866025i) q^{24} +(1.14575 - 1.98450i) q^{25} +(0.500000 + 0.866025i) q^{26} +1.00000 q^{27} +2.64575 q^{28} -6.29150 q^{29} +(0.822876 + 1.42526i) q^{30} +(3.64575 - 6.31463i) q^{31} +(0.500000 - 0.866025i) q^{32} +(2.32288 + 4.02334i) q^{33} +1.35425 q^{34} +(-2.17712 + 3.77089i) q^{35} +1.00000 q^{36} +(-0.177124 - 0.306788i) q^{37} +(2.50000 - 4.33013i) q^{38} +(-0.500000 + 0.866025i) q^{39} +(0.822876 + 1.42526i) q^{40} -7.64575 q^{41} +(1.32288 + 2.29129i) q^{42} +5.29150 q^{43} +(2.32288 + 4.02334i) q^{44} +(-0.822876 + 1.42526i) q^{45} +(-3.82288 + 6.62141i) q^{46} +(-1.50000 - 2.59808i) q^{47} +1.00000 q^{48} +(-3.50000 + 6.06218i) q^{49} +2.29150 q^{50} +(0.677124 + 1.17281i) q^{51} +(-0.500000 + 0.866025i) q^{52} +(1.50000 - 2.59808i) q^{53} +(0.500000 + 0.866025i) q^{54} -7.64575 q^{55} +(1.32288 + 2.29129i) q^{56} +5.00000 q^{57} +(-3.14575 - 5.44860i) q^{58} +(-3.96863 + 6.87386i) q^{59} +(-0.822876 + 1.42526i) q^{60} +(-1.96863 - 3.40976i) q^{61} +7.29150 q^{62} +(-1.32288 + 2.29129i) q^{63} +1.00000 q^{64} +(-0.822876 - 1.42526i) q^{65} +(-2.32288 + 4.02334i) q^{66} +(6.79150 - 11.7632i) q^{67} +(0.677124 + 1.17281i) q^{68} -7.64575 q^{69} -4.35425 q^{70} +5.70850 q^{71} +(0.500000 + 0.866025i) q^{72} +(4.17712 - 7.23499i) q^{73} +(0.177124 - 0.306788i) q^{74} +(1.14575 + 1.98450i) q^{75} +5.00000 q^{76} -12.2915 q^{77} -1.00000 q^{78} +(5.00000 + 8.66025i) q^{79} +(-0.822876 + 1.42526i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.82288 - 6.62141i) q^{82} -2.70850 q^{83} +(-1.32288 + 2.29129i) q^{84} -2.22876 q^{85} +(2.64575 + 4.58258i) q^{86} +(3.14575 - 5.44860i) q^{87} +(-2.32288 + 4.02334i) q^{88} +(-0.531373 - 0.920365i) q^{89} -1.64575 q^{90} +(-1.32288 - 2.29129i) q^{91} -7.64575 q^{92} +(3.64575 + 6.31463i) q^{93} +(1.50000 - 2.59808i) q^{94} +(-4.11438 + 7.12631i) q^{95} +(0.500000 + 0.866025i) q^{96} -14.9373 q^{97} -7.00000 q^{98} -4.64575 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{5} - 4 q^{6} - 4 q^{8} - 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^5 - 4 * q^6 - 4 * q^8 - 2 * q^9	\( 4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{5} - 4 q^{6} - 4 q^{8} - 2 q^{9} - 2 q^{10} + 4 q^{11} - 2 q^{12} + 4 q^{13} - 4 q^{15} - 2 q^{16} + 8 q^{17} + 2 q^{18} - 10 q^{19} - 4 q^{20} + 8 q^{22} + 10 q^{23} + 2 q^{24} - 6 q^{25} + 2 q^{26} + 4 q^{27} - 4 q^{29} - 2 q^{30} + 4 q^{31} + 2 q^{32} + 4 q^{33} + 16 q^{34} - 14 q^{35} + 4 q^{36} - 6 q^{37} + 10 q^{38} - 2 q^{39} - 2 q^{40} - 20 q^{41} + 4 q^{44} + 2 q^{45} - 10 q^{46} - 6 q^{47} + 4 q^{48} - 14 q^{49} - 12 q^{50} + 8 q^{51} - 2 q^{52} + 6 q^{53} + 2 q^{54} - 20 q^{55} + 20 q^{57} - 2 q^{58} + 2 q^{60} + 8 q^{61} + 8 q^{62} + 4 q^{64} + 2 q^{65} - 4 q^{66} + 6 q^{67} + 8 q^{68} - 20 q^{69} - 28 q^{70} + 44 q^{71} + 2 q^{72} + 22 q^{73} + 6 q^{74} - 6 q^{75} + 20 q^{76} - 28 q^{77} - 4 q^{78} + 20 q^{79} + 2 q^{80} - 2 q^{81} - 10 q^{82} - 32 q^{83} + 44 q^{85} + 2 q^{87} - 4 q^{88} - 18 q^{89} + 4 q^{90} - 20 q^{92} + 4 q^{93} + 6 q^{94} + 10 q^{95} + 2 q^{96} - 28 q^{97} - 28 q^{98} - 8 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^5 - 4 * q^6 - 4 * q^8 - 2 * q^9 - 2 * q^10 + 4 * q^11 - 2 * q^12 + 4 * q^13 - 4 * q^15 - 2 * q^16 + 8 * q^17 + 2 * q^18 - 10 * q^19 - 4 * q^20 + 8 * q^22 + 10 * q^23 + 2 * q^24 - 6 * q^25 + 2 * q^26 + 4 * q^27 - 4 * q^29 - 2 * q^30 + 4 * q^31 + 2 * q^32 + 4 * q^33 + 16 * q^34 - 14 * q^35 + 4 * q^36 - 6 * q^37 + 10 * q^38 - 2 * q^39 - 2 * q^40 - 20 * q^41 + 4 * q^44 + 2 * q^45 - 10 * q^46 - 6 * q^47 + 4 * q^48 - 14 * q^49 - 12 * q^50 + 8 * q^51 - 2 * q^52 + 6 * q^53 + 2 * q^54 - 20 * q^55 + 20 * q^57 - 2 * q^58 + 2 * q^60 + 8 * q^61 + 8 * q^62 + 4 * q^64 + 2 * q^65 - 4 * q^66 + 6 * q^67 + 8 * q^68 - 20 * q^69 - 28 * q^70 + 44 * q^71 + 2 * q^72 + 22 * q^73 + 6 * q^74 - 6 * q^75 + 20 * q^76 - 28 * q^77 - 4 * q^78 + 20 * q^79 + 2 * q^80 - 2 * q^81 - 10 * q^82 - 32 * q^83 + 44 * q^85 + 2 * q^87 - 4 * q^88 - 18 * q^89 + 4 * q^90 - 20 * q^92 + 4 * q^93 + 6 * q^94 + 10 * q^95 + 2 * q^96 - 28 * q^97 - 28 * q^98 - 8 * q^99

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