LMFDB - Embedded newform 546.2.i.j.79.2

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			79.2
Root			$1.32288 - 2.29129i$ of defining polynomial
Character	$\chi$	$=$	546.79
Dual form			546.2.i.j.235.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.82288 - 3.15731i) q^{5} -1.00000 q^{6} +(1.32288 - 2.29129i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.82288 - 3.15731i) q^{5} -1.00000 q^{6} +(1.32288 - 2.29129i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.82288 - 3.15731i) q^{10} +(-0.322876 - 0.559237i) q^{11} +(-0.500000 + 0.866025i) q^{12} +1.00000 q^{13} +(-1.32288 - 2.29129i) q^{14} -3.64575 q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.32288 + 5.75539i) q^{17} +(0.500000 + 0.866025i) q^{18} +(-2.50000 + 4.33013i) q^{19} -3.64575 q^{20} -2.64575 q^{21} -0.645751 q^{22} +(1.17712 - 2.03884i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-4.14575 - 7.18065i) q^{25} +(0.500000 - 0.866025i) q^{26} +1.00000 q^{27} -2.64575 q^{28} +4.29150 q^{29} +(-1.82288 + 3.15731i) q^{30} +(-1.64575 - 2.85052i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-0.322876 + 0.559237i) q^{33} +6.64575 q^{34} +(-4.82288 - 8.35347i) q^{35} +1.00000 q^{36} +(-2.82288 + 4.88936i) q^{37} +(2.50000 + 4.33013i) q^{38} +(-0.500000 - 0.866025i) q^{39} +(-1.82288 + 3.15731i) q^{40} -2.35425 q^{41} +(-1.32288 + 2.29129i) q^{42} -5.29150 q^{43} +(-0.322876 + 0.559237i) q^{44} +(1.82288 + 3.15731i) q^{45} +(-1.17712 - 2.03884i) q^{46} +(-1.50000 + 2.59808i) q^{47} +1.00000 q^{48} +(-3.50000 - 6.06218i) q^{49} -8.29150 q^{50} +(3.32288 - 5.75539i) q^{51} +(-0.500000 - 0.866025i) q^{52} +(1.50000 + 2.59808i) q^{53} +(0.500000 - 0.866025i) q^{54} -2.35425 q^{55} +(-1.32288 + 2.29129i) q^{56} +5.00000 q^{57} +(2.14575 - 3.71655i) q^{58} +(3.96863 + 6.87386i) q^{59} +(1.82288 + 3.15731i) q^{60} +(5.96863 - 10.3380i) q^{61} -3.29150 q^{62} +(1.32288 + 2.29129i) q^{63} +1.00000 q^{64} +(1.82288 - 3.15731i) q^{65} +(0.322876 + 0.559237i) q^{66} +(-3.79150 - 6.56708i) q^{67} +(3.32288 - 5.75539i) q^{68} -2.35425 q^{69} -9.64575 q^{70} +16.2915 q^{71} +(0.500000 - 0.866025i) q^{72} +(6.82288 + 11.8176i) q^{73} +(2.82288 + 4.88936i) q^{74} +(-4.14575 + 7.18065i) q^{75} +5.00000 q^{76} -1.70850 q^{77} -1.00000 q^{78} +(5.00000 - 8.66025i) q^{79} +(1.82288 + 3.15731i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-1.17712 + 2.03884i) q^{82} -13.2915 q^{83} +(1.32288 + 2.29129i) q^{84} +24.2288 q^{85} +(-2.64575 + 4.58258i) q^{86} +(-2.14575 - 3.71655i) q^{87} +(0.322876 + 0.559237i) q^{88} +(-8.46863 + 14.6681i) q^{89} +3.64575 q^{90} +(1.32288 - 2.29129i) q^{91} -2.35425 q^{92} +(-1.64575 + 2.85052i) q^{93} +(1.50000 + 2.59808i) q^{94} +(9.11438 + 15.7866i) q^{95} +(0.500000 - 0.866025i) q^{96} +0.937254 q^{97} -7.00000 q^{98} +0.645751 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 $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	1.82288	−	3.15731i	0.815215	−	1.41199i	−0.0939588	−	0.995576i	$-0.529952\pi$
$5$	1.82288	−	3.15731i	0.815215	−	1.41199i	0.909174	−	0.416417i	$-0.136714\pi$
$6$	−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
$10$	−1.82288	−	3.15731i	−0.576444	−	0.998430i
$11$	−0.322876	−	0.559237i	−0.0973507	−	0.168616i	0.813237	−	0.581933i	$-0.197704\pi$
$11$	−0.322876	−	0.559237i	−0.0973507	−	0.168616i	−0.910587	+	0.413317i	$0.864370\pi$
$12$	−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
$15$	−3.64575			−0.941329
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	3.32288	+	5.75539i	0.805916	+	1.39589i	0.915671	+	0.401928i	$0.131660\pi$
$17$	3.32288	+	5.75539i	0.805916	+	1.39589i	−0.109755	+	0.993959i	$0.535007\pi$
$18$	0.500000	+	0.866025i	0.117851	+	0.204124i
$19$	−2.50000	+	4.33013i	−0.573539	+	0.993399i	0.422659	+	0.906289i	$0.361097\pi$
$19$	−2.50000	+	4.33013i	−0.573539	+	0.993399i	−0.996199	+	0.0871106i	$0.972237\pi$
$20$	−3.64575			−0.815215
$21$	−2.64575			−0.577350
$22$	−0.645751			−0.137675
$23$	1.17712	−	2.03884i	0.245447	−	0.425127i	−0.716810	−	0.697269i	$-0.754398\pi$
$23$	1.17712	−	2.03884i	0.245447	−	0.425127i	0.962257	+	0.272141i	$0.0877318\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	−4.14575	−	7.18065i	−0.829150	−	1.43613i
$26$	0.500000	−	0.866025i	0.0980581	−	0.169842i
$27$	1.00000			0.192450
$28$	−2.64575			−0.500000
$29$	4.29150			0.796912			0.398456	−	0.917187i	$-0.369546\pi$
$29$	4.29150			0.796912			0.398456	+	0.917187i	$0.369546\pi$
$30$	−1.82288	+	3.15731i	−0.332810	+	0.576444i
$31$	−1.64575	−	2.85052i	−0.295586	−	0.511969i	0.679535	−	0.733643i	$-0.262181\pi$
$31$	−1.64575	−	2.85052i	−0.295586	−	0.511969i	−0.975121	+	0.221673i	$0.928848\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−0.322876	+	0.559237i	−0.0562054	+	0.0973507i
$34$	6.64575			1.13974
$35$	−4.82288	−	8.35347i	−0.815215	−	1.41199i
$36$	1.00000			0.166667
$37$	−2.82288	+	4.88936i	−0.464078	+	0.803806i	−0.999159	−	0.0409939i	$-0.986948\pi$
$37$	−2.82288	+	4.88936i	−0.464078	+	0.803806i	0.535081	+	0.844800i	$0.320281\pi$
$38$	2.50000	+	4.33013i	0.405554	+	0.702439i
$39$	−0.500000	−	0.866025i	−0.0800641	−	0.138675i
$40$	−1.82288	+	3.15731i	−0.288222	+	0.499215i
$41$	−2.35425			−0.367672			−0.183836	−	0.982957i	$-0.558852\pi$
$41$	−2.35425			−0.367672			−0.183836	+	0.982957i	$0.558852\pi$
$42$	−1.32288	+	2.29129i	−0.204124	+	0.353553i
$43$	−5.29150			−0.806947			−0.403473	−	0.914991i	$-0.632197\pi$
$43$	−5.29150			−0.806947			−0.403473	+	0.914991i	$0.632197\pi$
$44$	−0.322876	+	0.559237i	−0.0486753	+	0.0843082i
$45$	1.82288	+	3.15731i	0.271738	+	0.470664i
$46$	−1.17712	−	2.03884i	−0.173558	−	0.300610i
$47$	−1.50000	+	2.59808i	−0.218797	+	0.378968i	−0.954441	−	0.298401i	$-0.903547\pi$
$47$	−1.50000	+	2.59808i	−0.218797	+	0.378968i	0.735643	+	0.677369i	$0.236880\pi$
$48$	1.00000			0.144338
$49$	−3.50000	−	6.06218i	−0.500000	−	0.866025i
$50$	−8.29150			−1.17260
$51$	3.32288	−	5.75539i	0.465296	−	0.805916i
$52$	−0.500000	−	0.866025i	−0.0693375	−	0.120096i
$53$	1.50000	+	2.59808i	0.206041	+	0.356873i	0.950464	−	0.310835i	$-0.100609\pi$
$53$	1.50000	+	2.59808i	0.206041	+	0.356873i	−0.744423	+	0.667708i	$0.767275\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$	−2.35425			−0.317447
$56$	−1.32288	+	2.29129i	−0.176777	+	0.306186i
$57$	5.00000			0.662266
$58$	2.14575	−	3.71655i	0.281751	−	0.488007i
$59$	3.96863	+	6.87386i	0.516671	+	0.894901i	0.999813	+	0.0193585i	$0.00616237\pi$
$59$	3.96863	+	6.87386i	0.516671	+	0.894901i	−0.483141	+	0.875542i	$0.660504\pi$
$60$	1.82288	+	3.15731i	0.235332	+	0.407607i
$61$	5.96863	−	10.3380i	0.764204	−	1.32364i	−0.176462	−	0.984307i	$-0.556465\pi$
$61$	5.96863	−	10.3380i	0.764204	−	1.32364i	0.940666	−	0.339333i	$-0.110201\pi$
$62$	−3.29150			−0.418021
$63$	1.32288	+	2.29129i	0.166667	+	0.288675i
$64$	1.00000			0.125000
$65$	1.82288	−	3.15731i	0.226100	−	0.391617i
$66$	0.322876	+	0.559237i	0.0397432	+	0.0688373i
$67$	−3.79150	−	6.56708i	−0.463206	−	0.802296i	0.535913	−	0.844273i	$-0.319968\pi$
$67$	−3.79150	−	6.56708i	−0.463206	−	0.802296i	−0.999119	+	0.0419774i	$0.986634\pi$
$68$	3.32288	−	5.75539i	0.402958	−	0.697943i
$69$	−2.35425			−0.283418
$70$	−9.64575			−1.15289
$71$	16.2915			1.93345			0.966723	−	0.255826i	$-0.0823474\pi$
$71$	16.2915			1.93345			0.966723	+	0.255826i	$0.0823474\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$	6.82288	+	11.8176i	0.798557	+	1.38314i	0.920556	+	0.390611i	$0.127736\pi$
$73$	6.82288	+	11.8176i	0.798557	+	1.38314i	−0.121998	+	0.992530i	$0.538930\pi$
$74$	2.82288	+	4.88936i	0.328153	+	0.568377i
$75$	−4.14575	+	7.18065i	−0.478710	+	0.829150i
$76$	5.00000			0.573539
$77$	−1.70850			−0.194701
$78$	−1.00000			−0.113228
$79$	5.00000	−	8.66025i	0.562544	−	0.974355i	−0.434730	−	0.900561i	$-0.643156\pi$
$79$	5.00000	−	8.66025i	0.562544	−	0.974355i	0.997274	−	0.0737937i	$-0.0235106\pi$
$80$	1.82288	+	3.15731i	0.203804	+	0.352998i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−1.17712	+	2.03884i	−0.129992	+	0.225152i
$83$	−13.2915			−1.45893			−0.729466	−	0.684017i	$-0.760231\pi$
$83$	−13.2915			−1.45893			−0.729466	+	0.684017i	$0.760231\pi$
$84$	1.32288	+	2.29129i	0.144338	+	0.250000i
$85$	24.2288			2.62798
$86$	−2.64575	+	4.58258i	−0.285299	+	0.494152i
$87$	−2.14575	−	3.71655i	−0.230049	−	0.398456i
$88$	0.322876	+	0.559237i	0.0344187	+	0.0596149i
$89$	−8.46863	+	14.6681i	−0.897673	+	1.55481i	−0.0672111	+	0.997739i	$0.521410\pi$
$89$	−8.46863	+	14.6681i	−0.897673	+	1.55481i	−0.830462	+	0.557076i	$0.811923\pi$
$90$	3.64575			0.384296
$91$	1.32288	−	2.29129i	0.138675	−	0.240192i
$92$	−2.35425			−0.245447
$93$	−1.64575	+	2.85052i	−0.170656	+	0.295586i
$94$	1.50000	+	2.59808i	0.154713	+	0.267971i
$95$	9.11438	+	15.7866i	0.935115	+	1.61967i
$96$	0.500000	−	0.866025i	0.0510310	−	0.0883883i
$97$	0.937254			0.0951637			0.0475819	−	0.998867i	$-0.484849\pi$
$97$	0.937254			0.0951637			0.0475819	+	0.998867i	$0.484849\pi$
$98$	−7.00000			−0.707107
$99$	0.645751			0.0649004
$100$	−4.14575	+	7.18065i	−0.414575	+	0.718065i
$101$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$101$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$102$	−3.32288	−	5.75539i	−0.329014	−	0.569868i
$103$	2.64575	−	4.58258i	0.260694	−	0.451535i	−0.705733	−	0.708478i	$-0.749382\pi$
$103$	2.64575	−	4.58258i	0.260694	−	0.451535i	0.966426	+	0.256943i	$0.0827154\pi$
$104$	−1.00000			−0.0980581
$105$	−4.82288	+	8.35347i	−0.470664	+	0.815215i
$106$	3.00000			0.291386
$107$	6.00000	−	10.3923i	0.580042	−	1.00466i	−0.415432	−	0.909624i	$-0.636370\pi$
$107$	6.00000	−	10.3923i	0.580042	−	1.00466i	0.995474	−	0.0950377i	$-0.0302972\pi$
$108$	−0.500000	−	0.866025i	−0.0481125	−	0.0833333i
$109$	2.00000	+	3.46410i	0.191565	+	0.331801i	0.945769	−	0.324840i	$-0.105310\pi$
$109$	2.00000	+	3.46410i	0.191565	+	0.331801i	−0.754204	+	0.656640i	$0.771977\pi$
$110$	−1.17712	+	2.03884i	−0.112234	+	0.194396i
$111$	5.64575			0.535871
$112$	1.32288	+	2.29129i	0.125000	+	0.216506i
$113$	15.2288			1.43260			0.716300	−	0.697792i	$-0.245834\pi$
$113$	15.2288			1.43260			0.716300	+	0.697792i	$0.245834\pi$
$114$	2.50000	−	4.33013i	0.234146	−	0.405554i
$115$	−4.29150	−	7.43310i	−0.400185	−	0.693140i
$116$	−2.14575	−	3.71655i	−0.199228	−	0.345073i
$117$	−0.500000	+	0.866025i	−0.0462250	+	0.0800641i
$118$	7.93725			0.730683
$119$	17.5830			1.61183
$120$	3.64575			0.332810
$121$	5.29150	−	9.16515i	0.481046	−	0.833196i
$122$	−5.96863	−	10.3380i	−0.540374	−	0.935955i
$123$	1.17712	+	2.03884i	0.106138	+	0.183836i
$124$	−1.64575	+	2.85052i	−0.147793	+	0.255985i
$125$	−12.0000			−1.07331
$126$	2.64575			0.235702
$127$	−10.2288			−0.907655			−0.453828	−	0.891089i	$-0.649942\pi$
$127$	−10.2288			−0.907655			−0.453828	+	0.891089i	$0.649942\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	2.64575	+	4.58258i	0.232945	+	0.403473i
$130$	−1.82288	−	3.15731i	−0.159877	−	0.276915i
$131$	−5.46863	+	9.47194i	−0.477796	+	0.827567i	−0.999676	−	0.0254518i	$-0.991898\pi$
$131$	−5.46863	+	9.47194i	−0.477796	+	0.827567i	0.521880	+	0.853019i	$0.325231\pi$
$132$	0.645751			0.0562054
$133$	6.61438	+	11.4564i	0.573539	+	0.993399i
$134$	−7.58301			−0.655072
$135$	1.82288	−	3.15731i	0.156888	−	0.271738i
$136$	−3.32288	−	5.75539i	−0.284934	−	0.493521i
$137$	9.76013	+	16.9050i	0.833864	+	1.44430i	0.894952	+	0.446163i	$0.147210\pi$
$137$	9.76013	+	16.9050i	0.833864	+	1.44430i	−0.0610877	+	0.998132i	$0.519457\pi$
$138$	−1.17712	+	2.03884i	−0.100203	+	0.173558i
$139$	−22.2288			−1.88542			−0.942709	−	0.333615i	$-0.891731\pi$
$139$	−22.2288			−1.88542			−0.942709	+	0.333615i	$0.891731\pi$
$140$	−4.82288	+	8.35347i	−0.407607	+	0.705997i
$141$	3.00000			0.252646
$142$	8.14575	−	14.1089i	0.683576	−	1.18399i
$143$	−0.322876	−	0.559237i	−0.0270002	−	0.0467658i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	7.82288	−	13.5496i	0.649654	−	1.12523i
$146$	13.6458			1.12933
$147$	−3.50000	+	6.06218i	−0.288675	+	0.500000i
$148$	5.64575			0.464078
$149$	3.53137	−	6.11652i	0.289301	−	0.501085i	−0.684342	−	0.729161i	$-0.739910\pi$
$149$	3.53137	−	6.11652i	0.289301	−	0.501085i	0.973643	+	0.228077i	$0.0732437\pi$
$150$	4.14575	+	7.18065i	0.338499	+	0.586298i
$151$	−3.03137	−	5.25049i	−0.246690	−	0.427279i	0.715916	−	0.698187i	$-0.246009\pi$
$151$	−3.03137	−	5.25049i	−0.246690	−	0.427279i	−0.962605	+	0.270908i	$0.912676\pi$
$152$	2.50000	−	4.33013i	0.202777	−	0.351220i
$153$	−6.64575			−0.537277
$154$	−0.854249	+	1.47960i	−0.0688373	+	0.119230i
$155$	−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	$-0.200336\pi$
$157$	−1.32288	−	2.29129i	−0.105577	−	0.182865i	−0.913974	+	0.405773i	$0.867002\pi$
$158$	−5.00000	−	8.66025i	−0.397779	−	0.688973i
$159$	1.50000	−	2.59808i	0.118958	−	0.206041i
$160$	3.64575			0.288222
$161$	−3.11438	−	5.39426i	−0.245447	−	0.425127i
$162$	−1.00000			−0.0785674
$163$	−1.20850	+	2.09318i	−0.0946568	+	0.163950i	−0.909465	−	0.415780i	$-0.863509\pi$
$163$	−1.20850	+	2.09318i	−0.0946568	+	0.163950i	0.814809	+	0.579730i	$0.196842\pi$
$164$	1.17712	+	2.03884i	0.0919180	+	0.159207i
$165$	1.17712	+	2.03884i	0.0916390	+	0.158723i
$166$	−6.64575	+	11.5108i	−0.515810	+	0.893410i
$167$	−6.87451			−0.531965			−0.265983	−	0.963978i	$-0.585696\pi$
$167$	−6.87451			−0.531965			−0.265983	+	0.963978i	$0.585696\pi$
$168$	2.64575			0.204124
$169$	1.00000			0.0769231
$170$	12.1144	−	20.9827i	0.929130	−	1.60930i
$171$	−2.50000	−	4.33013i	−0.191180	−	0.331133i
$172$	2.64575	+	4.58258i	0.201737	+	0.349418i
$173$	11.1458	−	19.3050i	0.847396	−	1.46773i	−0.0361285	−	0.999347i	$-0.511503\pi$
$173$	11.1458	−	19.3050i	0.847396	−	1.46773i	0.883524	−	0.468385i	$-0.155164\pi$
$174$	−4.29150			−0.325338
$175$	−21.9373			−1.65830
$176$	0.645751			0.0486753
$177$	3.96863	−	6.87386i	0.298300	−	0.516671i
$178$	8.46863	+	14.6681i	0.634750	+	1.09942i
$179$	3.00000	+	5.19615i	0.224231	+	0.388379i	0.956088	−	0.293079i	$-0.0946798\pi$
$179$	3.00000	+	5.19615i	0.224231	+	0.388379i	−0.731858	+	0.681457i	$0.761346\pi$
$180$	1.82288	−	3.15731i	0.135869	−	0.235332i
$181$	14.6458			1.08861			0.544305	−	0.838887i	$-0.316793\pi$
$181$	14.6458			1.08861			0.544305	+	0.838887i	$0.316793\pi$
$182$	−1.32288	−	2.29129i	−0.0980581	−	0.169842i
$183$	−11.9373			−0.882427
$184$	−1.17712	+	2.03884i	−0.0867788	+	0.150305i
$185$	10.2915	+	17.8254i	0.756646	+	1.31055i
$186$	1.64575	+	2.85052i	0.120672	+	0.209011i
$187$	2.14575	−	3.71655i	0.156913	−	0.271781i
$188$	3.00000			0.218797
$189$	1.32288	−	2.29129i	0.0962250	−	0.166667i
$190$	18.2288			1.32245
$191$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$191$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	−9.46863	−	16.4001i	−0.681567	−	1.18051i	−0.974503	−	0.224376i	$-0.927966\pi$
$193$	−9.46863	−	16.4001i	−0.681567	−	1.18051i	0.292936	−	0.956132i	$-0.405368\pi$
$194$	0.468627	−	0.811686i	0.0336455	−	0.0582756i
$195$	−3.64575			−0.261078
$196$	−3.50000	+	6.06218i	−0.250000	+	0.433013i
$197$	−26.8118			−1.91026			−0.955129	−	0.296189i	$-0.904284\pi$
$197$	−26.8118			−1.91026			−0.955129	+	0.296189i	$0.904284\pi$
$198$	0.322876	−	0.559237i	0.0229458	−	0.0397432i
$199$	11.1144	+	19.2507i	0.787877	+	1.36464i	0.927265	+	0.374406i	$0.122153\pi$
$199$	11.1144	+	19.2507i	0.787877	+	1.36464i	−0.139388	+	0.990238i	$0.544513\pi$
$200$	4.14575	+	7.18065i	0.293149	+	0.507749i
$201$	−3.79150	+	6.56708i	−0.267432	+	0.463206i
$202$		0			0
$203$	5.67712	−	9.83307i	0.398456	−	0.690146i
$204$	−6.64575			−0.465296
$205$	−4.29150	+	7.43310i	−0.299732	+	0.519150i
$206$	−2.64575	−	4.58258i	−0.184338	−	0.319283i
$207$	1.17712	+	2.03884i	0.0818158	+	0.141709i
$208$	−0.500000	+	0.866025i	−0.0346688	+	0.0600481i
$209$	3.22876			0.223338
$210$	4.82288	+	8.35347i	0.332810	+	0.576444i
$211$	−6.35425			−0.437445			−0.218722	−	0.975787i	$-0.570189\pi$
$211$	−6.35425			−0.437445			−0.218722	+	0.975787i	$0.570189\pi$
$212$	1.50000	−	2.59808i	0.103020	−	0.178437i
$213$	−8.14575	−	14.1089i	−0.558138	−	0.966723i
$214$	−6.00000	−	10.3923i	−0.410152	−	0.710403i
$215$	−9.64575	+	16.7069i	−0.657835	+	1.13940i
$216$	−1.00000			−0.0680414
$217$	−8.70850			−0.591171
$218$	4.00000			0.270914
$219$	6.82288	−	11.8176i	0.461047	−	0.798557i
$220$	1.17712	+	2.03884i	0.0793617	+	0.137459i
$221$	3.32288	+	5.75539i	0.223521	+	0.387149i
$222$	2.82288	−	4.88936i	0.189459	−	0.328153i
$223$	−20.5203			−1.37414			−0.687069	−	0.726592i	$-0.741103\pi$
$223$	−20.5203			−1.37414			−0.687069	+	0.726592i	$0.741103\pi$
$224$	2.64575			0.176777
$225$	8.29150			0.552767
$226$	7.61438	−	13.1885i	0.506501	−	0.877285i
$227$	2.35425	+	4.07768i	0.156257	+	0.270645i	0.933516	−	0.358536i	$-0.116724\pi$
$227$	2.35425	+	4.07768i	0.156257	+	0.270645i	−0.777259	+	0.629181i	$0.783391\pi$
$228$	−2.50000	−	4.33013i	−0.165567	−	0.286770i
$229$	−13.2288	+	22.9129i	−0.874181	+	1.51413i	−0.0165480	+	0.999863i	$0.505268\pi$
$229$	−13.2288	+	22.9129i	−0.874181	+	1.51413i	−0.857633	+	0.514263i	$0.828066\pi$
$230$	−8.58301			−0.565947
$231$	0.854249	+	1.47960i	0.0562054	+	0.0973507i
$232$	−4.29150			−0.281751
$233$	−0.322876	+	0.559237i	−0.0211523	+	0.0366368i	−0.876408	−	0.481570i	$-0.840067\pi$
$233$	−0.322876	+	0.559237i	−0.0211523	+	0.0366368i	0.855256	+	0.518207i	$0.173400\pi$
$234$	0.500000	+	0.866025i	0.0326860	+	0.0566139i
$235$	5.46863	+	9.47194i	0.356734	+	0.617881i
$236$	3.96863	−	6.87386i	0.258336	−	0.447450i
$237$	−10.0000			−0.649570
$238$	8.79150	−	15.2273i	0.569868	−	0.987041i
$239$	3.00000			0.194054			0.0970269	−	0.995282i	$-0.469067\pi$
$239$	3.00000			0.194054			0.0970269	+	0.995282i	$0.469067\pi$
$240$	1.82288	−	3.15731i	0.117666	−	0.203804i
$241$	6.93725	+	12.0157i	0.446868	+	0.773998i	0.998180	−	0.0603011i	$-0.0192061\pi$
$241$	6.93725	+	12.0157i	0.446868	+	0.773998i	−0.551312	+	0.834299i	$0.685873\pi$
$242$	−5.29150	−	9.16515i	−0.340151	−	0.589158i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−11.9373			−0.764204
$245$	−25.5203			−1.63043
$246$	2.35425			0.150101
$247$	−2.50000	+	4.33013i	−0.159071	+	0.275519i
$248$	1.64575	+	2.85052i	0.104505	+	0.181009i
$249$	6.64575	+	11.5108i	0.421157	+	0.729466i
$250$	−6.00000	+	10.3923i	−0.379473	+	0.657267i
$251$	−13.2915			−0.838952			−0.419476	−	0.907766i	$-0.637786\pi$
$251$	−13.2915			−0.838952			−0.419476	+	0.907766i	$0.637786\pi$
$252$	1.32288	−	2.29129i	0.0833333	−	0.144338i
$253$	−1.52026			−0.0955779
$254$	−5.11438	+	8.85836i	−0.320905	+	0.555823i
$255$	−12.1144	−	20.9827i	−0.758632	−	1.31399i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	7.93725	−	13.7477i	0.495112	−	0.857560i	−0.504872	−	0.863194i	$-0.668460\pi$
$257$	7.93725	−	13.7477i	0.495112	−	0.857560i	0.999984	+	0.00563467i	$0.00179358\pi$
$258$	5.29150			0.329435
$259$	7.46863	+	12.9360i	0.464078	+	0.803806i
$260$	−3.64575			−0.226100
$261$	−2.14575	+	3.71655i	−0.132819	+	0.230049i
$262$	5.46863	+	9.47194i	0.337853	+	0.585178i
$263$	1.82288	+	3.15731i	0.112403	+	0.194688i	0.916739	−	0.399487i	$-0.130812\pi$
$263$	1.82288	+	3.15731i	0.112403	+	0.194688i	−0.804335	+	0.594175i	$0.797478\pi$
$264$	0.322876	−	0.559237i	0.0198716	−	0.0344187i
$265$	10.9373			0.671870
$266$	13.2288			0.811107
$267$	16.9373			1.03654
$268$	−3.79150	+	6.56708i	−0.231603	+	0.401148i
$269$	−3.43725	−	5.95350i	−0.209573	−	0.362991i	0.742007	−	0.670392i	$-0.233874\pi$
$269$	−3.43725	−	5.95350i	−0.209573	−	0.362991i	−0.951580	+	0.307401i	$0.900541\pi$
$270$	−1.82288	−	3.15731i	−0.110937	−	0.192148i
$271$	11.3229	−	19.6118i	0.687816	−	1.19133i	−0.284727	−	0.958609i	$-0.591903\pi$
$271$	11.3229	−	19.6118i	0.687816	−	1.19133i	0.972543	−	0.232723i	$-0.0747636\pi$
$272$	−6.64575			−0.402958
$273$	−2.64575			−0.160128
$274$	19.5203			1.17926
$275$	−2.67712	+	4.63692i	−0.161437	+	0.279617i
$276$	1.17712	+	2.03884i	0.0708546	+	0.122724i
$277$	−9.26013	−	16.0390i	−0.556387	−	0.963691i	−0.997794	−	0.0663840i	$-0.978854\pi$
$277$	−9.26013	−	16.0390i	−0.556387	−	0.963691i	0.441407	−	0.897307i	$-0.354480\pi$
$278$	−11.1144	+	19.2507i	−0.666596	+	1.15458i
$279$	3.29150			0.197057
$280$	4.82288	+	8.35347i	0.288222	+	0.499215i
$281$	−2.58301			−0.154089			−0.0770446	−	0.997028i	$-0.524548\pi$
$281$	−2.58301			−0.154089			−0.0770446	+	0.997028i	$0.524548\pi$
$282$	1.50000	−	2.59808i	0.0893237	−	0.154713i
$283$	5.53137	+	9.58062i	0.328806	+	0.569509i	0.982275	−	0.187444i	$-0.0600204\pi$
$283$	5.53137	+	9.58062i	0.328806	+	0.569509i	−0.653469	+	0.756953i	$0.726687\pi$
$284$	−8.14575	−	14.1089i	−0.483361	−	0.837207i
$285$	9.11438	−	15.7866i	0.539889	−	0.935115i
$286$	−0.645751			−0.0381841
$287$	−3.11438	+	5.39426i	−0.183836	+	0.318413i
$288$	−1.00000			−0.0589256
$289$	−13.5830	+	23.5265i	−0.799000	+	1.38391i
$290$	−7.82288	−	13.5496i	−0.459375	−	0.795661i
$291$	−0.468627	−	0.811686i	−0.0274714	−	0.0475819i
$292$	6.82288	−	11.8176i	0.399279	−	0.691571i
$293$	7.52026			0.439338			0.219669	−	0.975574i	$-0.429502\pi$
$293$	7.52026			0.439338			0.219669	+	0.975574i	$0.429502\pi$
$294$	3.50000	+	6.06218i	0.204124	+	0.353553i
$295$	28.9373			1.68479
$296$	2.82288	−	4.88936i	0.164076	−	0.284189i
$297$	−0.322876	−	0.559237i	−0.0187351	−	0.0324502i
$298$	−3.53137	−	6.11652i	−0.204567	−	0.354320i
$299$	1.17712	−	2.03884i	0.0680749	−	0.117909i
$300$	8.29150			0.478710
$301$	−7.00000	+	12.1244i	−0.403473	+	0.698836i
$302$	−6.06275			−0.348872
$303$		0			0
$304$	−2.50000	−	4.33013i	−0.143385	−	0.248350i
$305$	−21.7601	−	37.6897i	−1.24598	−	2.15810i
$306$	−3.32288	+	5.75539i	−0.189956	+	0.329014i
$307$	−9.58301			−0.546931			−0.273465	−	0.961882i	$-0.588170\pi$
$307$	−9.58301			−0.546931			−0.273465	+	0.961882i	$0.588170\pi$
$308$	0.854249	+	1.47960i	0.0486753	+	0.0843082i
$309$	−5.29150			−0.301023
$310$	−6.00000	+	10.3923i	−0.340777	+	0.590243i
$311$	0.531373	+	0.920365i	0.0301314	+	0.0521891i	0.880698	−	0.473678i	$-0.157074\pi$
$311$	0.531373	+	0.920365i	0.0301314	+	0.0521891i	−0.850566	+	0.525868i	$0.823741\pi$
$312$	0.500000	+	0.866025i	0.0283069	+	0.0490290i
$313$	−6.58301	+	11.4021i	−0.372093	+	0.644485i	−0.989887	−	0.141855i	$-0.954693\pi$
$313$	−6.58301	+	11.4021i	−0.372093	+	0.644485i	0.617794	+	0.786340i	$0.288027\pi$
$314$	−2.64575			−0.149308
$315$	9.64575			0.543477
$316$	−10.0000			−0.562544
$317$	6.64575	−	11.5108i	0.373263	−	0.646510i	−0.616803	−	0.787118i	$-0.711572\pi$
$317$	6.64575	−	11.5108i	0.373263	−	0.646510i	0.990065	+	0.140608i	$0.0449057\pi$
$318$	−1.50000	−	2.59808i	−0.0841158	−	0.145693i
$319$	−1.38562	−	2.39997i	−0.0775799	−	0.134372i
$320$	1.82288	−	3.15731i	0.101902	−	0.176499i
$321$	−12.0000			−0.669775
$322$	−6.22876			−0.347115
$323$	−33.2288			−1.84890
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	−4.14575	−	7.18065i	−0.229965	−	0.398311i
$326$	1.20850	+	2.09318i	0.0669325	+	0.115930i
$327$	2.00000	−	3.46410i	0.110600	−	0.191565i
$328$	2.35425			0.129992
$329$	3.96863	+	6.87386i	0.218797	+	0.378968i
$330$	2.35425			0.129597
$331$	−5.70850	+	9.88741i	−0.313767	+	0.543461i	−0.979175	−	0.203019i	$-0.934925\pi$
$331$	−5.70850	+	9.88741i	−0.313767	+	0.543461i	0.665407	+	0.746480i	$0.268258\pi$
$332$	6.64575	+	11.5108i	0.364733	+	0.631736i
$333$	−2.82288	−	4.88936i	−0.154693	−	0.267935i
$334$	−3.43725	+	5.95350i	−0.188078	+	0.325761i
$335$	−27.6458			−1.51045
$336$	1.32288	−	2.29129i	0.0721688	−	0.125000i
$337$	−15.5830			−0.848860			−0.424430	−	0.905461i	$-0.639526\pi$
$337$	−15.5830			−0.848860			−0.424430	+	0.905461i	$0.639526\pi$
$338$	0.500000	−	0.866025i	0.0271964	−	0.0471056i
$339$	−7.61438	−	13.1885i	−0.413556	−	0.716300i
$340$	−12.1144	−	20.9827i	−0.656994	−	1.13795i
$341$	−1.06275	+	1.84073i	−0.0575509	+	0.0996811i
$342$	−5.00000			−0.270369
$343$	−18.5203			−1.00000
$344$	5.29150			0.285299
$345$	−4.29150	+	7.43310i	−0.231047	+	0.400185i
$346$	−11.1458	−	19.3050i	−0.599199	−	1.03784i
$347$	−0.114378	−	0.198109i	−0.00614015	−	0.0106350i	0.862939	−	0.505308i	$-0.168621\pi$
$347$	−0.114378	−	0.198109i	−0.00614015	−	0.0106350i	−0.869079	+	0.494673i	$0.835288\pi$
$348$	−2.14575	+	3.71655i	−0.115024	+	0.199228i
$349$	18.9373			1.01369			0.506844	−	0.862038i	$-0.330812\pi$
$349$	18.9373			1.01369			0.506844	+	0.862038i	$0.330812\pi$
$350$	−10.9686	+	18.9982i	−0.586298	+	1.01550i
$351$	1.00000			0.0533761
$352$	0.322876	−	0.559237i	0.0172093	−	0.0298074i
$353$	10.2915	+	17.8254i	0.547761	+	0.948751i	0.998428	+	0.0560580i	$0.0178532\pi$
$353$	10.2915	+	17.8254i	0.547761	+	0.948751i	−0.450666	+	0.892693i	$0.648813\pi$
$354$	−3.96863	−	6.87386i	−0.210930	−	0.365342i
$355$	29.6974	−	51.4374i	1.57617	−	2.73001i
$356$	16.9373			0.897673
$357$	−8.79150	−	15.2273i	−0.465296	−	0.805916i
$358$	6.00000			0.317110
$359$	3.00000	−	5.19615i	0.158334	−	0.274242i	−0.775934	−	0.630814i	$-0.782721\pi$
$359$	3.00000	−	5.19615i	0.158334	−	0.274242i	0.934268	+	0.356572i	$0.116054\pi$
$360$	−1.82288	−	3.15731i	−0.0960740	−	0.166405i
$361$	−3.00000	−	5.19615i	−0.157895	−	0.273482i
$362$	7.32288	−	12.6836i	0.384882	−	0.666635i
$363$	−10.5830			−0.555464
$364$	−2.64575			−0.138675
$365$	49.7490			2.60398
$366$	−5.96863	+	10.3380i	−0.311985	+	0.540374i
$367$	0.291503	+	0.504897i	0.0152163	+	0.0263554i	0.873533	−	0.486764i	$-0.161823\pi$
$367$	0.291503	+	0.504897i	0.0152163	+	0.0263554i	−0.858317	+	0.513120i	$0.828490\pi$
$368$	1.17712	+	2.03884i	0.0613618	+	0.106282i
$369$	1.17712	−	2.03884i	0.0612786	−	0.106138i
$370$	20.5830			1.07006
$371$	7.93725			0.412082
$372$	3.29150			0.170656
$373$	−7.32288	+	12.6836i	−0.379164	+	0.656732i	−0.990941	−	0.134299i	$-0.957122\pi$
$373$	−7.32288	+	12.6836i	−0.379164	+	0.656732i	0.611777	+	0.791030i	$0.290455\pi$
$374$	−2.14575	−	3.71655i	−0.110954	−	0.192178i
$375$	6.00000	+	10.3923i	0.309839	+	0.536656i
$376$	1.50000	−	2.59808i	0.0773566	−	0.133986i
$377$	4.29150			0.221024
$378$	−1.32288	−	2.29129i	−0.0680414	−	0.117851i
$379$	−9.16601			−0.470826			−0.235413	−	0.971895i	$-0.575644\pi$
$379$	−9.16601			−0.470826			−0.235413	+	0.971895i	$0.575644\pi$
$380$	9.11438	−	15.7866i	0.467558	−	0.809834i
$381$	5.11438	+	8.85836i	0.262018	+	0.453828i
$382$		0			0
$383$	−12.8745	+	22.2993i	−0.657857	+	1.13944i	0.323313	+	0.946292i	$0.395203\pi$
$383$	−12.8745	+	22.2993i	−0.657857	+	1.13944i	−0.981169	+	0.193149i	$0.938130\pi$
$384$	−1.00000			−0.0510310
$385$	−3.11438	+	5.39426i	−0.158723	+	0.274917i
$386$	−18.9373			−0.963881
$387$	2.64575	−	4.58258i	0.134491	−	0.232945i
$388$	−0.468627	−	0.811686i	−0.0237909	−	0.0412071i
$389$	−3.85425	−	6.67575i	−0.195418	−	0.338474i	0.751619	−	0.659597i	$-0.229273\pi$
$389$	−3.85425	−	6.67575i	−0.195418	−	0.338474i	−0.947038	+	0.321123i	$0.895940\pi$
$390$	−1.82288	+	3.15731i	−0.0923049	+	0.159877i
$391$	15.6458			0.791240
$392$	3.50000	+	6.06218i	0.176777	+	0.306186i
$393$	10.9373			0.551711
$394$	−13.4059	+	23.2197i	−0.675379	+	1.16979i
$395$	−18.2288	−	31.5731i	−0.917188	−	1.58862i
$396$	−0.322876	−	0.559237i	−0.0162251	−	0.0281027i
$397$	7.46863	−	12.9360i	0.374840	−	0.649241i	−0.615463	−	0.788165i	$-0.711031\pi$
$397$	7.46863	−	12.9360i	0.374840	−	0.649241i	0.990303	+	0.138924i	$0.0443644\pi$
$398$	22.2288			1.11423
$399$	6.61438	−	11.4564i	0.331133	−	0.573539i
$400$	8.29150			0.414575
$401$	9.11438	−	15.7866i	0.455150	−	0.788343i	−0.543547	−	0.839379i	$-0.682919\pi$
$401$	9.11438	−	15.7866i	0.455150	−	0.788343i	0.998697	+	0.0510356i	$0.0162522\pi$
$402$	3.79150	+	6.56708i	0.189103	+	0.327536i
$403$	−1.64575	−	2.85052i	−0.0819807	−	0.141995i
$404$		0			0
$405$	−3.64575			−0.181159
$406$	−5.67712	−	9.83307i	−0.281751	−	0.488007i
$407$	3.64575			0.180713
$408$	−3.32288	+	5.75539i	−0.164507	+	0.284934i
$409$	13.4686	+	23.3283i	0.665981	+	1.15351i	0.979018	+	0.203772i	$0.0653201\pi$
$409$	13.4686	+	23.3283i	0.665981	+	1.15351i	−0.313038	+	0.949741i	$0.601347\pi$
$410$	4.29150	+	7.43310i	0.211942	+	0.367095i
$411$	9.76013	−	16.9050i	0.481432	−	0.833864i
$412$	−5.29150			−0.260694
$413$	21.0000			1.03334
$414$	2.35425			0.115705
$415$	−24.2288	+	41.9654i	−1.18934	+	2.06000i
$416$	0.500000	+	0.866025i	0.0245145	+	0.0424604i
$417$	11.1144	+	19.2507i	0.544273	+	0.942709i
$418$	1.61438	−	2.79619i	0.0789618	−	0.136766i
$419$	30.4575			1.48795			0.743973	−	0.668209i	$-0.232939\pi$
$419$	30.4575			1.48795			0.743973	+	0.668209i	$0.232939\pi$
$420$	9.64575			0.470664
$421$	−24.3542			−1.18695			−0.593477	−	0.804851i	$-0.702245\pi$
$421$	−24.3542			−1.18695			−0.593477	+	0.804851i	$0.702245\pi$
$422$	−3.17712	+	5.50294i	−0.154660	+	0.267879i
$423$	−1.50000	−	2.59808i	−0.0729325	−	0.126323i
$424$	−1.50000	−	2.59808i	−0.0728464	−	0.126174i
$425$	27.5516	−	47.7208i	1.33645	−	2.31480i
$426$	−16.2915			−0.789326
$427$	−15.7915	−	27.3517i	−0.764204	−	1.32364i
$428$	−12.0000			−0.580042
$429$	−0.322876	+	0.559237i	−0.0155886	+	0.0270002i
$430$	9.64575	+	16.7069i	0.465159	+	0.805680i
$431$	−10.2915	−	17.8254i	−0.495724	−	0.858620i	0.504264	−	0.863550i	$-0.331764\pi$
$431$	−10.2915	−	17.8254i	−0.495724	−	0.858620i	−0.999988	+	0.00493021i	$0.998431\pi$
$432$	−0.500000	+	0.866025i	−0.0240563	+	0.0416667i
$433$	−33.5830			−1.61390			−0.806948	−	0.590622i	$-0.798882\pi$
$433$	−33.5830			−1.61390			−0.806948	+	0.590622i	$0.798882\pi$
$434$	−4.35425	+	7.54178i	−0.209011	+	0.362017i
$435$	−15.6458			−0.750156
$436$	2.00000	−	3.46410i	0.0957826	−	0.165900i
$437$	5.88562	+	10.1942i	0.281547	+	0.487655i
$438$	−6.82288	−	11.8176i	−0.326010	−	0.564665i
$439$	−11.8229	+	20.4778i	−0.564275	+	0.977353i	0.432842	+	0.901470i	$0.357511\pi$
$439$	−11.8229	+	20.4778i	−0.564275	+	0.977353i	−0.997117	+	0.0758831i	$0.975822\pi$
$440$	2.35425			0.112234
$441$	7.00000			0.333333
$442$	6.64575			0.316106
$443$	−9.53137	+	16.5088i	−0.452849	+	0.784358i	−0.998562	−	0.0536147i	$-0.982926\pi$
$443$	−9.53137	+	16.5088i	−0.452849	+	0.784358i	0.545713	+	0.837972i	$0.316259\pi$
$444$	−2.82288	−	4.88936i	−0.133968	−	0.232039i
$445$	30.8745	+	53.4762i	1.46359	+	2.53502i
$446$	−10.2601	+	17.7711i	−0.485831	+	0.841484i
$447$	−7.06275			−0.334056
$448$	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	$0.408618\pi$
$450$	4.14575	−	7.18065i	0.195433	−	0.338499i
$451$	0.760130	+	1.31658i	0.0357931	+	0.0619955i
$452$	−7.61438	−	13.1885i	−0.358150	−	0.620334i
$453$	−3.03137	+	5.25049i	−0.142426	+	0.246690i
$454$	4.70850			0.220981
$455$	−4.82288	−	8.35347i	−0.226100	−	0.391617i
$456$	−5.00000			−0.234146
$457$	−16.1144	+	27.9109i	−0.753799	+	1.30562i	0.192170	+	0.981362i	$0.438447\pi$
$457$	−16.1144	+	27.9109i	−0.753799	+	1.30562i	−0.945969	+	0.324256i	$0.894886\pi$
$458$	13.2288	+	22.9129i	0.618139	+	1.07065i
$459$	3.32288	+	5.75539i	0.155099	+	0.268639i
$460$	−4.29150	+	7.43310i	−0.200092	+	0.346570i
$461$	−36.4575			−1.69800			−0.848998	−	0.528396i	$-0.822794\pi$
$461$	−36.4575			−1.69800			−0.848998	+	0.528396i	$0.822794\pi$
$462$	1.70850			0.0794865
$463$	25.1660			1.16956			0.584782	−	0.811191i	$-0.301180\pi$
$463$	25.1660			1.16956			0.584782	+	0.811191i	$0.301180\pi$
$464$	−2.14575	+	3.71655i	−0.0996140	+	0.172537i
$465$	6.00000	+	10.3923i	0.278243	+	0.481932i
$466$	0.322876	+	0.559237i	0.0149569	+	0.0259062i
$467$	18.7601	−	32.4935i	0.868115	−	1.50362i	0.00419497	−	0.999991i	$-0.498665\pi$
$467$	18.7601	−	32.4935i	0.868115	−	1.50362i	0.863920	−	0.503629i	$-0.168002\pi$
$468$	1.00000			0.0462250
$469$	−20.0627			−0.926412
$470$	10.9373			0.504498
$471$	−1.32288	+	2.29129i	−0.0609549	+	0.105577i
$472$	−3.96863	−	6.87386i	−0.182671	−	0.316395i
$473$	1.70850	+	2.95920i	0.0785568	+	0.136064i
$474$	−5.00000	+	8.66025i	−0.229658	+	0.397779i
$475$	41.4575			1.90220
$476$	−8.79150	−	15.2273i	−0.402958	−	0.697943i
$477$	−3.00000			−0.137361
$478$	1.50000	−	2.59808i	0.0686084	−	0.118833i
$479$	17.3745	+	30.0935i	0.793862	+	1.37501i	0.923560	+	0.383455i	$0.125266\pi$
$479$	17.3745	+	30.0935i	0.793862	+	1.37501i	−0.129698	+	0.991554i	$0.541401\pi$
$480$	−1.82288	−	3.15731i	−0.0832025	−	0.144111i
$481$	−2.82288	+	4.88936i	−0.128712	+	0.222936i
$482$	13.8745			0.631967
$483$	−3.11438	+	5.39426i	−0.141709	+	0.245447i
$484$	−10.5830			−0.481046
$485$	1.70850	−	2.95920i	0.0775789	−	0.134371i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	11.9686	+	20.7303i	0.542350	+	0.939378i	0.998769	+	0.0496129i	$0.0157987\pi$
$487$	11.9686	+	20.7303i	0.542350	+	0.939378i	−0.456418	+	0.889765i	$0.650868\pi$
$488$	−5.96863	+	10.3380i	−0.270187	+	0.467978i
$489$	2.41699			0.109300
$490$	−12.7601	+	22.1012i	−0.576444	+	0.998430i
$491$	11.1660			0.503915			0.251957	−	0.967738i	$-0.418926\pi$
$491$	11.1660			0.503915			0.251957	+	0.967738i	$0.418926\pi$
$492$	1.17712	−	2.03884i	0.0530689	−	0.0919180i
$493$	14.2601	+	24.6993i	0.642244	+	1.11240i
$494$	2.50000	+	4.33013i	0.112480	+	0.194822i
$495$	1.17712	−	2.03884i	0.0529078	−	0.0916390i
$496$	3.29150			0.147793
$497$	21.5516	−	37.3285i	0.966723	−	1.67441i
$498$	13.2915			0.595606
$499$	14.6458	−	25.3672i	0.655634	−	1.13559i	−0.326101	−	0.945335i	$-0.605735\pi$
$499$	14.6458	−	25.3672i	0.655634	−	1.13559i	0.981734	−	0.190256i	$-0.0609318\pi$
$500$	6.00000	+	10.3923i	0.268328	+	0.464758i
$501$	3.43725	+	5.95350i	0.153565	+	0.265983i
$502$	−6.64575	+	11.5108i	−0.296614	+	0.513751i
$503$	36.4575			1.62556			0.812780	−	0.582571i	$-0.197953\pi$
$503$	36.4575			1.62556			0.812780	+	0.582571i	$0.197953\pi$
$504$	−1.32288	−	2.29129i	−0.0589256	−	0.102062i
$505$		0			0
$506$	−0.760130	+	1.31658i	−0.0337919	+	0.0585293i
$507$	−0.500000	−	0.866025i	−0.0222058	−	0.0384615i
$508$	5.11438	+	8.85836i	0.226914	+	0.393026i
$509$	−12.0000	+	20.7846i	−0.531891	+	0.921262i	0.467416	+	0.884037i	$0.345185\pi$
$509$	−12.0000	+	20.7846i	−0.531891	+	0.921262i	−0.999307	+	0.0372243i	$0.988148\pi$
$510$	−24.2288			−1.07287
$511$	36.1033			1.59711
$512$	−1.00000			−0.0441942
$513$	−2.50000	+	4.33013i	−0.110378	+	0.191180i
$514$	−7.93725	−	13.7477i	−0.350097	−	0.606386i
$515$	−9.64575	−	16.7069i	−0.425043	−	0.736195i
$516$	2.64575	−	4.58258i	0.116473	−	0.201737i
$517$	1.93725			0.0852003
$518$	14.9373			0.656305
$519$	−22.2915			−0.978488
$520$	−1.82288	+	3.15731i	−0.0799384	+	0.138457i
$521$	−9.00000	−	15.5885i	−0.394297	−	0.682943i	0.598714	−	0.800963i	$-0.295679\pi$
$521$	−9.00000	−	15.5885i	−0.394297	−	0.682943i	−0.993011	+	0.118020i	$0.962345\pi$
$522$	2.14575	+	3.71655i	0.0939170	+	0.162669i
$523$	13.3542	−	23.1302i	0.583941	−	1.01141i	−0.411066	−	0.911606i	$-0.634843\pi$
$523$	13.3542	−	23.1302i	0.583941	−	1.01141i	0.995007	−	0.0998091i	$-0.0318232\pi$
$524$	10.9373			0.477796
$525$	10.9686	+	18.9982i	0.478710	+	0.829150i
$526$	3.64575			0.158962
$527$	10.9373	−	18.9439i	0.476434	−	0.825208i
$528$	−0.322876	−	0.559237i	−0.0140514	−	0.0243377i
$529$	8.72876	+	15.1186i	0.379511	+	0.657333i
$530$	5.46863	−	9.47194i	0.237542	−	0.411435i
$531$	−7.93725			−0.344447
$532$	6.61438	−	11.4564i	0.286770	−	0.496700i
$533$	−2.35425			−0.101974
$534$	8.46863	−	14.6681i	0.366473	−	0.634750i
$535$	−21.8745	−	37.8878i	−0.945717	−	1.63803i
$536$	3.79150	+	6.56708i	0.163768	+	0.283654i
$537$	3.00000	−	5.19615i	0.129460	−	0.224231i
$538$	−6.87451			−0.296381
$539$	−2.26013	+	3.91466i	−0.0973507	+	0.168616i
$540$	−3.64575			−0.156888
$541$	−20.8229	+	36.0663i	−0.895245	+	1.55061i	−0.0617447	+	0.998092i	$0.519666\pi$
$541$	−20.8229	+	36.0663i	−0.895245	+	1.55061i	−0.833501	+	0.552518i	$0.813667\pi$
$542$	−11.3229	−	19.6118i	−0.486359	−	0.842399i
$543$	−7.32288	−	12.6836i	−0.314255	−	0.544305i
$544$	−3.32288	+	5.75539i	−0.142467	+	0.246760i
$545$	14.5830			0.624667
$546$	−1.32288	+	2.29129i	−0.0566139	+	0.0980581i
$547$	−20.9373			−0.895212			−0.447606	−	0.894231i	$-0.647723\pi$
$547$	−20.9373			−0.895212			−0.447606	+	0.894231i	$0.647723\pi$
$548$	9.76013	−	16.9050i	0.416932	−	0.722148i
$549$	5.96863	+	10.3380i	0.254735	+	0.441214i
$550$	2.67712	+	4.63692i	0.114153	+	0.197719i
$551$	−10.7288	+	18.5828i	−0.457060	+	0.791652i
$552$	2.35425			0.100203
$553$	−13.2288	−	22.9129i	−0.562544	−	0.974355i
$554$	−18.5203			−0.786850
$555$	10.2915	−	17.8254i	0.436850	−	0.756646i
$556$	11.1144	+	19.2507i	0.471355	+	0.816410i
$557$	−5.58301	−	9.67005i	−0.236560	−	0.409733i	0.723165	−	0.690675i	$-0.242686\pi$
$557$	−5.58301	−	9.67005i	−0.236560	−	0.409733i	−0.959725	+	0.280942i	$0.909353\pi$
$558$	1.64575	−	2.85052i	0.0696702	−	0.120672i
$559$	−5.29150			−0.223807
$560$	9.64575			0.407607
$561$	−4.29150			−0.181187
$562$	−1.29150	+	2.23695i	−0.0544788	+	0.0943600i
$563$	13.5203	+	23.4178i	0.569811	+	0.986942i	0.996584	+	0.0825829i	$0.0263169\pi$
$563$	13.5203	+	23.4178i	0.569811	+	0.986942i	−0.426773	+	0.904359i	$0.640350\pi$
$564$	−1.50000	−	2.59808i	−0.0631614	−	0.109399i
$565$	27.7601	−	48.0820i	1.16788	−	2.02282i
$566$	11.0627			0.465002
$567$	−2.64575			−0.111111
$568$	−16.2915			−0.683576
$569$	16.6144	−	28.7769i	0.696511	−	1.20639i	−0.273158	−	0.961969i	$-0.588068\pi$
$569$	16.6144	−	28.7769i	0.696511	−	1.20639i	0.969669	−	0.244423i	$-0.0785986\pi$
$570$	−9.11438	−	15.7866i	−0.381759	−	0.661226i
$571$	8.00000	+	13.8564i	0.334790	+	0.579873i	0.983444	−	0.181210i	$-0.0580014\pi$
$571$	8.00000	+	13.8564i	0.334790	+	0.579873i	−0.648655	+	0.761083i	$0.724668\pi$
$572$	−0.322876	+	0.559237i	−0.0135001	+	0.0233829i
$573$		0			0
$574$	3.11438	+	5.39426i	0.129992	+	0.225152i
$575$	−19.5203			−0.814051
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	6.29150	+	10.8972i	0.261919	+	0.453656i	0.966752	−	0.255717i	$-0.0823114\pi$
$577$	6.29150	+	10.8972i	0.261919	+	0.453656i	−0.704833	+	0.709373i	$0.748978\pi$
$578$	13.5830	+	23.5265i	0.564979	+	0.978572i
$579$	−9.46863	+	16.4001i	−0.393503	+	0.681567i
$580$	−15.6458			−0.649654
$581$	−17.5830	+	30.4547i	−0.729466	+	1.26347i
$582$	−0.937254			−0.0388504
$583$	0.968627	−	1.67771i	0.0401164	−	0.0694837i
$584$	−6.82288	−	11.8176i	−0.282333	−	0.489014i
$585$	1.82288	+	3.15731i	0.0753666	+	0.130539i
$586$	3.76013	−	6.51274i	0.155330	−	0.269039i
$587$	31.9373			1.31819			0.659096	−	0.752059i	$-0.270939\pi$
$587$	31.9373			1.31819			0.659096	+	0.752059i	$0.270939\pi$
$588$	7.00000			0.288675
$589$	16.4575			0.678120
$590$	14.4686	−	25.0604i	0.595664	−	1.03172i
$591$	13.4059	+	23.2197i	0.551444	+	0.955129i
$592$	−2.82288	−	4.88936i	−0.116019	−	0.200952i
$593$	−21.7601	+	37.6897i	−0.893581	+	1.54773i	−0.0580309	+	0.998315i	$0.518482\pi$
$593$	−21.7601	+	37.6897i	−0.893581	+	1.54773i	−0.835551	+	0.549414i	$0.814851\pi$
$594$	−0.645751			−0.0264955
$595$	32.0516	−	55.5151i	1.31399	−	2.27590i
$596$	−7.06275			−0.289301
$597$	11.1144	−	19.2507i	0.454881	−	0.787877i
$598$	−1.17712	−	2.03884i	−0.0481362	−	0.0833743i
$599$	16.4059	+	28.4158i	0.670326	+	1.16104i	0.977812	+	0.209486i	$0.0671791\pi$
$599$	16.4059	+	28.4158i	0.670326	+	1.16104i	−0.307485	+	0.951553i	$0.599488\pi$
$600$	4.14575	−	7.18065i	0.169250	−	0.293149i
$601$	14.8745			0.606744			0.303372	−	0.952872i	$-0.401888\pi$
$601$	14.8745			0.606744			0.303372	+	0.952872i	$0.401888\pi$
$602$	7.00000	+	12.1244i	0.285299	+	0.494152i
$603$	7.58301			0.308804
$604$	−3.03137	+	5.25049i	−0.123345	+	0.213639i
$605$	−19.2915	−	33.4139i	−0.784311	−	1.35847i
$606$		0			0
$607$	−8.40588	+	14.5594i	−0.341184	+	0.590948i	−0.984653	−	0.174524i	$-0.944161\pi$
$607$	−8.40588	+	14.5594i	−0.341184	+	0.590948i	0.643469	+	0.765472i	$0.277495\pi$
$608$	−5.00000			−0.202777
$609$	−11.3542			−0.460097
$610$	−43.5203			−1.76208
$611$	−1.50000	+	2.59808i	−0.0606835	+	0.105107i
$612$	3.32288	+	5.75539i	0.134319	+	0.232648i
$613$	−20.9373	−	36.2644i	−0.845648	−	1.46470i	−0.885058	−	0.465482i	$-0.845881\pi$
$613$	−20.9373	−	36.2644i	−0.845648	−	1.46470i	0.0394098	−	0.999223i	$-0.487452\pi$
$614$	−4.79150	+	8.29913i	−0.193369	+	0.334925i
$615$	8.58301			0.346100
$616$	1.70850			0.0688373
$617$	−10.7085			−0.431108			−0.215554	−	0.976492i	$-0.569156\pi$
$617$	−10.7085			−0.431108			−0.215554	+	0.976492i	$0.569156\pi$
$618$	−2.64575	+	4.58258i	−0.106428	+	0.184338i
$619$	20.8745	+	36.1557i	0.839017	+	1.45322i	0.890717	+	0.454558i	$0.150203\pi$
$619$	20.8745	+	36.1557i	0.839017	+	1.45322i	−0.0516999	+	0.998663i	$0.516464\pi$
$620$	6.00000	+	10.3923i	0.240966	+	0.417365i
$621$	1.17712	−	2.03884i	0.0472364	−	0.0818158i
$622$	1.06275			0.0426122
$623$	22.4059	+	38.8081i	0.897673	+	1.55481i
$624$	1.00000			0.0400320
$625$	−1.14575	+	1.98450i	−0.0458301	+	0.0793800i
$626$	6.58301	+	11.4021i	0.263110	+	0.455720i
$627$	−1.61438	−	2.79619i	−0.0644721	−	0.111669i
$628$	−1.32288	+	2.29129i	−0.0527885	+	0.0914323i
$629$	−37.5203			−1.49603
$630$	4.82288	−	8.35347i	0.192148	−	0.332810i
$631$	14.4575			0.575545			0.287772	−	0.957699i	$-0.407085\pi$
$631$	14.4575			0.575545			0.287772	+	0.957699i	$0.407085\pi$
$632$	−5.00000	+	8.66025i	−0.198889	+	0.344486i
$633$	3.17712	+	5.50294i	0.126279	+	0.218722i
$634$	−6.64575	−	11.5108i	−0.263937	−	0.457151i
$635$	−18.6458	+	32.2954i	−0.739934	+	1.28160i
$636$	−3.00000			−0.118958
$637$	−3.50000	−	6.06218i	−0.138675	−	0.240192i
$638$	−2.77124			−0.109715
$639$	−8.14575	+	14.1089i	−0.322241	+	0.558138i
$640$	−1.82288	−	3.15731i	−0.0720555	−	0.124804i
$641$	10.7085	+	18.5477i	0.422960	+	0.732589i	0.996228	−	0.0867798i	$-0.0276577\pi$
$641$	10.7085	+	18.5477i	0.422960	+	0.732589i	−0.573267	+	0.819368i	$0.694324\pi$
$642$	−6.00000	+	10.3923i	−0.236801	+	0.410152i
$643$	−10.8745			−0.428849			−0.214424	−	0.976741i	$-0.568788\pi$
$643$	−10.8745			−0.428849			−0.214424	+	0.976741i	$0.568788\pi$
$644$	−3.11438	+	5.39426i	−0.122724	+	0.212564i
$645$	19.2915			0.759602
$646$	−16.6144	+	28.7769i	−0.653684	+	1.13221i
$647$	−12.8745	−	22.2993i	−0.506149	−	0.876676i	−0.999975	−	0.00711502i	$-0.997735\pi$
$647$	−12.8745	−	22.2993i	−0.506149	−	0.876676i	0.493826	−	0.869561i	$-0.335598\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	2.56275	−	4.43881i	0.100597	−	0.174238i
$650$	−8.29150			−0.325219
$651$	4.35425	+	7.54178i	0.170656	+	0.295586i
$652$	2.41699			0.0946568
$653$	−6.00000	+	10.3923i	−0.234798	+	0.406682i	−0.959214	−	0.282681i	$-0.908776\pi$
$653$	−6.00000	+	10.3923i	−0.234798	+	0.406682i	0.724416	+	0.689363i	$0.242110\pi$
$654$	−2.00000	−	3.46410i	−0.0782062	−	0.135457i
$655$	19.9373	+	34.5323i	0.779013	+	1.34929i
$656$	1.17712	−	2.03884i	0.0459590	−	0.0796033i
$657$	−13.6458			−0.532371
$658$	7.93725			0.309426
$659$	−16.9373			−0.659782			−0.329891	−	0.944019i	$-0.607012\pi$
$659$	−16.9373			−0.659782			−0.329891	+	0.944019i	$0.607012\pi$
$660$	1.17712	−	2.03884i	0.0458195	−	0.0793617i
$661$	−7.76013	−	13.4409i	−0.301834	−	0.522792i	0.674717	−	0.738076i	$-0.264266\pi$
$661$	−7.76013	−	13.4409i	−0.301834	−	0.522792i	−0.976551	+	0.215284i	$0.930932\pi$
$662$	5.70850	+	9.88741i	0.221867	+	0.384285i
$663$	3.32288	−	5.75539i	0.129050	−	0.223521i
$664$	13.2915			0.515810
$665$	48.2288			1.87023
$666$	−5.64575			−0.218768
$667$	5.05163	−	8.74968i	0.195600	−	0.338789i
$668$	3.43725	+	5.95350i	0.132991	+	0.230348i
$669$	10.2601	+	17.7711i	0.396680	+	0.687069i
$670$	−13.8229	+	23.9419i	−0.534024	+	0.924957i
$671$	−7.70850			−0.297583
$672$	−1.32288	−	2.29129i	−0.0510310	−	0.0883883i
$673$	−6.58301			−0.253756			−0.126878	−	0.991918i	$-0.540496\pi$
$673$	−6.58301			−0.253756			−0.126878	+	0.991918i	$0.540496\pi$
$674$	−7.79150	+	13.4953i	−0.300117	+	0.519819i
$675$	−4.14575	−	7.18065i	−0.159570	−	0.276383i
$676$	−0.500000	−	0.866025i	−0.0192308	−	0.0333087i
$677$	−10.0830	+	17.4643i	−0.387521	+	0.671207i	−0.992115	−	0.125327i	$-0.960002\pi$
$677$	−10.0830	+	17.4643i	−0.387521	+	0.671207i	0.604594	+	0.796534i	$0.293335\pi$
$678$	−15.2288			−0.584857
$679$	1.23987	−	2.14752i	0.0475819	−	0.0824142i
$680$	−24.2288			−0.929130
$681$	2.35425	−	4.07768i	0.0902150	−	0.156257i
$682$	1.06275	+	1.84073i	0.0406947	+	0.0704852i
$683$	−9.64575	−	16.7069i	−0.369084	−	0.639273i	0.620338	−	0.784334i	$-0.286995\pi$
$683$	−9.64575	−	16.7069i	−0.369084	−	0.639273i	−0.989423	+	0.145061i	$0.953662\pi$
$684$	−2.50000	+	4.33013i	−0.0955899	+	0.165567i
$685$	71.1660			2.71911
$686$	−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
$690$	4.29150	+	7.43310i	0.163375	+	0.282973i
$691$	20.0203	−	34.6761i	0.761607	−	1.31914i	−0.180416	−	0.983590i	$-0.557744\pi$
$691$	20.0203	−	34.6761i	0.761607	−	1.31914i	0.942022	−	0.335551i	$-0.108922\pi$
$692$	−22.2915			−0.847396
$693$	0.854249	−	1.47960i	0.0324502	−	0.0562054i
$694$	−0.228757			−0.00868348
$695$	−40.5203	+	70.1831i	−1.53702	+	2.66220i
$696$	2.14575	+	3.71655i	0.0813345	+	0.140875i
$697$	−7.82288	−	13.5496i	−0.296313	−	0.513228i
$698$	9.46863	−	16.4001i	0.358393	−	0.620755i
$699$	0.645751			0.0244246
$700$	10.9686	+	18.9982i	0.414575	+	0.718065i
$701$	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
$703$	−14.1144	−	24.4468i	−0.532334	−	0.922029i
$704$	−0.322876	−	0.559237i	−0.0121688	−	0.0210770i
$705$	5.46863	−	9.47194i	0.205960	−	0.356734i
$706$	20.5830			0.774652
$707$		0			0
$708$	−7.93725			−0.298300
$709$	−3.23987	+	5.61162i	−0.121676	+	0.210749i	−0.920429	−	0.390911i	$-0.872160\pi$
$709$	−3.23987	+	5.61162i	−0.121676	+	0.210749i	0.798753	+	0.601659i	$0.205494\pi$
$710$	−29.6974	−	51.4374i	−1.11452	−	1.93041i
$711$	5.00000	+	8.66025i	0.187515	+	0.324785i
$712$	8.46863	−	14.6681i	0.317375	−	0.549710i
$713$	−7.74902			−0.290203
$714$	−17.5830			−0.658027
$715$	−2.35425			−0.0880439
$716$	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
$719$	−22.2915	+	38.6100i	−0.831333	+	1.43991i	0.0656489	+	0.997843i	$0.479088\pi$
$719$	−22.2915	+	38.6100i	−0.831333	+	1.43991i	−0.896982	+	0.442068i	$0.854245\pi$
$720$	−3.64575			−0.135869
$721$	−7.00000	−	12.1244i	−0.260694	−	0.451535i
$722$	−6.00000			−0.223297
$723$	6.93725	−	12.0157i	0.257999	−	0.446868i
$724$	−7.32288	−	12.6836i	−0.272153	−	0.471382i
$725$	−17.7915	−	30.8158i	−0.660760	−	1.14447i
$726$	−5.29150	+	9.16515i	−0.196386	+	0.340151i
$727$	−16.4575			−0.610375			−0.305188	−	0.952292i	$-0.598719\pi$
$727$	−16.4575			−0.610375			−0.305188	+	0.952292i	$0.598719\pi$
$728$	−1.32288	+	2.29129i	−0.0490290	+	0.0849208i
$729$	1.00000			0.0370370
$730$	24.8745	−	43.0839i	0.920647	−	1.59461i
$731$	−17.5830	−	30.4547i	−0.650331	−	1.12641i
$732$	5.96863	+	10.3380i	0.220607	+	0.382102i
$733$	−7.11438	+	12.3225i	−0.262776	+	0.455141i	−0.966978	−	0.254858i	$-0.917971\pi$
$733$	−7.11438	+	12.3225i	−0.262776	+	0.455141i	0.704203	+	0.709999i	$0.251305\pi$
$734$	0.583005			0.0215191
$735$	12.7601	+	22.1012i	0.470664	+	0.815215i
$736$	2.35425			0.0867788
$737$	−2.44837	+	4.24070i	−0.0901868	+	0.156208i
$738$	−1.17712	−	2.03884i	−0.0433305	−	0.0750507i
$739$	8.64575	+	14.9749i	0.318039	+	0.550860i	0.980079	−	0.198609i	$-0.0636423\pi$
$739$	8.64575	+	14.9749i	0.318039	+	0.550860i	−0.662040	+	0.749469i	$0.730309\pi$
$740$	10.2915	−	17.8254i	0.378323	−	0.655275i
$741$	5.00000			0.183680
$742$	3.96863	−	6.87386i	0.145693	−	0.252347i
$743$	−51.4575			−1.88779			−0.943897	−	0.330241i	$-0.892870\pi$
$743$	−51.4575			−1.88779			−0.943897	+	0.330241i	$0.892870\pi$
$744$	1.64575	−	2.85052i	0.0603362	−	0.104505i
$745$	−12.8745	−	22.2993i	−0.471685	−	0.816983i
$746$	7.32288	+	12.6836i	0.268110	+	0.464379i
$747$	6.64575	−	11.5108i	0.243155	−	0.421157i
$748$	−4.29150			−0.156913
$749$	−15.8745	−	27.4955i	−0.580042	−	1.00466i
$750$	12.0000			0.438178
$751$	16.5830	−	28.7226i	0.605122	−	1.04810i	−0.386910	−	0.922118i	$-0.626457\pi$
$751$	16.5830	−	28.7226i	0.605122	−	1.04810i	0.992032	−	0.125985i	$-0.0402092\pi$
$752$	−1.50000	−	2.59808i	−0.0546994	−	0.0947421i
$753$	6.64575	+	11.5108i	0.242185	+	0.419476i
$754$	2.14575	−	3.71655i	0.0781437	−	0.135349i
$755$	−22.1033			−0.804420
$756$	−2.64575			−0.0962250
$757$	26.6458			0.968456			0.484228	−	0.874942i	$-0.339100\pi$
$757$	26.6458			0.968456			0.484228	+	0.874942i	$0.339100\pi$
$758$	−4.58301	+	7.93800i	−0.166462	+	0.288321i
$759$	0.760130	+	1.31658i	0.0275910	+	0.0477889i
$760$	−9.11438	−	15.7866i	−0.330613	−	0.572639i
$761$	−3.64575	+	6.31463i	−0.132158	+	0.228905i	−0.924508	−	0.381162i	$-0.875524\pi$
$761$	−3.64575	+	6.31463i	−0.132158	+	0.228905i	0.792350	+	0.610067i	$0.208857\pi$
$762$	10.2288			0.370549
$763$	10.5830			0.383131
$764$		0			0
$765$	−12.1144	+	20.9827i	−0.437996	+	0.758632i
$766$	12.8745	+	22.2993i	0.465175	+	0.805707i
$767$	3.96863	+	6.87386i	0.143299	+	0.248201i
$768$	−0.500000	+	0.866025i	−0.0180422	+	0.0312500i
$769$	5.64575			0.203591			0.101795	−	0.994805i	$-0.467541\pi$
$769$	5.64575			0.203591			0.101795	+	0.994805i	$0.467541\pi$
$770$	3.11438	+	5.39426i	0.112234	+	0.194396i
$771$	−15.8745			−0.571706
$772$	−9.46863	+	16.4001i	−0.340783	+	0.590254i
$773$	−20.1660	−	34.9286i

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)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.82288 - 3.15731i) q^{5} -1.00000 q^{6} +(1.32288 - 2.29129i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.82288 - 3.15731i) q^{5} -1.00000 q^{6} +(1.32288 - 2.29129i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.82288 - 3.15731i) q^{10} +(-0.322876 - 0.559237i) q^{11} +(-0.500000 + 0.866025i) q^{12} +1.00000 q^{13} +(-1.32288 - 2.29129i) q^{14} -3.64575 q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.32288 + 5.75539i) q^{17} +(0.500000 + 0.866025i) q^{18} +(-2.50000 + 4.33013i) q^{19} -3.64575 q^{20} -2.64575 q^{21} -0.645751 q^{22} +(1.17712 - 2.03884i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-4.14575 - 7.18065i) q^{25} +(0.500000 - 0.866025i) q^{26} +1.00000 q^{27} -2.64575 q^{28} +4.29150 q^{29} +(-1.82288 + 3.15731i) q^{30} +(-1.64575 - 2.85052i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-0.322876 + 0.559237i) q^{33} +6.64575 q^{34} +(-4.82288 - 8.35347i) q^{35} +1.00000 q^{36} +(-2.82288 + 4.88936i) q^{37} +(2.50000 + 4.33013i) q^{38} +(-0.500000 - 0.866025i) q^{39} +(-1.82288 + 3.15731i) q^{40} -2.35425 q^{41} +(-1.32288 + 2.29129i) q^{42} -5.29150 q^{43} +(-0.322876 + 0.559237i) q^{44} +(1.82288 + 3.15731i) q^{45} +(-1.17712 - 2.03884i) q^{46} +(-1.50000 + 2.59808i) q^{47} +1.00000 q^{48} +(-3.50000 - 6.06218i) q^{49} -8.29150 q^{50} +(3.32288 - 5.75539i) q^{51} +(-0.500000 - 0.866025i) q^{52} +(1.50000 + 2.59808i) q^{53} +(0.500000 - 0.866025i) q^{54} -2.35425 q^{55} +(-1.32288 + 2.29129i) q^{56} +5.00000 q^{57} +(2.14575 - 3.71655i) q^{58} +(3.96863 + 6.87386i) q^{59} +(1.82288 + 3.15731i) q^{60} +(5.96863 - 10.3380i) q^{61} -3.29150 q^{62} +(1.32288 + 2.29129i) q^{63} +1.00000 q^{64} +(1.82288 - 3.15731i) q^{65} +(0.322876 + 0.559237i) q^{66} +(-3.79150 - 6.56708i) q^{67} +(3.32288 - 5.75539i) q^{68} -2.35425 q^{69} -9.64575 q^{70} +16.2915 q^{71} +(0.500000 - 0.866025i) q^{72} +(6.82288 + 11.8176i) q^{73} +(2.82288 + 4.88936i) q^{74} +(-4.14575 + 7.18065i) q^{75} +5.00000 q^{76} -1.70850 q^{77} -1.00000 q^{78} +(5.00000 - 8.66025i) q^{79} +(1.82288 + 3.15731i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-1.17712 + 2.03884i) q^{82} -13.2915 q^{83} +(1.32288 + 2.29129i) q^{84} +24.2288 q^{85} +(-2.64575 + 4.58258i) q^{86} +(-2.14575 - 3.71655i) q^{87} +(0.322876 + 0.559237i) q^{88} +(-8.46863 + 14.6681i) q^{89} +3.64575 q^{90} +(1.32288 - 2.29129i) q^{91} -2.35425 q^{92} +(-1.64575 + 2.85052i) q^{93} +(1.50000 + 2.59808i) q^{94} +(9.11438 + 15.7866i) q^{95} +(0.500000 - 0.866025i) q^{96} +0.937254 q^{97} -7.00000 q^{98} +0.645751 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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