LMFDB - Embedded newform 546.2.i.h.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:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
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			$-0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	546.235
Dual form			546.2.i.h.79.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.707107 - 1.22474i) q^{5} +1.00000 q^{6} +(-1.62132 + 2.09077i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.707107 - 1.22474i) q^{5} +1.00000 q^{6} +(-1.62132 + 2.09077i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.707107 + 1.22474i) q^{10} +(1.20711 - 2.09077i) q^{11} +(-0.500000 - 0.866025i) q^{12} +1.00000 q^{13} +(2.62132 + 0.358719i) q^{14} +1.41421 q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.62132 - 2.80821i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(-1.50000 - 2.59808i) q^{19} +1.41421 q^{20} +(-1.00000 - 2.44949i) q^{21} -2.41421 q^{22} +(-2.53553 - 4.39167i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(1.50000 - 2.59808i) q^{25} +(-0.500000 - 0.866025i) q^{26} +1.00000 q^{27} +(-1.00000 - 2.44949i) q^{28} +5.00000 q^{29} +(-0.707107 - 1.22474i) q^{30} +(-0.585786 + 1.01461i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(1.20711 + 2.09077i) q^{33} -3.24264 q^{34} +(3.70711 + 0.507306i) q^{35} +1.00000 q^{36} +(-4.53553 - 7.85578i) q^{37} +(-1.50000 + 2.59808i) q^{38} +(-0.500000 + 0.866025i) q^{39} +(-0.707107 - 1.22474i) q^{40} +7.41421 q^{41} +(-1.62132 + 2.09077i) q^{42} -0.828427 q^{43} +(1.20711 + 2.09077i) q^{44} +(-0.707107 + 1.22474i) q^{45} +(-2.53553 + 4.39167i) q^{46} +(-4.50000 - 7.79423i) q^{47} +1.00000 q^{48} +(-1.74264 - 6.77962i) q^{49} -3.00000 q^{50} +(1.62132 + 2.80821i) q^{51} +(-0.500000 + 0.866025i) q^{52} +(5.15685 - 8.93193i) q^{53} +(-0.500000 - 0.866025i) q^{54} -3.41421 q^{55} +(-1.62132 + 2.09077i) q^{56} +3.00000 q^{57} +(-2.50000 - 4.33013i) q^{58} +(-5.20711 + 9.01897i) q^{59} +(-0.707107 + 1.22474i) q^{60} +(-1.62132 - 2.80821i) q^{61} +1.17157 q^{62} +(2.62132 + 0.358719i) q^{63} +1.00000 q^{64} +(-0.707107 - 1.22474i) q^{65} +(1.20711 - 2.09077i) q^{66} +(1.67157 - 2.89525i) q^{67} +(1.62132 + 2.80821i) q^{68} +5.07107 q^{69} +(-1.41421 - 3.46410i) q^{70} -1.00000 q^{71} +(-0.500000 - 0.866025i) q^{72} +(-6.53553 + 11.3199i) q^{73} +(-4.53553 + 7.85578i) q^{74} +(1.50000 + 2.59808i) q^{75} +3.00000 q^{76} +(2.41421 + 5.91359i) q^{77} +1.00000 q^{78} +(4.65685 + 8.06591i) q^{79} +(-0.707107 + 1.22474i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.70711 - 6.42090i) q^{82} +3.65685 q^{83} +(2.62132 + 0.358719i) q^{84} -4.58579 q^{85} +(0.414214 + 0.717439i) q^{86} +(-2.50000 + 4.33013i) q^{87} +(1.20711 - 2.09077i) q^{88} +(-1.12132 - 1.94218i) q^{89} +1.41421 q^{90} +(-1.62132 + 2.09077i) q^{91} +5.07107 q^{92} +(-0.585786 - 1.01461i) q^{93} +(-4.50000 + 7.79423i) q^{94} +(-2.12132 + 3.67423i) q^{95} +(-0.500000 - 0.866025i) q^{96} -11.8995 q^{97} +(-5.00000 + 4.89898i) q^{98} -2.41421 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 4 q^{6} + 2 q^{7} + 4 q^{8} - 2 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 4 * q^6 + 2 * q^7 + 4 * q^8 - 2 * q^9	$ 4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 4 q^{6} + 2 q^{7} + 4 q^{8} - 2 q^{9} + 2 q^{11} - 2 q^{12} + 4 q^{13} + 2 q^{14} - 2 q^{16} - 2 q^{17} - 2 q^{18} - 6 q^{19} - 4 q^{21} - 4 q^{22} + 4 q^{23} - 2 q^{24} + 6 q^{25} - 2 q^{26} + 4 q^{27} - 4 q^{28} + 20 q^{29} - 8 q^{31} - 2 q^{32} + 2 q^{33} + 4 q^{34} + 12 q^{35} + 4 q^{36} - 4 q^{37} - 6 q^{38} - 2 q^{39} + 24 q^{41} + 2 q^{42} + 8 q^{43} + 2 q^{44} + 4 q^{46} - 18 q^{47} + 4 q^{48} + 10 q^{49} - 12 q^{50} - 2 q^{51} - 2 q^{52} - 2 q^{53} - 2 q^{54} - 8 q^{55} + 2 q^{56} + 12 q^{57} - 10 q^{58} - 18 q^{59} + 2 q^{61} + 16 q^{62} + 2 q^{63} + 4 q^{64} + 2 q^{66} + 18 q^{67} - 2 q^{68} - 8 q^{69} - 4 q^{71} - 2 q^{72} - 12 q^{73} - 4 q^{74} + 6 q^{75} + 12 q^{76} + 4 q^{77} + 4 q^{78} - 4 q^{79} - 2 q^{81} - 12 q^{82} - 8 q^{83} + 2 q^{84} - 24 q^{85} - 4 q^{86} - 10 q^{87} + 2 q^{88} + 4 q^{89} + 2 q^{91} - 8 q^{92} - 8 q^{93} - 18 q^{94} - 2 q^{96} - 8 q^{97} - 20 q^{98} - 4 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 4 * q^6 + 2 * q^7 + 4 * q^8 - 2 * q^9 + 2 * q^11 - 2 * q^12 + 4 * q^13 + 2 * q^14 - 2 * q^16 - 2 * q^17 - 2 * q^18 - 6 * q^19 - 4 * q^21 - 4 * q^22 + 4 * q^23 - 2 * q^24 + 6 * q^25 - 2 * q^26 + 4 * q^27 - 4 * q^28 + 20 * q^29 - 8 * q^31 - 2 * q^32 + 2 * q^33 + 4 * q^34 + 12 * q^35 + 4 * q^36 - 4 * q^37 - 6 * q^38 - 2 * q^39 + 24 * q^41 + 2 * q^42 + 8 * q^43 + 2 * q^44 + 4 * q^46 - 18 * q^47 + 4 * q^48 + 10 * q^49 - 12 * q^50 - 2 * q^51 - 2 * q^52 - 2 * q^53 - 2 * q^54 - 8 * q^55 + 2 * q^56 + 12 * q^57 - 10 * q^58 - 18 * q^59 + 2 * q^61 + 16 * q^62 + 2 * q^63 + 4 * q^64 + 2 * q^66 + 18 * q^67 - 2 * q^68 - 8 * q^69 - 4 * q^71 - 2 * q^72 - 12 * q^73 - 4 * q^74 + 6 * q^75 + 12 * q^76 + 4 * q^77 + 4 * q^78 - 4 * q^79 - 2 * q^81 - 12 * q^82 - 8 * q^83 + 2 * q^84 - 24 * q^85 - 4 * q^86 - 10 * q^87 + 2 * q^88 + 4 * q^89 + 2 * q^91 - 8 * q^92 - 8 * q^93 - 18 * q^94 - 2 * q^96 - 8 * q^97 - 20 * q^98 - 4 * 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
$5$	−0.707107	−	1.22474i	−0.316228	−	0.547723i	0.663470	−	0.748203i	$-0.269083\pi$
$5$	−0.707107	−	1.22474i	−0.316228	−	0.547723i	−0.979698	+	0.200480i	$0.935750\pi$
$6$	1.00000			0.408248
$7$	−1.62132	+	2.09077i	−0.612801	+	0.790237i
$7$	−1.62132	+	2.09077i	−0.612801	+	0.790237i
$8$	1.00000			0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−0.707107	+	1.22474i	−0.223607	+	0.387298i
$11$	1.20711	−	2.09077i	0.363956	−	0.630391i	−0.624652	−	0.780903i	$-0.714759\pi$
$11$	1.20711	−	2.09077i	0.363956	−	0.630391i	0.988608	+	0.150513i	$0.0480924\pi$
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	1.00000			0.277350
$13$	1.00000			0.277350
$14$	2.62132	+	0.358719i	0.700577	+	0.0958718i
$15$	1.41421			0.365148
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.62132	−	2.80821i	0.393228	−	0.681091i	−0.599645	−	0.800266i	$-0.704692\pi$
$17$	1.62132	−	2.80821i	0.393228	−	0.681091i	0.992873	+	0.119175i	$0.0380250\pi$
$18$	−0.500000	+	0.866025i	−0.117851	+	0.204124i
$19$	−1.50000	−	2.59808i	−0.344124	−	0.596040i	0.641071	−	0.767482i	$-0.278491\pi$
$19$	−1.50000	−	2.59808i	−0.344124	−	0.596040i	−0.985194	+	0.171442i	$0.945157\pi$
$20$	1.41421			0.316228
$21$	−1.00000	−	2.44949i	−0.218218	−	0.534522i
$22$	−2.41421			−0.514712
$23$	−2.53553	−	4.39167i	−0.528695	−	0.915727i	−0.999440	−	0.0334578i	$-0.989348\pi$
$23$	−2.53553	−	4.39167i	−0.528695	−	0.915727i	0.470745	−	0.882269i	$-0.343985\pi$
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	1.50000	−	2.59808i	0.300000	−	0.519615i
$26$	−0.500000	−	0.866025i	−0.0980581	−	0.169842i
$27$	1.00000			0.192450
$28$	−1.00000	−	2.44949i	−0.188982	−	0.462910i
$29$	5.00000			0.928477			0.464238	−	0.885710i	$-0.346328\pi$
$29$	5.00000			0.928477			0.464238	+	0.885710i	$0.346328\pi$
$30$	−0.707107	−	1.22474i	−0.129099	−	0.223607i
$31$	−0.585786	+	1.01461i	−0.105210	+	0.182230i	−0.913824	−	0.406110i	$-0.866885\pi$
$31$	−0.585786	+	1.01461i	−0.105210	+	0.182230i	0.808614	+	0.588340i	$0.200218\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	1.20711	+	2.09077i	0.210130	+	0.363956i
$34$	−3.24264			−0.556108
$35$	3.70711	+	0.507306i	0.626615	+	0.0857504i
$36$	1.00000			0.166667
$37$	−4.53553	−	7.85578i	−0.745637	−	1.29148i	−0.949896	−	0.312565i	$-0.898812\pi$
$37$	−4.53553	−	7.85578i	−0.745637	−	1.29148i	0.204259	−	0.978917i	$-0.434521\pi$
$38$	−1.50000	+	2.59808i	−0.243332	+	0.421464i
$39$	−0.500000	+	0.866025i	−0.0800641	+	0.138675i
$40$	−0.707107	−	1.22474i	−0.111803	−	0.193649i
$41$	7.41421			1.15791			0.578953	−	0.815361i	$-0.303462\pi$
$41$	7.41421			1.15791			0.578953	+	0.815361i	$0.303462\pi$
$42$	−1.62132	+	2.09077i	−0.250175	+	0.322613i
$43$	−0.828427			−0.126334			−0.0631670	−	0.998003i	$-0.520120\pi$
$43$	−0.828427			−0.126334			−0.0631670	+	0.998003i	$0.520120\pi$
$44$	1.20711	+	2.09077i	0.181978	+	0.315195i
$45$	−0.707107	+	1.22474i	−0.105409	+	0.182574i
$46$	−2.53553	+	4.39167i	−0.373844	+	0.647517i
$47$	−4.50000	−	7.79423i	−0.656392	−	1.13691i	−0.981543	−	0.191243i	$-0.938748\pi$
$47$	−4.50000	−	7.79423i	−0.656392	−	1.13691i	0.325150	−	0.945662i	$-0.394585\pi$
$48$	1.00000			0.144338
$49$	−1.74264	−	6.77962i	−0.248949	−	0.968517i
$50$	−3.00000			−0.424264
$51$	1.62132	+	2.80821i	0.227030	+	0.393228i
$52$	−0.500000	+	0.866025i	−0.0693375	+	0.120096i
$53$	5.15685	−	8.93193i	0.708348	−	1.22690i	−0.257121	−	0.966379i	$-0.582774\pi$
$53$	5.15685	−	8.93193i	0.708348	−	1.22690i	0.965469	−	0.260516i	$-0.0838928\pi$
$54$	−0.500000	−	0.866025i	−0.0680414	−	0.117851i
$55$	−3.41421			−0.460372
$56$	−1.62132	+	2.09077i	−0.216658	+	0.279391i
$57$	3.00000			0.397360
$58$	−2.50000	−	4.33013i	−0.328266	−	0.568574i
$59$	−5.20711	+	9.01897i	−0.677908	+	1.17417i	0.297702	+	0.954659i	$0.403780\pi$
$59$	−5.20711	+	9.01897i	−0.677908	+	1.17417i	−0.975610	+	0.219512i	$0.929554\pi$
$60$	−0.707107	+	1.22474i	−0.0912871	+	0.158114i
$61$	−1.62132	−	2.80821i	−0.207589	−	0.359554i	0.743366	−	0.668885i	$-0.233228\pi$
$61$	−1.62132	−	2.80821i	−0.207589	−	0.359554i	−0.950954	+	0.309331i	$0.899895\pi$
$62$	1.17157			0.148790
$63$	2.62132	+	0.358719i	0.330255	+	0.0451944i
$64$	1.00000			0.125000
$65$	−0.707107	−	1.22474i	−0.0877058	−	0.151911i
$66$	1.20711	−	2.09077i	0.148585	−	0.257356i
$67$	1.67157	−	2.89525i	0.204215	−	0.353711i	−0.745667	−	0.666319i	$-0.767869\pi$
$67$	1.67157	−	2.89525i	0.204215	−	0.353711i	0.949882	+	0.312608i	$0.101202\pi$
$68$	1.62132	+	2.80821i	0.196614	+	0.340545i
$69$	5.07107			0.610485
$70$	−1.41421	−	3.46410i	−0.169031	−	0.414039i
$71$	−1.00000			−0.118678			−0.0593391	−	0.998238i	$-0.518899\pi$
$71$	−1.00000			−0.118678			−0.0593391	+	0.998238i	$0.518899\pi$
$72$	−0.500000	−	0.866025i	−0.0589256	−	0.102062i
$73$	−6.53553	+	11.3199i	−0.764926	+	1.32489i	0.175359	+	0.984505i	$0.443891\pi$
$73$	−6.53553	+	11.3199i	−0.764926	+	1.32489i	−0.940285	+	0.340387i	$0.889442\pi$
$74$	−4.53553	+	7.85578i	−0.527245	+	0.913215i
$75$	1.50000	+	2.59808i	0.173205	+	0.300000i
$76$	3.00000			0.344124
$77$	2.41421	+	5.91359i	0.275125	+	0.673916i
$78$	1.00000			0.113228
$79$	4.65685	+	8.06591i	0.523937	+	0.907486i	0.999612	+	0.0278643i	$0.00887063\pi$
$79$	4.65685	+	8.06591i	0.523937	+	0.907486i	−0.475675	+	0.879621i	$0.657796\pi$
$80$	−0.707107	+	1.22474i	−0.0790569	+	0.136931i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−3.70711	−	6.42090i	−0.409381	−	0.709069i
$83$	3.65685			0.401392			0.200696	−	0.979654i	$-0.435680\pi$
$83$	3.65685			0.401392			0.200696	+	0.979654i	$0.435680\pi$
$84$	2.62132	+	0.358719i	0.286009	+	0.0391395i
$85$	−4.58579			−0.497398
$86$	0.414214	+	0.717439i	0.0446658	+	0.0773634i
$87$	−2.50000	+	4.33013i	−0.268028	+	0.464238i
$88$	1.20711	−	2.09077i	0.128678	−	0.222877i
$89$	−1.12132	−	1.94218i	−0.118860	−	0.205871i	0.800456	−	0.599391i	$-0.204591\pi$
$89$	−1.12132	−	1.94218i	−0.118860	−	0.205871i	−0.919316	+	0.393520i	$0.871257\pi$
$90$	1.41421			0.149071
$91$	−1.62132	+	2.09077i	−0.169961	+	0.219172i
$92$	5.07107			0.528695
$93$	−0.585786	−	1.01461i	−0.0607432	−	0.105210i
$94$	−4.50000	+	7.79423i	−0.464140	+	0.803913i
$95$	−2.12132	+	3.67423i	−0.217643	+	0.376969i
$96$	−0.500000	−	0.866025i	−0.0510310	−	0.0883883i
$97$	−11.8995			−1.20821			−0.604105	−	0.796904i	$-0.706469\pi$
$97$	−11.8995			−1.20821			−0.604105	+	0.796904i	$0.706469\pi$
$98$	−5.00000	+	4.89898i	−0.505076	+	0.494872i
$99$	−2.41421			−0.242638
$100$	1.50000	+	2.59808i	0.150000	+	0.259808i
$101$	3.41421	−	5.91359i	0.339727	−	0.588424i	−0.644654	−	0.764474i	$-0.722999\pi$
$101$	3.41421	−	5.91359i	0.339727	−	0.588424i	0.984381	+	0.176050i	$0.0563320\pi$
$102$	1.62132	−	2.80821i	0.160535	−	0.278054i
$103$	5.24264	+	9.08052i	0.516573	+	0.894730i	0.999815	+	0.0192435i	$0.00612576\pi$
$103$	5.24264	+	9.08052i	0.516573	+	0.894730i	−0.483242	+	0.875487i	$0.660541\pi$
$104$	1.00000			0.0980581
$105$	−2.29289	+	2.95680i	−0.223763	+	0.288554i
$106$	−10.3137			−1.00176
$107$	−1.17157	−	2.02922i	−0.113260	−	0.196172i	0.803823	−	0.594869i	$-0.202796\pi$
$107$	−1.17157	−	2.02922i	−0.113260	−	0.196172i	−0.917083	+	0.398696i	$0.869463\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	4.82843	−	8.36308i	0.462479	−	0.801038i	−0.536604	−	0.843834i	$-0.680293\pi$
$109$	4.82843	−	8.36308i	0.462479	−	0.801038i	0.999084	+	0.0427961i	$0.0136266\pi$
$110$	1.70711	+	2.95680i	0.162766	+	0.281919i
$111$	9.07107			0.860988
$112$	2.62132	+	0.358719i	0.247691	+	0.0338958i
$113$	8.07107			0.759262			0.379631	−	0.925138i	$-0.376051\pi$
$113$	8.07107			0.759262			0.379631	+	0.925138i	$0.376051\pi$
$114$	−1.50000	−	2.59808i	−0.140488	−	0.243332i
$115$	−3.58579	+	6.21076i	−0.334376	+	0.579157i
$116$	−2.50000	+	4.33013i	−0.232119	+	0.402042i
$117$	−0.500000	−	0.866025i	−0.0462250	−	0.0800641i
$118$	10.4142			0.958706
$119$	3.24264	+	7.94282i	0.297252	+	0.728117i
$120$	1.41421			0.129099
$121$	2.58579	+	4.47871i	0.235071	+	0.407156i
$122$	−1.62132	+	2.80821i	−0.146787	+	0.254243i
$123$	−3.70711	+	6.42090i	−0.334259	+	0.578953i
$124$	−0.585786	−	1.01461i	−0.0526052	−	0.0911148i
$125$	−11.3137			−1.01193
$126$	−1.00000	−	2.44949i	−0.0890871	−	0.218218i
$127$	−9.89949			−0.878438			−0.439219	−	0.898380i	$-0.644745\pi$
$127$	−9.89949			−0.878438			−0.439219	+	0.898380i	$0.644745\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	0.414214	−	0.717439i	0.0364695	−	0.0631670i
$130$	−0.707107	+	1.22474i	−0.0620174	+	0.107417i
$131$	4.94975	+	8.57321i	0.432461	+	0.749045i	0.997085	−	0.0763036i	$-0.0243118\pi$
$131$	4.94975	+	8.57321i	0.432461	+	0.749045i	−0.564623	+	0.825349i	$0.690978\pi$
$132$	−2.41421			−0.210130
$133$	7.86396	+	1.07616i	0.681892	+	0.0933148i
$134$	−3.34315			−0.288804
$135$	−0.707107	−	1.22474i	−0.0608581	−	0.105409i
$136$	1.62132	−	2.80821i	0.139027	−	0.240802i
$137$	−0.535534	+	0.927572i	−0.0457537	+	0.0792478i	−0.887995	−	0.459852i	$-0.847902\pi$
$137$	−0.535534	+	0.927572i	−0.0457537	+	0.0792478i	0.842242	+	0.539100i	$0.181236\pi$
$138$	−2.53553	−	4.39167i	−0.215839	−	0.373844i
$139$	21.2132			1.79928			0.899640	−	0.436632i	$-0.143829\pi$
$139$	21.2132			1.79928			0.899640	+	0.436632i	$0.143829\pi$
$140$	−2.29289	+	2.95680i	−0.193785	+	0.249895i
$141$	9.00000			0.757937
$142$	0.500000	+	0.866025i	0.0419591	+	0.0726752i
$143$	1.20711	−	2.09077i	0.100943	−	0.174839i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−3.53553	−	6.12372i	−0.293610	−	0.508548i
$146$	13.0711			1.08177
$147$	6.74264	+	1.88064i	0.556124	+	0.155112i
$148$	9.07107			0.745637
$149$	1.94975	+	3.37706i	0.159730	+	0.276660i	0.934771	−	0.355251i	$-0.115604\pi$
$149$	1.94975	+	3.37706i	0.159730	+	0.276660i	−0.775042	+	0.631910i	$0.782271\pi$
$150$	1.50000	−	2.59808i	0.122474	−	0.212132i
$151$	5.20711	−	9.01897i	0.423748	−	0.733954i	−0.572554	−	0.819867i	$-0.694047\pi$
$151$	5.20711	−	9.01897i	0.423748	−	0.733954i	0.996303	+	0.0859132i	$0.0273808\pi$
$152$	−1.50000	−	2.59808i	−0.121666	−	0.210732i
$153$	−3.24264			−0.262152
$154$	3.91421	−	5.04757i	0.315416	−	0.406744i
$155$	1.65685			0.133082
$156$	−0.500000	−	0.866025i	−0.0400320	−	0.0693375i
$157$	−11.0355	+	19.1141i	−0.880731	+	1.52547i	−0.0302023	+	0.999544i	$0.509615\pi$
$157$	−11.0355	+	19.1141i	−0.880731	+	1.52547i	−0.850529	+	0.525928i	$0.823718\pi$
$158$	4.65685	−	8.06591i	0.370479	−	0.641689i
$159$	5.15685	+	8.93193i	0.408965	+	0.708348i
$160$	1.41421			0.111803
$161$	13.2929	+	1.81909i	1.04763	+	0.143364i
$162$	1.00000			0.0785674
$163$	5.57107	+	9.64937i	0.436360	+	0.755797i	0.997406	−	0.0719876i	$-0.0229342\pi$
$163$	5.57107	+	9.64937i	0.436360	+	0.755797i	−0.561046	+	0.827785i	$0.689601\pi$
$164$	−3.70711	+	6.42090i	−0.289476	+	0.501388i
$165$	1.70711	−	2.95680i	0.132898	−	0.230186i
$166$	−1.82843	−	3.16693i	−0.141913	−	0.245801i
$167$	−10.3137			−0.798099			−0.399049	−	0.916929i	$-0.630660\pi$
$167$	−10.3137			−0.798099			−0.399049	+	0.916929i	$0.630660\pi$
$168$	−1.00000	−	2.44949i	−0.0771517	−	0.188982i
$169$	1.00000			0.0769231
$170$	2.29289	+	3.97141i	0.175857	+	0.304593i
$171$	−1.50000	+	2.59808i	−0.114708	+	0.198680i
$172$	0.414214	−	0.717439i	0.0315835	−	0.0547042i
$173$	1.15685	+	2.00373i	0.0879540	+	0.152341i	0.906646	−	0.421892i	$-0.138634\pi$
$173$	1.15685	+	2.00373i	0.0879540	+	0.152341i	−0.818692	+	0.574233i	$0.805300\pi$
$174$	5.00000			0.379049
$175$	3.00000	+	7.34847i	0.226779	+	0.555492i
$176$	−2.41421			−0.181978
$177$	−5.20711	−	9.01897i	−0.391390	−	0.677908i
$178$	−1.12132	+	1.94218i	−0.0840465	+	0.145573i
$179$	11.8284	−	20.4874i	0.884098	−	1.53130i	0.0373543	−	0.999302i	$-0.488107\pi$
$179$	11.8284	−	20.4874i	0.884098	−	1.53130i	0.846744	−	0.532001i	$-0.178560\pi$
$180$	−0.707107	−	1.22474i	−0.0527046	−	0.0912871i
$181$	−14.4142			−1.07140			−0.535700	−	0.844408i	$-0.679952\pi$
$181$	−14.4142			−1.07140			−0.535700	+	0.844408i	$0.679952\pi$
$182$	2.62132	+	0.358719i	0.194305	+	0.0265901i
$183$	3.24264			0.239703
$184$	−2.53553	−	4.39167i	−0.186922	−	0.323758i
$185$	−6.41421	+	11.1097i	−0.471582	+	0.816805i
$186$	−0.585786	+	1.01461i	−0.0429519	+	0.0743950i
$187$	−3.91421	−	6.77962i	−0.286236	−	0.495775i
$188$	9.00000			0.656392
$189$	−1.62132	+	2.09077i	−0.117934	+	0.152081i
$190$	4.24264			0.307794
$191$	−6.82843	−	11.8272i	−0.494088	−	0.855785i	0.505889	−	0.862599i	$-0.331164\pi$
$191$	−6.82843	−	11.8272i	−0.494088	−	0.855785i	−0.999977	+	0.00681360i	$0.997831\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	12.1213	−	20.9947i	0.872512	−	1.51123i	0.0131218	−	0.999914i	$-0.495823\pi$
$193$	12.1213	−	20.9947i	0.872512	−	1.51123i	0.859390	−	0.511321i	$-0.170844\pi$
$194$	5.94975	+	10.3053i	0.427167	+	0.739875i
$195$	1.41421			0.101274
$196$	6.74264	+	1.88064i	0.481617	+	0.134331i
$197$	−21.5563			−1.53583			−0.767913	−	0.640554i	$-0.778705\pi$
$197$	−21.5563			−1.53583			−0.767913	+	0.640554i	$0.778705\pi$
$198$	1.20711	+	2.09077i	0.0857853	+	0.148585i
$199$	−6.70711	+	11.6170i	−0.475454	+	0.823511i	−0.999605	−	0.0281148i	$-0.991050\pi$
$199$	−6.70711	+	11.6170i	−0.475454	+	0.823511i	0.524151	+	0.851626i	$0.324383\pi$
$200$	1.50000	−	2.59808i	0.106066	−	0.183712i
$201$	1.67157	+	2.89525i	0.117904	+	0.204215i
$202$	−6.82843			−0.480446
$203$	−8.10660	+	10.4539i	−0.568972	+	0.733717i
$204$	−3.24264			−0.227030
$205$	−5.24264	−	9.08052i	−0.366162	−	0.634211i
$206$	5.24264	−	9.08052i	0.365272	−	0.632670i
$207$	−2.53553	+	4.39167i	−0.176232	+	0.305242i
$208$	−0.500000	−	0.866025i	−0.0346688	−	0.0600481i
$209$	−7.24264			−0.500984
$210$	3.70711	+	0.507306i	0.255815	+	0.0350074i
$211$	8.38478			0.577232			0.288616	−	0.957445i	$-0.406805\pi$
$211$	8.38478			0.577232			0.288616	+	0.957445i	$0.406805\pi$
$212$	5.15685	+	8.93193i	0.354174	+	0.613448i
$213$	0.500000	−	0.866025i	0.0342594	−	0.0593391i
$214$	−1.17157	+	2.02922i	−0.0800871	+	0.138715i
$215$	0.585786	+	1.01461i	0.0399503	+	0.0691960i
$216$	1.00000			0.0680414
$217$	−1.17157	−	2.86976i	−0.0795315	−	0.194812i
$218$	−9.65685			−0.654045
$219$	−6.53553	−	11.3199i	−0.441630	−	0.764926i
$220$	1.70711	−	2.95680i	0.115093	−	0.199347i
$221$	1.62132	−	2.80821i	0.109062	−	0.188901i
$222$	−4.53553	−	7.85578i	−0.304405	−	0.527245i
$223$	−15.3848			−1.03024			−0.515120	−	0.857118i	$-0.672253\pi$
$223$	−15.3848			−1.03024			−0.515120	+	0.857118i	$0.672253\pi$
$224$	−1.00000	−	2.44949i	−0.0668153	−	0.163663i
$225$	−3.00000			−0.200000
$226$	−4.03553	−	6.98975i	−0.268440	−	0.464951i
$227$	−1.07107	+	1.85514i	−0.0710893	+	0.123130i	−0.899379	−	0.437170i	$-0.855981\pi$
$227$	−1.07107	+	1.85514i	−0.0710893	+	0.123130i	0.828290	+	0.560300i	$0.189314\pi$
$228$	−1.50000	+	2.59808i	−0.0993399	+	0.172062i
$229$	6.41421	+	11.1097i	0.423863	+	0.734153i	0.996314	−	0.0857869i	$-0.0273404\pi$
$229$	6.41421	+	11.1097i	0.423863	+	0.734153i	−0.572450	+	0.819939i	$0.694007\pi$
$230$	7.17157			0.472880
$231$	−6.32843	−	0.866025i	−0.416380	−	0.0569803i
$232$	5.00000			0.328266
$233$	−10.8640	−	18.8169i	−0.711722	−	1.23274i	−0.964210	−	0.265138i	$-0.914582\pi$
$233$	−10.8640	−	18.8169i	−0.711722	−	1.23274i	0.252489	−	0.967600i	$-0.418751\pi$
$234$	−0.500000	+	0.866025i	−0.0326860	+	0.0566139i
$235$	−6.36396	+	11.0227i	−0.415139	+	0.719042i
$236$	−5.20711	−	9.01897i	−0.338954	−	0.587085i
$237$	−9.31371			−0.604990
$238$	5.25736	−	6.77962i	0.340784	−	0.439457i
$239$	−19.4853			−1.26040			−0.630199	−	0.776434i	$-0.717027\pi$
$239$	−19.4853			−1.26040			−0.630199	+	0.776434i	$0.717027\pi$
$240$	−0.707107	−	1.22474i	−0.0456435	−	0.0790569i
$241$	−0.242641	+	0.420266i	−0.0156299	+	0.0270717i	−0.873735	−	0.486403i	$-0.838309\pi$
$241$	−0.242641	+	0.420266i	−0.0156299	+	0.0270717i	0.858105	+	0.513475i	$0.171642\pi$
$242$	2.58579	−	4.47871i	0.166221	−	0.287903i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	3.24264			0.207589
$245$	−7.07107	+	6.92820i	−0.451754	+	0.442627i
$246$	7.41421			0.472713
$247$	−1.50000	−	2.59808i	−0.0954427	−	0.165312i
$248$	−0.585786	+	1.01461i	−0.0371975	+	0.0644279i
$249$	−1.82843	+	3.16693i	−0.115872	+	0.200696i
$250$	5.65685	+	9.79796i	0.357771	+	0.619677i
$251$	7.17157			0.452666			0.226333	−	0.974050i	$-0.427326\pi$
$251$	7.17157			0.452666			0.226333	+	0.974050i	$0.427326\pi$
$252$	−1.62132	+	2.09077i	−0.102134	+	0.131706i
$253$	−12.2426			−0.769688
$254$	4.94975	+	8.57321i	0.310575	+	0.537931i
$255$	2.29289	−	3.97141i	0.143587	−	0.248699i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−8.89949	−	15.4144i	−0.555135	−	0.961522i	−0.997893	−	0.0648812i	$-0.979333\pi$
$257$	−8.89949	−	15.4144i	−0.555135	−	0.961522i	0.442758	−	0.896641i	$-0.354000\pi$
$258$	−0.828427			−0.0515756
$259$	23.7782	+	3.25397i	1.47750	+	0.202192i
$260$	1.41421			0.0877058
$261$	−2.50000	−	4.33013i	−0.154746	−	0.268028i
$262$	4.94975	−	8.57321i	0.305796	−	0.529655i
$263$	−11.7782	+	20.4004i	−0.726273	+	1.25794i	0.232174	+	0.972674i	$0.425416\pi$
$263$	−11.7782	+	20.4004i	−0.726273	+	1.25794i	−0.958448	+	0.285268i	$0.907917\pi$
$264$	1.20711	+	2.09077i	0.0742923	+	0.128678i
$265$	−14.5858			−0.895998
$266$	−3.00000	−	7.34847i	−0.183942	−	0.450564i
$267$	2.24264			0.137247
$268$	1.67157	+	2.89525i	0.102108	+	0.176855i
$269$	13.1569	−	22.7883i	0.802188	−	1.38943i	−0.115986	−	0.993251i	$-0.537003\pi$
$269$	13.1569	−	22.7883i	0.802188	−	1.38943i	0.918173	−	0.396179i	$-0.129664\pi$
$270$	−0.707107	+	1.22474i	−0.0430331	+	0.0745356i
$271$	−10.6924	−	18.5198i	−0.649516	−	1.12500i	−0.983239	−	0.182324i	$-0.941638\pi$
$271$	−10.6924	−	18.5198i	−0.649516	−	1.12500i	0.333722	−	0.942671i	$-0.391695\pi$
$272$	−3.24264			−0.196614
$273$	−1.00000	−	2.44949i	−0.0605228	−	0.148250i
$274$	1.07107			0.0647056
$275$	−3.62132	−	6.27231i	−0.218374	−	0.378235i
$276$	−2.53553	+	4.39167i	−0.152621	+	0.264348i
$277$	6.79289	−	11.7656i	0.408145	−	0.706929i	−0.586537	−	0.809923i	$-0.699509\pi$
$277$	6.79289	−	11.7656i	0.408145	−	0.706929i	0.994682	+	0.102994i	$0.0328423\pi$
$278$	−10.6066	−	18.3712i	−0.636142	−	1.10183i
$279$	1.17157			0.0701402
$280$	3.70711	+	0.507306i	0.221542	+	0.0303173i
$281$	−15.3137			−0.913539			−0.456770	−	0.889585i	$-0.650994\pi$
$281$	−15.3137			−0.913539			−0.456770	+	0.889585i	$0.650994\pi$
$282$	−4.50000	−	7.79423i	−0.267971	−	0.464140i
$283$	−1.46447	+	2.53653i	−0.0870535	+	0.150781i	−0.906264	−	0.422711i	$-0.861078\pi$
$283$	−1.46447	+	2.53653i	−0.0870535	+	0.150781i	0.819211	+	0.573492i	$0.194412\pi$
$284$	0.500000	−	0.866025i	0.0296695	−	0.0513892i
$285$	−2.12132	−	3.67423i	−0.125656	−	0.217643i
$286$	−2.41421			−0.142755
$287$	−12.0208	+	15.5014i	−0.709566	+	0.915020i
$288$	1.00000			0.0589256
$289$	3.24264	+	5.61642i	0.190744	+	0.330378i
$290$	−3.53553	+	6.12372i	−0.207614	+	0.359597i
$291$	5.94975	−	10.3053i	0.348780	−	0.604105i
$292$	−6.53553	−	11.3199i	−0.382463	−	0.662446i
$293$	6.72792			0.393049			0.196525	−	0.980499i	$-0.437034\pi$
$293$	6.72792			0.393049			0.196525	+	0.980499i	$0.437034\pi$
$294$	−1.74264	−	6.77962i	−0.101633	−	0.395395i
$295$	14.7279			0.857493
$296$	−4.53553	−	7.85578i	−0.263623	−	0.456608i
$297$	1.20711	−	2.09077i	0.0700434	−	0.121319i
$298$	1.94975	−	3.37706i	0.112946	−	0.195628i
$299$	−2.53553	−	4.39167i	−0.146634	−	0.253977i
$300$	−3.00000			−0.173205
$301$	1.34315	−	1.73205i	0.0774176	−	0.0998337i
$302$	−10.4142			−0.599271
$303$	3.41421	+	5.91359i	0.196141	+	0.339727i
$304$	−1.50000	+	2.59808i	−0.0860309	+	0.149010i
$305$	−2.29289	+	3.97141i	−0.131291	+	0.227402i
$306$	1.62132	+	2.80821i	0.0926847	+	0.160535i
$307$	25.6274			1.46263			0.731317	−	0.682038i	$-0.238906\pi$
$307$	25.6274			1.46263			0.731317	+	0.682038i	$0.238906\pi$
$308$	−6.32843	−	0.866025i	−0.360596	−	0.0493464i
$309$	−10.4853			−0.596487
$310$	−0.828427	−	1.43488i	−0.0470515	−	0.0814956i
$311$	4.70711	−	8.15295i	0.266916	−	0.462311i	−0.701148	−	0.713016i	$-0.747329\pi$
$311$	4.70711	−	8.15295i	0.266916	−	0.462311i	0.968064	+	0.250704i	$0.0806622\pi$
$312$	−0.500000	+	0.866025i	−0.0283069	+	0.0490290i
$313$	5.07107	+	8.78335i	0.286634	+	0.496464i	0.973004	−	0.230788i	$-0.0741304\pi$
$313$	5.07107	+	8.78335i	0.286634	+	0.496464i	−0.686370	+	0.727252i	$0.740797\pi$
$314$	22.0711			1.24554
$315$	−1.41421	−	3.46410i	−0.0796819	−	0.195180i
$316$	−9.31371			−0.523937
$317$	2.41421	+	4.18154i	0.135596	+	0.234859i	0.925825	−	0.377953i	$-0.123372\pi$
$317$	2.41421	+	4.18154i	0.135596	+	0.234859i	−0.790229	+	0.612811i	$0.790038\pi$
$318$	5.15685	−	8.93193i	0.289182	−	0.500878i
$319$	6.03553	−	10.4539i	0.337925	−	0.585303i
$320$	−0.707107	−	1.22474i	−0.0395285	−	0.0684653i
$321$	2.34315			0.130782
$322$	−5.07107	−	12.4215i	−0.282600	−	0.692225i
$323$	−9.72792			−0.541276
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	1.50000	−	2.59808i	0.0832050	−	0.144115i
$326$	5.57107	−	9.64937i	0.308553	−	0.534429i
$327$	4.82843	+	8.36308i	0.267013	+	0.462479i
$328$	7.41421			0.409381
$329$	23.5919	+	3.22848i	1.30066	+	0.177992i
$330$	−3.41421			−0.187946
$331$	2.75736	+	4.77589i	0.151558	+	0.262506i	0.931800	−	0.362971i	$-0.118238\pi$
$331$	2.75736	+	4.77589i	0.151558	+	0.262506i	−0.780242	+	0.625477i	$0.784904\pi$
$332$	−1.82843	+	3.16693i	−0.100348	+	0.173808i
$333$	−4.53553	+	7.85578i	−0.248546	+	0.430494i
$334$	5.15685	+	8.93193i	0.282171	+	0.488734i
$335$	−4.72792			−0.258314
$336$	−1.62132	+	2.09077i	−0.0884503	+	0.114061i
$337$	17.3431			0.944741			0.472371	−	0.881400i	$-0.343398\pi$
$337$	17.3431			0.944741			0.472371	+	0.881400i	$0.343398\pi$
$338$	−0.500000	−	0.866025i	−0.0271964	−	0.0471056i
$339$	−4.03553	+	6.98975i	−0.219180	+	0.379631i
$340$	2.29289	−	3.97141i	0.124350	−	0.215380i
$341$	1.41421	+	2.44949i	0.0765840	+	0.132647i
$342$	3.00000			0.162221
$343$	17.0000	+	7.34847i	0.917914	+	0.396780i
$344$	−0.828427			−0.0446658
$345$	−3.58579	−	6.21076i	−0.193052	−	0.334376i
$346$	1.15685	−	2.00373i	0.0621929	−	0.107721i
$347$	−7.12132	+	12.3345i	−0.382293	+	0.662150i	−0.991390	−	0.130946i	$-0.958199\pi$
$347$	−7.12132	+	12.3345i	−0.382293	+	0.662150i	0.609097	+	0.793096i	$0.291532\pi$
$348$	−2.50000	−	4.33013i	−0.134014	−	0.232119i
$349$	2.58579			0.138414			0.0692070	−	0.997602i	$-0.477953\pi$
$349$	2.58579			0.138414			0.0692070	+	0.997602i	$0.477953\pi$
$350$	4.86396	−	6.27231i	0.259990	−	0.335269i
$351$	1.00000			0.0533761
$352$	1.20711	+	2.09077i	0.0643390	+	0.111438i
$353$	16.3137	−	28.2562i	0.868291	−	1.50392i	0.00454930	−	0.999990i	$-0.498552\pi$
$353$	16.3137	−	28.2562i	0.868291	−	1.50392i	0.863742	−	0.503935i	$-0.168115\pi$
$354$	−5.20711	+	9.01897i	−0.276755	+	0.479353i
$355$	0.707107	+	1.22474i	0.0375293	+	0.0650027i
$356$	2.24264			0.118860
$357$	−8.50000	−	1.16320i	−0.449868	−	0.0615630i
$358$	−23.6569			−1.25030
$359$	−17.7279	−	30.7057i	−0.935644	−	1.62058i	−0.773482	−	0.633819i	$-0.781487\pi$
$359$	−17.7279	−	30.7057i	−0.935644	−	1.62058i	−0.162162	−	0.986764i	$-0.551847\pi$
$360$	−0.707107	+	1.22474i	−0.0372678	+	0.0645497i
$361$	5.00000	−	8.66025i	0.263158	−	0.455803i
$362$	7.20711	+	12.4831i	0.378797	+	0.656096i
$363$	−5.17157			−0.271437
$364$	−1.00000	−	2.44949i	−0.0524142	−	0.128388i
$365$	18.4853			0.967564
$366$	−1.62132	−	2.80821i	−0.0847478	−	0.146787i
$367$	−7.00000	+	12.1244i	−0.365397	+	0.632886i	−0.988840	−	0.148983i	$-0.952400\pi$
$367$	−7.00000	+	12.1244i	−0.365397	+	0.632886i	0.623443	+	0.781869i	$0.285733\pi$
$368$	−2.53553	+	4.39167i	−0.132174	+	0.228932i
$369$	−3.70711	−	6.42090i	−0.192984	−	0.334259i
$370$	12.8284			0.666918
$371$	10.3137	+	25.2633i	0.535461	+	1.31161i
$372$	1.17157			0.0607432
$373$	15.4497	+	26.7597i	0.799958	+	1.38557i	0.919643	+	0.392755i	$0.128478\pi$
$373$	15.4497	+	26.7597i	0.799958	+	1.38557i	−0.119685	+	0.992812i	$0.538189\pi$
$374$	−3.91421	+	6.77962i	−0.202399	+	0.350566i
$375$	5.65685	−	9.79796i	0.292119	−	0.505964i
$376$	−4.50000	−	7.79423i	−0.232070	−	0.401957i
$377$	5.00000			0.257513
$378$	2.62132	+	0.358719i	0.134826	+	0.0184505i
$379$	−22.3431			−1.14769			−0.573845	−	0.818964i	$-0.694549\pi$
$379$	−22.3431			−1.14769			−0.573845	+	0.818964i	$0.694549\pi$
$380$	−2.12132	−	3.67423i	−0.108821	−	0.188484i
$381$	4.94975	−	8.57321i	0.253583	−	0.439219i
$382$	−6.82843	+	11.8272i	−0.349373	+	0.605131i
$383$	5.24264	+	9.08052i	0.267886	+	0.463993i	0.968316	−	0.249729i	$-0.0803415\pi$
$383$	5.24264	+	9.08052i	0.267886	+	0.463993i	−0.700429	+	0.713722i	$0.747008\pi$
$384$	1.00000			0.0510310
$385$	5.53553	−	7.13834i	0.282117	−	0.363803i
$386$	−24.2426			−1.23392
$387$	0.414214	+	0.717439i	0.0210557	+	0.0364695i
$388$	5.94975	−	10.3053i	0.302053	−	0.523171i
$389$	−11.5000	+	19.9186i	−0.583073	+	1.00991i	0.412039	+	0.911166i	$0.364817\pi$
$389$	−11.5000	+	19.9186i	−0.583073	+	1.00991i	−0.995113	+	0.0987463i	$0.968517\pi$
$390$	−0.707107	−	1.22474i	−0.0358057	−	0.0620174i
$391$	−16.4437			−0.831591
$392$	−1.74264	−	6.77962i	−0.0880166	−	0.342422i
$393$	−9.89949			−0.499363
$394$	10.7782	+	18.6683i	0.542997	+	0.940498i
$395$	6.58579	−	11.4069i	0.331367	−	0.573944i
$396$	1.20711	−	2.09077i	0.0606594	−	0.105065i
$397$	14.1213	+	24.4588i	0.708729	+	1.22755i	0.965329	+	0.261037i	$0.0840643\pi$
$397$	14.1213	+	24.4588i	0.708729	+	1.22755i	−0.256600	+	0.966518i	$0.582602\pi$
$398$	13.4142			0.672394
$399$	−4.86396	+	6.27231i	−0.243503	+	0.314008i
$400$	−3.00000			−0.150000
$401$	−2.46447	−	4.26858i	−0.123070	−	0.213163i	0.797907	−	0.602780i	$-0.205940\pi$
$401$	−2.46447	−	4.26858i	−0.123070	−	0.213163i	−0.920977	+	0.389618i	$0.872607\pi$
$402$	1.67157	−	2.89525i	0.0833705	−	0.144402i
$403$	−0.585786	+	1.01461i	−0.0291801	+	0.0505414i
$404$	3.41421	+	5.91359i	0.169863	+	0.294212i
$405$	1.41421			0.0702728
$406$	13.1066	+	1.79360i	0.650470	+	0.0890147i
$407$	−21.8995			−1.08552
$408$	1.62132	+	2.80821i	0.0802673	+	0.139027i
$409$	2.70711	−	4.68885i	0.133858	−	0.231849i	−0.791303	−	0.611425i	$-0.790597\pi$
$409$	2.70711	−	4.68885i	0.133858	−	0.231849i	0.925161	+	0.379576i	$0.123930\pi$
$410$	−5.24264	+	9.08052i	−0.258916	+	0.448455i
$411$	−0.535534	−	0.927572i	−0.0264159	−	0.0457537i
$412$	−10.4853			−0.516573
$413$	−10.4142	−	25.5095i	−0.512450	−	1.25524i
$414$	5.07107			0.249229
$415$	−2.58579	−	4.47871i	−0.126931	−	0.219851i
$416$	−0.500000	+	0.866025i	−0.0245145	+	0.0424604i
$417$	−10.6066	+	18.3712i	−0.519408	+	0.899640i
$418$	3.62132	+	6.27231i	0.177125	+	0.306789i
$419$	23.4558			1.14589			0.572946	−	0.819593i	$-0.305800\pi$
$419$	23.4558			1.14589			0.572946	+	0.819593i	$0.305800\pi$
$420$	−1.41421	−	3.46410i	−0.0690066	−	0.169031i
$421$	13.4142			0.653769			0.326884	−	0.945064i	$-0.394001\pi$
$421$	13.4142			0.653769			0.326884	+	0.945064i	$0.394001\pi$
$422$	−4.19239	−	7.26143i	−0.204082	−	0.353481i
$423$	−4.50000	+	7.79423i	−0.218797	+	0.378968i
$424$	5.15685	−	8.93193i	0.250439	−	0.433773i
$425$	−4.86396	−	8.42463i	−0.235937	−	0.408654i
$426$	−1.00000			−0.0484502
$427$	8.50000	+	1.16320i	0.411344	+	0.0562911i
$428$	2.34315			0.113260
$429$	1.20711	+	2.09077i	0.0582797	+	0.100943i
$430$	0.585786	−	1.01461i	0.0282491	−	0.0489289i
$431$	1.24264	−	2.15232i	0.0598559	−	0.103673i	−0.834545	−	0.550940i	$-0.814269\pi$
$431$	1.24264	−	2.15232i	0.0598559	−	0.103673i	0.894401	+	0.447267i	$0.147603\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	−19.0000			−0.913082			−0.456541	−	0.889702i	$-0.650912\pi$
$433$	−19.0000			−0.913082			−0.456541	+	0.889702i	$0.650912\pi$
$434$	−1.89949	+	2.44949i	−0.0911787	+	0.117579i
$435$	7.07107			0.339032
$436$	4.82843	+	8.36308i	0.231240	+	0.400519i
$437$	−7.60660	+	13.1750i	−0.363873	+	0.630247i
$438$	−6.53553	+	11.3199i	−0.312280	+	0.540885i
$439$	6.70711	+	11.6170i	0.320113	+	0.554452i	0.980511	−	0.196464i	$-0.0629459\pi$
$439$	6.70711	+	11.6170i	0.320113	+	0.554452i	−0.660398	+	0.750915i	$0.729613\pi$
$440$	−3.41421			−0.162766
$441$	−5.00000	+	4.89898i	−0.238095	+	0.233285i
$442$	−3.24264			−0.154237
$443$	1.36396	+	2.36245i	0.0648037	+	0.112243i	0.896607	−	0.442827i	$-0.146025\pi$
$443$	1.36396	+	2.36245i	0.0648037	+	0.112243i	−0.831803	+	0.555071i	$0.812691\pi$
$444$	−4.53553	+	7.85578i	−0.215247	+	0.372819i
$445$	−1.58579	+	2.74666i	−0.0751735	+	0.130204i
$446$	7.69239	+	13.3236i	0.364245	+	0.630891i
$447$	−3.89949			−0.184440
$448$	−1.62132	+	2.09077i	−0.0766002	+	0.0987796i
$449$	33.9411			1.60178			0.800890	−	0.598811i	$-0.204360\pi$
$449$	33.9411			1.60178			0.800890	+	0.598811i	$0.204360\pi$
$450$	1.50000	+	2.59808i	0.0707107	+	0.122474i
$451$	8.94975	−	15.5014i	0.421427	−	0.729933i
$452$	−4.03553	+	6.98975i	−0.189816	+	0.328770i
$453$	5.20711	+	9.01897i	0.244651	+	0.423748i
$454$	2.14214			0.100535
$455$	3.70711	+	0.507306i	0.173792	+	0.0237829i
$456$	3.00000			0.140488
$457$	−13.6066	−	23.5673i	−0.636490	−	1.10243i	−0.986197	−	0.165574i	$-0.947052\pi$
$457$	−13.6066	−	23.5673i	−0.636490	−	1.10243i	0.349707	−	0.936859i	$-0.386281\pi$
$458$	6.41421	−	11.1097i	0.299717	−	0.519124i
$459$	1.62132	−	2.80821i	0.0756768	−	0.131076i
$460$	−3.58579	−	6.21076i	−0.167188	−	0.289578i
$461$	17.4558			0.813000			0.406500	−	0.913651i	$-0.366749\pi$
$461$	17.4558			0.813000			0.406500	+	0.913651i	$0.366749\pi$
$462$	2.41421	+	5.91359i	0.112319	+	0.275125i
$463$	29.9411			1.39148			0.695741	−	0.718293i	$-0.255076\pi$
$463$	29.9411			1.39148			0.695741	+	0.718293i	$0.255076\pi$
$464$	−2.50000	−	4.33013i	−0.116060	−	0.201021i
$465$	−0.828427	+	1.43488i	−0.0384174	+	0.0665409i
$466$	−10.8640	+	18.8169i	−0.503263	+	0.871678i
$467$	−4.12132	−	7.13834i	−0.190712	−	0.330323i	0.754774	−	0.655984i	$-0.227746\pi$
$467$	−4.12132	−	7.13834i	−0.190712	−	0.330323i	−0.945486	+	0.325662i	$0.894413\pi$
$468$	1.00000			0.0462250
$469$	3.34315	+	8.18900i	0.154372	+	0.378133i
$470$	12.7279			0.587095
$471$	−11.0355	−	19.1141i	−0.508491	−	0.880731i
$472$	−5.20711	+	9.01897i	−0.239677	+	0.415132i
$473$	−1.00000	+	1.73205i	−0.0459800	+	0.0796398i
$474$	4.65685	+	8.06591i	0.213896	+	0.370479i
$475$	−9.00000			−0.412948
$476$	−8.50000	−	1.16320i	−0.389597	−	0.0533151i
$477$	−10.3137			−0.472232
$478$	9.74264	+	16.8747i	0.445618	+	0.771833i
$479$	1.42893	−	2.47498i	0.0652896	−	0.113085i	−0.831533	−	0.555476i	$-0.812536\pi$
$479$	1.42893	−	2.47498i	0.0652896	−	0.113085i	0.896822	+	0.442391i	$0.145870\pi$
$480$	−0.707107	+	1.22474i	−0.0322749	+	0.0559017i
$481$	−4.53553	−	7.85578i	−0.206803	−	0.358193i
$482$	0.485281			0.0221040
$483$	−8.22183	+	10.6024i	−0.374106	+	0.482428i
$484$	−5.17157			−0.235071
$485$	8.41421	+	14.5738i	0.382070	+	0.661764i
$486$	−0.500000	+	0.866025i	−0.0226805	+	0.0392837i
$487$	−0.863961	+	1.49642i	−0.0391498	+	0.0678095i	−0.884936	−	0.465712i	$-0.845798\pi$
$487$	−0.863961	+	1.49642i	−0.0391498	+	0.0678095i	0.845787	+	0.533521i	$0.179132\pi$
$488$	−1.62132	−	2.80821i	−0.0733937	−	0.127122i
$489$	−11.1421			−0.503865
$490$	9.53553	+	2.65962i	0.430772	+	0.120150i
$491$	30.2843			1.36671			0.683355	−	0.730086i	$-0.260520\pi$
$491$	30.2843			1.36671			0.683355	+	0.730086i	$0.260520\pi$
$492$	−3.70711	−	6.42090i	−0.167129	−	0.289476i
$493$	8.10660	−	14.0410i	0.365103	−	0.632377i
$494$	−1.50000	+	2.59808i	−0.0674882	+	0.116893i
$495$	1.70711	+	2.95680i	0.0767287	+	0.132898i
$496$	1.17157			0.0526052
$497$	1.62132	−	2.09077i	0.0727262	−	0.0937839i
$498$	3.65685			0.163868
$499$	15.0000	+	25.9808i	0.671492	+	1.16306i	0.977481	+	0.211024i	$0.0676797\pi$
$499$	15.0000	+	25.9808i	0.671492	+	1.16306i	−0.305989	+	0.952035i	$0.598987\pi$
$500$	5.65685	−	9.79796i	0.252982	−	0.438178i
$501$	5.15685	−	8.93193i	0.230391	−	0.399049i
$502$	−3.58579	−	6.21076i	−0.160041	−	0.277200i
$503$	−3.79899			−0.169389			−0.0846943	−	0.996407i	$-0.526991\pi$
$503$	−3.79899			−0.169389			−0.0846943	+	0.996407i	$0.526991\pi$
$504$	2.62132	+	0.358719i	0.116763	+	0.0159786i
$505$	−9.65685			−0.429724
$506$	6.12132	+	10.6024i	0.272126	+	0.471336i
$507$	−0.500000	+	0.866025i	−0.0222058	+	0.0384615i
$508$	4.94975	−	8.57321i	0.219610	−	0.380375i
$509$	10.4853	+	18.1610i	0.464752	+	0.804974i	0.999190	−	0.0402335i	$-0.0128102\pi$
$509$	10.4853	+	18.1610i	0.464752	+	0.804974i	−0.534438	+	0.845207i	$0.679477\pi$
$510$	−4.58579			−0.203062
$511$	−13.0711	−	32.0174i	−0.578230	−	1.41637i
$512$	1.00000			0.0441942
$513$	−1.50000	−	2.59808i	−0.0662266	−	0.114708i
$514$	−8.89949	+	15.4144i	−0.392540	+	0.679899i
$515$	7.41421	−	12.8418i	0.326709	−	0.565877i
$516$	0.414214	+	0.717439i	0.0182347	+	0.0315835i
$517$	−21.7279			−0.955593
$518$	−9.07107	−	22.2195i	−0.398560	−	0.976268i
$519$	−2.31371			−0.101561
$520$	−0.707107	−	1.22474i	−0.0310087	−	0.0537086i
$521$	7.00000	−	12.1244i	0.306676	−	0.531178i	−0.670957	−	0.741496i	$-0.734117\pi$
$521$	7.00000	−	12.1244i	0.306676	−	0.531178i	0.977633	+	0.210318i	$0.0674500\pi$
$522$	−2.50000	+	4.33013i	−0.109422	+	0.189525i
$523$	16.0711	+	27.8359i	0.702739	+	1.21718i	0.967501	+	0.252866i	$0.0813730\pi$
$523$	16.0711	+	27.8359i	0.702739	+	1.21718i	−0.264763	+	0.964314i	$0.585294\pi$
$524$	−9.89949			−0.432461
$525$	−7.86396	−	1.07616i	−0.343211	−	0.0469674i
$526$	23.5563			1.02711
$527$	1.89949	+	3.29002i	0.0827433	+	0.143316i
$528$	1.20711	−	2.09077i	0.0525326	−	0.0909891i
$529$	−1.35786	+	2.35189i	−0.0590376	+	0.102256i
$530$	7.29289	+	12.6317i	0.316783	+	0.548684i
$531$	10.4142			0.451938
$532$	−4.86396	+	6.27231i	−0.210879	+	0.271939i
$533$	7.41421			0.321145
$534$	−1.12132	−	1.94218i	−0.0485243	−	0.0840465i
$535$	−1.65685	+	2.86976i	−0.0716321	+	0.124070i
$536$	1.67157	−	2.89525i	0.0722010	−	0.125056i
$537$	11.8284	+	20.4874i	0.510434	+	0.884098i
$538$	−26.3137			−1.13446
$539$	−16.2782	−	4.54026i	−0.701151	−	0.195563i
$540$	1.41421			0.0608581
$541$	20.4350	+	35.3945i	0.878571	+	1.52173i	0.852910	+	0.522058i	$0.174836\pi$
$541$	20.4350	+	35.3945i	0.878571	+	1.52173i	0.0256606	+	0.999671i	$0.491831\pi$
$542$	−10.6924	+	18.5198i	−0.459277	+	0.795492i
$543$	7.20711	−	12.4831i	0.309287	−	0.535700i
$544$	1.62132	+	2.80821i	0.0695135	+	0.120401i
$545$	−13.6569			−0.584995
$546$	−1.62132	+	2.09077i	−0.0693861	+	0.0894767i
$547$	−14.2426			−0.608971			−0.304486	−	0.952517i	$-0.598485\pi$
$547$	−14.2426			−0.608971			−0.304486	+	0.952517i	$0.598485\pi$
$548$	−0.535534	−	0.927572i	−0.0228769	−	0.0396239i
$549$	−1.62132	+	2.80821i	−0.0691963	+	0.119851i
$550$	−3.62132	+	6.27231i	−0.154414	+	0.267452i
$551$	−7.50000	−	12.9904i	−0.319511	−	0.553409i
$552$	5.07107			0.215839
$553$	−24.4142	−	3.34101i	−1.03820	−	0.142074i
$554$	−13.5858			−0.577205
$555$	−6.41421	−	11.1097i	−0.272268	−	0.471582i
$556$	−10.6066	+	18.3712i	−0.449820	+	0.779111i
$557$	−11.4853	+	19.8931i	−0.486647	+	0.842897i	−0.999882	−	0.0153507i	$-0.995114\pi$
$557$	−11.4853	+	19.8931i	−0.486647	+	0.842897i	0.513235	+	0.858248i	$0.328447\pi$
$558$	−0.585786	−	1.01461i	−0.0247983	−	0.0429519i
$559$	−0.828427			−0.0350387
$560$	−1.41421	−	3.46410i	−0.0597614	−	0.146385i
$561$	7.82843			0.330516
$562$	7.65685	+	13.2621i	0.322985	+	0.559426i
$563$	−8.24264	+	14.2767i	−0.347386	+	0.601690i	−0.985784	−	0.168016i	$-0.946264\pi$
$563$	−8.24264	+	14.2767i	−0.347386	+	0.601690i	0.638398	+	0.769706i	$0.279597\pi$
$564$	−4.50000	+	7.79423i	−0.189484	+	0.328196i
$565$	−5.70711	−	9.88500i	−0.240100	−	0.415865i
$566$	2.92893			0.123112
$567$	−1.00000	−	2.44949i	−0.0419961	−	0.102869i
$568$	−1.00000			−0.0419591
$569$	14.2071	+	24.6074i	0.595593	+	1.03160i	0.993463	+	0.114155i	$0.0364162\pi$
$569$	14.2071	+	24.6074i	0.595593	+	1.03160i	−0.397870	+	0.917442i	$0.630250\pi$
$570$	−2.12132	+	3.67423i	−0.0888523	+	0.153897i
$571$	−4.82843	+	8.36308i	−0.202063	+	0.349984i	−0.949193	−	0.314694i	$-0.898098\pi$
$571$	−4.82843	+	8.36308i	−0.202063	+	0.349984i	0.747130	+	0.664678i	$0.231431\pi$
$572$	1.20711	+	2.09077i	0.0504717	+	0.0874195i
$573$	13.6569			0.570523
$574$	19.4350	+	2.65962i	0.811202	+	0.111011i
$575$	−15.2132			−0.634434
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	9.00000	−	15.5885i	0.374675	−	0.648956i	−0.615603	−	0.788056i	$-0.711088\pi$
$577$	9.00000	−	15.5885i	0.374675	−	0.648956i	0.990278	+	0.139100i	$0.0444210\pi$
$578$	3.24264	−	5.61642i	0.134876	−	0.233612i
$579$	12.1213	+	20.9947i	0.503745	+	0.872512i
$580$	7.07107			0.293610
$581$	−5.92893	+	7.64564i	−0.245974	+	0.317195i
$582$	−11.8995			−0.493250
$583$	−12.4497	−	21.5636i	−0.515616	−	0.893073i
$584$	−6.53553	+	11.3199i	−0.270442	+	0.468420i
$585$	−0.707107	+	1.22474i	−0.0292353	+	0.0506370i
$586$	−3.36396	−	5.82655i	−0.138964	−	0.240693i
$587$	2.75736			0.113808			0.0569042	−	0.998380i	$-0.481877\pi$
$587$	2.75736			0.113808			0.0569042	+	0.998380i	$0.481877\pi$
$588$	−5.00000	+	4.89898i	−0.206197	+	0.202031i
$589$	3.51472			0.144821
$590$	−7.36396	−	12.7548i	−0.303169	−	0.525105i
$591$	10.7782	−	18.6683i	0.443355	−	0.767913i
$592$	−4.53553	+	7.85578i	−0.186409	+	0.322870i
$593$	15.7071	+	27.2055i	0.645014	+	1.11720i	0.984298	+	0.176513i	$0.0564816\pi$
$593$	15.7071	+	27.2055i	0.645014	+	1.11720i	−0.339285	+	0.940684i	$0.610185\pi$
$594$	−2.41421			−0.0990564
$595$	7.43503	−	9.58783i	0.304806	−	0.393063i
$596$	−3.89949			−0.159730
$597$	−6.70711	−	11.6170i	−0.274504	−	0.475454i
$598$	−2.53553	+	4.39167i	−0.103686	+	0.179589i
$599$	−19.4350	+	33.6625i	−0.794094	+	1.37541i	0.129319	+	0.991603i	$0.458721\pi$
$599$	−19.4350	+	33.6625i	−0.794094	+	1.37541i	−0.923413	+	0.383808i	$0.874613\pi$
$600$	1.50000	+	2.59808i	0.0612372	+	0.106066i
$601$	−12.1716			−0.496489			−0.248244	−	0.968697i	$-0.579854\pi$
$601$	−12.1716			−0.496489			−0.248244	+	0.968697i	$0.579854\pi$
$602$	−2.17157	−	0.297173i	−0.0885067	−	0.0121119i
$603$	−3.34315			−0.136143
$604$	5.20711	+	9.01897i	0.211874	+	0.366977i
$605$	3.65685	−	6.33386i	0.148672	−	0.257508i
$606$	3.41421	−	5.91359i	0.138693	−	0.240223i
$607$	−6.46447	−	11.1968i	−0.262385	−	0.454463i	0.704491	−	0.709713i	$-0.251176\pi$
$607$	−6.46447	−	11.1968i	−0.262385	−	0.454463i	−0.966875	+	0.255250i	$0.917842\pi$
$608$	3.00000			0.121666
$609$	−5.00000	−	12.2474i	−0.202610	−	0.496292i
$610$	4.58579			0.185673
$611$	−4.50000	−	7.79423i	−0.182051	−	0.315321i
$612$	1.62132	−	2.80821i	0.0655380	−	0.113515i
$613$	−1.89949	+	3.29002i	−0.0767199	+	0.132883i	−0.901833	−	0.432085i	$-0.857778\pi$
$613$	−1.89949	+	3.29002i	−0.0767199	+	0.132883i	0.825113	+	0.564968i	$0.191111\pi$
$614$	−12.8137	−	22.1940i	−0.517119	−	0.895677i
$615$	10.4853			0.422807
$616$	2.41421	+	5.91359i	0.0972714	+	0.238265i
$617$	10.4853			0.422122			0.211061	−	0.977473i	$-0.432308\pi$
$617$	10.4853			0.422122			0.211061	+	0.977473i	$0.432308\pi$
$618$	5.24264	+	9.08052i	0.210890	+	0.365272i
$619$	3.72792	−	6.45695i	0.149838	−	0.259527i	−0.781330	−	0.624119i	$-0.785458\pi$
$619$	3.72792	−	6.45695i	0.149838	−	0.259527i	0.931167	+	0.364592i	$0.118792\pi$
$620$	−0.828427	+	1.43488i	−0.0332704	+	0.0576261i
$621$	−2.53553	−	4.39167i	−0.101747	−	0.176232i
$622$	−9.41421			−0.377476
$623$	5.87868	+	0.804479i	0.235524	+	0.0322308i
$624$	1.00000			0.0400320
$625$	0.500000	+	0.866025i	0.0200000	+	0.0346410i
$626$	5.07107	−	8.78335i	0.202681	−	0.351053i
$627$	3.62132	−	6.27231i	0.144622	−	0.250492i
$628$	−11.0355	−	19.1141i	−0.440366	−	0.762736i
$629$	−29.4142			−1.17282
$630$	−2.29289	+	2.95680i	−0.0913511	+	0.117802i
$631$	−8.62742			−0.343452			−0.171726	−	0.985145i	$-0.554934\pi$
$631$	−8.62742			−0.343452			−0.171726	+	0.985145i	$0.554934\pi$
$632$	4.65685	+	8.06591i	0.185240	+	0.320845i
$633$	−4.19239	+	7.26143i	−0.166632	+	0.288616i
$634$	2.41421	−	4.18154i	0.0958807	−	0.166070i
$635$	7.00000	+	12.1244i	0.277787	+	0.481140i
$636$	−10.3137			−0.408965
$637$	−1.74264	−	6.77962i	−0.0690459	−	0.268618i
$638$	−12.0711			−0.477898
$639$	0.500000	+	0.866025i	0.0197797	+	0.0342594i
$640$	−0.707107	+	1.22474i	−0.0279508	+	0.0484123i
$641$	−19.4142	+	33.6264i	−0.766815	+	1.32816i	0.172466	+	0.985015i	$0.444826\pi$
$641$	−19.4142	+	33.6264i	−0.766815	+	1.32816i	−0.939281	+	0.343148i	$0.888507\pi$
$642$	−1.17157	−	2.02922i	−0.0462383	−	0.0800871i
$643$	13.6863			0.539735			0.269867	−	0.962898i	$-0.413020\pi$
$643$	13.6863			0.539735			0.269867	+	0.962898i	$0.413020\pi$
$644$	−8.22183	+	10.6024i	−0.323985	+	0.417795i
$645$	−1.17157			−0.0461306
$646$	4.86396	+	8.42463i	0.191370	+	0.331463i
$647$	8.31371	−	14.3998i	0.326846	−	0.566113i	−0.655039	−	0.755595i	$-0.727348\pi$
$647$	8.31371	−	14.3998i	0.326846	−	0.566113i	0.981884	+	0.189482i	$0.0606810\pi$
$648$	−0.500000	+	0.866025i	−0.0196419	+	0.0340207i
$649$	12.5711	+	21.7737i	0.493458	+	0.854694i
$650$	−3.00000			−0.117670
$651$	3.07107	+	0.420266i	0.120365	+	0.0164715i
$652$	−11.1421			−0.436360
$653$	23.5563	+	40.8008i	0.921831	+	1.59666i	0.796580	+	0.604533i	$0.206640\pi$
$653$	23.5563	+	40.8008i	0.921831	+	1.59666i	0.125251	+	0.992125i	$0.460026\pi$
$654$	4.82843	−	8.36308i	0.188806	−	0.327022i
$655$	7.00000	−	12.1244i	0.273513	−	0.473738i
$656$	−3.70711	−	6.42090i	−0.144738	−	0.250694i
$657$	13.0711			0.509951
$658$	−9.00000	−	22.0454i	−0.350857	−	0.859419i
$659$	5.27208			0.205371			0.102685	−	0.994714i	$-0.467256\pi$
$659$	5.27208			0.205371			0.102685	+	0.994714i	$0.467256\pi$
$660$	1.70711	+	2.95680i	0.0664490	+	0.115093i
$661$	−8.77817	+	15.2042i	−0.341431	+	0.591377i	−0.984699	−	0.174265i	$-0.944245\pi$
$661$	−8.77817	+	15.2042i	−0.341431	+	0.591377i	0.643267	+	0.765642i	$0.277578\pi$
$662$	2.75736	−	4.77589i	0.107168	−	0.185620i
$663$	1.62132	+	2.80821i	0.0629669	+	0.109062i
$664$	3.65685			0.141913
$665$	−4.24264	−	10.3923i	−0.164523	−	0.402996i
$666$	9.07107			0.351497
$667$	−12.6777	−	21.9584i	−0.490881	−	0.850231i
$668$	5.15685	−	8.93193i	0.199525	−	0.345587i
$669$	7.69239	−	13.3236i	0.297405	−	0.515120i
$670$	2.36396	+	4.09450i	0.0913278	+	0.158184i
$671$	−7.82843			−0.302213
$672$	2.62132	+	0.358719i	0.101120	+	0.0138379i
$673$	−6.82843			−0.263217			−0.131608	−	0.991302i	$-0.542014\pi$
$673$	−6.82843			−0.263217			−0.131608	+	0.991302i	$0.542014\pi$
$674$	−8.67157	−	15.0196i	−0.334017	−	0.578534i
$675$	1.50000	−	2.59808i	0.0577350	−	0.100000i
$676$	−0.500000	+	0.866025i	−0.0192308	+	0.0333087i
$677$	−16.9142	−	29.2963i	−0.650066	−	1.12595i	−0.983106	−	0.183035i	$-0.941408\pi$
$677$	−16.9142	−	29.2963i	−0.650066	−	1.12595i	0.333040	−	0.942913i	$-0.391925\pi$
$678$	8.07107			0.309967
$679$	19.2929	−	24.8791i	0.740393	−	0.954773i
$680$	−4.58579			−0.175857
$681$	−1.07107	−	1.85514i	−0.0410434	−	0.0710893i
$682$	1.41421	−	2.44949i	0.0541530	−	0.0937958i
$683$	22.7279	−	39.3659i	0.869660	−	1.50629i	0.00731507	−	0.999973i	$-0.497672\pi$
$683$	22.7279	−	39.3659i	0.869660	−	1.50629i	0.862345	−	0.506322i	$-0.168995\pi$
$684$	−1.50000	−	2.59808i	−0.0573539	−	0.0993399i
$685$	1.51472			0.0578744
$686$	−2.13604	−	18.3967i	−0.0815543	−	0.702388i
$687$	−12.8284			−0.489435
$688$	0.414214	+	0.717439i	0.0157917	+	0.0273521i
$689$	5.15685	−	8.93193i	0.196461	−	0.340280i
$690$	−3.58579	+	6.21076i	−0.136509	+	0.236440i
$691$	8.57107	+	14.8455i	0.326059	+	0.564750i	0.981726	−	0.190300i	$-0.0609459\pi$
$691$	8.57107	+	14.8455i	0.326059	+	0.564750i	−0.655667	+	0.755050i	$0.727613\pi$
$692$	−2.31371			−0.0879540
$693$	3.91421	−	5.04757i	0.148689	−	0.191741i
$694$	14.2426			0.540643
$695$	−15.0000	−	25.9808i	−0.568982	−	0.985506i
$696$	−2.50000	+	4.33013i	−0.0947623	+	0.164133i
$697$	12.0208	−	20.8207i	0.455321	−	0.788639i
$698$	−1.29289	−	2.23936i	−0.0489367	−	0.0847609i
$699$	21.7279			0.821825
$700$	−7.86396	−	1.07616i	−0.297230	−	0.0406750i
$701$	31.5147			1.19029			0.595147	−	0.803617i	$-0.297094\pi$
$701$	31.5147			1.19029			0.595147	+	0.803617i	$0.297094\pi$
$702$	−0.500000	−	0.866025i	−0.0188713	−	0.0326860i
$703$	−13.6066	+	23.5673i	−0.513183	+	0.888859i
$704$	1.20711	−	2.09077i	0.0454945	−	0.0787989i
$705$	−6.36396	−	11.0227i	−0.239681	−	0.415139i
$706$	−32.6274			−1.22795
$707$	6.82843	+	16.7262i	0.256809	+	0.629052i
$708$	10.4142			0.391390
$709$	−8.02082	−	13.8925i	−0.301228	−	0.521742i	0.675186	−	0.737647i	$-0.264063\pi$
$709$	−8.02082	−	13.8925i	−0.301228	−	0.521742i	−0.976414	+	0.215905i	$0.930730\pi$
$710$	0.707107	−	1.22474i	0.0265372	−	0.0459639i
$711$	4.65685	−	8.06591i	0.174646	−	0.302495i
$712$	−1.12132	−	1.94218i	−0.0420233	−	0.0727864i
$713$	5.94113			0.222497
$714$	3.24264	+	7.94282i	0.121353	+	0.297252i
$715$	−3.41421			−0.127684
$716$	11.8284	+	20.4874i	0.442049	+	0.765651i
$717$	9.74264	−	16.8747i	0.363846	−	0.630199i
$718$	−17.7279	+	30.7057i	−0.661600	+	1.14593i
$719$	−17.1421	−	29.6910i	−0.639294	−	1.10729i	−0.985588	−	0.169163i	$-0.945893\pi$
$719$	−17.1421	−	29.6910i	−0.639294	−	1.10729i	0.346294	−	0.938126i	$-0.387440\pi$
$720$	1.41421			0.0527046
$721$	−27.4853	−	3.76127i	−1.02361	−	0.140077i
$722$	−10.0000			−0.372161
$723$	−0.242641	−	0.420266i	−0.00902390	−	0.0156299i
$724$	7.20711	−	12.4831i	0.267850	−	0.463930i
$725$	7.50000	−	12.9904i	0.278543	−	0.482451i
$726$	2.58579	+	4.47871i	0.0959675	+	0.166221i
$727$	−33.1716			−1.23027			−0.615133	−	0.788424i	$-0.710898\pi$
$727$	−33.1716			−1.23027			−0.615133	+	0.788424i	$0.710898\pi$
$728$	−1.62132	+	2.09077i	−0.0600901	+	0.0774891i
$729$	1.00000			0.0370370
$730$	−9.24264	−	16.0087i	−0.342085	−	0.592509i
$731$	−1.34315	+	2.32640i	−0.0496780	+	0.0860449i
$732$	−1.62132	+	2.80821i	−0.0599257	+	0.103794i
$733$	−26.5061	−	45.9099i	−0.979025	−	1.69572i	−0.665957	−	0.745991i	$-0.731976\pi$
$733$	−26.5061	−	45.9099i	−0.979025	−	1.69572i	−0.313068	−	0.949731i	$-0.601357\pi$
$734$	14.0000			0.516749
$735$	−2.46447	−	9.58783i	−0.0909032	−	0.353652i
$736$	5.07107			0.186922
$737$	−4.03553	−	6.98975i	−0.148651	−	0.257471i
$738$	−3.70711	+	6.42090i	−0.136460	+	0.236356i
$739$	13.4853	−	23.3572i	0.496064	−	0.859208i	−0.503926	−	0.863747i	$-0.668111\pi$
$739$	13.4853	−	23.3572i	0.496064	−	0.859208i	0.999990	+	0.00453885i	$0.00144476\pi$
$740$	−6.41421	−	11.1097i	−0.235791	−	0.408402i
$741$	3.00000			0.110208
$742$	16.7218	−	21.5636i	0.613878	−	0.791624i
$743$	−5.48528			−0.201235			−0.100618	−	0.994925i	$-0.532082\pi$
$743$	−5.48528			−0.201235			−0.100618	+	0.994925i	$0.532082\pi$
$744$	−0.585786	−	1.01461i	−0.0214760	−	0.0371975i
$745$	2.75736	−	4.77589i	0.101022	−	0.174975i
$746$	15.4497	−	26.7597i	0.565655	−	0.979744i
$747$	−1.82843	−	3.16693i	−0.0668987	−	0.115872i
$748$	7.82843			0.286236
$749$	6.14214	+	0.840532i	0.224429	+	0.0307124i
$750$	−11.3137			−0.413118
$751$	22.8284	+	39.5400i	0.833021	+	1.44283i	0.895631	+	0.444797i	$0.146724\pi$
$751$	22.8284	+	39.5400i	0.833021	+	1.44283i	−0.0626103	+	0.998038i	$0.519943\pi$
$752$	−4.50000	+	7.79423i	−0.164098	+	0.284226i
$753$	−3.58579	+	6.21076i	−0.130673	+	0.226333i
$754$	−2.50000	−	4.33013i	−0.0910446	−	0.157694i
$755$	−14.7279			−0.536004
$756$	−1.00000	−	2.44949i	−0.0363696	−	0.0890871i
$757$	54.5563			1.98288			0.991442	−	0.130547i	$-0.0416734\pi$
$757$	54.5563			1.98288			0.991442	+	0.130547i	$0.0416734\pi$
$758$	11.1716	+	19.3497i	0.405770	+	0.702814i
$759$	6.12132	−	10.6024i	0.222190	−	0.384844i
$760$	−2.12132	+	3.67423i	−0.0769484	+	0.133278i
$761$	23.0711	+	39.9603i	0.836326	+	1.44856i	0.892947	+	0.450163i	$0.148634\pi$
$761$	23.0711	+	39.9603i	0.836326	+	1.44856i	−0.0566210	+	0.998396i	$0.518033\pi$
$762$	−9.89949			−0.358621
$763$	9.65685	+	23.6544i	0.349602	+	0.856346i
$764$	13.6569			0.494088
$765$	2.29289	+	3.97141i	0.0828997	+	0.143587i
$766$	5.24264	−	9.08052i	0.189424	−	0.328093i
$767$	−5.20711	+	9.01897i	−0.188018	+	0.325656i
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$	−21.0711			−0.759842			−0.379921	−	0.925019i	$-0.624049\pi$
$769$	−21.0711			−0.759842			−0.379921	+	0.925019i	$0.624049\pi$
$770$	−8.94975	−	1.22474i	−0.322527	−	0.0441367i
$771$	17.7990			0.641015

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)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.707107 - 1.22474i) q^{5} +1.00000 q^{6} +(-1.62132 + 2.09077i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.707107 - 1.22474i) q^{5} +1.00000 q^{6} +(-1.62132 + 2.09077i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.707107 + 1.22474i) q^{10} +(1.20711 - 2.09077i) q^{11} +(-0.500000 - 0.866025i) q^{12} +1.00000 q^{13} +(2.62132 + 0.358719i) q^{14} +1.41421 q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.62132 - 2.80821i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(-1.50000 - 2.59808i) q^{19} +1.41421 q^{20} +(-1.00000 - 2.44949i) q^{21} -2.41421 q^{22} +(-2.53553 - 4.39167i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(1.50000 - 2.59808i) q^{25} +(-0.500000 - 0.866025i) q^{26} +1.00000 q^{27} +(-1.00000 - 2.44949i) q^{28} +5.00000 q^{29} +(-0.707107 - 1.22474i) q^{30} +(-0.585786 + 1.01461i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(1.20711 + 2.09077i) q^{33} -3.24264 q^{34} +(3.70711 + 0.507306i) q^{35} +1.00000 q^{36} +(-4.53553 - 7.85578i) q^{37} +(-1.50000 + 2.59808i) q^{38} +(-0.500000 + 0.866025i) q^{39} +(-0.707107 - 1.22474i) q^{40} +7.41421 q^{41} +(-1.62132 + 2.09077i) q^{42} -0.828427 q^{43} +(1.20711 + 2.09077i) q^{44} +(-0.707107 + 1.22474i) q^{45} +(-2.53553 + 4.39167i) q^{46} +(-4.50000 - 7.79423i) q^{47} +1.00000 q^{48} +(-1.74264 - 6.77962i) q^{49} -3.00000 q^{50} +(1.62132 + 2.80821i) q^{51} +(-0.500000 + 0.866025i) q^{52} +(5.15685 - 8.93193i) q^{53} +(-0.500000 - 0.866025i) q^{54} -3.41421 q^{55} +(-1.62132 + 2.09077i) q^{56} +3.00000 q^{57} +(-2.50000 - 4.33013i) q^{58} +(-5.20711 + 9.01897i) q^{59} +(-0.707107 + 1.22474i) q^{60} +(-1.62132 - 2.80821i) q^{61} +1.17157 q^{62} +(2.62132 + 0.358719i) q^{63} +1.00000 q^{64} +(-0.707107 - 1.22474i) q^{65} +(1.20711 - 2.09077i) q^{66} +(1.67157 - 2.89525i) q^{67} +(1.62132 + 2.80821i) q^{68} +5.07107 q^{69} +(-1.41421 - 3.46410i) q^{70} -1.00000 q^{71} +(-0.500000 - 0.866025i) q^{72} +(-6.53553 + 11.3199i) q^{73} +(-4.53553 + 7.85578i) q^{74} +(1.50000 + 2.59808i) q^{75} +3.00000 q^{76} +(2.41421 + 5.91359i) q^{77} +1.00000 q^{78} +(4.65685 + 8.06591i) q^{79} +(-0.707107 + 1.22474i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.70711 - 6.42090i) q^{82} +3.65685 q^{83} +(2.62132 + 0.358719i) q^{84} -4.58579 q^{85} +(0.414214 + 0.717439i) q^{86} +(-2.50000 + 4.33013i) q^{87} +(1.20711 - 2.09077i) q^{88} +(-1.12132 - 1.94218i) q^{89} +1.41421 q^{90} +(-1.62132 + 2.09077i) q^{91} +5.07107 q^{92} +(-0.585786 - 1.01461i) q^{93} +(-4.50000 + 7.79423i) q^{94} +(-2.12132 + 3.67423i) q^{95} +(-0.500000 - 0.866025i) q^{96} -11.8995 q^{97} +(-5.00000 + 4.89898i) q^{98} -2.41421 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 4 q^{6} + 2 q^{7} + 4 q^{8} - 2 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 4 * q^6 + 2 * q^7 + 4 * q^8 - 2 * q^9	\( 4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 4 q^{6} + 2 q^{7} + 4 q^{8} - 2 q^{9} + 2 q^{11} - 2 q^{12} + 4 q^{13} + 2 q^{14} - 2 q^{16} - 2 q^{17} - 2 q^{18} - 6 q^{19} - 4 q^{21} - 4 q^{22} + 4 q^{23} - 2 q^{24} + 6 q^{25} - 2 q^{26} + 4 q^{27} - 4 q^{28} + 20 q^{29} - 8 q^{31} - 2 q^{32} + 2 q^{33} + 4 q^{34} + 12 q^{35} + 4 q^{36} - 4 q^{37} - 6 q^{38} - 2 q^{39} + 24 q^{41} + 2 q^{42} + 8 q^{43} + 2 q^{44} + 4 q^{46} - 18 q^{47} + 4 q^{48} + 10 q^{49} - 12 q^{50} - 2 q^{51} - 2 q^{52} - 2 q^{53} - 2 q^{54} - 8 q^{55} + 2 q^{56} + 12 q^{57} - 10 q^{58} - 18 q^{59} + 2 q^{61} + 16 q^{62} + 2 q^{63} + 4 q^{64} + 2 q^{66} + 18 q^{67} - 2 q^{68} - 8 q^{69} - 4 q^{71} - 2 q^{72} - 12 q^{73} - 4 q^{74} + 6 q^{75} + 12 q^{76} + 4 q^{77} + 4 q^{78} - 4 q^{79} - 2 q^{81} - 12 q^{82} - 8 q^{83} + 2 q^{84} - 24 q^{85} - 4 q^{86} - 10 q^{87} + 2 q^{88} + 4 q^{89} + 2 q^{91} - 8 q^{92} - 8 q^{93} - 18 q^{94} - 2 q^{96} - 8 q^{97} - 20 q^{98} - 4 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 4 * q^6 + 2 * q^7 + 4 * q^8 - 2 * q^9 + 2 * q^11 - 2 * q^12 + 4 * q^13 + 2 * q^14 - 2 * q^16 - 2 * q^17 - 2 * q^18 - 6 * q^19 - 4 * q^21 - 4 * q^22 + 4 * q^23 - 2 * q^24 + 6 * q^25 - 2 * q^26 + 4 * q^27 - 4 * q^28 + 20 * q^29 - 8 * q^31 - 2 * q^32 + 2 * q^33 + 4 * q^34 + 12 * q^35 + 4 * q^36 - 4 * q^37 - 6 * q^38 - 2 * q^39 + 24 * q^41 + 2 * q^42 + 8 * q^43 + 2 * q^44 + 4 * q^46 - 18 * q^47 + 4 * q^48 + 10 * q^49 - 12 * q^50 - 2 * q^51 - 2 * q^52 - 2 * q^53 - 2 * q^54 - 8 * q^55 + 2 * q^56 + 12 * q^57 - 10 * q^58 - 18 * q^59 + 2 * q^61 + 16 * q^62 + 2 * q^63 + 4 * q^64 + 2 * q^66 + 18 * q^67 - 2 * q^68 - 8 * q^69 - 4 * q^71 - 2 * q^72 - 12 * q^73 - 4 * q^74 + 6 * q^75 + 12 * q^76 + 4 * q^77 + 4 * q^78 - 4 * q^79 - 2 * q^81 - 12 * q^82 - 8 * q^83 + 2 * q^84 - 24 * q^85 - 4 * q^86 - 10 * q^87 + 2 * q^88 + 4 * q^89 + 2 * q^91 - 8 * q^92 - 8 * q^93 - 18 * q^94 - 2 * q^96 - 8 * q^97 - 20 * q^98 - 4 * q^99

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