LMFDB - Embedded newform 462.2.g.e.419.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(419,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("462.419");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.g (of order $2$, degree $1$, 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:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.342102016.5
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + x^{6} + 4x^{4} + 4x^{2} + 16 $ x^8 + x^6 + 4x^4 + 4x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			419.4
Root			$-1.17915 - 0.780776i$ of defining polynomial
Character	$\chi$	$=$	462.419
Dual form			462.2.g.e.419.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(1.51022 - 0.848071i) q^{3} -1.00000 q^{4} -1.69614 q^{5} +(-0.848071 - 1.51022i) q^{6} +(-2.56155 - 0.662153i) q^{7} +1.00000i q^{8} +(1.56155 - 2.56155i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(1.51022 - 0.848071i) q^{3} -1.00000 q^{4} -1.69614 q^{5} +(-0.848071 - 1.51022i) q^{6} +(-2.56155 - 0.662153i) q^{7} +1.00000i q^{8} +(1.56155 - 2.56155i) q^{9} +1.69614i q^{10} -1.00000i q^{11} +(-1.51022 + 0.848071i) q^{12} -4.34475i q^{13} +(-0.662153 + 2.56155i) q^{14} +(-2.56155 + 1.43845i) q^{15} +1.00000 q^{16} -4.71659 q^{17} +(-2.56155 - 1.56155i) q^{18} -6.41273i q^{19} +1.69614 q^{20} +(-4.43007 + 1.17238i) q^{21} -1.00000 q^{22} +6.00000i q^{23} +(0.848071 + 1.51022i) q^{24} -2.12311 q^{25} -4.34475 q^{26} +(0.185917 - 5.19283i) q^{27} +(2.56155 + 0.662153i) q^{28} +2.00000i q^{29} +(1.43845 + 2.56155i) q^{30} -1.32431i q^{31} -1.00000i q^{32} +(-0.848071 - 1.51022i) q^{33} +4.71659i q^{34} +(4.34475 + 1.12311i) q^{35} +(-1.56155 + 2.56155i) q^{36} +8.24621 q^{37} -6.41273 q^{38} +(-3.68466 - 6.56155i) q^{39} -1.69614i q^{40} +7.36520 q^{41} +(1.17238 + 4.43007i) q^{42} +11.1231 q^{43} +1.00000i q^{44} +(-2.64861 + 4.34475i) q^{45} +6.00000 q^{46} -7.36520 q^{47} +(1.51022 - 0.848071i) q^{48} +(6.12311 + 3.39228i) q^{49} +2.12311i q^{50} +(-7.12311 + 4.00000i) q^{51} +4.34475i q^{52} +2.00000i q^{53} +(-5.19283 - 0.185917i) q^{54} +1.69614i q^{55} +(0.662153 - 2.56155i) q^{56} +(-5.43845 - 9.68466i) q^{57} +2.00000 q^{58} +11.7100 q^{59} +(2.56155 - 1.43845i) q^{60} -1.69614i q^{61} -1.32431 q^{62} +(-5.69614 + 5.52757i) q^{63} -1.00000 q^{64} +7.36932i q^{65} +(-1.51022 + 0.848071i) q^{66} -12.0000 q^{67} +4.71659 q^{68} +(5.08842 + 9.06134i) q^{69} +(1.12311 - 4.34475i) q^{70} -9.36932i q^{71} +(2.56155 + 1.56155i) q^{72} -8.68951i q^{73} -8.24621i q^{74} +(-3.20636 + 1.80054i) q^{75} +6.41273i q^{76} +(-0.662153 + 2.56155i) q^{77} +(-6.56155 + 3.68466i) q^{78} -6.87689 q^{79} -1.69614 q^{80} +(-4.12311 - 8.00000i) q^{81} -7.36520i q^{82} +6.41273 q^{83} +(4.43007 - 1.17238i) q^{84} +8.00000 q^{85} -11.1231i q^{86} +(1.69614 + 3.02045i) q^{87} +1.00000 q^{88} +6.78456 q^{89} +(4.34475 + 2.64861i) q^{90} +(-2.87689 + 11.1293i) q^{91} -6.00000i q^{92} +(-1.12311 - 2.00000i) q^{93} +7.36520i q^{94} +10.8769i q^{95} +(-0.848071 - 1.51022i) q^{96} +6.04090i q^{97} +(3.39228 - 6.12311i) q^{98} +(-2.56155 - 1.56155i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4} - 4 q^{7} - 4 q^{9}+O(q^{10}) $ 8 * q - 8 * q^4 - 4 * q^7 - 4 * q^9	$ 8 q - 8 q^{4} - 4 q^{7} - 4 q^{9} - 4 q^{15} + 8 q^{16} - 4 q^{18} + 12 q^{21} - 8 q^{22} + 16 q^{25} + 4 q^{28} + 28 q^{30} + 4 q^{36} + 20 q^{39} - 8 q^{42} + 56 q^{43} + 48 q^{46} + 16 q^{49} - 24 q^{51} - 60 q^{57} + 16 q^{58} + 4 q^{60} - 32 q^{63} - 8 q^{64} - 96 q^{67} - 24 q^{70} + 4 q^{72} - 36 q^{78} - 88 q^{79} - 12 q^{84} + 64 q^{85} + 8 q^{88} - 56 q^{91} + 24 q^{93} - 4 q^{99}+O(q^{100}) $ 8 * q - 8 * q^4 - 4 * q^7 - 4 * q^9 - 4 * q^15 + 8 * q^16 - 4 * q^18 + 12 * q^21 - 8 * q^22 + 16 * q^25 + 4 * q^28 + 28 * q^30 + 4 * q^36 + 20 * q^39 - 8 * q^42 + 56 * q^43 + 48 * q^46 + 16 * q^49 - 24 * q^51 - 60 * q^57 + 16 * q^58 + 4 * q^60 - 32 * q^63 - 8 * q^64 - 96 * q^67 - 24 * q^70 + 4 * q^72 - 36 * q^78 - 88 * q^79 - 12 * q^84 + 64 * q^85 + 8 * q^88 - 56 * q^91 + 24 * q^93 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	1.51022	−	0.848071i	0.871928	−	0.489634i
$3$	1.51022	−	0.848071i	0.871928	−	0.489634i
$4$	−1.00000			−0.500000
$5$	−1.69614			−0.758537			−0.379269	−	0.925287i	$-0.623824\pi$
$5$	−1.69614			−0.758537			−0.379269	+	0.925287i	$0.623824\pi$
$6$	−0.848071	−	1.51022i	−0.346223	−	0.616546i
$7$	−2.56155	−	0.662153i	−0.968176	−	0.250270i
$7$	−2.56155	−	0.662153i	−0.968176	−	0.250270i
$8$			1.00000i			0.353553i
$9$	1.56155	−	2.56155i	0.520518	−	0.853851i
$10$			1.69614i			0.536367i
$11$		−	1.00000i		−	0.301511i
$11$		−	1.00000i		−	0.301511i
$12$	−1.51022	+	0.848071i	−0.435964	+	0.244817i
$13$		−	4.34475i		−	1.20502i	−0.798112	−	0.602509i	$-0.794168\pi$
$13$		−	4.34475i		−	1.20502i	0.798112	−	0.602509i	$-0.205832\pi$
$14$	−0.662153	+	2.56155i	−0.176968	+	0.684604i
$15$	−2.56155	+	1.43845i	−0.661390	+	0.371405i
$16$	1.00000			0.250000
$17$	−4.71659			−1.14394			−0.571970	−	0.820274i	$-0.693821\pi$
$17$	−4.71659			−1.14394			−0.571970	+	0.820274i	$0.693821\pi$
$18$	−2.56155	−	1.56155i	−0.603764	−	0.368062i
$19$		−	6.41273i		−	1.47118i	−0.677426	−	0.735591i	$-0.736905\pi$
$19$		−	6.41273i		−	1.47118i	0.677426	−	0.735591i	$-0.263095\pi$
$20$	1.69614			0.379269
$21$	−4.43007	+	1.17238i	−0.966721	+	0.255834i
$22$	−1.00000			−0.213201
$23$			6.00000i			1.25109i	0.780189	+	0.625543i	$0.215123\pi$
$23$			6.00000i			1.25109i	−0.780189	+	0.625543i	$0.784877\pi$
$24$	0.848071	+	1.51022i	0.173112	+	0.308273i
$25$	−2.12311			−0.424621
$26$	−4.34475			−0.852077
$27$	0.185917	−	5.19283i	0.0357798	−	0.999360i
$28$	2.56155	+	0.662153i	0.484088	+	0.125135i
$29$			2.00000i			0.371391i	0.982607	+	0.185695i	$0.0594537\pi$
$29$			2.00000i			0.371391i	−0.982607	+	0.185695i	$0.940546\pi$
$30$	1.43845	+	2.56155i	0.262623	+	0.467673i
$31$		−	1.32431i		−	0.237853i	−0.992903	−	0.118926i	$-0.962055\pi$
$31$		−	1.32431i		−	0.237853i	0.992903	−	0.118926i	$-0.0379452\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−0.848071	−	1.51022i	−0.147630	−	0.262896i
$34$			4.71659i			0.808888i
$35$	4.34475	+	1.12311i	0.734398	+	0.189839i
$36$	−1.56155	+	2.56155i	−0.260259	+	0.426925i
$37$	8.24621			1.35567			0.677834	−	0.735215i	$-0.262919\pi$
$37$	8.24621			1.35567			0.677834	+	0.735215i	$0.262919\pi$
$38$	−6.41273			−1.04028
$39$	−3.68466	−	6.56155i	−0.590018	−	1.05069i
$40$		−	1.69614i		−	0.268183i
$41$	7.36520			1.15025			0.575126	−	0.818065i	$-0.304953\pi$
$41$	7.36520			1.15025			0.575126	+	0.818065i	$0.304953\pi$
$42$	1.17238	+	4.43007i	0.180902	+	0.683575i
$43$	11.1231			1.69626			0.848129	−	0.529790i	$-0.177729\pi$
$43$	11.1231			1.69626			0.848129	+	0.529790i	$0.177729\pi$
$44$			1.00000i			0.150756i
$45$	−2.64861	+	4.34475i	−0.394832	+	0.647678i
$46$	6.00000			0.884652
$47$	−7.36520			−1.07433			−0.537163	−	0.843479i	$-0.680504\pi$
$47$	−7.36520			−1.07433			−0.537163	+	0.843479i	$0.680504\pi$
$48$	1.51022	−	0.848071i	0.217982	−	0.122408i
$49$	6.12311	+	3.39228i	0.874729	+	0.484612i
$50$			2.12311i			0.300252i
$51$	−7.12311	+	4.00000i	−0.997434	+	0.560112i
$52$			4.34475i			0.602509i
$53$			2.00000i			0.274721i	0.990521	+	0.137361i	$0.0438619\pi$
$53$			2.00000i			0.274721i	−0.990521	+	0.137361i	$0.956138\pi$
$54$	−5.19283	−	0.185917i	−0.706654	−	0.0253001i
$55$			1.69614i			0.228708i
$56$	0.662153	−	2.56155i	0.0884840	−	0.342302i
$57$	−5.43845	−	9.68466i	−0.720340	−	1.28276i
$58$	2.00000			0.262613
$59$	11.7100			1.52451			0.762253	−	0.647279i	$-0.224093\pi$
$59$	11.7100			1.52451			0.762253	+	0.647279i	$0.224093\pi$
$60$	2.56155	−	1.43845i	0.330695	−	0.185703i
$61$		−	1.69614i		−	0.217169i	−0.994087	−	0.108584i	$-0.965368\pi$
$61$		−	1.69614i		−	0.217169i	0.994087	−	0.108584i	$-0.0346317\pi$
$62$	−1.32431			−0.168187
$63$	−5.69614	+	5.52757i	−0.717646	+	0.696408i
$64$	−1.00000			−0.125000
$65$			7.36932i			0.914051i
$66$	−1.51022	+	0.848071i	−0.185896	+	0.104390i
$67$	−12.0000			−1.46603			−0.733017	−	0.680211i	$-0.761888\pi$
$67$	−12.0000			−1.46603			−0.733017	+	0.680211i	$0.761888\pi$
$68$	4.71659			0.571970
$69$	5.08842	+	9.06134i	0.612574	+	1.09086i
$70$	1.12311	−	4.34475i	0.134237	−	0.519298i
$71$		−	9.36932i		−	1.11193i	−0.831205	−	0.555967i	$-0.812348\pi$
$71$		−	9.36932i		−	1.11193i	0.831205	−	0.555967i	$-0.187652\pi$
$72$	2.56155	+	1.56155i	0.301882	+	0.184031i
$73$		−	8.68951i		−	1.01703i	−0.861053	−	0.508515i	$-0.830195\pi$
$73$		−	8.68951i		−	1.01703i	0.861053	−	0.508515i	$-0.169805\pi$
$74$		−	8.24621i		−	0.958603i
$75$	−3.20636	+	1.80054i	−0.370239	+	0.207909i
$76$			6.41273i			0.735591i
$77$	−0.662153	+	2.56155i	−0.0754594	+	0.291916i
$78$	−6.56155	+	3.68466i	−0.742950	+	0.417205i
$79$	−6.87689			−0.773711			−0.386856	−	0.922140i	$-0.626439\pi$
$79$	−6.87689			−0.773711			−0.386856	+	0.922140i	$0.626439\pi$
$80$	−1.69614			−0.189634
$81$	−4.12311	−	8.00000i	−0.458123	−	0.888889i
$82$		−	7.36520i		−	0.813351i
$83$	6.41273			0.703889			0.351944	−	0.936021i	$-0.385521\pi$
$83$	6.41273			0.703889			0.351944	+	0.936021i	$0.385521\pi$
$84$	4.43007	−	1.17238i	0.483360	−	0.127917i
$85$	8.00000			0.867722
$86$		−	11.1231i		−	1.19944i
$87$	1.69614	+	3.02045i	0.181845	+	0.323826i
$88$	1.00000			0.106600
$89$	6.78456			0.719162			0.359581	−	0.933114i	$-0.382920\pi$
$89$	6.78456			0.719162			0.359581	+	0.933114i	$0.382920\pi$
$90$	4.34475	+	2.64861i	0.457977	+	0.279188i
$91$	−2.87689	+	11.1293i	−0.301580	+	1.16667i
$92$		−	6.00000i		−	0.625543i
$93$	−1.12311	−	2.00000i	−0.116461	−	0.207390i
$94$			7.36520i			0.759663i
$95$			10.8769i			1.11595i
$96$	−0.848071	−	1.51022i	−0.0865558	−	0.154137i
$97$			6.04090i			0.613360i	0.951813	+	0.306680i	$0.0992181\pi$
$97$			6.04090i			0.613360i	−0.951813	+	0.306680i	$0.900782\pi$
$98$	3.39228	−	6.12311i	0.342672	−	0.618527i
$99$	−2.56155	−	1.56155i	−0.257446	−	0.156942i
$100$	2.12311			0.212311
$101$	−7.73704			−0.769864			−0.384932	−	0.922945i	$-0.625775\pi$
$101$	−7.73704			−0.769864			−0.384932	+	0.922945i	$0.625775\pi$
$102$	4.00000	+	7.12311i	0.396059	+	0.705293i
$103$			3.97292i			0.391464i	0.980657	+	0.195732i	$0.0627082\pi$
$103$			3.97292i			0.391464i	−0.980657	+	0.195732i	$0.937292\pi$
$104$	4.34475			0.426038
$105$	7.51403	−	1.98852i	0.733294	−	0.194059i
$106$	2.00000			0.194257
$107$		−	14.2462i		−	1.37723i	−0.725126	−	0.688617i	$-0.758218\pi$
$107$		−	14.2462i		−	1.37723i	0.725126	−	0.688617i	$-0.241782\pi$
$108$	−0.185917	+	5.19283i	−0.0178899	+	0.499680i
$109$	5.12311			0.490705			0.245352	−	0.969434i	$-0.421096\pi$
$109$	5.12311			0.490705			0.245352	+	0.969434i	$0.421096\pi$
$110$	1.69614			0.161721
$111$	12.4536	−	6.99337i	1.18205	−	0.663781i
$112$	−2.56155	−	0.662153i	−0.242044	−	0.0625676i
$113$		−	2.87689i		−	0.270635i	−0.990802	−	0.135318i	$-0.956794\pi$
$113$		−	2.87689i		−	0.270635i	0.990802	−	0.135318i	$-0.0432055\pi$
$114$	−9.68466	+	5.43845i	−0.907051	+	0.509357i
$115$		−	10.1768i		−	0.948996i
$116$		−	2.00000i		−	0.185695i
$117$	−11.1293	−	6.78456i	−1.02891	−	0.627233i
$118$		−	11.7100i		−	1.07799i
$119$	12.0818	+	3.12311i	1.10754	+	0.286295i
$120$	−1.43845	−	2.56155i	−0.131312	−	0.233837i
$121$	−1.00000			−0.0909091
$122$	−1.69614			−0.153561
$123$	11.1231	−	6.24621i	1.00294	−	0.563202i
$124$			1.32431i			0.118926i
$125$	12.0818			1.08063
$126$	5.52757	+	5.69614i	0.492435	+	0.507453i
$127$	14.2462			1.26415			0.632073	−	0.774909i	$-0.282204\pi$
$127$	14.2462			1.26415			0.632073	+	0.774909i	$0.282204\pi$
$128$			1.00000i			0.0883883i
$129$	16.7984	−	9.43318i	1.47901	−	0.830545i
$130$	7.36932			0.646332
$131$	−15.8459			−1.38446			−0.692232	−	0.721675i	$-0.743372\pi$
$131$	−15.8459			−1.38446			−0.692232	+	0.721675i	$0.743372\pi$
$132$	0.848071	+	1.51022i	0.0738151	+	0.131448i
$133$	−4.24621	+	16.4265i	−0.368193	+	1.42436i
$134$			12.0000i			1.03664i
$135$	−0.315342	+	8.80776i	−0.0271403	+	0.758052i
$136$		−	4.71659i		−	0.404444i
$137$			16.4924i			1.40904i	0.709683	+	0.704521i	$0.248838\pi$
$137$			16.4924i			1.40904i	−0.709683	+	0.704521i	$0.751162\pi$
$138$	9.06134	−	5.08842i	0.771353	−	0.433155i
$139$		−	21.1431i		−	1.79334i	−0.442702	−	0.896669i	$-0.645980\pi$
$139$		−	21.1431i		−	1.79334i	0.442702	−	0.896669i	$-0.354020\pi$
$140$	−4.34475	−	1.12311i	−0.367199	−	0.0949197i
$141$	−11.1231	+	6.24621i	−0.936734	+	0.526026i
$142$	−9.36932			−0.786256
$143$	−4.34475			−0.363327
$144$	1.56155	−	2.56155i	0.130129	−	0.213463i
$145$		−	3.39228i		−	0.281714i
$146$	−8.68951			−0.719149
$147$	12.1242	−	0.0697197i	0.999983	−	0.00575038i
$148$	−8.24621			−0.677834
$149$			4.24621i			0.347863i	0.984758	+	0.173932i	$0.0556472\pi$
$149$			4.24621i			0.347863i	−0.984758	+	0.173932i	$0.944353\pi$
$150$	1.80054	+	3.20636i	0.147014	+	0.261799i
$151$	−1.75379			−0.142721			−0.0713607	−	0.997451i	$-0.522734\pi$
$151$	−1.75379			−0.142721			−0.0713607	+	0.997451i	$0.522734\pi$
$152$	6.41273			0.520141
$153$	−7.36520	+	12.0818i	−0.595441	+	0.976755i
$154$	2.56155	+	0.662153i	0.206416	+	0.0533578i
$155$			2.24621i			0.180420i
$156$	3.68466	+	6.56155i	0.295009	+	0.525345i
$157$			24.5354i			1.95814i	0.203525	+	0.979070i	$0.434760\pi$
$157$			24.5354i			1.95814i	−0.203525	+	0.979070i	$0.565240\pi$
$158$			6.87689i			0.547096i
$159$	1.69614	+	3.02045i	0.134513	+	0.239537i
$160$			1.69614i			0.134092i
$161$	3.97292	−	15.3693i	0.313110	−	1.21127i
$162$	−8.00000	+	4.12311i	−0.628539	+	0.323942i
$163$	16.0000			1.25322			0.626608	−	0.779334i	$-0.284443\pi$
$163$	16.0000			1.25322			0.626608	+	0.779334i	$0.284443\pi$
$164$	−7.36520			−0.575126
$165$	1.43845	+	2.56155i	0.111983	+	0.199417i
$166$		−	6.41273i		−	0.497724i
$167$	6.04090			0.467459			0.233729	−	0.972302i	$-0.424907\pi$
$167$	6.04090			0.467459			0.233729	+	0.972302i	$0.424907\pi$
$168$	−1.17238	−	4.43007i	−0.0904509	−	0.341787i
$169$	−5.87689			−0.452069
$170$		−	8.00000i		−	0.613572i
$171$	−16.4265	−	10.0138i	−1.25617	−	0.765776i
$172$	−11.1231			−0.848129
$173$	−13.0343			−0.990977			−0.495488	−	0.868615i	$-0.665011\pi$
$173$	−13.0343			−0.990977			−0.495488	+	0.868615i	$0.665011\pi$
$174$	3.02045	−	1.69614i	0.228980	−	0.128584i
$175$	5.43845	+	1.40582i	0.411108	+	0.106270i
$176$		−	1.00000i		−	0.0753778i
$177$	17.6847	−	9.93087i	1.32926	−	0.746450i
$178$		−	6.78456i		−	0.508525i
$179$		−	14.2462i		−	1.06481i	−0.846489	−	0.532406i	$-0.821288\pi$
$179$		−	14.2462i		−	1.06481i	0.846489	−	0.532406i	$-0.178712\pi$
$180$	2.64861	−	4.34475i	0.197416	−	0.323839i
$181$			3.02045i			0.224508i	0.993680	+	0.112254i	$0.0358070\pi$
$181$			3.02045i			0.224508i	−0.993680	+	0.112254i	$0.964193\pi$
$182$	11.1293	+	2.87689i	0.824960	+	0.213250i
$183$	−1.43845	−	2.56155i	−0.106333	−	0.189355i
$184$	−6.00000			−0.442326
$185$	−13.9867			−1.02833
$186$	−2.00000	+	1.12311i	−0.146647	+	0.0823501i
$187$			4.71659i			0.344911i
$188$	7.36520			0.537163
$189$	−3.91468	+	13.1786i	−0.284751	+	0.958601i
$190$	10.8769			0.789093
$191$		−	9.36932i		−	0.677940i	−0.940797	−	0.338970i	$-0.889921\pi$
$191$		−	9.36932i		−	0.677940i	0.940797	−	0.338970i	$-0.110079\pi$
$192$	−1.51022	+	0.848071i	−0.108991	+	0.0612042i
$193$	−9.36932			−0.674418			−0.337209	−	0.941430i	$-0.609483\pi$
$193$	−9.36932			−0.674418			−0.337209	+	0.941430i	$0.609483\pi$
$194$	6.04090			0.433711
$195$	6.24970	+	11.1293i	0.447550	+	0.796987i
$196$	−6.12311	−	3.39228i	−0.437365	−	0.242306i
$197$			14.4924i			1.03254i	0.856425	+	0.516271i	$0.172680\pi$
$197$			14.4924i			1.03254i	−0.856425	+	0.516271i	$0.827320\pi$
$198$	−1.56155	+	2.56155i	−0.110975	+	0.182042i
$199$			1.32431i			0.0938776i	0.998898	+	0.0469388i	$0.0149466\pi$
$199$			1.32431i			0.0938776i	−0.998898	+	0.0469388i	$0.985053\pi$
$200$		−	2.12311i		−	0.150126i
$201$	−18.1227	+	10.1768i	−1.27828	+	0.717819i
$202$			7.73704i			0.544376i
$203$	1.32431	−	5.12311i	0.0929481	−	0.359572i
$204$	7.12311	−	4.00000i	0.498717	−	0.280056i
$205$	−12.4924			−0.872509
$206$	3.97292			0.276807
$207$	15.3693	+	9.36932i	1.06824	+	0.651213i
$208$		−	4.34475i		−	0.301255i
$209$	−6.41273			−0.443578
$210$	−1.98852	−	7.51403i	−0.137221	−	0.518517i
$211$	−1.36932			−0.0942677			−0.0471338	−	0.998889i	$-0.515009\pi$
$211$	−1.36932			−0.0942677			−0.0471338	+	0.998889i	$0.515009\pi$
$212$		−	2.00000i		−	0.137361i
$213$	−7.94584	−	14.1498i	−0.544440	−	0.969526i
$214$	−14.2462			−0.973851
$215$	−18.8664			−1.28667
$216$	5.19283	+	0.185917i	0.353327	+	0.0126501i
$217$	−0.876894	+	3.39228i	−0.0595275	+	0.230283i
$218$		−	5.12311i		−	0.346980i
$219$	−7.36932	−	13.1231i	−0.497972	−	0.886777i
$220$		−	1.69614i		−	0.114354i
$221$			20.4924i			1.37847i
$222$	−6.99337	−	12.4536i	−0.469364	−	0.835833i
$223$			2.06798i			0.138482i	0.997600	+	0.0692409i	$0.0220577\pi$
$223$			2.06798i			0.138482i	−0.997600	+	0.0692409i	$0.977942\pi$
$224$	−0.662153	+	2.56155i	−0.0442420	+	0.171151i
$225$	−3.31534	+	5.43845i	−0.221023	+	0.362563i
$226$	−2.87689			−0.191368
$227$	−3.02045			−0.200474			−0.100237	−	0.994964i	$-0.531960\pi$
$227$	−3.02045			−0.200474			−0.100237	+	0.994964i	$0.531960\pi$
$228$	5.43845	+	9.68466i	0.360170	+	0.641382i
$229$			9.06134i			0.598790i	0.954129	+	0.299395i	$0.0967849\pi$
$229$			9.06134i			0.598790i	−0.954129	+	0.299395i	$0.903215\pi$
$230$	−10.1768			−0.671041
$231$	1.17238	+	4.43007i	0.0771368	+	0.291477i
$232$	−2.00000			−0.131306
$233$			8.87689i			0.581545i	0.956792	+	0.290772i	$0.0939122\pi$
$233$			8.87689i			0.581545i	−0.956792	+	0.290772i	$0.906088\pi$
$234$	−6.78456	+	11.1293i	−0.443521	+	0.727546i
$235$	12.4924			0.814916
$236$	−11.7100			−0.762253
$237$	−10.3857	+	5.83209i	−0.674621	+	0.378835i
$238$	3.12311	−	12.0818i	0.202441	−	0.783146i
$239$		−	19.3693i		−	1.25290i	−0.779463	−	0.626448i	$-0.784508\pi$
$239$		−	19.3693i		−	1.25290i	0.779463	−	0.626448i	$-0.215492\pi$
$240$	−2.56155	+	1.43845i	−0.165348	+	0.0928514i
$241$		−	12.0818i		−	0.778257i	−0.921184	−	0.389128i	$-0.872776\pi$
$241$		−	12.0818i		−	0.778257i	0.921184	−	0.389128i	$-0.127224\pi$
$242$			1.00000i			0.0642824i
$243$	−13.0114	−	8.58511i	−0.834680	−	0.550735i
$244$			1.69614i			0.108584i
$245$	−10.3857	−	5.75379i	−0.663515	−	0.367596i
$246$	−6.24621	−	11.1231i	−0.398244	−	0.709183i
$247$	−27.8617			−1.77280
$248$	1.32431			0.0840936
$249$	9.68466	−	5.43845i	0.613740	−	0.344648i
$250$		−	12.0818i		−	0.764120i
$251$	−14.3586			−0.906305			−0.453152	−	0.891433i	$-0.649701\pi$
$251$	−14.3586			−0.906305			−0.453152	+	0.891433i	$0.649701\pi$
$252$	5.69614	−	5.52757i	0.358823	−	0.348204i
$253$	6.00000			0.377217
$254$		−	14.2462i		−	0.893887i
$255$	12.0818	−	6.78456i	0.756591	−	0.424866i
$256$	1.00000			0.0625000
$257$	−4.13595			−0.257993			−0.128997	−	0.991645i	$-0.541176\pi$
$257$	−4.13595			−0.257993			−0.128997	+	0.991645i	$0.541176\pi$
$258$	−9.43318	−	16.7984i	−0.587284	−	1.04582i
$259$	−21.1231	−	5.46026i	−1.31253	−	0.339284i
$260$		−	7.36932i		−	0.457026i
$261$	5.12311	+	3.12311i	0.317112	+	0.193315i
$262$			15.8459i			0.978963i
$263$			14.2462i			0.878459i	0.898375	+	0.439230i	$0.144749\pi$
$263$			14.2462i			0.878459i	−0.898375	+	0.439230i	$0.855251\pi$
$264$	1.51022	−	0.848071i	0.0929479	−	0.0521951i
$265$		−	3.39228i		−	0.208386i
$266$	16.4265	+	4.24621i	1.00718	+	0.260352i
$267$	10.2462	−	5.75379i	0.627058	−	0.352126i
$268$	12.0000			0.733017
$269$	−1.69614			−0.103416			−0.0517078	−	0.998662i	$-0.516466\pi$
$269$	−1.69614			−0.103416			−0.0517078	+	0.998662i	$0.516466\pi$
$270$	8.80776	+	0.315342i	0.536023	+	0.0191911i
$271$		−	13.4061i		−	0.814362i	−0.913347	−	0.407181i	$-0.866512\pi$
$271$		−	13.4061i		−	0.814362i	0.913347	−	0.407181i	$-0.133488\pi$
$272$	−4.71659			−0.285985
$273$	5.09369	+	19.2476i	0.308284	+	1.16492i
$274$	16.4924			0.996344
$275$			2.12311i			0.128028i
$276$	−5.08842	−	9.06134i	−0.306287	−	0.545429i
$277$	−13.6155			−0.818078			−0.409039	−	0.912517i	$-0.634136\pi$
$277$	−13.6155			−0.818078			−0.409039	+	0.912517i	$0.634136\pi$
$278$	−21.1431			−1.26808
$279$	−3.39228	−	2.06798i	−0.203091	−	0.123806i
$280$	−1.12311	+	4.34475i	−0.0671184	+	0.259649i
$281$			16.8769i			1.00679i	0.864056	+	0.503396i	$0.167916\pi$
$281$			16.8769i			1.00679i	−0.864056	+	0.503396i	$0.832084\pi$
$282$	6.24621	+	11.1231i	0.371956	+	0.662371i
$283$		−	14.3586i		−	0.853528i	−0.904363	−	0.426764i	$-0.859653\pi$
$283$		−	14.3586i		−	0.853528i	0.904363	−	0.426764i	$-0.140347\pi$
$284$			9.36932i			0.555967i
$285$	9.22437	+	16.4265i	0.546405	+	0.973025i
$286$			4.34475i			0.256911i
$287$	−18.8664	−	4.87689i	−1.11365	−	0.287874i
$288$	−2.56155	−	1.56155i	−0.150941	−	0.0920154i
$289$	5.24621			0.308601
$290$	−3.39228			−0.199202
$291$	5.12311	+	9.12311i	0.300322	+	0.534806i
$292$			8.68951i			0.508515i
$293$	3.60109			0.210378			0.105189	−	0.994452i	$-0.466455\pi$
$293$	3.60109			0.210378			0.105189	+	0.994452i	$0.466455\pi$
$294$	−0.0697197	−	12.1242i	−0.00406614	−	0.707095i
$295$	−19.8617			−1.15640
$296$			8.24621i			0.479301i
$297$	−5.19283	−	0.185917i	−0.301318	−	0.0107880i
$298$	4.24621			0.245976
$299$	26.0685			1.50758
$300$	3.20636	−	1.80054i	0.185120	−	0.103954i
$301$	−28.4924	−	7.36520i	−1.64228	−	0.424523i
$302$			1.75379i			0.100919i
$303$	−11.6847	+	6.56155i	−0.671266	+	0.376951i
$304$		−	6.41273i		−	0.367795i
$305$			2.87689i			0.164730i
$306$	12.0818	+	7.36520i	0.690670	+	0.421041i
$307$			27.1840i			1.55147i	0.631056	+	0.775737i	$0.282622\pi$
$307$			27.1840i			1.55147i	−0.631056	+	0.775737i	$0.717378\pi$
$308$	0.662153	−	2.56155i	0.0377297	−	0.145958i
$309$	3.36932	+	6.00000i	0.191674	+	0.341328i
$310$	2.24621			0.127576
$311$	26.9752			1.52962			0.764812	−	0.644253i	$-0.222832\pi$
$311$	26.9752			1.52962			0.764812	+	0.644253i	$0.222832\pi$
$312$	6.56155	−	3.68466i	0.371475	−	0.208603i
$313$			8.68951i			0.491160i	0.969376	+	0.245580i	$0.0789784\pi$
$313$			8.68951i			0.491160i	−0.969376	+	0.245580i	$0.921022\pi$
$314$	24.5354			1.38461
$315$	9.66146	−	9.37553i	0.544362	−	0.528251i
$316$	6.87689			0.386856
$317$		−	24.7386i		−	1.38946i	−0.719271	−	0.694730i	$-0.755524\pi$
$317$		−	24.7386i		−	1.38946i	0.719271	−	0.694730i	$-0.244476\pi$
$318$	3.02045	−	1.69614i	0.169378	−	0.0951149i
$319$	2.00000			0.111979
$320$	1.69614			0.0948172
$321$	−12.0818	−	21.5150i	−0.674340	−	1.20085i
$322$	−15.3693	−	3.97292i	−0.856499	−	0.221402i
$323$			30.2462i			1.68294i
$324$	4.12311	+	8.00000i	0.229061	+	0.444444i
$325$			9.22437i			0.511676i
$326$		−	16.0000i		−	0.886158i
$327$	7.73704	−	4.34475i	0.427859	−	0.240265i
$328$			7.36520i			0.406675i
$329$	18.8664	+	4.87689i	1.04014	+	0.268872i
$330$	2.56155	−	1.43845i	0.141009	−	0.0791839i
$331$	20.0000			1.09930			0.549650	−	0.835395i	$-0.314761\pi$
$331$	20.0000			1.09930			0.549650	+	0.835395i	$0.314761\pi$
$332$	−6.41273			−0.351944
$333$	12.8769	−	21.1231i	0.705649	−	1.15754i
$334$		−	6.04090i		−	0.330543i
$335$	20.3537			1.11204
$336$	−4.43007	+	1.17238i	−0.241680	+	0.0639584i
$337$	21.3693			1.16406			0.582030	−	0.813167i	$-0.302258\pi$
$337$	21.3693			1.16406			0.582030	+	0.813167i	$0.302258\pi$
$338$			5.87689i			0.319661i
$339$	−2.43981	−	4.34475i	−0.132512	−	0.235975i
$340$	−8.00000			−0.433861
$341$	−1.32431			−0.0717152
$342$	−10.0138	+	16.4265i	−0.541485	+	0.888246i
$343$	−13.4384	−	12.7439i	−0.725608	−	0.688108i
$344$			11.1231i			0.599718i
$345$	−8.63068	−	15.3693i	−0.464660	−	0.827456i
$346$			13.0343i			0.700726i
$347$			4.00000i			0.214731i	0.994220	+	0.107366i	$0.0342415\pi$
$347$			4.00000i			0.214731i	−0.994220	+	0.107366i	$0.965758\pi$
$348$	−1.69614	−	3.02045i	−0.0909227	−	0.161913i
$349$			31.1570i			1.66779i	0.551921	+	0.833897i	$0.313895\pi$
$349$			31.1570i			1.66779i	−0.551921	+	0.833897i	$0.686105\pi$
$350$	1.40582	−	5.43845i	0.0751443	−	0.290697i
$351$	−22.5616	−	0.807764i	−1.20425	−	0.0431153i
$352$	−1.00000			−0.0533002
$353$	14.7304			0.784020			0.392010	−	0.919961i	$-0.371780\pi$
$353$	14.7304			0.784020			0.392010	+	0.919961i	$0.371780\pi$
$354$	−9.93087	−	17.6847i	−0.527820	−	0.939929i
$355$			15.8917i			0.843443i
$356$	−6.78456			−0.359581
$357$	20.8948	−	5.52962i	1.10587	−	0.292659i
$358$	−14.2462			−0.752936
$359$			1.12311i			0.0592752i	0.999561	+	0.0296376i	$0.00943533\pi$
$359$			1.12311i			0.0592752i	−0.999561	+	0.0296376i	$0.990565\pi$
$360$	−4.34475	−	2.64861i	−0.228989	−	0.139594i
$361$	−22.1231			−1.16437
$362$	3.02045			0.158751
$363$	−1.51022	+	0.848071i	−0.0792662	+	0.0445122i
$364$	2.87689	−	11.1293i	0.150790	−	0.583335i
$365$			14.7386i			0.771455i
$366$	−2.56155	+	1.43845i	−0.133895	+	0.0751888i
$367$		−	30.3675i		−	1.58517i	−0.609761	−	0.792586i	$-0.708734\pi$
$367$		−	30.3675i		−	1.58517i	0.609761	−	0.792586i	$-0.291266\pi$
$368$			6.00000i			0.312772i
$369$	11.5012	−	18.8664i	0.598726	−	0.982143i
$370$			13.9867i			0.727136i
$371$	1.32431	−	5.12311i	0.0687546	−	0.265978i
$372$	1.12311	+	2.00000i	0.0582303	+	0.103695i
$373$	17.6155			0.912097			0.456049	−	0.889955i	$-0.349264\pi$
$373$	17.6155			0.912097			0.456049	+	0.889955i	$0.349264\pi$
$374$	4.71659			0.243889
$375$	18.2462	−	10.2462i	0.942230	−	0.529112i
$376$		−	7.36520i		−	0.379831i
$377$	8.68951			0.447533
$378$	13.1786	+	3.91468i	0.677834	+	0.201350i
$379$	30.7386			1.57894			0.789469	−	0.613791i	$-0.210356\pi$
$379$	30.7386			1.57894			0.789469	+	0.613791i	$0.210356\pi$
$380$		−	10.8769i		−	0.557973i
$381$	21.5150	−	12.0818i	1.10225	−	0.618969i
$382$	−9.36932			−0.479376
$383$	−33.0161			−1.68705			−0.843523	−	0.537094i	$-0.819522\pi$
$383$	−33.0161			−1.68705			−0.843523	+	0.537094i	$0.819522\pi$
$384$	0.848071	+	1.51022i	0.0432779	+	0.0770683i
$385$	1.12311	−	4.34475i	0.0572388	−	0.221429i
$386$			9.36932i			0.476886i
$387$	17.3693	−	28.4924i	0.882932	−	1.44835i
$388$		−	6.04090i		−	0.306680i
$389$		−	4.24621i		−	0.215291i	−0.994189	−	0.107646i	$-0.965669\pi$
$389$		−	4.24621i		−	0.215291i	0.994189	−	0.107646i	$-0.0343312\pi$
$390$	11.1293	−	6.24970i	0.563555	−	0.316466i
$391$		−	28.2995i		−	1.43117i
$392$	−3.39228	+	6.12311i	−0.171336	+	0.309264i
$393$	−23.9309	+	13.4384i	−1.20715	+	0.677880i
$394$	14.4924			0.730118
$395$	11.6642			0.586889
$396$	2.56155	+	1.56155i	0.128723	+	0.0784710i
$397$		−	9.06134i		−	0.454776i	−0.973804	−	0.227388i	$-0.926981\pi$
$397$		−	9.06134i		−	0.454776i	0.973804	−	0.227388i	$-0.0730185\pi$
$398$	1.32431			0.0663815
$399$	7.51814	+	28.4089i	0.376378	+	1.42222i
$400$	−2.12311			−0.106155
$401$			19.3693i			0.967258i	0.875273	+	0.483629i	$0.160682\pi$
$401$			19.3693i			0.967258i	−0.875273	+	0.483629i	$0.839318\pi$
$402$	10.1768	+	18.1227i	0.507575	+	0.903877i
$403$	−5.75379			−0.286617
$404$	7.73704			0.384932
$405$	6.99337	+	13.5691i	0.347503	+	0.674255i
$406$	−5.12311	−	1.32431i	−0.254255	−	0.0657242i
$407$		−	8.24621i		−	0.408750i
$408$	−4.00000	−	7.12311i	−0.198030	−	0.352646i
$409$		−	24.1636i		−	1.19481i	−0.801939	−	0.597406i	$-0.796198\pi$
$409$		−	24.1636i		−	1.19481i	0.801939	−	0.597406i	$-0.203802\pi$
$410$			12.4924i			0.616957i
$411$	13.9867	+	24.9073i	0.689915	+	1.22858i
$412$		−	3.97292i		−	0.195732i
$413$	−29.9957	−	7.75379i	−1.47599	−	0.381539i
$414$	9.36932	−	15.3693i	0.460477	−	0.755361i
$415$	−10.8769			−0.533926
$416$	−4.34475			−0.213019
$417$	−17.9309	−	31.9309i	−0.878078	−	1.56366i
$418$			6.41273i			0.313657i
$419$	−22.6305			−1.10557			−0.552785	−	0.833324i	$-0.686435\pi$
$419$	−22.6305			−1.10557			−0.552785	+	0.833324i	$0.686435\pi$
$420$	−7.51403	+	1.98852i	−0.366647	+	0.0970297i
$421$	−8.24621			−0.401896			−0.200948	−	0.979602i	$-0.564402\pi$
$421$	−8.24621			−0.401896			−0.200948	+	0.979602i	$0.564402\pi$
$422$			1.36932i			0.0666573i
$423$	−11.5012	+	18.8664i	−0.559205	+	0.917314i
$424$	−2.00000			−0.0971286
$425$	10.0138			0.485741
$426$	−14.1498	+	7.94584i	−0.685558	+	0.384977i
$427$	−1.12311	+	4.34475i	−0.0543509	+	0.210257i
$428$			14.2462i			0.688617i
$429$	−6.56155	+	3.68466i	−0.316795	+	0.177897i
$430$			18.8664i			0.909816i
$431$		−	29.6155i		−	1.42653i	−0.700895	−	0.713265i	$-0.747216\pi$
$431$		−	29.6155i		−	1.42653i	0.700895	−	0.713265i	$-0.252784\pi$
$432$	0.185917	−	5.19283i	0.00894494	−	0.249840i
$433$			10.1768i			0.489068i	0.969641	+	0.244534i	$0.0786350\pi$
$433$			10.1768i			0.489068i	−0.969641	+	0.244534i	$0.921365\pi$
$434$	3.39228	+	0.876894i	0.162835	+	0.0420923i
$435$	−2.87689	−	5.12311i	−0.137937	−	0.245634i
$436$	−5.12311			−0.245352
$437$	38.4764			1.84057
$438$	−13.1231	+	7.36932i	−0.627046	+	0.352120i
$439$			36.4084i			1.73768i	0.495094	+	0.868839i	$0.335133\pi$
$439$			36.4084i			1.73768i	−0.495094	+	0.868839i	$0.664867\pi$
$440$	−1.69614			−0.0808604
$441$	18.2511	−	10.3874i	0.869098	−	0.494640i
$442$	20.4924			0.974725
$443$			22.7386i			1.08035i	0.841554	+	0.540173i	$0.181641\pi$
$443$			22.7386i			1.08035i	−0.841554	+	0.540173i	$0.818359\pi$
$444$	−12.4536	+	6.99337i	−0.591023	+	0.331891i
$445$	−11.5076			−0.545511
$446$	2.06798			0.0979215
$447$	3.60109	+	6.41273i	0.170326	+	0.303312i
$448$	2.56155	+	0.662153i	0.121022	+	0.0312838i
$449$		−	34.2462i		−	1.61618i	−0.589060	−	0.808089i	$-0.700502\pi$
$449$		−	34.2462i		−	1.61618i	0.589060	−	0.808089i	$-0.299498\pi$
$450$	5.43845	+	3.31534i	0.256371	+	0.156287i
$451$		−	7.36520i		−	0.346814i
$452$			2.87689i			0.135318i
$453$	−2.64861	+	1.48734i	−0.124443	+	0.0698812i
$454$			3.02045i			0.141757i
$455$	4.87962	−	18.8769i	0.228760	−	0.884962i
$456$	9.68466	−	5.43845i	0.453526	−	0.254679i
$457$	−15.6155			−0.730464			−0.365232	−	0.930917i	$-0.619010\pi$
$457$	−15.6155			−0.730464			−0.365232	+	0.930917i	$0.619010\pi$
$458$	9.06134			0.423409
$459$	−0.876894	+	24.4924i	−0.0409299	+	1.14321i
$460$			10.1768i			0.474498i
$461$	−24.6984			−1.15032			−0.575161	−	0.818040i	$-0.695060\pi$
$461$	−24.6984			−1.15032			−0.575161	+	0.818040i	$0.695060\pi$
$462$	4.43007	−	1.17238i	0.206106	−	0.0545439i
$463$	−7.36932			−0.342481			−0.171241	−	0.985229i	$-0.554778\pi$
$463$	−7.36932			−0.342481			−0.171241	+	0.985229i	$0.554778\pi$
$464$			2.00000i			0.0928477i
$465$	1.90495	+	3.39228i	0.0883397	+	0.157313i
$466$	8.87689			0.411214
$467$	24.5354			1.13536			0.567682	−	0.823248i	$-0.307840\pi$
$467$	24.5354			1.13536			0.567682	+	0.823248i	$0.307840\pi$
$468$	11.1293	+	6.78456i	0.514453	+	0.313617i
$469$	30.7386	+	7.94584i	1.41938	+	0.366905i
$470$		−	12.4924i		−	0.576232i
$471$	20.8078	+	37.0540i	0.958771	+	1.70736i
$472$			11.7100i			0.538994i
$473$		−	11.1231i		−	0.511441i
$474$	5.83209	+	10.3857i	0.267877	+	0.477029i
$475$			13.6149i			0.624695i
$476$	−12.0818	−	3.12311i	−0.553768	−	0.143147i
$477$	5.12311	+	3.12311i	0.234571	+	0.142997i
$478$	−19.3693			−0.885932
$479$	26.0685			1.19110			0.595551	−	0.803318i	$-0.296934\pi$
$479$	26.0685			1.19110			0.595551	+	0.803318i	$0.296934\pi$
$480$	1.43845	+	2.56155i	0.0656558	+	0.116918i
$481$		−	35.8278i		−	1.63361i
$482$	−12.0818			−0.550311
$483$	−7.03426	−	26.5804i	−0.320070	−	1.20945i
$484$	1.00000			0.0454545
$485$		−	10.2462i		−	0.465256i
$486$	−8.58511	+	13.0114i	−0.389428	+	0.590208i
$487$	3.50758			0.158944			0.0794718	−	0.996837i	$-0.474677\pi$
$487$	3.50758			0.158944			0.0794718	+	0.996837i	$0.474677\pi$
$488$	1.69614			0.0767807
$489$	24.1636	−	13.5691i	1.09272	−	0.613617i
$490$	−5.75379	+	10.3857i	−0.259930	+	0.469176i
$491$		−	34.7386i		−	1.56773i	−0.620930	−	0.783866i	$-0.713245\pi$
$491$		−	34.7386i		−	1.56773i	0.620930	−	0.783866i	$-0.286755\pi$
$492$	−11.1231	+	6.24621i	−0.501468	+	0.281601i
$493$		−	9.43318i		−	0.424849i
$494$			27.8617i			1.25356i
$495$	4.34475	+	2.64861i	0.195282	+	0.119046i
$496$		−	1.32431i		−	0.0594631i
$497$	−6.20393	+	24.0000i	−0.278284	+	1.07655i
$498$	−5.43845	−	9.68466i	−0.243703	−	0.433980i
$499$	24.0000			1.07439			0.537194	−	0.843459i	$-0.319484\pi$
$499$	24.0000			1.07439			0.537194	+	0.843459i	$0.319484\pi$
$500$	−12.0818			−0.540314
$501$	9.12311	−	5.12311i	0.407590	−	0.228883i
$502$			14.3586i			0.640854i
$503$	−1.16128			−0.0517788			−0.0258894	−	0.999665i	$-0.508242\pi$
$503$	−1.16128			−0.0517788			−0.0258894	+	0.999665i	$0.508242\pi$
$504$	−5.52757	−	5.69614i	−0.246217	−	0.253726i
$505$	13.1231			0.583971
$506$		−	6.00000i		−	0.266733i
$507$	−8.87543	+	4.98402i	−0.394172	+	0.221348i
$508$	−14.2462			−0.632073
$509$	17.1702			0.761056			0.380528	−	0.924769i	$-0.375742\pi$
$509$	17.1702			0.761056			0.380528	+	0.924769i	$0.375742\pi$
$510$	−6.78456	−	12.0818i	−0.300426	−	0.534991i
$511$	−5.75379	+	22.2586i	−0.254533	+	0.984664i
$512$		−	1.00000i		−	0.0441942i
$513$	−33.3002	−	1.19224i	−1.47024	−	0.0526385i
$514$			4.13595i			0.182429i
$515$		−	6.73863i		−	0.296940i
$516$	−16.7984	+	9.43318i	−0.739507	+	0.415273i
$517$			7.36520i			0.323921i
$518$	−5.46026	+	21.1231i	−0.239910	+	0.928096i
$519$	−19.6847	+	11.0540i	−0.864061	+	0.485216i
$520$	−7.36932			−0.323166
$521$	12.8255			0.561894			0.280947	−	0.959723i	$-0.409352\pi$
$521$	12.8255			0.561894			0.280947	+	0.959723i	$0.409352\pi$
$522$	3.12311	−	5.12311i	0.136695	−	0.224232i
$523$			17.3332i			0.757930i	0.925411	+	0.378965i	$0.123720\pi$
$523$			17.3332i			0.757930i	−0.925411	+	0.378965i	$0.876280\pi$
$524$	15.8459			0.692232
$525$	9.40551	−	2.48908i	0.410490	−	0.108632i
$526$	14.2462			0.621164
$527$			6.24621i			0.272089i
$528$	−0.848071	−	1.51022i	−0.0369075	−	0.0657241i
$529$	−13.0000			−0.565217
$530$	−3.39228			−0.147351
$531$	18.2857	−	29.9957i	0.793533	−	1.30170i
$532$	4.24621	−	16.4265i	0.184097	−	0.712181i
$533$		−	32.0000i		−	1.38607i
$534$	−5.75379	−	10.2462i	−0.248991	−	0.443397i
$535$			24.1636i			1.04468i
$536$		−	12.0000i		−	0.518321i
$537$	−12.0818	−	21.5150i	−0.521368	−	0.928439i
$538$			1.69614i			0.0731258i
$539$	3.39228	−	6.12311i	0.146116	−	0.263741i
$540$	0.315342	−	8.80776i	0.0135701	−	0.379026i
$541$	21.6155			0.929324			0.464662	−	0.885488i	$-0.346176\pi$
$541$	21.6155			0.929324			0.464662	+	0.885488i	$0.346176\pi$
$542$	−13.4061			−0.575841
$543$	2.56155	+	4.56155i	0.109927	+	0.195755i
$544$			4.71659i			0.202222i
$545$	−8.68951			−0.372218
$546$	19.2476	−	5.09369i	0.823720	−	0.217990i
$547$	−19.1231			−0.817645			−0.408822	−	0.912614i	$-0.634060\pi$
$547$	−19.1231			−0.817645			−0.408822	+	0.912614i	$0.634060\pi$
$548$		−	16.4924i		−	0.704521i
$549$	−4.34475	−	2.64861i	−0.185430	−	0.113040i
$550$	2.12311			0.0905295
$551$	12.8255			0.546383
$552$	−9.06134	+	5.08842i	−0.385676	+	0.216578i
$553$	17.6155	+	4.55356i	0.749088	+	0.193637i
$554$			13.6155i			0.578468i
$555$	−21.1231	+	11.8617i	−0.896626	+	0.503503i
$556$			21.1431i			0.896669i
$557$			22.4924i			0.953035i	0.879165	+	0.476517i	$0.158101\pi$
$557$			22.4924i			0.953035i	−0.879165	+	0.476517i	$0.841899\pi$
$558$	−2.06798	+	3.39228i	−0.0875444	+	0.143607i
$559$		−	48.3272i		−	2.04402i
$560$	4.34475	+	1.12311i	0.183599	+	0.0474599i
$561$	4.00000	+	7.12311i	0.168880	+	0.300738i
$562$	16.8769			0.711909
$563$	−26.4404			−1.11433			−0.557164	−	0.830402i	$-0.688111\pi$
$563$	−26.4404			−1.11433			−0.557164	+	0.830402i	$0.688111\pi$
$564$	11.1231	−	6.24621i	0.468367	−	0.263013i
$565$			4.87962i			0.205287i
$566$	−14.3586			−0.603536
$567$	5.26433	+	23.2226i	0.221081	+	0.975255i
$568$	9.36932			0.393128
$569$			15.7538i			0.660433i	0.943905	+	0.330217i	$0.107122\pi$
$569$			15.7538i			0.660433i	−0.943905	+	0.330217i	$0.892878\pi$
$570$	16.4265	−	9.22437i	0.688032	−	0.386366i
$571$	−27.1231			−1.13507			−0.567533	−	0.823350i	$-0.692102\pi$
$571$	−27.1231			−1.13507			−0.567533	+	0.823350i	$0.692102\pi$
$572$	4.34475			0.181663
$573$	−7.94584	−	14.1498i	−0.331942	−	0.591115i
$574$	−4.87689	+	18.8664i	−0.203558	+	0.787466i
$575$		−	12.7386i		−	0.531238i
$576$	−1.56155	+	2.56155i	−0.0650647	+	0.106731i
$577$		−	10.9205i		−	0.454627i	−0.973822	−	0.227313i	$-0.927006\pi$
$577$		−	10.9205i		−	0.454627i	0.973822	−	0.227313i	$-0.0729942\pi$
$578$		−	5.24621i		−	0.218214i
$579$	−14.1498	+	7.94584i	−0.588044	+	0.330218i
$580$			3.39228i			0.140857i
$581$	−16.4265	−	4.24621i	−0.681488	−	0.176163i
$582$	9.12311	−	5.12311i	0.378165	−	0.212360i
$583$	2.00000			0.0828315
$584$	8.68951			0.359574
$585$	18.8769	+	11.5076i	0.780464	+	0.475780i
$586$		−	3.60109i		−	0.148760i
$587$	−1.11550			−0.0460417			−0.0230209	−	0.999735i	$-0.507328\pi$
$587$	−1.11550			−0.0460417			−0.0230209	+	0.999735i	$0.507328\pi$
$588$	−12.1242	+	0.0697197i	−0.499992	+	0.00287519i
$589$	−8.49242			−0.349924
$590$			19.8617i			0.817695i
$591$	12.2906	+	21.8868i	0.505568	+	0.900303i
$592$	8.24621			0.338917
$593$	33.4337			1.37296			0.686479	−	0.727149i	$-0.259155\pi$
$593$	33.4337			1.37296			0.686479	+	0.727149i	$0.259155\pi$
$594$	−0.185917	+	5.19283i	−0.00762827	+	0.213064i
$595$	−20.4924	−	5.29723i	−0.840107	−	0.217165i
$596$		−	4.24621i		−	0.173932i
$597$	1.12311	+	2.00000i	0.0459657	+	0.0818546i
$598$		−	26.0685i		−	1.06602i
$599$		−	36.1080i		−	1.47533i	−0.675166	−	0.737665i	$-0.735928\pi$
$599$		−	36.1080i		−	1.47533i	0.675166	−	0.737665i	$-0.264072\pi$
$600$	−1.80054	−	3.20636i	−0.0735069	−	0.130899i
$601$		−	15.4741i		−	0.631201i	−0.948892	−	0.315600i	$-0.897794\pi$
$601$		−	15.4741i		−	0.631201i	0.948892	−	0.315600i	$-0.102206\pi$
$602$	−7.36520	+	28.4924i	−0.300183	+	1.16126i
$603$	−18.7386	+	30.7386i	−0.763096	+	1.25177i
$604$	1.75379			0.0713607
$605$	1.69614			0.0689579
$606$	6.56155	+	11.6847i	0.266545	+	0.474657i
$607$			21.6780i			0.879883i	0.898026	+	0.439941i	$0.145001\pi$
$607$			21.6780i			0.879883i	−0.898026	+	0.439941i	$0.854999\pi$
$608$	−6.41273			−0.260071
$609$	−2.34475	−	8.86014i	−0.0950143	−	0.359031i
$610$	2.87689			0.116482
$611$			32.0000i			1.29458i
$612$	7.36520	−	12.0818i	0.297721	−	0.488377i
$613$	35.3693			1.42855			0.714277	−	0.699863i	$-0.246756\pi$
$613$	35.3693			1.42855			0.714277	+	0.699863i	$0.246756\pi$
$614$	27.1840			1.09706
$615$	−18.8664	+	10.5945i	−0.760765	+	0.427210i
$616$	−2.56155	−	0.662153i	−0.103208	−	0.0266789i
$617$			21.6155i			0.870208i	0.900380	+	0.435104i	$0.143288\pi$
$617$			21.6155i			0.870208i	−0.900380	+	0.435104i	$0.856712\pi$
$618$	6.00000	−	3.36932i	0.241355	−	0.135534i
$619$			34.5492i			1.38865i	0.719661	+	0.694325i	$0.244297\pi$
$619$			34.5492i			1.38865i	−0.719661	+	0.694325i	$0.755703\pi$
$620$		−	2.24621i		−	0.0902100i
$621$	31.1570	+	1.11550i	1.25029	+	0.0447636i
$622$		−	26.9752i		−	1.08161i
$623$	−17.3790	−	4.49242i	−0.696276	−	0.179985i
$624$	−3.68466	−	6.56155i	−0.147504	−	0.262672i
$625$	−9.87689			−0.395076
$626$	8.68951			0.347303
$627$	−9.68466	+	5.43845i	−0.386768	+	0.217191i
$628$		−	24.5354i		−	0.979070i
$629$	−38.8940			−1.55080
$630$	−9.37553	−	9.66146i	−0.373530	−	0.384922i
$631$	18.8769			0.751477			0.375739	−	0.926726i	$-0.377389\pi$
$631$	18.8769			0.751477			0.375739	+	0.926726i	$0.377389\pi$
$632$		−	6.87689i		−	0.273548i
$633$	−2.06798	+	1.16128i	−0.0821946	+	0.0461566i
$634$	−24.7386			−0.982497
$635$	−24.1636			−0.958903
$636$	−1.69614	−	3.02045i	−0.0672564	−	0.119769i
$637$	14.7386	−	26.6034i	0.583966	−	1.05406i
$638$		−	2.00000i		−	0.0791808i
$639$	−24.0000	−	14.6307i	−0.949425	−	0.578781i
$640$		−	1.69614i		−	0.0670459i
$641$			12.6307i			0.498882i	0.968390	+	0.249441i	$0.0802469\pi$
$641$			12.6307i			0.498882i	−0.968390	+	0.249441i	$0.919753\pi$
$642$	−21.5150	+	12.0818i	−0.849128	+	0.476830i
$643$		−	25.1161i		−	0.990481i	−0.868756	−	0.495240i	$-0.835080\pi$
$643$		−	25.1161i		−	0.990481i	0.868756	−	0.495240i	$-0.164920\pi$
$644$	−3.97292	+	15.3693i	−0.156555	+	0.605636i
$645$	−28.4924	+	16.0000i	−1.12189	+	0.629999i
$646$	30.2462			1.19002
$647$	−28.8802			−1.13540			−0.567698	−	0.823237i	$-0.692166\pi$
$647$	−28.8802			−1.13540			−0.567698	+	0.823237i	$0.692166\pi$
$648$	8.00000	−	4.12311i	0.314270	−	0.161971i
$649$		−	11.7100i		−	0.459656i
$650$	9.22437			0.361810
$651$	1.55259	+	5.86677i	0.0608507	+	0.229937i
$652$	−16.0000			−0.626608
$653$		−	6.49242i		−	0.254068i	−0.991898	−	0.127034i	$-0.959454\pi$
$653$		−	6.49242i		−	0.254068i	0.991898	−	0.127034i	$-0.0405458\pi$
$654$	−4.34475	−	7.73704i	−0.169893	−	0.302542i
$655$	26.8769			1.05017
$656$	7.36520			0.287563
$657$	−22.2586	−	13.5691i	−0.868392	−	0.529382i
$658$	4.87689	−	18.8664i	0.190121	−	0.735487i
$659$		−	7.50758i		−	0.292454i	−0.989251	−	0.146227i	$-0.953287\pi$
$659$		−	7.50758i		−	0.292454i	0.989251	−	0.146227i	$-0.0467129\pi$
$660$	−1.43845	−	2.56155i	−0.0559915	−	0.0997083i
$661$			15.1022i			0.587409i	0.955896	+	0.293705i	$0.0948882\pi$
$661$			15.1022i			0.587409i	−0.955896	+	0.293705i	$0.905112\pi$
$662$		−	20.0000i		−	0.777322i
$663$	17.3790	+	30.9481i	0.674945	+	1.20193i
$664$			6.41273i			0.248862i
$665$	7.20217	−	27.8617i	0.279288	−	1.08043i
$666$	−21.1231	−	12.8769i	−0.818504	−	0.498970i
$667$	−12.0000			−0.464642
$668$	−6.04090			−0.233729
$669$	1.75379	+	3.12311i	0.0678054	+	0.120746i
$670$		−	20.3537i		−	0.786332i
$671$	−1.69614			−0.0654788
$672$	1.17238	+	4.43007i	0.0452254	+	0.170894i
$673$	−2.49242			−0.0960758			−0.0480379	−	0.998846i	$-0.515297\pi$
$673$	−2.49242			−0.0960758			−0.0480379	+	0.998846i	$0.515297\pi$
$674$		−	21.3693i		−	0.823115i
$675$	−0.394722	+	11.0249i	−0.0151928	+	0.424349i
$676$	5.87689			0.226034
$677$	−13.7779			−0.529529			−0.264764	−	0.964313i	$-0.585294\pi$
$677$	−13.7779			−0.529529			−0.264764	+	0.964313i	$0.585294\pi$
$678$	−4.34475	+	2.43981i	−0.166859	+	0.0937003i
$679$	4.00000	−	15.4741i	0.153506	−	0.593840i
$680$			8.00000i			0.306786i
$681$	−4.56155	+	2.56155i	−0.174799	+	0.0981589i
$682$			1.32431i			0.0507103i
$683$		−	30.2462i		−	1.15734i	−0.815562	−	0.578670i	$-0.803572\pi$
$683$		−	30.2462i		−	1.15734i	0.815562	−	0.578670i	$-0.196428\pi$
$684$	16.4265	+	10.0138i	0.628085	+	0.382888i
$685$		−	27.9735i		−	1.06881i
$686$	−12.7439	+	13.4384i	−0.486566	+	0.513082i
$687$	7.68466	+	13.6847i	0.293188	+	0.522102i
$688$	11.1231			0.424064
$689$	8.68951			0.331044
$690$	−15.3693	+	8.63068i	−0.585100	+	0.328564i
$691$			12.6167i			0.479960i	0.970778	+	0.239980i	$0.0771409\pi$
$691$			12.6167i			0.479960i	−0.970778	+	0.239980i	$0.922859\pi$
$692$	13.0343			0.495488
$693$	5.52757	+	5.69614i	0.209975	+	0.216379i
$694$	4.00000			0.151838
$695$			35.8617i			1.36031i
$696$	−3.02045	+	1.69614i	−0.114490	+	0.0642921i
$697$	−34.7386			−1.31582
$698$	31.1570			1.17931
$699$	7.52823	+	13.4061i	0.284744	+	0.507065i
$700$	−5.43845	−	1.40582i	−0.205554	−	0.0531351i
$701$		−	12.2462i		−	0.462533i	−0.972890	−	0.231267i	$-0.925713\pi$
$701$		−	12.2462i		−	0.462533i	0.972890	−	0.231267i	$-0.0742869\pi$
$702$	−0.807764	+	22.5616i	−0.0304871	+	0.851531i
$703$		−	52.8807i		−	1.99443i
$704$			1.00000i			0.0376889i
$705$	18.8664	−	10.5945i	0.710548	−	0.399010i
$706$		−	14.7304i		−	0.554386i
$707$	19.8188	+	5.12311i	0.745364	+	0.192674i
$708$	−17.6847	+	9.93087i	−0.664630	+	0.373225i
$709$	36.7386			1.37975			0.689874	−	0.723929i	$-0.257666\pi$
$709$	36.7386			1.37975			0.689874	+	0.723929i	$0.257666\pi$
$710$	15.8917			0.596404
$711$	−10.7386	+	17.6155i	−0.402730	+	0.660634i
$712$			6.78456i			0.254262i
$713$	7.94584			0.297574
$714$	−5.52962	−	20.8948i	−0.206941	−	0.781969i
$715$	7.36932			0.275597
$716$			14.2462i			0.532406i
$717$	−16.4265	−	29.2520i	−0.613461	−	1.09244i
$718$	1.12311			0.0419139
$719$	−0.580639			−0.0216542			−0.0108271	−	0.999941i	$-0.503446\pi$
$719$	−0.580639			−0.0216542			−0.0108271	+	0.999941i	$0.503446\pi$
$720$	−2.64861	+	4.34475i	−0.0987080	+	0.161919i
$721$	2.63068	−	10.1768i	0.0979718	−	0.379006i
$722$			22.1231i			0.823337i
$723$	−10.2462	−	18.2462i	−0.381061	−	0.678584i
$724$		−	3.02045i		−	0.112254i
$725$		−	4.24621i		−	0.157700i
$726$	0.848071	+	1.51022i	0.0314748	+	0.0560497i
$727$		−	39.0570i		−	1.44854i	−0.689514	−	0.724272i	$-0.742176\pi$
$727$		−	39.0570i		−	1.44854i	0.689514	−	0.724272i	$-0.257824\pi$
$728$	−11.1293	−	2.87689i	−0.412480	−	0.106625i
$729$	−26.9309	−	1.93087i	−0.997440	−	0.0715137i
$730$	14.7386			0.545501
$731$	−52.4631			−1.94042
$732$	1.43845	+	2.56155i	0.0531665	+	0.0946777i
$733$			22.0498i			0.814429i	0.913333	+	0.407215i	$0.133500\pi$
$733$			22.0498i			0.814429i	−0.913333	+	0.407215i	$0.866500\pi$
$734$	−30.3675			−1.12089
$735$	−20.5643	+	0.118254i	−0.758525	+	0.00436188i
$736$	6.00000			0.221163
$737$			12.0000i			0.442026i
$738$	−18.8664	−	11.5012i	−0.694480	−	0.423363i
$739$	38.3542			1.41088			0.705440	−	0.708769i	$-0.250749\pi$
$739$	38.3542			1.41088			0.705440	+	0.708769i	$0.250749\pi$
$740$	13.9867			0.514163
$741$	−42.0775	+	23.6287i	−1.54575	+	0.868023i
$742$	−5.12311	−	1.32431i	−0.188075	−	0.0486168i
$743$		−	2.87689i		−	0.105543i	−0.998607	−	0.0527715i	$-0.983195\pi$
$743$		−	2.87689i		−	0.105543i	0.998607	−	0.0527715i	$-0.0168055\pi$
$744$	2.00000	−	1.12311i	0.0733236	−	0.0411750i
$745$		−	7.20217i		−	0.263867i
$746$		−	17.6155i		−	0.644950i
$747$	10.0138	−	16.4265i	0.366386	−	0.601016i
$748$		−	4.71659i		−	0.172456i
$749$	−9.43318	+	36.4924i	−0.344681	+	1.33340i
$750$	−10.2462	−	18.2462i	−0.374139	−	0.666257i
$751$	−11.5076			−0.419917			−0.209959	−	0.977710i	$-0.567333\pi$
$751$	−11.5076			−0.419917			−0.209959	+	0.977710i	$0.567333\pi$
$752$	−7.36520			−0.268581
$753$	−21.6847	+	12.1771i	−0.790233	+	0.443757i
$754$		−	8.68951i		−	0.316453i
$755$	2.97467			0.108259
$756$	3.91468	−	13.1786i	0.142376	−	0.479301i
$757$	−0.246211			−0.00894870			−0.00447435	−	0.999990i	$-0.501424\pi$
$757$	−0.246211			−0.00894870			−0.00447435	+	0.999990i	$0.501424\pi$
$758$		−	30.7386i		−	1.11648i
$759$	9.06134	−	5.08842i	0.328906	−	0.184698i
$760$	−10.8769			−0.394546
$761$	18.2857			0.662857			0.331428	−	0.943480i	$-0.392469\pi$
$761$	18.2857			0.662857			0.331428	+	0.943480i	$0.392469\pi$
$762$	−12.0818	−	21.5150i	−0.437677	−	0.779405i
$763$	−13.1231	−	3.39228i	−0.475088	−	0.122809i
$764$			9.36932i			0.338970i
$765$	12.4924	−	20.4924i	0.451664	−	0.740905i
$766$			33.0161i			1.19292i
$767$		−	50.8769i		−	1.83706i
$768$	1.51022	−	0.848071i	0.0544955	−	0.0306021i
$769$			48.3272i			1.74272i	0.490642	+	0.871361i	$0.336762\pi$
$769$			48.3272i			1.74272i	−0.490642	+	0.871361i	$0.663238\pi$
$770$	−4.34475	−	1.12311i	−0.156574	−	0.0404739i
$771$	−6.24621	+	3.50758i	−0.224952	+	0.126322i
$772$	9.36932			0.337209
$773$	−39.4289			−1.41816			−0.709079	−	0.705129i	$-0.750889\pi$
$773$	−39.4289			−1.41816			−0.709079	+	0.705129i	$0.750889\pi$
$774$	−28.4924	−	17.3693i	−1.02414	−	0.624327i
$775$			2.81164i			0.100997i
$776$	−6.04090			−0.216856
$777$	−36.5313	+	9.66767i	−1.31055	+	0.346826i
$778$	−4.24621			−0.152234
$779$		−	47.2311i		−	1.69223i
$780$	−6.24970	−	11.1293i	−0.223775	−	0.398494i
$781$	−9.36932			−0.335261
$782$	−28.2995			−1.01199
$783$	10.3857	+	0.371834i	0.371153	+	0.0132883i
$784$	6.12311	+	3.39228i	0.218682	+	0.121153i
$785$		−	41.6155i		−	1.48532i
$786$	13.4384	+	23.9309i	0.479334	+	0.853586i
$787$			13.1973i			0.470433i	0.971943	+	0.235216i	$0.0755799\pi$
$787$			13.1973i			0.470433i	−0.971943	+	0.235216i	$0.924420\pi$
$788$		−	14.4924i		−	0.516271i
$789$	12.0818	+	21.5150i	0.430123	+	0.765953i
$790$		−	11.6642i		−	0.414993i
$791$	−1.90495	+	7.36932i	−0.0677321	+	0.262023i
$792$	1.56155	−	2.56155i	0.0554874	−	0.0910208i
$793$	−7.36932			−0.261692
$794$	−9.06134			−0.321575
$795$	−2.87689	−	5.12311i	−0.102033	−	0.181698i
$796$		−	1.32431i		−	0.0469388i
$797$	−2.11375			−0.0748729			−0.0374364	−	0.999299i	$-0.511919\pi$
$797$	−2.11375			−0.0748729			−0.0374364	+	0.999299i	$0.511919\pi$
$798$	28.4089	−	7.51814i	1.00566	−	0.266139i
$799$	34.7386			1.22896
$800$			2.12311i			0.0750631i
$801$	10.5945	−	17.3790i	0.374337	−	0.614057i
$802$	19.3693			0.683954
$803$	−8.68951			−0.306646
$804$	18.1227	−	10.1768i	0.639138	−	0.358910i
$805$	−6.73863	+	26.0685i	−0.237506	+	0.918795i
$806$			5.75379i			0.202669i
$807$	−2.56155	+	1.43845i	−0.0901709	+	0.0506357i
$808$		−	7.73704i		−	0.272188i
$809$			16.7386i			0.588499i	0.955729	+	0.294250i	$0.0950697\pi$
$809$			16.7386i			0.588499i	−0.955729	+	0.294250i	$0.904930\pi$
$810$	13.5691	−	6.99337i	0.476771	−	0.245722i
$811$			38.1045i			1.33803i	0.743248	+	0.669016i	$0.233284\pi$
$811$			38.1045i			1.33803i	−0.743248	+	0.669016i	$0.766716\pi$
$812$	−1.32431	+	5.12311i	−0.0464741	+	0.179786i
$813$	−11.3693	−	20.2462i	−0.398739	−	0.710066i
$814$	−8.24621			−0.289030
$815$	−27.1383			−0.950612
$816$	−7.12311	+	4.00000i	−0.249359	+	0.140028i
$817$		−	71.3295i		−	2.49550i
$818$	−24.1636			−0.844860
$819$	24.0159	+	24.7483i	0.839184	+	0.864777i
$820$	12.4924			0.436254
$821$		−	13.5076i		−	0.471418i	−0.971824	−	0.235709i	$-0.924259\pi$
$821$		−	13.5076i		−	0.471418i	0.971824	−	0.235709i	$-0.0757412\pi$
$822$	24.9073	−	13.9867i	0.868740	−	0.487843i
$823$	13.1231			0.457443			0.228721	−	0.973492i	$-0.426546\pi$
$823$	13.1231			0.457443			0.228721	+	0.973492i	$0.426546\pi$
$824$	−3.97292			−0.138403
$825$	1.80054	+	3.20636i	0.0626869	+	0.111631i
$826$	−7.75379	+	29.9957i	−0.269789	+	1.04368i
$827$			24.4924i			0.851685i	0.904797	+	0.425842i	$0.140022\pi$
$827$			24.4924i			0.851685i	−0.904797	+	0.425842i	$0.859978\pi$
$828$	−15.3693	−	9.36932i	−0.534121	−	0.325606i
$829$			27.9277i			0.969969i	0.874523	+	0.484985i	$0.161175\pi$
$829$			27.9277i			0.969969i	−0.874523	+	0.484985i	$0.838825\pi$
$830$			10.8769i			0.377543i
$831$	−20.5625	+	11.5469i	−0.713305	+	0.400558i
$832$			4.34475i			0.150627i
$833$	−28.8802	−	16.0000i	−1.00064	−	0.554367i
$834$	−31.9309	+	17.9309i	−1.10568	+	0.620895i
$835$	−10.2462			−0.354585
$836$	6.41273			0.221789
$837$	−6.87689	−	0.246211i	−0.237700	−	0.00851031i
$838$			22.6305i			0.781757i
$839$	22.4217			0.774082			0.387041	−	0.922063i	$-0.373497\pi$
$839$	22.4217			0.774082			0.387041	+	0.922063i	$0.373497\pi$
$840$	1.98852	+	7.51403i	0.0686104	+	0.259259i
$841$	25.0000			0.862069
$842$			8.24621i			0.284183i
$843$	14.3128	+	25.4879i	0.492959	+	0.877850i
$844$	1.36932			0.0471338
$845$	9.96804			0.342911
$846$	18.8664	+	11.5012i	0.648639	+	0.395418i
$847$	2.56155	+	0.662153i	0.0880160	+	0.0227519i
$848$			2.00000i			0.0686803i
$849$	−12.1771	−	21.6847i	−0.417916	−	0.744216i
$850$		−	10.0138i		−	0.343471i
$851$			49.4773i			1.69606i
$852$	7.94584	+	14.1498i	0.272220	+	0.484763i
$853$		−	42.0775i		−	1.44071i	−0.693608	−	0.720353i	$-0.743980\pi$
$853$		−	42.0775i		−	1.44071i	0.693608	−	0.720353i	$-0.256020\pi$
$854$	4.34475	+	1.12311i	0.148674	+	0.0384319i
$855$	27.8617	+	16.9848i	0.952851	+	0.580869i
$856$	14.2462			0.486925
$857$	55.6924			1.90242			0.951208	−	0.308552i	$-0.0998443\pi$
$857$	55.6924			1.90242			0.951208	+	0.308552i	$0.0998443\pi$
$858$	3.68466	+	6.56155i	0.125792	+	0.224008i
$859$			40.1725i			1.37067i	0.728229	+	0.685334i	$0.240344\pi$
$859$			40.1725i			1.37067i	−0.728229	+	0.685334i	$0.759656\pi$
$860$	18.8664			0.643337
$861$	−32.6284	+	8.63480i	−1.11197	+	0.294273i
$862$	−29.6155			−1.00871
$863$		−	17.3693i		−	0.591258i	−0.955303	−	0.295629i	$-0.904471\pi$
$863$		−	17.3693i		−	0.591258i	0.955303	−	0.295629i	$-0.0955293\pi$
$864$	−5.19283	−	0.185917i	−0.176664	−	0.00632503i
$865$	22.1080			0.751693
$866$	10.1768			0.345823
$867$	7.92295	−	4.44916i	0.269078	−	0.151101i
$868$	0.876894	−	3.39228i	0.0297637	−	0.115142i
$869$			6.87689i			0.233283i
$870$	−5.12311	+	2.87689i	−0.173690	+	0.0975359i
$871$			52.1371i			1.76660i
$872$			5.12311i			0.173490i
$873$	15.4741	+	9.43318i	0.523718	+	0.319265i
$874$		−	38.4764i		−	1.30148i
$875$	−30.9481	−	8.00000i	−1.04624	−	0.270449i
$876$	7.36932	+	13.1231i	0.248986	+	0.443389i
$877$	14.8769			0.502357			0.251179	−	0.967941i	$-0.419182\pi$
$877$	14.8769			0.502357			0.251179	+	0.967941i	$0.419182\pi$
$878$	36.4084			1.22872
$879$	5.43845	−	3.05398i	0.183434	−	0.103008i
$880$			1.69614i			0.0571769i
$881$	32.4355			1.09278			0.546390	−	0.837531i	$-0.316002\pi$
$881$	32.4355			1.09278			0.546390	+	0.837531i	$0.316002\pi$
$882$	−10.3874	−	18.2511i	−0.349763	−	0.614545i
$883$	28.4924			0.958846			0.479423	−	0.877584i	$-0.340846\pi$
$883$	28.4924			0.958846			0.479423	+	0.877584i	$0.340846\pi$
$884$		−	20.4924i		−	0.689235i
$885$	−29.9957	+	16.8442i	−1.00829	+	0.566210i
$886$	22.7386			0.763919
$887$	−20.7713			−0.697432			−0.348716	−	0.937228i	$-0.613382\pi$
$887$	−20.7713			−0.697432			−0.348716	+	0.937228i	$0.613382\pi$
$888$	6.99337	+	12.4536i	0.234682	+	0.417916i
$889$	−36.4924	−	9.43318i	−1.22392	−	0.316379i
$890$			11.5076i			0.385735i
$891$	−8.00000	+	4.12311i	−0.268010	+	0.138129i
$892$		−	2.06798i		−	0.0692409i
$893$			47.2311i			1.58053i
$894$	6.41273	−	3.60109i	0.214474	−	0.120438i
$895$			24.1636i			0.807700i
$896$	0.662153	−	2.56155i	0.0221210	−	0.0855755i
$897$	39.3693	−	22.1080i	1.31450	−	0.738163i
$898$	−34.2462			−1.14281
$899$	2.64861			0.0883362
$900$	3.31534	−	5.43845i	0.110511	−	0.181282i
$901$		−	9.43318i		−	0.314265i
$902$	−7.36520			−0.245234
$903$	−49.2762	+	13.0405i	−1.63981	+	0.433960i
$904$	2.87689			0.0956841
$905$		−	5.12311i		−	0.170298i
$906$	1.48734	+	2.64861i	0.0494134	+	0.0879943i
$907$	−4.49242			−0.149168			−0.0745842	−	0.997215i	$-0.523763\pi$
$907$	−4.49242			−0.149168			−0.0745842	+	0.997215i	$0.523763\pi$
$908$	3.02045			0.100237
$909$	−12.0818	+	19.8188i	−0.400728	+	0.657349i
$910$	−18.8769	−	4.87962i	−0.625763	−	0.161758i
$911$			18.4924i			0.612681i	0.951922	+	0.306341i	$0.0991047\pi$
$911$			18.4924i			0.612681i	−0.951922	+	0.306341i	$0.900895\pi$
$912$	−5.43845	−	9.68466i	−0.180085	−	0.320691i
$913$		−	6.41273i		−	0.212230i
$914$			15.6155i			0.516516i
$915$	2.43981	+	4.34475i	0.0806576	+	0.143633i
$916$		−	9.06134i		−	0.299395i
$917$	40.5901	+	10.4924i	1.34040	+	0.346490i
$918$	24.4924	+	0.876894i	0.808370	+	0.0289418i
$919$	55.8617			1.84271			0.921354	−	0.388724i	$-0.127084\pi$
$919$	55.8617			1.84271			0.921354	+	0.388724i	$0.127084\pi$
$920$	10.1768			0.335521
$921$	23.0540	+	41.0540i	0.759654	+	1.35277i
$922$			24.6984i			0.813400i
$923$	−40.7074			−1.33990
$924$	−1.17238	−	4.43007i	−0.0385684	−	0.145739i
$925$	−17.5076			−0.575646
$926$			7.36932i			0.242171i
$927$	10.1768	+	6.20393i	0.334251	+	0.203764i
$928$	2.00000			0.0656532
$929$	42.6123			1.39807			0.699033	−	0.715090i	$-0.253614\pi$
$929$	42.6123			1.39807			0.699033	+	0.715090i	$0.253614\pi$
$930$	3.39228	−	1.90495i	0.111237	−	0.0624656i
$931$	21.7538	−	39.2658i	0.712952	−	1.28689i
$932$		−	8.87689i		−	0.290772i
$933$	40.7386	−	22.8769i	1.33372	−	0.748956i
$934$		−	24.5354i		−	0.802823i
$935$		−	8.00000i		−	0.261628i
$936$	6.78456	−	11.1293i	0.221760	−	0.363773i
$937$		−	10.1768i		−	0.332463i	−0.986087	−	0.166232i	$-0.946840\pi$
$937$		−	10.1768i		−	0.332463i	0.986087	−	0.166232i	$-0.0531599\pi$
$938$	7.94584	−	30.7386i	0.259441	−	1.00365i
$939$	7.36932	+	13.1231i	0.240489	+	0.428256i
$940$	−12.4924			−0.407458
$941$	15.6829			0.511247			0.255624	−	0.966776i	$-0.417719\pi$
$941$	15.6829			0.511247			0.255624	+	0.966776i	$0.417719\pi$
$942$	37.0540	−	20.8078i	1.20728	−	0.677954i
$943$			44.1912i			1.43906i
$944$	11.7100			0.381127
$945$	6.63986	−	22.3527i	0.215995	−	0.727135i
$946$	−11.1231			−0.361643
$947$			40.0000i			1.29983i	0.760009	+	0.649913i	$0.225195\pi$
$947$			40.0000i			1.29983i	−0.760009	+	0.649913i	$0.774805\pi$
$948$	10.3857	−	5.83209i	0.337310	−	0.189418i
$949$	−37.7538			−1.22554
$950$	13.6149			0.441726
$951$	−20.9801	−	37.3609i	−0.680327	−	1.21151i
$952$	−3.12311	+	12.0818i	−0.101220	+	0.391573i
$953$			17.3693i			0.562647i	0.959613	+	0.281324i	$0.0907735\pi$
$953$			17.3693i			0.562647i	−0.959613	+	0.281324i	$0.909227\pi$
$954$	3.12311	−	5.12311i	0.101114	−	0.165867i
$955$			15.8917i			0.514243i
$956$			19.3693i			0.626448i
$957$	3.02045	−	1.69614i	0.0976372	−	0.0548285i
$958$		−	26.0685i		−	0.842236i
$959$	10.9205	−	42.2462i	0.352642	−	1.36420i
$960$	2.56155	−	1.43845i	0.0826738	−	0.0464257i
$961$	29.2462			0.943426
$962$	−35.8278			−1.15513
$963$	−36.4924	−	22.2462i	−1.17595	−	0.716874i
$964$			12.0818i			0.389128i
$965$	15.8917			0.511571
$966$	−26.5804	+	7.03426i	−0.855211	+	0.226324i
$967$	6.24621			0.200865			0.100432	−	0.994944i	$-0.467977\pi$
$967$	6.24621			0.200865			0.100432	+	0.994944i	$0.467977\pi$
$968$		−	1.00000i		−	0.0321412i
$969$	25.6509	+	45.6786i	0.824026	+	1.46741i
$970$	−10.2462			−0.328986
$971$	26.4404			0.848512			0.424256	−	0.905542i	$-0.360536\pi$
$971$	26.4404			0.848512			0.424256	+	0.905542i	$0.360536\pi$
$972$	13.0114	+	8.58511i	0.417340	+	0.275367i
$973$	−14.0000	+	54.1593i	−0.448819	+	1.73627i
$974$		−	3.50758i		−	0.112390i
$975$	7.82292	+	13.9309i	0.250534	+	0.446145i
$976$		−	1.69614i		−	0.0542922i
$977$		−	6.73863i		−	0.215588i	−0.994173	−	0.107794i	$-0.965621\pi$
$977$		−	6.73863i		−	0.215588i	0.994173	−	0.107794i	$-0.0343787\pi$
$978$	−13.5691	−	24.1636i	−0.433893	−	0.772666i
$979$		−	6.78456i		−	0.216836i
$980$	10.3857	+	5.75379i	0.331757	+	0.183798i
$981$	8.00000	−	13.1231i	0.255420	−	0.418989i
$982$	−34.7386			−1.10855
$983$	−39.4746			−1.25905			−0.629523	−	0.776982i	$-0.716749\pi$
$983$	−39.4746			−1.25905			−0.629523	+	0.776982i	$0.716749\pi$
$984$	6.24621	+	11.1231i	0.199122	+	0.354592i
$985$		−	24.5812i		−	0.783222i
$986$	−9.43318			−0.300414
$987$	32.6284	−	8.63480i	1.03857	−	0.274849i
$988$	27.8617			0.886400
$989$			66.7386i			2.12217i
$990$	2.64861	−	4.34475i	0.0841785	−	0.138085i
$991$	−9.61553			−0.305447			−0.152724	−	0.988269i	$-0.548804\pi$
$991$	−9.61553			−0.305447			−0.152724	+	0.988269i	$0.548804\pi$
$992$	−1.32431			−0.0420468
$993$	30.2045	−	16.9614i	0.958510	−	0.538254i
$994$	24.0000	+	6.20393i	0.761234	+	0.196777i
$995$		−	2.24621i		−	0.0712097i
$996$	−9.68466	+	5.43845i	−0.306870	+	0.172324i
$997$			12.6167i			0.399573i	0.979839	+	0.199787i	$0.0640249\pi$
$997$			12.6167i			0.399573i	−0.979839	+	0.199787i	$0.935975\pi$
$998$		−	24.0000i		−	0.759707i
$999$	1.53311	−	42.8211i	0.0485055	−	1.35480i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.g.e.419.4	yes	8
3.2	odd	2	inner	462.2.g.e.419.5	yes	8
7.6	odd	2	inner	462.2.g.e.419.1	✓	8
21.20	even	2	inner	462.2.g.e.419.8	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.g.e.419.1	✓	8	7.6	odd	2	inner
462.2.g.e.419.4	yes	8	1.1	even	1	trivial
462.2.g.e.419.5	yes	8	3.2	odd	2	inner
462.2.g.e.419.8	yes	8	21.20	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(1.51022 - 0.848071i) q^{3} -1.00000 q^{4} -1.69614 q^{5} +(-0.848071 - 1.51022i) q^{6} +(-2.56155 - 0.662153i) q^{7} +1.00000i q^{8} +(1.56155 - 2.56155i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(1.51022 - 0.848071i) q^{3} -1.00000 q^{4} -1.69614 q^{5} +(-0.848071 - 1.51022i) q^{6} +(-2.56155 - 0.662153i) q^{7} +1.00000i q^{8} +(1.56155 - 2.56155i) q^{9} +1.69614i q^{10} -1.00000i q^{11} +(-1.51022 + 0.848071i) q^{12} -4.34475i q^{13} +(-0.662153 + 2.56155i) q^{14} +(-2.56155 + 1.43845i) q^{15} +1.00000 q^{16} -4.71659 q^{17} +(-2.56155 - 1.56155i) q^{18} -6.41273i q^{19} +1.69614 q^{20} +(-4.43007 + 1.17238i) q^{21} -1.00000 q^{22} +6.00000i q^{23} +(0.848071 + 1.51022i) q^{24} -2.12311 q^{25} -4.34475 q^{26} +(0.185917 - 5.19283i) q^{27} +(2.56155 + 0.662153i) q^{28} +2.00000i q^{29} +(1.43845 + 2.56155i) q^{30} -1.32431i q^{31} -1.00000i q^{32} +(-0.848071 - 1.51022i) q^{33} +4.71659i q^{34} +(4.34475 + 1.12311i) q^{35} +(-1.56155 + 2.56155i) q^{36} +8.24621 q^{37} -6.41273 q^{38} +(-3.68466 - 6.56155i) q^{39} -1.69614i q^{40} +7.36520 q^{41} +(1.17238 + 4.43007i) q^{42} +11.1231 q^{43} +1.00000i q^{44} +(-2.64861 + 4.34475i) q^{45} +6.00000 q^{46} -7.36520 q^{47} +(1.51022 - 0.848071i) q^{48} +(6.12311 + 3.39228i) q^{49} +2.12311i q^{50} +(-7.12311 + 4.00000i) q^{51} +4.34475i q^{52} +2.00000i q^{53} +(-5.19283 - 0.185917i) q^{54} +1.69614i q^{55} +(0.662153 - 2.56155i) q^{56} +(-5.43845 - 9.68466i) q^{57} +2.00000 q^{58} +11.7100 q^{59} +(2.56155 - 1.43845i) q^{60} -1.69614i q^{61} -1.32431 q^{62} +(-5.69614 + 5.52757i) q^{63} -1.00000 q^{64} +7.36932i q^{65} +(-1.51022 + 0.848071i) q^{66} -12.0000 q^{67} +4.71659 q^{68} +(5.08842 + 9.06134i) q^{69} +(1.12311 - 4.34475i) q^{70} -9.36932i q^{71} +(2.56155 + 1.56155i) q^{72} -8.68951i q^{73} -8.24621i q^{74} +(-3.20636 + 1.80054i) q^{75} +6.41273i q^{76} +(-0.662153 + 2.56155i) q^{77} +(-6.56155 + 3.68466i) q^{78} -6.87689 q^{79} -1.69614 q^{80} +(-4.12311 - 8.00000i) q^{81} -7.36520i q^{82} +6.41273 q^{83} +(4.43007 - 1.17238i) q^{84} +8.00000 q^{85} -11.1231i q^{86} +(1.69614 + 3.02045i) q^{87} +1.00000 q^{88} +6.78456 q^{89} +(4.34475 + 2.64861i) q^{90} +(-2.87689 + 11.1293i) q^{91} -6.00000i q^{92} +(-1.12311 - 2.00000i) q^{93} +7.36520i q^{94} +10.8769i q^{95} +(-0.848071 - 1.51022i) q^{96} +6.04090i q^{97} +(3.39228 - 6.12311i) q^{98} +(-2.56155 - 1.56155i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} - 4 q^{7} - 4 q^{9}+O(q^{10}) \) 8 * q - 8 * q^4 - 4 * q^7 - 4 * q^9	\( 8 q - 8 q^{4} - 4 q^{7} - 4 q^{9} - 4 q^{15} + 8 q^{16} - 4 q^{18} + 12 q^{21} - 8 q^{22} + 16 q^{25} + 4 q^{28} + 28 q^{30} + 4 q^{36} + 20 q^{39} - 8 q^{42} + 56 q^{43} + 48 q^{46} + 16 q^{49} - 24 q^{51} - 60 q^{57} + 16 q^{58} + 4 q^{60} - 32 q^{63} - 8 q^{64} - 96 q^{67} - 24 q^{70} + 4 q^{72} - 36 q^{78} - 88 q^{79} - 12 q^{84} + 64 q^{85} + 8 q^{88} - 56 q^{91} + 24 q^{93} - 4 q^{99}+O(q^{100}) \) 8 * q - 8 * q^4 - 4 * q^7 - 4 * q^9 - 4 * q^15 + 8 * q^16 - 4 * q^18 + 12 * q^21 - 8 * q^22 + 16 * q^25 + 4 * q^28 + 28 * q^30 + 4 * q^36 + 20 * q^39 - 8 * q^42 + 56 * q^43 + 48 * q^46 + 16 * q^49 - 24 * q^51 - 60 * q^57 + 16 * q^58 + 4 * q^60 - 32 * q^63 - 8 * q^64 - 96 * q^67 - 24 * q^70 + 4 * q^72 - 36 * q^78 - 88 * q^79 - 12 * q^84 + 64 * q^85 + 8 * q^88 - 56 * q^91 + 24 * q^93 - 4 * q^99

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