LMFDB - Embedded newform 462.2.g.e.419.5

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			419.5
Root			$1.17915 + 0.780776i$ of defining polynomial
Character	$\chi$	$=$	462.419
Dual form			462.2.g.e.419.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(-1.51022 - 0.848071i) q^{3} -1.00000 q^{4} +1.69614 q^{5} +(0.848071 - 1.51022i) q^{6} +(-2.56155 - 0.662153i) q^{7} -1.00000i q^{8} +(1.56155 + 2.56155i) q^{9} +O(q^{10})$	\(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} +(3.30697 + 3.17238i) 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} +(-3.17238 + 3.30697i) 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} +(-2.30386 - 7.59554i) 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} +(-3.30697 - 3.17238i) 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	$-0.376176\pi$
$5$	1.69614			0.758537			0.379269	+	0.925287i	$0.376176\pi$
$6$	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	$-0.306179\pi$
$17$	4.71659			1.14394			0.571970	+	0.820274i	$0.306179\pi$
$18$	−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
$21$	3.30697	+	3.17238i	0.721639	+	0.692270i
$22$	−1.00000			−0.213201
$23$		−	6.00000i		−	1.25109i	−0.780189	−	0.625543i	$-0.784877\pi$
$23$		−	6.00000i		−	1.25109i	0.780189	−	0.625543i	$-0.215123\pi$
$24$	−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	$-0.940546\pi$
$29$		−	2.00000i		−	0.371391i	0.982607	−	0.185695i	$-0.0594537\pi$
$30$	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	$-0.695047\pi$
$41$	−7.36520			−1.15025			−0.575126	+	0.818065i	$0.695047\pi$
$42$	−3.17238	+	3.30697i	−0.489508	+	0.510276i
$43$	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	$-0.319496\pi$
$47$	7.36520			1.07433			0.537163	+	0.843479i	$0.319496\pi$
$48$	−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	$-0.956138\pi$
$53$		−	2.00000i		−	0.274721i	0.990521	−	0.137361i	$-0.0438619\pi$
$54$	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	$-0.775907\pi$
$59$	−11.7100			−1.52451			−0.762253	+	0.647279i	$0.775907\pi$
$60$	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
$63$	−2.30386	−	7.59554i	−0.290259	−	0.956948i
$64$	−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	$0.187652\pi$
$71$			9.36932i			1.11193i	−0.831205	+	0.555967i	$0.812348\pi$
$72$	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	$-0.614479\pi$
$83$	−6.41273			−0.703889			−0.351944	+	0.936021i	$0.614479\pi$
$84$	−3.30697	−	3.17238i	−0.360820	−	0.346135i
$85$	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	$-0.617080\pi$
$89$	−6.78456			−0.719162			−0.359581	+	0.933114i	$0.617080\pi$
$90$	−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	$-0.374225\pi$
$101$	7.73704			0.769864			0.384932	+	0.922945i	$0.374225\pi$
$102$	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
$105$	5.60908	+	5.38080i	0.547390	+	0.525112i
$106$	2.00000			0.194257
$107$			14.2462i			1.37723i	0.725126	+	0.688617i	$0.241782\pi$
$107$			14.2462i			1.37723i	−0.725126	+	0.688617i	$0.758218\pi$
$108$	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	$0.0432055\pi$
$113$			2.87689i			0.270635i	−0.990802	+	0.135318i	$0.956794\pi$
$114$	−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
$126$	7.59554	−	2.30386i	0.676665	−	0.205244i
$127$	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	$-0.256628\pi$
$131$	15.8459			1.38446			0.692232	+	0.721675i	$0.256628\pi$
$132$	−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	$-0.751162\pi$
$137$		−	16.4924i		−	1.40904i	0.709683	−	0.704521i	$-0.248838\pi$
$138$	−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
$147$	−6.37037	−	10.3159i	−0.525419	−	0.850844i
$148$	−8.24621			−0.677834
$149$		−	4.24621i		−	0.347863i	−0.984758	−	0.173932i	$-0.944353\pi$
$149$		−	4.24621i		−	0.347863i	0.984758	−	0.173932i	$-0.0556472\pi$
$150$	−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	$-0.575093\pi$
$167$	−6.04090			−0.467459			−0.233729	+	0.972302i	$0.575093\pi$
$168$	3.17238	−	3.30697i	0.244754	−	0.255138i
$169$	−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	$-0.334989\pi$
$173$	13.0343			0.990977			0.495488	+	0.868615i	$0.334989\pi$
$174$	−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	$0.178712\pi$
$179$			14.2462i			1.06481i	−0.846489	+	0.532406i	$0.821288\pi$
$180$	−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
$189$	−2.96221	+	13.4248i	−0.215469	+	0.976511i
$190$	10.8769			0.789093
$191$			9.36932i			0.677940i	0.940797	+	0.338970i	$0.110079\pi$
$191$			9.36932i			0.677940i	−0.940797	+	0.338970i	$0.889921\pi$
$192$	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	$-0.827320\pi$
$197$		−	14.4924i		−	1.03254i	0.856425	−	0.516271i	$-0.172680\pi$
$198$	−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
$210$	−5.38080	+	5.60908i	−0.371310	+	0.387063i
$211$	−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	$-0.468040\pi$
$227$	3.02045			0.200474			0.100237	+	0.994964i	$0.468040\pi$
$228$	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
$231$	−3.17238	+	3.30697i	−0.208727	+	0.217582i
$232$	−2.00000			−0.131306
$233$		−	8.87689i		−	0.581545i	−0.956792	−	0.290772i	$-0.906088\pi$
$233$		−	8.87689i		−	0.581545i	0.956792	−	0.290772i	$-0.0939122\pi$
$234$	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	$0.215492\pi$
$239$			19.3693i			1.25290i	−0.779463	+	0.626448i	$0.784508\pi$
$240$	−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	$-0.350299\pi$
$251$	14.3586			0.906305			0.453152	+	0.891433i	$0.350299\pi$
$252$	2.30386	+	7.59554i	0.145129	+	0.478474i
$253$	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	$-0.458824\pi$
$257$	4.13595			0.257993			0.128997	+	0.991645i	$0.458824\pi$
$258$	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	$-0.855251\pi$
$263$		−	14.2462i		−	0.878459i	0.898375	−	0.439230i	$-0.144749\pi$
$264$	−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	$-0.483534\pi$
$269$	1.69614			0.103416			0.0517078	+	0.998662i	$0.483534\pi$
$270$	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
$273$	13.7832	−	14.3680i	0.834197	−	0.869588i
$274$	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	$-0.832084\pi$
$281$		−	16.8769i		−	1.00679i	0.864056	−	0.503396i	$-0.167916\pi$
$282$	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	$-0.533545\pi$
$293$	−3.60109			−0.210378			−0.105189	+	0.994452i	$0.533545\pi$
$294$	10.3159	−	6.37037i	0.601637	−	0.371527i
$295$	−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	$-0.777168\pi$
$311$	−26.9752			−1.52962			−0.764812	+	0.644253i	$0.777168\pi$
$312$	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
$315$	−3.90767	−	12.8831i	−0.220172	−	0.725881i
$316$	6.87689			0.386856
$317$			24.7386i			1.38946i	0.719271	+	0.694730i	$0.244476\pi$
$317$			24.7386i			1.38946i	−0.719271	+	0.694730i	$0.755524\pi$
$318$	−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
$336$	3.30697	+	3.17238i	0.180410	+	0.173067i
$337$	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	$-0.965758\pi$
$347$		−	4.00000i		−	0.214731i	0.994220	−	0.107366i	$-0.0342415\pi$
$348$	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	$-0.628220\pi$
$353$	−14.7304			−0.784020			−0.392010	+	0.919961i	$0.628220\pi$
$354$	−9.93087	+	17.6847i	−0.527820	+	0.939929i
$355$			15.8917i			0.843443i
$356$	6.78456			0.359581
$357$	15.5976	+	14.9628i	0.825512	+	0.791915i
$358$	−14.2462			−0.752936
$359$		−	1.12311i		−	0.0592752i	−0.999561	−	0.0296376i	$-0.990565\pi$
$359$		−	1.12311i		−	0.0592752i	0.999561	−	0.0296376i	$-0.00943533\pi$
$360$	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
$378$	−13.4248	−	2.96221i	−0.690497	−	0.152360i
$379$	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	$-0.180478\pi$
$383$	33.0161			1.68705			0.843523	+	0.537094i	$0.180478\pi$
$384$	−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	$0.0343312\pi$
$389$			4.24621i			0.215291i	−0.994189	+	0.107646i	$0.965669\pi$
$390$	−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
$399$	20.3436	−	21.2067i	1.01845	−	1.06166i
$400$	−2.12311			−0.106155
$401$		−	19.3693i		−	0.967258i	−0.875273	−	0.483629i	$-0.839318\pi$
$401$		−	19.3693i		−	0.967258i	0.875273	−	0.483629i	$-0.160682\pi$
$402$	−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	$-0.313565\pi$
$419$	22.6305			1.10557			0.552785	+	0.833324i	$0.313565\pi$
$420$	−5.60908	−	5.38080i	−0.273695	−	0.262556i
$421$	−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	$0.252784\pi$
$431$			29.6155i			1.42653i	−0.700895	+	0.713265i	$0.747216\pi$
$432$	−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
$441$	0.872043	+	20.9819i	0.0415259	+	0.999137i
$442$	20.4924			0.974725
$443$		−	22.7386i		−	1.08035i	−0.841554	−	0.540173i	$-0.818359\pi$
$443$		−	22.7386i		−	1.08035i	0.841554	−	0.540173i	$-0.181641\pi$
$444$	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	$0.299498\pi$
$449$			34.2462i			1.61618i	−0.589060	+	0.808089i	$0.700502\pi$
$450$	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	$-0.304940\pi$
$461$	24.6984			1.15032			0.575161	+	0.818040i	$0.304940\pi$
$462$	−3.30697	−	3.17238i	−0.153854	−	0.147592i
$463$	−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	$-0.692160\pi$
$467$	−24.5354			−1.13536			−0.567682	+	0.823248i	$0.692160\pi$
$468$	−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	$-0.703066\pi$
$479$	−26.0685			−1.19110			−0.595551	+	0.803318i	$0.703066\pi$
$480$	1.43845	−	2.56155i	0.0656558	−	0.116918i
$481$		−	35.8278i		−	1.63361i
$482$	12.0818			0.550311
$483$	19.0343	−	19.8418i	0.866089	−	0.902833i
$484$	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	$0.286755\pi$
$491$			34.7386i			1.56773i	−0.620930	+	0.783866i	$0.713245\pi$
$492$	−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	$-0.491758\pi$
$503$	1.16128			0.0517788			0.0258894	+	0.999665i	$0.491758\pi$
$504$	−7.59554	+	2.30386i	−0.338332	+	0.102622i
$505$	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	$-0.624258\pi$
$509$	−17.1702			−0.761056			−0.380528	+	0.924769i	$0.624258\pi$
$510$	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	$-0.590648\pi$
$521$	−12.8255			−0.561894			−0.280947	+	0.959723i	$0.590648\pi$
$522$	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
$525$	−7.02104	−	6.73529i	−0.306423	−	0.293952i
$526$	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
$546$	14.3680	+	13.7832i	0.614892	+	0.589867i
$547$	−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	$-0.841899\pi$
$557$		−	22.4924i		−	0.953035i	0.879165	−	0.476517i	$-0.158101\pi$
$558$	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	$-0.311889\pi$
$563$	26.4404			1.11433			0.557164	+	0.830402i	$0.311889\pi$
$564$	11.1231	+	6.24621i	0.468367	+	0.263013i
$565$			4.87962i			0.205287i
$566$	14.3586			0.603536
$567$	15.8588	−	17.7623i	0.666006	−	0.745946i
$568$	9.36932			0.393128
$569$		−	15.7538i		−	0.660433i	−0.943905	−	0.330217i	$-0.892878\pi$
$569$		−	15.7538i		−	0.660433i	0.943905	−	0.330217i	$-0.107122\pi$
$570$	−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	$-0.492672\pi$
$587$	1.11550			0.0460417			0.0230209	+	0.999735i	$0.492672\pi$
$588$	6.37037	+	10.3159i	0.262709	+	0.425422i
$589$	−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	$-0.740845\pi$
$593$	−33.4337			−1.37296			−0.686479	+	0.727149i	$0.740845\pi$
$594$	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	$0.264072\pi$
$599$			36.1080i			1.47533i	−0.675166	+	0.737665i	$0.735928\pi$
$600$	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
$609$	6.34475	−	6.61393i	0.257102	−	0.268010i
$610$	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	$-0.856712\pi$
$617$		−	21.6155i		−	0.870208i	0.900380	−	0.435104i	$-0.143288\pi$
$618$	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
$630$	12.8831	−	3.90767i	0.513275	−	0.155685i
$631$	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	$-0.919753\pi$
$641$		−	12.6307i		−	0.498882i	0.968390	−	0.249441i	$-0.0802469\pi$
$642$	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	$-0.307834\pi$
$647$	28.8802			1.13540			0.567698	+	0.823237i	$0.307834\pi$
$648$	8.00000	+	4.12311i	0.314270	+	0.161971i
$649$		−	11.7100i		−	0.459656i
$650$	−9.22437			−0.361810
$651$	4.20120	−	4.37944i	0.164658	−	0.171644i
$652$	−16.0000			−0.626608
$653$			6.49242i			0.254068i	0.991898	+	0.127034i	$0.0405458\pi$
$653$			6.49242i			0.254068i	−0.991898	+	0.127034i	$0.959454\pi$
$654$	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	$0.0467129\pi$
$659$			7.50758i			0.292454i	−0.989251	+	0.146227i	$0.953287\pi$
$660$	−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
$672$	−3.17238	+	3.30697i	−0.122377	+	0.127569i
$673$	−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	$-0.414706\pi$
$677$	13.7779			0.529529			0.264764	+	0.964313i	$0.414706\pi$
$678$	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	$0.196428\pi$
$683$			30.2462i			1.15734i	−0.815562	+	0.578670i	$0.803572\pi$
$684$	−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
$693$	7.59554	−	2.30386i	0.288531	−	0.0875164i
$694$	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	$0.0742869\pi$
$701$			12.2462i			0.462533i	−0.972890	+	0.231267i	$0.925713\pi$
$702$	−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
$714$	−14.9628	+	15.5976i	−0.559969	+	0.583725i
$715$	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	$-0.496554\pi$
$719$	0.580639			0.0216542			0.0108271	+	0.999941i	$0.496554\pi$
$720$	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
$735$	−10.8050	−	17.4973i	−0.398550	−	0.645397i
$736$	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	$0.0168055\pi$
$743$			2.87689i			0.105543i	−0.998607	+	0.0527715i	$0.983195\pi$
$744$	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
$756$	2.96221	−	13.4248i	0.107735	−	0.488255i
$757$	−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	$-0.607531\pi$
$761$	−18.2857			−0.662857			−0.331428	+	0.943480i	$0.607531\pi$
$762$	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	$-0.249111\pi$
$773$	39.4289			1.41816			0.709079	+	0.705129i	$0.249111\pi$
$774$	−28.4924	+	17.3693i	−1.02414	+	0.624327i
$775$			2.81164i			0.100997i
$776$	6.04090			0.216856
$777$	27.2699	+	26.1601i	0.978304	+	0.938488i
$778$	−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	$-0.488081\pi$
$797$	2.11375			0.0748729			0.0374364	+	0.999299i	$0.488081\pi$
$798$	21.2067	+	20.3436i	0.750708	+	0.720156i
$799$	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	$-0.904930\pi$
$809$		−	16.7386i		−	0.588499i	0.955729	−	0.294250i	$-0.0950697\pi$
$810$	−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
$819$	−33.0008	+	10.0097i	−1.15314	+	0.349767i
$820$	12.4924			0.436254
$821$			13.5076i			0.471418i	0.971824	+	0.235709i	$0.0757412\pi$
$821$			13.5076i			0.471418i	−0.971824	+	0.235709i	$0.924259\pi$
$822$	−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	$-0.859978\pi$
$827$		−	24.4924i		−	0.851685i	0.904797	−	0.425842i	$-0.140022\pi$
$828$	−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	$-0.626503\pi$
$839$	−22.4217			−0.774082			−0.387041	+	0.922063i	$0.626503\pi$
$840$	5.38080	−	5.60908i	0.185655	−	0.193532i
$841$	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	$-0.900156\pi$
$857$	−55.6924			−1.90242			−0.951208	+	0.308552i	$0.900156\pi$
$858$	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
$861$	−24.3565	−	23.3652i	−0.830066	−	0.796284i
$862$	−29.6155			−1.00871
$863$			17.3693i			0.591258i	0.955303	+	0.295629i	$0.0955293\pi$
$863$			17.3693i			0.591258i	−0.955303	+	0.295629i	$0.904471\pi$
$864$	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	$-0.683998\pi$
$881$	−32.4355			−1.09278			−0.546390	+	0.837531i	$0.683998\pi$
$882$	−20.9819	+	0.872043i	−0.706497	+	0.0293632i
$883$	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	$-0.386618\pi$
$887$	20.7713			0.697432			0.348716	+	0.937228i	$0.386618\pi$
$888$	−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
$903$	36.7837	+	35.2867i	1.22409	+	1.17427i
$904$	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	$-0.900895\pi$
$911$		−	18.4924i		−	0.612681i	0.951922	−	0.306341i	$-0.0991047\pi$
$912$	−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
$924$	3.17238	−	3.30697i	0.104364	−	0.108791i
$925$	−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	$-0.746386\pi$
$929$	−42.6123			−1.39807			−0.699033	+	0.715090i	$0.746386\pi$
$930$	−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	$-0.582281\pi$
$941$	−15.6829			−0.511247			−0.255624	+	0.966776i	$0.582281\pi$
$942$	37.0540	+	20.8078i	1.20728	+	0.677954i
$943$			44.1912i			1.43906i
$944$	−11.7100			−0.381127
$945$	−5.02433	+	22.7704i	−0.163441	+	0.740720i
$946$	−11.1231			−0.361643
$947$		−	40.0000i		−	1.29983i	−0.760009	−	0.649913i	$-0.774805\pi$
$947$		−	40.0000i		−	1.29983i	0.760009	−	0.649913i	$-0.225195\pi$
$948$	−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	$-0.909227\pi$
$953$		−	17.3693i		−	0.562647i	0.959613	−	0.281324i	$-0.0907735\pi$
$954$	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
$966$	19.8418	+	19.0343i	0.638399	+	0.612417i
$967$	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	$-0.639464\pi$
$971$	−26.4404			−0.848512			−0.424256	+	0.905542i	$0.639464\pi$
$972$	−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	$0.0343787\pi$
$977$			6.73863i			0.215588i	−0.994173	+	0.107794i	$0.965621\pi$
$978$	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	$-0.283251\pi$
$983$	39.4746			1.25905			0.629523	+	0.776982i	$0.283251\pi$
$984$	6.24621	−	11.1231i	0.199122	−	0.354592i
$985$		−	24.5812i		−	0.783222i
$986$	9.43318			0.300414
$987$	24.3565	+	23.3652i	0.775275	+	0.743723i
$988$	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.419.5	yes	8
3.2	odd	2	inner	462.2.g.e.419.4	yes	8
7.6	odd	2	inner	462.2.g.e.419.8	yes	8
21.20	even	2	inner	462.2.g.e.419.1	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.g.e.419.1	✓	8	21.20	even	2	inner
462.2.g.e.419.4	yes	8	3.2	odd	2	inner
462.2.g.e.419.5	yes	8	1.1	even	1	trivial
462.2.g.e.419.8	yes	8	7.6	odd	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} +(3.30697 + 3.17238i) 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} +(-3.17238 + 3.30697i) 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} +(-2.30386 - 7.59554i) 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} +(-3.30697 - 3.17238i) 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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