LMFDB - Embedded newform 124.2.d.a.123.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [124,2,Mod(123,124)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(124, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("124.123");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 124 = 2^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	124.d (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:	$0.990144985064$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 9 $ x^4 + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			123.4
Root			$-1.22474 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	124.123
Dual form			124.2.d.a.123.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.00000i) q^{2} +2.44949 q^{3} -2.00000i q^{4} +1.00000 q^{5} +(-2.44949 + 2.44949i) q^{6} -3.00000i q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000 q^{9} +O(q^{10})$	\(q+(-1.00000 + 1.00000i) q^{2} +2.44949 q^{3} -2.00000i q^{4} +1.00000 q^{5} +(-2.44949 + 2.44949i) q^{6} -3.00000i q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000 q^{9} +(-1.00000 + 1.00000i) q^{10} -4.89898 q^{11} -4.89898i q^{12} +2.44949i q^{13} +(3.00000 + 3.00000i) q^{14} +2.44949 q^{15} -4.00000 q^{16} +7.34847i q^{17} +(-3.00000 + 3.00000i) q^{18} +1.00000i q^{19} -2.00000i q^{20} -7.34847i q^{21} +(4.89898 - 4.89898i) q^{22} +2.44949 q^{23} +(4.89898 + 4.89898i) q^{24} -4.00000 q^{25} +(-2.44949 - 2.44949i) q^{26} -6.00000 q^{28} -2.44949i q^{29} +(-2.44949 + 2.44949i) q^{30} +(-2.44949 - 5.00000i) q^{31} +(4.00000 - 4.00000i) q^{32} -12.0000 q^{33} +(-7.34847 - 7.34847i) q^{34} -3.00000i q^{35} -6.00000i q^{36} -4.89898i q^{37} +(-1.00000 - 1.00000i) q^{38} +6.00000i q^{39} +(2.00000 + 2.00000i) q^{40} +7.00000 q^{41} +(7.34847 + 7.34847i) q^{42} +2.44949 q^{43} +9.79796i q^{44} +3.00000 q^{45} +(-2.44949 + 2.44949i) q^{46} +2.00000i q^{47} -9.79796 q^{48} -2.00000 q^{49} +(4.00000 - 4.00000i) q^{50} +18.0000i q^{51} +4.89898 q^{52} -9.79796i q^{53} -4.89898 q^{55} +(6.00000 - 6.00000i) q^{56} +2.44949i q^{57} +(2.44949 + 2.44949i) q^{58} +11.0000i q^{59} -4.89898i q^{60} +12.2474i q^{61} +(7.44949 + 2.55051i) q^{62} -9.00000i q^{63} +8.00000i q^{64} +2.44949i q^{65} +(12.0000 - 12.0000i) q^{66} -8.00000i q^{67} +14.6969 q^{68} +6.00000 q^{69} +(3.00000 + 3.00000i) q^{70} -5.00000i q^{71} +(6.00000 + 6.00000i) q^{72} -9.79796i q^{73} +(4.89898 + 4.89898i) q^{74} -9.79796 q^{75} +2.00000 q^{76} +14.6969i q^{77} +(-6.00000 - 6.00000i) q^{78} +12.2474 q^{79} -4.00000 q^{80} -9.00000 q^{81} +(-7.00000 + 7.00000i) q^{82} -9.79796 q^{83} -14.6969 q^{84} +7.34847i q^{85} +(-2.44949 + 2.44949i) q^{86} -6.00000i q^{87} +(-9.79796 - 9.79796i) q^{88} -2.44949i q^{89} +(-3.00000 + 3.00000i) q^{90} +7.34847 q^{91} -4.89898i q^{92} +(-6.00000 - 12.2474i) q^{93} +(-2.00000 - 2.00000i) q^{94} +1.00000i q^{95} +(9.79796 - 9.79796i) q^{96} +13.0000 q^{97} +(2.00000 - 2.00000i) q^{98} -14.6969 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + 4 q^{5} + 8 q^{8} + 12 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 + 4 * q^5 + 8 * q^8 + 12 * q^9	$ 4 q - 4 q^{2} + 4 q^{5} + 8 q^{8} + 12 q^{9} - 4 q^{10} + 12 q^{14} - 16 q^{16} - 12 q^{18} - 16 q^{25} - 24 q^{28} + 16 q^{32} - 48 q^{33} - 4 q^{38} + 8 q^{40} + 28 q^{41} + 12 q^{45} - 8 q^{49} + 16 q^{50} + 24 q^{56} + 20 q^{62} + 48 q^{66} + 24 q^{69} + 12 q^{70} + 24 q^{72} + 8 q^{76} - 24 q^{78} - 16 q^{80} - 36 q^{81} - 28 q^{82} - 12 q^{90} - 24 q^{93} - 8 q^{94} + 52 q^{97} + 8 q^{98}+O(q^{100}) $ 4 * q - 4 * q^2 + 4 * q^5 + 8 * q^8 + 12 * q^9 - 4 * q^10 + 12 * q^14 - 16 * q^16 - 12 * q^18 - 16 * q^25 - 24 * q^28 + 16 * q^32 - 48 * q^33 - 4 * q^38 + 8 * q^40 + 28 * q^41 + 12 * q^45 - 8 * q^49 + 16 * q^50 + 24 * q^56 + 20 * q^62 + 48 * q^66 + 24 * q^69 + 12 * q^70 + 24 * q^72 + 8 * q^76 - 24 * q^78 - 16 * q^80 - 36 * q^81 - 28 * q^82 - 12 * q^90 - 24 * q^93 - 8 * q^94 + 52 * q^97 + 8 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/124\mathbb{Z}\right)^\times$.

$n$	$63$	$65$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−1.00000	+	1.00000i	−0.707107	+	0.707107i
$2$	−1.00000	+	1.00000i	−0.707107	+	0.707107i
$3$	2.44949			1.41421			0.707107	−	0.707107i	$-0.250000\pi$
$3$	2.44949			1.41421			0.707107	+	0.707107i	$0.250000\pi$
$4$		−	2.00000i		−	1.00000i
$5$	1.00000			0.447214			0.223607	−	0.974679i	$-0.428217\pi$
$5$	1.00000			0.447214			0.223607	+	0.974679i	$0.428217\pi$
$6$	−2.44949	+	2.44949i	−1.00000	+	1.00000i
$7$		−	3.00000i		−	1.13389i	−0.823754	−	0.566947i	$-0.808125\pi$
$7$		−	3.00000i		−	1.13389i	0.823754	−	0.566947i	$-0.191875\pi$
$8$	2.00000	+	2.00000i	0.707107	+	0.707107i
$9$	3.00000			1.00000
$10$	−1.00000	+	1.00000i	−0.316228	+	0.316228i
$11$	−4.89898			−1.47710			−0.738549	−	0.674200i	$-0.764489\pi$
$11$	−4.89898			−1.47710			−0.738549	+	0.674200i	$0.764489\pi$
$12$		−	4.89898i		−	1.41421i
$13$			2.44949i			0.679366i	0.940540	+	0.339683i	$0.110320\pi$
$13$			2.44949i			0.679366i	−0.940540	+	0.339683i	$0.889680\pi$
$14$	3.00000	+	3.00000i	0.801784	+	0.801784i
$15$	2.44949			0.632456
$16$	−4.00000			−1.00000
$17$			7.34847i			1.78227i	0.453743	+	0.891133i	$0.350089\pi$
$17$			7.34847i			1.78227i	−0.453743	+	0.891133i	$0.649911\pi$
$18$	−3.00000	+	3.00000i	−0.707107	+	0.707107i
$19$			1.00000i			0.229416i	0.993399	+	0.114708i	$0.0365932\pi$
$19$			1.00000i			0.229416i	−0.993399	+	0.114708i	$0.963407\pi$
$20$		−	2.00000i		−	0.447214i
$21$		−	7.34847i		−	1.60357i
$22$	4.89898	−	4.89898i	1.04447	−	1.04447i
$23$	2.44949			0.510754			0.255377	−	0.966842i	$-0.417800\pi$
$23$	2.44949			0.510754			0.255377	+	0.966842i	$0.417800\pi$
$24$	4.89898	+	4.89898i	1.00000	+	1.00000i
$25$	−4.00000			−0.800000
$26$	−2.44949	−	2.44949i	−0.480384	−	0.480384i
$27$		0			0
$28$	−6.00000			−1.13389
$29$		−	2.44949i		−	0.454859i	−0.973795	−	0.227429i	$-0.926968\pi$
$29$		−	2.44949i		−	0.454859i	0.973795	−	0.227429i	$-0.0730321\pi$
$30$	−2.44949	+	2.44949i	−0.447214	+	0.447214i
$31$	−2.44949	−	5.00000i	−0.439941	−	0.898027i
$31$	−2.44949	−	5.00000i	−0.439941	−	0.898027i
$32$	4.00000	−	4.00000i	0.707107	−	0.707107i
$33$	−12.0000			−2.08893
$34$	−7.34847	−	7.34847i	−1.26025	−	1.26025i
$35$		−	3.00000i		−	0.507093i
$36$		−	6.00000i		−	1.00000i
$37$		−	4.89898i		−	0.805387i	−0.915335	−	0.402694i	$-0.868074\pi$
$37$		−	4.89898i		−	0.805387i	0.915335	−	0.402694i	$-0.131926\pi$
$38$	−1.00000	−	1.00000i	−0.162221	−	0.162221i
$39$			6.00000i			0.960769i
$40$	2.00000	+	2.00000i	0.316228	+	0.316228i
$41$	7.00000			1.09322			0.546608	−	0.837389i	$-0.315919\pi$
$41$	7.00000			1.09322			0.546608	+	0.837389i	$0.315919\pi$
$42$	7.34847	+	7.34847i	1.13389	+	1.13389i
$43$	2.44949			0.373544			0.186772	−	0.982403i	$-0.440197\pi$
$43$	2.44949			0.373544			0.186772	+	0.982403i	$0.440197\pi$
$44$			9.79796i			1.47710i
$45$	3.00000			0.447214
$46$	−2.44949	+	2.44949i	−0.361158	+	0.361158i
$47$			2.00000i			0.291730i	0.989305	+	0.145865i	$0.0465965\pi$
$47$			2.00000i			0.291730i	−0.989305	+	0.145865i	$0.953403\pi$
$48$	−9.79796			−1.41421
$49$	−2.00000			−0.285714
$50$	4.00000	−	4.00000i	0.565685	−	0.565685i
$51$			18.0000i			2.52050i
$52$	4.89898			0.679366
$53$		−	9.79796i		−	1.34585i	−0.739709	−	0.672927i	$-0.765037\pi$
$53$		−	9.79796i		−	1.34585i	0.739709	−	0.672927i	$-0.234963\pi$
$54$		0			0
$55$	−4.89898			−0.660578
$56$	6.00000	−	6.00000i	0.801784	−	0.801784i
$57$			2.44949i			0.324443i
$58$	2.44949	+	2.44949i	0.321634	+	0.321634i
$59$			11.0000i			1.43208i	0.698060	+	0.716039i	$0.254047\pi$
$59$			11.0000i			1.43208i	−0.698060	+	0.716039i	$0.745953\pi$
$60$		−	4.89898i		−	0.632456i
$61$			12.2474i			1.56813i	0.620682	+	0.784063i	$0.286856\pi$
$61$			12.2474i			1.56813i	−0.620682	+	0.784063i	$0.713144\pi$
$62$	7.44949	+	2.55051i	0.946086	+	0.323915i
$63$		−	9.00000i		−	1.13389i
$64$			8.00000i			1.00000i
$65$			2.44949i			0.303822i
$66$	12.0000	−	12.0000i	1.47710	−	1.47710i
$67$		−	8.00000i		−	0.977356i	−0.872464	−	0.488678i	$-0.837479\pi$
$67$		−	8.00000i		−	0.977356i	0.872464	−	0.488678i	$-0.162521\pi$
$68$	14.6969			1.78227
$69$	6.00000			0.722315
$70$	3.00000	+	3.00000i	0.358569	+	0.358569i
$71$		−	5.00000i		−	0.593391i	−0.954972	−	0.296695i	$-0.904115\pi$
$71$		−	5.00000i		−	0.593391i	0.954972	−	0.296695i	$-0.0958846\pi$
$72$	6.00000	+	6.00000i	0.707107	+	0.707107i
$73$		−	9.79796i		−	1.14676i	−0.819288	−	0.573382i	$-0.805631\pi$
$73$		−	9.79796i		−	1.14676i	0.819288	−	0.573382i	$-0.194369\pi$
$74$	4.89898	+	4.89898i	0.569495	+	0.569495i
$75$	−9.79796			−1.13137
$76$	2.00000			0.229416
$77$			14.6969i			1.67487i
$78$	−6.00000	−	6.00000i	−0.679366	−	0.679366i
$79$	12.2474			1.37795			0.688973	−	0.724787i	$-0.258062\pi$
$79$	12.2474			1.37795			0.688973	+	0.724787i	$0.258062\pi$
$80$	−4.00000			−0.447214
$81$	−9.00000			−1.00000
$82$	−7.00000	+	7.00000i	−0.773021	+	0.773021i
$83$	−9.79796			−1.07547			−0.537733	−	0.843115i	$-0.680719\pi$
$83$	−9.79796			−1.07547			−0.537733	+	0.843115i	$0.680719\pi$
$84$	−14.6969			−1.60357
$85$			7.34847i			0.797053i
$86$	−2.44949	+	2.44949i	−0.264135	+	0.264135i
$87$		−	6.00000i		−	0.643268i
$88$	−9.79796	−	9.79796i	−1.04447	−	1.04447i
$89$		−	2.44949i		−	0.259645i	−0.991537	−	0.129823i	$-0.958559\pi$
$89$		−	2.44949i		−	0.259645i	0.991537	−	0.129823i	$-0.0414408\pi$
$90$	−3.00000	+	3.00000i	−0.316228	+	0.316228i
$91$	7.34847			0.770329
$92$		−	4.89898i		−	0.510754i
$93$	−6.00000	−	12.2474i	−0.622171	−	1.27000i
$94$	−2.00000	−	2.00000i	−0.206284	−	0.206284i
$95$			1.00000i			0.102598i
$96$	9.79796	−	9.79796i	1.00000	−	1.00000i
$97$	13.0000			1.31995			0.659975	−	0.751288i	$-0.270567\pi$
$97$	13.0000			1.31995			0.659975	+	0.751288i	$0.270567\pi$
$98$	2.00000	−	2.00000i	0.202031	−	0.202031i
$99$	−14.6969			−1.47710
$100$			8.00000i			0.800000i
$101$	−13.0000			−1.29355			−0.646774	−	0.762682i	$-0.723882\pi$
$101$	−13.0000			−1.29355			−0.646774	+	0.762682i	$0.723882\pi$
$102$	−18.0000	−	18.0000i	−1.78227	−	1.78227i
$103$		−	1.00000i		−	0.0985329i	−0.998786	−	0.0492665i	$-0.984312\pi$
$103$		−	1.00000i		−	0.0985329i	0.998786	−	0.0492665i	$-0.0156884\pi$
$104$	−4.89898	+	4.89898i	−0.480384	+	0.480384i
$105$		−	7.34847i		−	0.717137i
$106$	9.79796	+	9.79796i	0.951662	+	0.951662i
$107$			7.00000i			0.676716i	0.941018	+	0.338358i	$0.109871\pi$
$107$			7.00000i			0.676716i	−0.941018	+	0.338358i	$0.890129\pi$
$108$		0			0
$109$	5.00000			0.478913			0.239457	−	0.970907i	$-0.423031\pi$
$109$	5.00000			0.478913			0.239457	+	0.970907i	$0.423031\pi$
$110$	4.89898	−	4.89898i	0.467099	−	0.467099i
$111$		−	12.0000i		−	1.13899i
$112$			12.0000i			1.13389i
$113$	−1.00000			−0.0940721			−0.0470360	−	0.998893i	$-0.514978\pi$
$113$	−1.00000			−0.0940721			−0.0470360	+	0.998893i	$0.514978\pi$
$114$	−2.44949	−	2.44949i	−0.229416	−	0.229416i
$115$	2.44949			0.228416
$116$	−4.89898			−0.454859
$117$			7.34847i			0.679366i
$118$	−11.0000	−	11.0000i	−1.01263	−	1.01263i
$119$	22.0454			2.02090
$120$	4.89898	+	4.89898i	0.447214	+	0.447214i
$121$	13.0000			1.18182
$122$	−12.2474	−	12.2474i	−1.10883	−	1.10883i
$123$	17.1464			1.54604
$124$	−10.0000	+	4.89898i	−0.898027	+	0.439941i
$125$	−9.00000			−0.804984
$126$	9.00000	+	9.00000i	0.801784	+	0.801784i
$127$	4.89898			0.434714			0.217357	−	0.976092i	$-0.430256\pi$
$127$	4.89898			0.434714			0.217357	+	0.976092i	$0.430256\pi$
$128$	−8.00000	−	8.00000i	−0.707107	−	0.707107i
$129$	6.00000			0.528271
$130$	−2.44949	−	2.44949i	−0.214834	−	0.214834i
$131$			10.0000i			0.873704i	0.899533	+	0.436852i	$0.143907\pi$
$131$			10.0000i			0.873704i	−0.899533	+	0.436852i	$0.856093\pi$
$132$			24.0000i			2.08893i
$133$	3.00000			0.260133
$134$	8.00000	+	8.00000i	0.691095	+	0.691095i
$135$		0			0
$136$	−14.6969	+	14.6969i	−1.26025	+	1.26025i
$137$		−	17.1464i		−	1.46492i	−0.680811	−	0.732459i	$-0.738373\pi$
$137$		−	17.1464i		−	1.46492i	0.680811	−	0.732459i	$-0.261627\pi$
$138$	−6.00000	+	6.00000i	−0.510754	+	0.510754i
$139$		0			0			−	1.00000i	$-0.5\pi$
$139$		0			0				1.00000i	$0.5\pi$
$140$	−6.00000			−0.507093
$141$			4.89898i			0.412568i
$142$	5.00000	+	5.00000i	0.419591	+	0.419591i
$143$		−	12.0000i		−	1.00349i
$144$	−12.0000			−1.00000
$145$		−	2.44949i		−	0.203419i
$146$	9.79796	+	9.79796i	0.810885	+	0.810885i
$147$	−4.89898			−0.404061
$148$	−9.79796			−0.805387
$149$	20.0000			1.63846			0.819232	−	0.573462i	$-0.194400\pi$
$149$	20.0000			1.63846			0.819232	+	0.573462i	$0.194400\pi$
$150$	9.79796	−	9.79796i	0.800000	−	0.800000i
$151$	−17.1464			−1.39536			−0.697678	−	0.716411i	$-0.745783\pi$
$151$	−17.1464			−1.39536			−0.697678	+	0.716411i	$0.745783\pi$
$152$	−2.00000	+	2.00000i	−0.162221	+	0.162221i
$153$			22.0454i			1.78227i
$154$	−14.6969	−	14.6969i	−1.18431	−	1.18431i
$155$	−2.44949	−	5.00000i	−0.196748	−	0.401610i
$156$	12.0000			0.960769
$157$	3.00000			0.239426			0.119713	−	0.992809i	$-0.461803\pi$
$157$	3.00000			0.239426			0.119713	+	0.992809i	$0.461803\pi$
$158$	−12.2474	+	12.2474i	−0.974355	+	0.974355i
$159$		−	24.0000i		−	1.90332i
$160$	4.00000	−	4.00000i	0.316228	−	0.316228i
$161$		−	7.34847i		−	0.579141i
$162$	9.00000	−	9.00000i	0.707107	−	0.707107i
$163$			9.00000i			0.704934i	0.935824	+	0.352467i	$0.114657\pi$
$163$			9.00000i			0.704934i	−0.935824	+	0.352467i	$0.885343\pi$
$164$		−	14.0000i		−	1.09322i
$165$	−12.0000			−0.934199
$166$	9.79796	−	9.79796i	0.760469	−	0.760469i
$167$	−19.5959			−1.51638			−0.758189	−	0.652035i	$-0.773915\pi$
$167$	−19.5959			−1.51638			−0.758189	+	0.652035i	$0.773915\pi$
$168$	14.6969	−	14.6969i	1.13389	−	1.13389i
$169$	7.00000			0.538462
$170$	−7.34847	−	7.34847i	−0.563602	−	0.563602i
$171$			3.00000i			0.229416i
$172$		−	4.89898i		−	0.373544i
$173$	−16.0000			−1.21646			−0.608229	−	0.793762i	$-0.708120\pi$
$173$	−16.0000			−1.21646			−0.608229	+	0.793762i	$0.708120\pi$
$174$	6.00000	+	6.00000i	0.454859	+	0.454859i
$175$			12.0000i			0.907115i
$176$	19.5959			1.47710
$177$			26.9444i			2.02526i
$178$	2.44949	+	2.44949i	0.183597	+	0.183597i
$179$	12.2474			0.915417			0.457709	−	0.889102i	$-0.348670\pi$
$179$	12.2474			0.915417			0.457709	+	0.889102i	$0.348670\pi$
$180$		−	6.00000i		−	0.447214i
$181$			12.2474i			0.910346i	0.890403	+	0.455173i	$0.150423\pi$
$181$			12.2474i			0.910346i	−0.890403	+	0.455173i	$0.849577\pi$
$182$	−7.34847	+	7.34847i	−0.544705	+	0.544705i
$183$			30.0000i			2.21766i
$184$	4.89898	+	4.89898i	0.361158	+	0.361158i
$185$		−	4.89898i		−	0.360180i
$186$	18.2474	+	6.24745i	1.33797	+	0.458085i
$187$		−	36.0000i		−	2.63258i
$188$	4.00000			0.291730
$189$		0			0
$190$	−1.00000	−	1.00000i	−0.0725476	−	0.0725476i
$191$		−	5.00000i		−	0.361787i	−0.983503	−	0.180894i	$-0.942101\pi$
$191$		−	5.00000i		−	0.361787i	0.983503	−	0.180894i	$-0.0578990\pi$
$192$			19.5959i			1.41421i
$193$	9.00000			0.647834			0.323917	−	0.946085i	$-0.395000\pi$
$193$	9.00000			0.647834			0.323917	+	0.946085i	$0.395000\pi$
$194$	−13.0000	+	13.0000i	−0.933346	+	0.933346i
$195$			6.00000i			0.429669i
$196$			4.00000i			0.285714i
$197$		−	4.89898i		−	0.349038i	−0.984654	−	0.174519i	$-0.944163\pi$
$197$		−	4.89898i		−	0.349038i	0.984654	−	0.174519i	$-0.0558370\pi$
$198$	14.6969	−	14.6969i	1.04447	−	1.04447i
$199$		0			0			−	1.00000i	$-0.5\pi$
$199$		0			0				1.00000i	$0.5\pi$
$200$	−8.00000	−	8.00000i	−0.565685	−	0.565685i
$201$		−	19.5959i		−	1.38219i
$202$	13.0000	−	13.0000i	0.914677	−	0.914677i
$203$	−7.34847			−0.515761
$204$	36.0000			2.52050
$205$	7.00000			0.488901
$206$	1.00000	+	1.00000i	0.0696733	+	0.0696733i
$207$	7.34847			0.510754
$208$		−	9.79796i		−	0.679366i
$209$		−	4.89898i		−	0.338869i
$210$	7.34847	+	7.34847i	0.507093	+	0.507093i
$211$			15.0000i			1.03264i	0.856395	+	0.516321i	$0.172699\pi$
$211$			15.0000i			1.03264i	−0.856395	+	0.516321i	$0.827301\pi$
$212$	−19.5959			−1.34585
$213$		−	12.2474i		−	0.839181i
$214$	−7.00000	−	7.00000i	−0.478510	−	0.478510i
$215$	2.44949			0.167054
$216$		0			0
$217$	−15.0000	+	7.34847i	−1.01827	+	0.498847i
$218$	−5.00000	+	5.00000i	−0.338643	+	0.338643i
$219$		−	24.0000i		−	1.62177i
$220$			9.79796i			0.660578i
$221$	−18.0000			−1.21081
$222$	12.0000	+	12.0000i	0.805387	+	0.805387i
$223$	14.6969			0.984180			0.492090	−	0.870544i	$-0.336233\pi$
$223$	14.6969			0.984180			0.492090	+	0.870544i	$0.336233\pi$
$224$	−12.0000	−	12.0000i	−0.801784	−	0.801784i
$225$	−12.0000			−0.800000
$226$	1.00000	−	1.00000i	0.0665190	−	0.0665190i
$227$			22.0000i			1.46019i	0.683345	+	0.730096i	$0.260525\pi$
$227$			22.0000i			1.46019i	−0.683345	+	0.730096i	$0.739475\pi$
$228$	4.89898			0.324443
$229$			9.79796i			0.647467i	0.946148	+	0.323734i	$0.104938\pi$
$229$			9.79796i			0.647467i	−0.946148	+	0.323734i	$0.895062\pi$
$230$	−2.44949	+	2.44949i	−0.161515	+	0.161515i
$231$			36.0000i			2.36863i
$232$	4.89898	−	4.89898i	0.321634	−	0.321634i
$233$	−1.00000			−0.0655122			−0.0327561	−	0.999463i	$-0.510428\pi$
$233$	−1.00000			−0.0655122			−0.0327561	+	0.999463i	$0.510428\pi$
$234$	−7.34847	−	7.34847i	−0.480384	−	0.480384i
$235$			2.00000i			0.130466i
$236$	22.0000			1.43208
$237$	30.0000			1.94871
$238$	−22.0454	+	22.0454i	−1.42899	+	1.42899i
$239$	−12.2474			−0.792222			−0.396111	−	0.918203i	$-0.629640\pi$
$239$	−12.2474			−0.792222			−0.396111	+	0.918203i	$0.629640\pi$
$240$	−9.79796			−0.632456
$241$		−	24.4949i		−	1.57786i	−0.614486	−	0.788928i	$-0.710637\pi$
$241$		−	24.4949i		−	1.57786i	0.614486	−	0.788928i	$-0.289363\pi$
$242$	−13.0000	+	13.0000i	−0.835672	+	0.835672i
$243$	−22.0454			−1.41421
$244$	24.4949			1.56813
$245$	−2.00000			−0.127775
$246$	−17.1464	+	17.1464i	−1.09322	+	1.09322i
$247$	−2.44949			−0.155857
$248$	5.10102	−	14.8990i	0.323915	−	0.946086i
$249$	−24.0000			−1.52094
$250$	9.00000	−	9.00000i	0.569210	−	0.569210i
$251$	7.34847			0.463831			0.231916	−	0.972736i	$-0.425501\pi$
$251$	7.34847			0.463831			0.231916	+	0.972736i	$0.425501\pi$
$252$	−18.0000			−1.13389
$253$	−12.0000			−0.754434
$254$	−4.89898	+	4.89898i	−0.307389	+	0.307389i
$255$			18.0000i			1.12720i
$256$	16.0000			1.00000
$257$	13.0000			0.810918			0.405459	−	0.914113i	$-0.367112\pi$
$257$	13.0000			0.810918			0.405459	+	0.914113i	$0.367112\pi$
$258$	−6.00000	+	6.00000i	−0.373544	+	0.373544i
$259$	−14.6969			−0.913223
$260$	4.89898			0.303822
$261$		−	7.34847i		−	0.454859i
$262$	−10.0000	−	10.0000i	−0.617802	−	0.617802i
$263$	2.44949			0.151042			0.0755210	−	0.997144i	$-0.475938\pi$
$263$	2.44949			0.151042			0.0755210	+	0.997144i	$0.475938\pi$
$264$	−24.0000	−	24.0000i	−1.47710	−	1.47710i
$265$		−	9.79796i		−	0.601884i
$266$	−3.00000	+	3.00000i	−0.183942	+	0.183942i
$267$		−	6.00000i		−	0.367194i
$268$	−16.0000			−0.977356
$269$			9.79796i			0.597392i	0.954348	+	0.298696i	$0.0965517\pi$
$269$			9.79796i			0.597392i	−0.954348	+	0.298696i	$0.903448\pi$
$270$		0			0
$271$	7.34847			0.446388			0.223194	−	0.974774i	$-0.428352\pi$
$271$	7.34847			0.446388			0.223194	+	0.974774i	$0.428352\pi$
$272$		−	29.3939i		−	1.78227i
$273$	18.0000			1.08941
$274$	17.1464	+	17.1464i	1.03585	+	1.03585i
$275$	19.5959			1.18168
$276$		−	12.0000i		−	0.722315i
$277$		−	17.1464i		−	1.03023i	−0.857121	−	0.515115i	$-0.827749\pi$
$277$		−	17.1464i		−	1.03023i	0.857121	−	0.515115i	$-0.172251\pi$
$278$		0			0
$279$	−7.34847	−	15.0000i	−0.439941	−	0.898027i
$280$	6.00000	−	6.00000i	0.358569	−	0.358569i
$281$	−13.0000			−0.775515			−0.387757	−	0.921761i	$-0.626750\pi$
$281$	−13.0000			−0.775515			−0.387757	+	0.921761i	$0.626750\pi$
$282$	−4.89898	−	4.89898i	−0.291730	−	0.291730i
$283$		−	6.00000i		−	0.356663i	−0.983970	−	0.178331i	$-0.942930\pi$
$283$		−	6.00000i		−	0.356663i	0.983970	−	0.178331i	$-0.0570699\pi$
$284$	−10.0000			−0.593391
$285$			2.44949i			0.145095i
$286$	12.0000	+	12.0000i	0.709575	+	0.709575i
$287$		−	21.0000i		−	1.23959i
$288$	12.0000	−	12.0000i	0.707107	−	0.707107i
$289$	−37.0000			−2.17647
$290$	2.44949	+	2.44949i	0.143839	+	0.143839i
$291$	31.8434			1.86669
$292$	−19.5959			−1.14676
$293$	4.00000			0.233682			0.116841	−	0.993151i	$-0.462723\pi$
$293$	4.00000			0.233682			0.116841	+	0.993151i	$0.462723\pi$
$294$	4.89898	−	4.89898i	0.285714	−	0.285714i
$295$			11.0000i			0.640445i
$296$	9.79796	−	9.79796i	0.569495	−	0.569495i
$297$		0			0
$298$	−20.0000	+	20.0000i	−1.15857	+	1.15857i
$299$			6.00000i			0.346989i
$300$			19.5959i			1.13137i
$301$		−	7.34847i		−	0.423559i
$302$	17.1464	−	17.1464i	0.986666	−	0.986666i
$303$	−31.8434			−1.82935
$304$		−	4.00000i		−	0.229416i
$305$			12.2474i			0.701287i
$306$	−22.0454	−	22.0454i	−1.26025	−	1.26025i
$307$		−	13.0000i		−	0.741949i	−0.928643	−	0.370975i	$-0.879024\pi$
$307$		−	13.0000i		−	0.741949i	0.928643	−	0.370975i	$-0.120976\pi$
$308$	29.3939			1.67487
$309$		−	2.44949i		−	0.139347i
$310$	7.44949	+	2.55051i	0.423103	+	0.144859i
$311$			5.00000i			0.283524i	0.989901	+	0.141762i	$0.0452768\pi$
$311$			5.00000i			0.283524i	−0.989901	+	0.141762i	$0.954723\pi$
$312$	−12.0000	+	12.0000i	−0.679366	+	0.679366i
$313$			26.9444i			1.52299i	0.648173	+	0.761493i	$0.275534\pi$
$313$			26.9444i			1.52299i	−0.648173	+	0.761493i	$0.724466\pi$
$314$	−3.00000	+	3.00000i	−0.169300	+	0.169300i
$315$		−	9.00000i		−	0.507093i
$316$		−	24.4949i		−	1.37795i
$317$	−17.0000			−0.954815			−0.477408	−	0.878682i	$-0.658423\pi$
$317$	−17.0000			−0.954815			−0.477408	+	0.878682i	$0.658423\pi$
$318$	24.0000	+	24.0000i	1.34585	+	1.34585i
$319$			12.0000i			0.671871i
$320$			8.00000i			0.447214i
$321$			17.1464i			0.957020i
$322$	7.34847	+	7.34847i	0.409514	+	0.409514i
$323$	−7.34847			−0.408880
$324$			18.0000i			1.00000i
$325$		−	9.79796i		−	0.543493i
$326$	−9.00000	−	9.00000i	−0.498464	−	0.498464i
$327$	12.2474			0.677285
$328$	14.0000	+	14.0000i	0.773021	+	0.773021i
$329$	6.00000			0.330791
$330$	12.0000	−	12.0000i	0.660578	−	0.660578i
$331$	−4.89898			−0.269272			−0.134636	−	0.990895i	$-0.542987\pi$
$331$	−4.89898			−0.269272			−0.134636	+	0.990895i	$0.542987\pi$
$332$			19.5959i			1.07547i
$333$		−	14.6969i		−	0.805387i
$334$	19.5959	−	19.5959i	1.07224	−	1.07224i
$335$		−	8.00000i		−	0.437087i
$336$			29.3939i			1.60357i
$337$			7.34847i			0.400297i	0.979766	+	0.200148i	$0.0641424\pi$
$337$			7.34847i			0.400297i	−0.979766	+	0.200148i	$0.935858\pi$
$338$	−7.00000	+	7.00000i	−0.380750	+	0.380750i
$339$	−2.44949			−0.133038
$340$	14.6969			0.797053
$341$	12.0000	+	24.4949i	0.649836	+	1.32647i
$342$	−3.00000	−	3.00000i	−0.162221	−	0.162221i
$343$		−	15.0000i		−	0.809924i
$344$	4.89898	+	4.89898i	0.264135	+	0.264135i
$345$	6.00000			0.323029
$346$	16.0000	−	16.0000i	0.860165	−	0.860165i
$347$	−7.34847			−0.394486			−0.197243	−	0.980355i	$-0.563199\pi$
$347$	−7.34847			−0.394486			−0.197243	+	0.980355i	$0.563199\pi$
$348$	−12.0000			−0.643268
$349$		0			0			−	1.00000i	$-0.5\pi$
$349$		0			0				1.00000i	$0.5\pi$
$350$	−12.0000	−	12.0000i	−0.641427	−	0.641427i
$351$		0			0
$352$	−19.5959	+	19.5959i	−1.04447	+	1.04447i
$353$			14.6969i			0.782239i	0.920340	+	0.391120i	$0.127912\pi$
$353$			14.6969i			0.782239i	−0.920340	+	0.391120i	$0.872088\pi$
$354$	−26.9444	−	26.9444i	−1.43208	−	1.43208i
$355$		−	5.00000i		−	0.265372i
$356$	−4.89898			−0.259645
$357$	54.0000			2.85798
$358$	−12.2474	+	12.2474i	−0.647298	+	0.647298i
$359$		−	29.0000i		−	1.53056i	−0.643697	−	0.765281i	$-0.722600\pi$
$359$		−	29.0000i		−	1.53056i	0.643697	−	0.765281i	$-0.277400\pi$
$360$	6.00000	+	6.00000i	0.316228	+	0.316228i
$361$	18.0000			0.947368
$362$	−12.2474	−	12.2474i	−0.643712	−	0.643712i
$363$	31.8434			1.67134
$364$		−	14.6969i		−	0.770329i
$365$		−	9.79796i		−	0.512849i
$366$	−30.0000	−	30.0000i	−1.56813	−	1.56813i
$367$	4.89898			0.255725			0.127862	−	0.991792i	$-0.459188\pi$
$367$	4.89898			0.255725			0.127862	+	0.991792i	$0.459188\pi$
$368$	−9.79796			−0.510754
$369$	21.0000			1.09322
$370$	4.89898	+	4.89898i	0.254686	+	0.254686i
$371$	−29.3939			−1.52605
$372$	−24.4949	+	12.0000i	−1.27000	+	0.622171i
$373$	19.0000			0.983783			0.491891	−	0.870657i	$-0.336306\pi$
$373$	19.0000			0.983783			0.491891	+	0.870657i	$0.336306\pi$
$374$	36.0000	+	36.0000i	1.86152	+	1.86152i
$375$	−22.0454			−1.13842
$376$	−4.00000	+	4.00000i	−0.206284	+	0.206284i
$377$	6.00000			0.309016
$378$		0			0
$379$			6.00000i			0.308199i	0.988055	+	0.154100i	$0.0492477\pi$
$379$			6.00000i			0.308199i	−0.988055	+	0.154100i	$0.950752\pi$
$380$	2.00000			0.102598
$381$	12.0000			0.614779
$382$	5.00000	+	5.00000i	0.255822	+	0.255822i
$383$	14.6969			0.750978			0.375489	−	0.926827i	$-0.377475\pi$
$383$	14.6969			0.750978			0.375489	+	0.926827i	$0.377475\pi$
$384$	−19.5959	−	19.5959i	−1.00000	−	1.00000i
$385$			14.6969i			0.749025i
$386$	−9.00000	+	9.00000i	−0.458088	+	0.458088i
$387$	7.34847			0.373544
$388$		−	26.0000i		−	1.31995i
$389$		−	14.6969i		−	0.745164i	−0.927999	−	0.372582i	$-0.878472\pi$
$389$		−	14.6969i		−	0.745164i	0.927999	−	0.372582i	$-0.121528\pi$
$390$	−6.00000	−	6.00000i	−0.303822	−	0.303822i
$391$			18.0000i			0.910299i
$392$	−4.00000	−	4.00000i	−0.202031	−	0.202031i
$393$			24.4949i			1.23560i
$394$	4.89898	+	4.89898i	0.246807	+	0.246807i
$395$	12.2474			0.616236
$396$			29.3939i			1.47710i
$397$	−17.0000			−0.853206			−0.426603	−	0.904439i	$-0.640290\pi$
$397$	−17.0000			−0.853206			−0.426603	+	0.904439i	$0.640290\pi$
$398$		0			0
$399$	7.34847			0.367884
$400$	16.0000			0.800000
$401$		−	12.2474i		−	0.611608i	−0.952094	−	0.305804i	$-0.901075\pi$
$401$		−	12.2474i		−	0.611608i	0.952094	−	0.305804i	$-0.0989253\pi$
$402$	19.5959	+	19.5959i	0.977356	+	0.977356i
$403$	12.2474	−	6.00000i	0.610089	−	0.298881i
$404$			26.0000i			1.29355i
$405$	−9.00000			−0.447214
$406$	7.34847	−	7.34847i	0.364698	−	0.364698i
$407$			24.0000i			1.18964i
$408$	−36.0000	+	36.0000i	−1.78227	+	1.78227i
$409$			22.0454i			1.09008i	0.838412	+	0.545038i	$0.183485\pi$
$409$			22.0454i			1.09008i	−0.838412	+	0.545038i	$0.816515\pi$
$410$	−7.00000	+	7.00000i	−0.345705	+	0.345705i
$411$		−	42.0000i		−	2.07171i
$412$	−2.00000			−0.0985329
$413$	33.0000			1.62382
$414$	−7.34847	+	7.34847i	−0.361158	+	0.361158i
$415$	−9.79796			−0.480963
$416$	9.79796	+	9.79796i	0.480384	+	0.480384i
$417$		0			0
$418$	4.89898	+	4.89898i	0.239617	+	0.239617i
$419$			1.00000i			0.0488532i	0.999702	+	0.0244266i	$0.00777600\pi$
$419$			1.00000i			0.0488532i	−0.999702	+	0.0244266i	$0.992224\pi$
$420$	−14.6969			−0.717137
$421$	−33.0000			−1.60832			−0.804161	−	0.594412i	$-0.797385\pi$
$421$	−33.0000			−1.60832			−0.804161	+	0.594412i	$0.797385\pi$
$422$	−15.0000	−	15.0000i	−0.730189	−	0.730189i
$423$			6.00000i			0.291730i
$424$	19.5959	−	19.5959i	0.951662	−	0.951662i
$425$		−	29.3939i		−	1.42581i
$426$	12.2474	+	12.2474i	0.593391	+	0.593391i
$427$	36.7423			1.77809
$428$	14.0000			0.676716
$429$		−	29.3939i		−	1.41915i
$430$	−2.44949	+	2.44949i	−0.118125	+	0.118125i
$431$			20.0000i			0.963366i	0.876346	+	0.481683i	$0.159974\pi$
$431$			20.0000i			0.963366i	−0.876346	+	0.481683i	$0.840026\pi$
$432$		0			0
$433$		−	22.0454i		−	1.05943i	−0.848174	−	0.529717i	$-0.822298\pi$
$433$		−	22.0454i		−	1.05943i	0.848174	−	0.529717i	$-0.177702\pi$
$434$	7.65153	−	22.3485i	0.367285	−	1.07276i
$435$		−	6.00000i		−	0.287678i
$436$		−	10.0000i		−	0.478913i
$437$			2.44949i			0.117175i
$438$	24.0000	+	24.0000i	1.14676	+	1.14676i
$439$			31.0000i			1.47955i	0.672855	+	0.739775i	$0.265068\pi$
$439$			31.0000i			1.47955i	−0.672855	+	0.739775i	$0.734932\pi$
$440$	−9.79796	−	9.79796i	−0.467099	−	0.467099i
$441$	−6.00000			−0.285714
$442$	18.0000	−	18.0000i	0.856173	−	0.856173i
$443$		−	11.0000i		−	0.522626i	−0.965254	−	0.261313i	$-0.915845\pi$
$443$		−	11.0000i		−	0.522626i	0.965254	−	0.261313i	$-0.0841554\pi$
$444$	−24.0000			−1.13899
$445$		−	2.44949i		−	0.116117i
$446$	−14.6969	+	14.6969i	−0.695920	+	0.695920i
$447$	48.9898			2.31714
$448$	24.0000			1.13389
$449$			9.79796i			0.462394i	0.972907	+	0.231197i	$0.0742642\pi$
$449$			9.79796i			0.462394i	−0.972907	+	0.231197i	$0.925736\pi$
$450$	12.0000	−	12.0000i	0.565685	−	0.565685i
$451$	−34.2929			−1.61479
$452$			2.00000i			0.0940721i
$453$	−42.0000			−1.97333
$454$	−22.0000	−	22.0000i	−1.03251	−	1.03251i
$455$	7.34847			0.344502
$456$	−4.89898	+	4.89898i	−0.229416	+	0.229416i
$457$		−	4.89898i		−	0.229165i	−0.993414	−	0.114582i	$-0.963447\pi$
$457$		−	4.89898i		−	0.229165i	0.993414	−	0.114582i	$-0.0365530\pi$
$458$	−9.79796	−	9.79796i	−0.457829	−	0.457829i
$459$		0			0
$460$		−	4.89898i		−	0.228416i
$461$			24.4949i			1.14084i	0.821353	+	0.570421i	$0.193220\pi$
$461$			24.4949i			1.14084i	−0.821353	+	0.570421i	$0.806780\pi$
$462$	−36.0000	−	36.0000i	−1.67487	−	1.67487i
$463$	−34.2929			−1.59372			−0.796862	−	0.604161i	$-0.793508\pi$
$463$	−34.2929			−1.59372			−0.796862	+	0.604161i	$0.793508\pi$
$464$			9.79796i			0.454859i
$465$	−6.00000	−	12.2474i	−0.278243	−	0.567962i
$466$	1.00000	−	1.00000i	0.0463241	−	0.0463241i
$467$		−	13.0000i		−	0.601568i	−0.953692	−	0.300784i	$-0.902752\pi$
$467$		−	13.0000i		−	0.601568i	0.953692	−	0.300784i	$-0.0972484\pi$
$468$	14.6969			0.679366
$469$	−24.0000			−1.10822
$470$	−2.00000	−	2.00000i	−0.0922531	−	0.0922531i
$471$	7.34847			0.338600
$472$	−22.0000	+	22.0000i	−1.01263	+	1.01263i
$473$	−12.0000			−0.551761
$474$	−30.0000	+	30.0000i	−1.37795	+	1.37795i
$475$		−	4.00000i		−	0.183533i
$476$		−	44.0908i		−	2.02090i
$477$		−	29.3939i		−	1.34585i
$478$	12.2474	−	12.2474i	0.560185	−	0.560185i
$479$			11.0000i			0.502603i	0.967909	+	0.251301i	$0.0808585\pi$
$479$			11.0000i			0.502603i	−0.967909	+	0.251301i	$0.919141\pi$
$480$	9.79796	−	9.79796i	0.447214	−	0.447214i
$481$	12.0000			0.547153
$482$	24.4949	+	24.4949i	1.11571	+	1.11571i
$483$		−	18.0000i		−	0.819028i
$484$		−	26.0000i		−	1.18182i
$485$	13.0000			0.590300
$486$	22.0454	−	22.0454i	1.00000	−	1.00000i
$487$	−31.8434			−1.44296			−0.721480	−	0.692435i	$-0.756538\pi$
$487$	−31.8434			−1.44296			−0.721480	+	0.692435i	$0.756538\pi$
$488$	−24.4949	+	24.4949i	−1.10883	+	1.10883i
$489$			22.0454i			0.996928i
$490$	2.00000	−	2.00000i	0.0903508	−	0.0903508i
$491$	−29.3939			−1.32653			−0.663264	−	0.748386i	$-0.730829\pi$
$491$	−29.3939			−1.32653			−0.663264	+	0.748386i	$0.730829\pi$
$492$		−	34.2929i		−	1.54604i
$493$	18.0000			0.810679
$494$	2.44949	−	2.44949i	0.110208	−	0.110208i
$495$	−14.6969			−0.660578
$496$	9.79796	+	20.0000i	0.439941	+	0.898027i
$497$	−15.0000			−0.672842
$498$	24.0000	−	24.0000i	1.07547	−	1.07547i
$499$		0			0			−	1.00000i	$-0.5\pi$
$499$		0			0				1.00000i	$0.5\pi$
$500$			18.0000i			0.804984i
$501$	−48.0000			−2.14448
$502$	−7.34847	+	7.34847i	−0.327978	+	0.327978i
$503$		−	11.0000i		−	0.490466i	−0.969464	−	0.245233i	$-0.921136\pi$
$503$		−	11.0000i		−	0.490466i	0.969464	−	0.245233i	$-0.0788644\pi$
$504$	18.0000	−	18.0000i	0.801784	−	0.801784i
$505$	−13.0000			−0.578492
$506$	12.0000	−	12.0000i	0.533465	−	0.533465i
$507$	17.1464			0.761500
$508$		−	9.79796i		−	0.434714i
$509$			22.0454i			0.977146i	0.872523	+	0.488573i	$0.162482\pi$
$509$			22.0454i			0.977146i	−0.872523	+	0.488573i	$0.837518\pi$
$510$	−18.0000	−	18.0000i	−0.797053	−	0.797053i
$511$	−29.3939			−1.30031
$512$	−16.0000	+	16.0000i	−0.707107	+	0.707107i
$513$		0			0
$514$	−13.0000	+	13.0000i	−0.573405	+	0.573405i
$515$		−	1.00000i		−	0.0440653i
$516$		−	12.0000i		−	0.528271i
$517$		−	9.79796i		−	0.430914i
$518$	14.6969	−	14.6969i	0.645746	−	0.645746i
$519$	−39.1918			−1.72033
$520$	−4.89898	+	4.89898i	−0.214834	+	0.214834i
$521$	−8.00000			−0.350486			−0.175243	−	0.984525i	$-0.556071\pi$
$521$	−8.00000			−0.350486			−0.175243	+	0.984525i	$0.556071\pi$
$522$	7.34847	+	7.34847i	0.321634	+	0.321634i
$523$	2.44949			0.107109			0.0535544	−	0.998565i	$-0.482945\pi$
$523$	2.44949			0.107109			0.0535544	+	0.998565i	$0.482945\pi$
$524$	20.0000			0.873704
$525$			29.3939i			1.28285i
$526$	−2.44949	+	2.44949i	−0.106803	+	0.106803i
$527$	36.7423	−	18.0000i	1.60052	−	0.784092i
$528$	48.0000			2.08893
$529$	−17.0000			−0.739130
$530$	9.79796	+	9.79796i	0.425596	+	0.425596i
$531$			33.0000i			1.43208i
$532$		−	6.00000i		−	0.260133i
$533$			17.1464i			0.742694i
$534$	6.00000	+	6.00000i	0.259645	+	0.259645i
$535$			7.00000i			0.302636i
$536$	16.0000	−	16.0000i	0.691095	−	0.691095i
$537$	30.0000			1.29460
$538$	−9.79796	−	9.79796i	−0.422420	−	0.422420i
$539$	9.79796			0.422028
$540$		0			0
$541$	−3.00000			−0.128980			−0.0644900	−	0.997918i	$-0.520542\pi$
$541$	−3.00000			−0.128980			−0.0644900	+	0.997918i	$0.520542\pi$
$542$	−7.34847	+	7.34847i	−0.315644	+	0.315644i
$543$			30.0000i			1.28742i
$544$	29.3939	+	29.3939i	1.26025	+	1.26025i
$545$	5.00000			0.214176
$546$	−18.0000	+	18.0000i	−0.770329	+	0.770329i
$547$			37.0000i			1.58201i	0.611812	+	0.791003i	$0.290441\pi$
$547$			37.0000i			1.58201i	−0.611812	+	0.791003i	$0.709559\pi$
$548$	−34.2929			−1.46492
$549$			36.7423i			1.56813i
$550$	−19.5959	+	19.5959i	−0.835573	+	0.835573i
$551$	2.44949			0.104352
$552$	12.0000	+	12.0000i	0.510754	+	0.510754i
$553$		−	36.7423i		−	1.56244i
$554$	17.1464	+	17.1464i	0.728482	+	0.728482i
$555$		−	12.0000i		−	0.509372i
$556$		0			0
$557$		−	29.3939i		−	1.24546i	−0.782437	−	0.622729i	$-0.786024\pi$
$557$		−	29.3939i		−	1.24546i	0.782437	−	0.622729i	$-0.213976\pi$
$558$	22.3485	+	7.65153i	0.946086	+	0.323915i
$559$			6.00000i			0.253773i
$560$			12.0000i			0.507093i
$561$		−	88.1816i		−	3.72303i
$562$	13.0000	−	13.0000i	0.548372	−	0.548372i
$563$		−	11.0000i		−	0.463595i	−0.972764	−	0.231797i	$-0.925539\pi$
$563$		−	11.0000i		−	0.463595i	0.972764	−	0.231797i	$-0.0744606\pi$
$564$	9.79796			0.412568
$565$	−1.00000			−0.0420703
$566$	6.00000	+	6.00000i	0.252199	+	0.252199i
$567$			27.0000i			1.13389i
$568$	10.0000	−	10.0000i	0.419591	−	0.419591i
$569$			9.79796i			0.410752i	0.978683	+	0.205376i	$0.0658417\pi$
$569$			9.79796i			0.410752i	−0.978683	+	0.205376i	$0.934158\pi$
$570$	−2.44949	−	2.44949i	−0.102598	−	0.102598i
$571$	−17.1464			−0.717556			−0.358778	−	0.933423i	$-0.616806\pi$
$571$	−17.1464			−0.717556			−0.358778	+	0.933423i	$0.616806\pi$
$572$	−24.0000			−1.00349
$573$		−	12.2474i		−	0.511645i
$574$	21.0000	+	21.0000i	0.876523	+	0.876523i
$575$	−9.79796			−0.408603
$576$			24.0000i			1.00000i
$577$	−12.0000			−0.499567			−0.249783	−	0.968302i	$-0.580359\pi$
$577$	−12.0000			−0.499567			−0.249783	+	0.968302i	$0.580359\pi$
$578$	37.0000	−	37.0000i	1.53900	−	1.53900i
$579$	22.0454			0.916176
$580$	−4.89898			−0.203419
$581$			29.3939i			1.21946i
$582$	−31.8434	+	31.8434i	−1.31995	+	1.31995i
$583$			48.0000i			1.98796i
$584$	19.5959	−	19.5959i	0.810885	−	0.810885i
$585$			7.34847i			0.303822i
$586$	−4.00000	+	4.00000i	−0.165238	+	0.165238i
$587$	4.89898			0.202203			0.101101	−	0.994876i	$-0.467763\pi$
$587$	4.89898			0.202203			0.101101	+	0.994876i	$0.467763\pi$
$588$			9.79796i			0.404061i
$589$	5.00000	−	2.44949i	0.206021	−	0.100929i
$590$	−11.0000	−	11.0000i	−0.452863	−	0.452863i
$591$		−	12.0000i		−	0.493614i
$592$			19.5959i			0.805387i
$593$	29.0000			1.19089			0.595444	−	0.803397i	$-0.296976\pi$
$593$	29.0000			1.19089			0.595444	+	0.803397i	$0.296976\pi$
$594$		0			0
$595$	22.0454			0.903774
$596$		−	40.0000i		−	1.63846i
$597$		0			0
$598$	−6.00000	−	6.00000i	−0.245358	−	0.245358i
$599$		−	19.0000i		−	0.776319i	−0.921592	−	0.388159i	$-0.873111\pi$
$599$		−	19.0000i		−	0.776319i	0.921592	−	0.388159i	$-0.126889\pi$
$600$	−19.5959	−	19.5959i	−0.800000	−	0.800000i
$601$			12.2474i			0.499584i	0.968300	+	0.249792i	$0.0803622\pi$
$601$			12.2474i			0.499584i	−0.968300	+	0.249792i	$0.919638\pi$
$602$	7.34847	+	7.34847i	0.299501	+	0.299501i
$603$		−	24.0000i		−	0.977356i
$604$			34.2929i			1.39536i
$605$	13.0000			0.528525
$606$	31.8434	−	31.8434i	1.29355	−	1.29355i
$607$			2.00000i			0.0811775i	0.999176	+	0.0405887i	$0.0129233\pi$
$607$			2.00000i			0.0811775i	−0.999176	+	0.0405887i	$0.987077\pi$
$608$	4.00000	+	4.00000i	0.162221	+	0.162221i
$609$	−18.0000			−0.729397
$610$	−12.2474	−	12.2474i	−0.495885	−	0.495885i
$611$	−4.89898			−0.198191
$612$	44.0908			1.78227
$613$			39.1918i			1.58294i	0.611206	+	0.791472i	$0.290685\pi$
$613$			39.1918i			1.58294i	−0.611206	+	0.791472i	$0.709315\pi$
$614$	13.0000	+	13.0000i	0.524637	+	0.524637i
$615$	17.1464			0.691411
$616$	−29.3939	+	29.3939i	−1.18431	+	1.18431i
$617$	8.00000			0.322068			0.161034	−	0.986949i	$-0.448517\pi$
$617$	8.00000			0.322068			0.161034	+	0.986949i	$0.448517\pi$
$618$	2.44949	+	2.44949i	0.0985329	+	0.0985329i
$619$	12.2474			0.492267			0.246133	−	0.969236i	$-0.420840\pi$
$619$	12.2474			0.492267			0.246133	+	0.969236i	$0.420840\pi$
$620$	−10.0000	+	4.89898i	−0.401610	+	0.196748i
$621$		0			0
$622$	−5.00000	−	5.00000i	−0.200482	−	0.200482i
$623$	−7.34847			−0.294410
$624$		−	24.0000i		−	0.960769i
$625$	11.0000			0.440000
$626$	−26.9444	−	26.9444i	−1.07691	−	1.07691i
$627$		−	12.0000i		−	0.479234i
$628$		−	6.00000i		−	0.239426i
$629$	36.0000			1.43541
$630$	9.00000	+	9.00000i	0.358569	+	0.358569i
$631$	44.0908			1.75523			0.877614	−	0.479368i	$-0.159134\pi$
$631$	44.0908			1.75523			0.877614	+	0.479368i	$0.159134\pi$
$632$	24.4949	+	24.4949i	0.974355	+	0.974355i
$633$			36.7423i			1.46038i
$634$	17.0000	−	17.0000i	0.675156	−	0.675156i
$635$	4.89898			0.194410
$636$	−48.0000			−1.90332
$637$		−	4.89898i		−	0.194105i
$638$	−12.0000	−	12.0000i	−0.475085	−	0.475085i
$639$		−	15.0000i		−	0.593391i
$640$	−8.00000	−	8.00000i	−0.316228	−	0.316228i
$641$		−	24.4949i		−	0.967490i	−0.875209	−	0.483745i	$-0.839276\pi$
$641$		−	24.4949i		−	0.967490i	0.875209	−	0.483745i	$-0.160724\pi$
$642$	−17.1464	−	17.1464i	−0.676716	−	0.676716i
$643$	14.6969			0.579591			0.289795	−	0.957089i	$-0.406413\pi$
$643$	14.6969			0.579591			0.289795	+	0.957089i	$0.406413\pi$
$644$	−14.6969			−0.579141
$645$	6.00000			0.236250
$646$	7.34847	−	7.34847i	0.289122	−	0.289122i
$647$	−19.5959			−0.770395			−0.385198	−	0.922834i	$-0.625867\pi$
$647$	−19.5959			−0.770395			−0.385198	+	0.922834i	$0.625867\pi$
$648$	−18.0000	−	18.0000i	−0.707107	−	0.707107i
$649$		−	53.8888i		−	2.11532i
$650$	9.79796	+	9.79796i	0.384308	+	0.384308i
$651$	−36.7423	+	18.0000i	−1.44005	+	0.705476i
$652$	18.0000			0.704934
$653$	4.00000			0.156532			0.0782660	−	0.996933i	$-0.475062\pi$
$653$	4.00000			0.156532			0.0782660	+	0.996933i	$0.475062\pi$
$654$	−12.2474	+	12.2474i	−0.478913	+	0.478913i
$655$			10.0000i			0.390732i
$656$	−28.0000			−1.09322
$657$		−	29.3939i		−	1.14676i
$658$	−6.00000	+	6.00000i	−0.233904	+	0.233904i
$659$		−	19.0000i		−	0.740135i	−0.929005	−	0.370067i	$-0.879335\pi$
$659$		−	19.0000i		−	0.740135i	0.929005	−	0.370067i	$-0.120665\pi$
$660$			24.0000i			0.934199i
$661$	−43.0000			−1.67251			−0.836253	−	0.548344i	$-0.815259\pi$
$661$	−43.0000			−1.67251			−0.836253	+	0.548344i	$0.815259\pi$
$662$	4.89898	−	4.89898i	0.190404	−	0.190404i
$663$	−44.0908			−1.71235
$664$	−19.5959	−	19.5959i	−0.760469	−	0.760469i
$665$	3.00000			0.116335
$666$	14.6969	+	14.6969i	0.569495	+	0.569495i
$667$		−	6.00000i		−	0.232321i
$668$			39.1918i			1.51638i
$669$	36.0000			1.39184
$670$	8.00000	+	8.00000i	0.309067	+	0.309067i
$671$		−	60.0000i		−	2.31627i
$672$	−29.3939	−	29.3939i	−1.13389	−	1.13389i
$673$		−	22.0454i		−	0.849788i	−0.905243	−	0.424894i	$-0.860311\pi$
$673$		−	22.0454i		−	0.849788i	0.905243	−	0.424894i	$-0.139689\pi$
$674$	−7.34847	−	7.34847i	−0.283052	−	0.283052i
$675$		0			0
$676$		−	14.0000i		−	0.538462i
$677$		−	4.89898i		−	0.188283i	−0.995559	−	0.0941415i	$-0.969989\pi$
$677$		−	4.89898i		−	0.188283i	0.995559	−	0.0941415i	$-0.0300106\pi$
$678$	2.44949	−	2.44949i	0.0940721	−	0.0940721i
$679$		−	39.0000i		−	1.49668i
$680$	−14.6969	+	14.6969i	−0.563602	+	0.563602i
$681$			53.8888i			2.06502i
$682$	−36.4949	−	12.4949i	−1.39746	−	0.478454i
$683$			29.0000i			1.10965i	0.831966	+	0.554827i	$0.187216\pi$
$683$			29.0000i			1.10965i	−0.831966	+	0.554827i	$0.812784\pi$
$684$	6.00000			0.229416
$685$		−	17.1464i		−	0.655131i
$686$	15.0000	+	15.0000i	0.572703	+	0.572703i
$687$			24.0000i			0.915657i
$688$	−9.79796			−0.373544
$689$	24.0000			0.914327
$690$	−6.00000	+	6.00000i	−0.228416	+	0.228416i
$691$			15.0000i			0.570627i	0.958434	+	0.285313i	$0.0920977\pi$
$691$			15.0000i			0.570627i	−0.958434	+	0.285313i	$0.907902\pi$
$692$			32.0000i			1.21646i
$693$			44.0908i			1.67487i
$694$	7.34847	−	7.34847i	0.278944	−	0.278944i
$695$		0			0
$696$	12.0000	−	12.0000i	0.454859	−	0.454859i
$697$			51.4393i			1.94840i
$698$		0			0
$699$	−2.44949			−0.0926482
$700$	24.0000			0.907115
$701$	−13.0000			−0.491003			−0.245502	−	0.969396i	$-0.578953\pi$
$701$	−13.0000			−0.491003			−0.245502	+	0.969396i	$0.578953\pi$
$702$		0			0
$703$	4.89898			0.184769
$704$		−	39.1918i		−	1.47710i
$705$			4.89898i			0.184506i
$706$	−14.6969	−	14.6969i	−0.553127	−	0.553127i
$707$			39.0000i			1.46675i
$708$	53.8888			2.02526
$709$		−	14.6969i		−	0.551955i	−0.961164	−	0.275978i	$-0.910998\pi$
$709$		−	14.6969i		−	0.551955i	0.961164	−	0.275978i	$-0.0890015\pi$
$710$	5.00000	+	5.00000i	0.187647	+	0.187647i
$711$	36.7423			1.37795
$712$	4.89898	−	4.89898i	0.183597	−	0.183597i
$713$	−6.00000	−	12.2474i	−0.224702	−	0.458671i
$714$	−54.0000	+	54.0000i	−2.02090	+	2.02090i
$715$		−	12.0000i		−	0.448775i
$716$		−	24.4949i		−	0.915417i
$717$	−30.0000			−1.12037
$718$	29.0000	+	29.0000i	1.08227	+	1.08227i
$719$	36.7423			1.37026			0.685129	−	0.728422i	$-0.259746\pi$
$719$	36.7423			1.37026			0.685129	+	0.728422i	$0.259746\pi$
$720$	−12.0000			−0.447214
$721$	−3.00000			−0.111726
$722$	−18.0000	+	18.0000i	−0.669891	+	0.669891i
$723$		−	60.0000i		−	2.23142i
$724$	24.4949			0.910346
$725$			9.79796i			0.363887i
$726$	−31.8434	+	31.8434i	−1.18182	+	1.18182i
$727$		−	33.0000i		−	1.22390i	−0.790896	−	0.611951i	$-0.790385\pi$
$727$		−	33.0000i		−	1.22390i	0.790896	−	0.611951i	$-0.209615\pi$
$728$	14.6969	+	14.6969i	0.544705	+	0.544705i
$729$	−27.0000			−1.00000
$730$	9.79796	+	9.79796i	0.362639	+	0.362639i
$731$			18.0000i			0.665754i
$732$	60.0000			2.21766
$733$	9.00000			0.332423			0.166211	−	0.986090i	$-0.446847\pi$
$733$	9.00000			0.332423			0.166211	+	0.986090i	$0.446847\pi$
$734$	−4.89898	+	4.89898i	−0.180825	+	0.180825i
$735$	−4.89898			−0.180702
$736$	9.79796	−	9.79796i	0.361158	−	0.361158i
$737$			39.1918i			1.44365i
$738$	−21.0000	+	21.0000i	−0.773021	+	0.773021i
$739$	−36.7423			−1.35159			−0.675795	−	0.737090i	$-0.736199\pi$
$739$	−36.7423			−1.35159			−0.675795	+	0.737090i	$0.736199\pi$
$740$	−9.79796			−0.360180
$741$	−6.00000			−0.220416
$742$	29.3939	−	29.3939i	1.07908	−	1.07908i
$743$	51.4393			1.88712			0.943562	−	0.331195i	$-0.107452\pi$
$743$	51.4393			1.88712			0.943562	+	0.331195i	$0.107452\pi$
$744$	12.4949	−	36.4949i	0.458085	−	1.33797i
$745$	20.0000			0.732743
$746$	−19.0000	+	19.0000i	−0.695639	+	0.695639i
$747$	−29.3939			−1.07547
$748$	−72.0000			−2.63258
$749$	21.0000			0.767323
$750$	22.0454	−	22.0454i	0.804984	−	0.804984i
$751$		−	25.0000i		−	0.912263i	−0.889912	−	0.456131i	$-0.849235\pi$
$751$		−	25.0000i		−	0.912263i	0.889912	−	0.456131i	$-0.150765\pi$
$752$		−	8.00000i		−	0.291730i
$753$	18.0000			0.655956
$754$	−6.00000	+	6.00000i	−0.218507	+	0.218507i
$755$	−17.1464			−0.624022
$756$		0			0
$757$		−	17.1464i		−	0.623198i	−0.950214	−	0.311599i	$-0.899136\pi$
$757$		−	17.1464i		−	0.623198i	0.950214	−	0.311599i	$-0.100864\pi$
$758$	−6.00000	−	6.00000i	−0.217930	−	0.217930i
$759$	−29.3939			−1.06693
$760$	−2.00000	+	2.00000i	−0.0725476	+	0.0725476i
$761$		−	24.4949i		−	0.887939i	−0.896042	−	0.443970i	$-0.853570\pi$
$761$		−	24.4949i		−	0.887939i	0.896042	−	0.443970i	$-0.146430\pi$
$762$	−12.0000	+	12.0000i	−0.434714	+	0.434714i
$763$		−	15.0000i		−	0.543036i
$764$	−10.0000			−0.361787
$765$			22.0454i			0.797053i
$766$	−14.6969	+	14.6969i	−0.531022	+	0.531022i
$767$	−26.9444			−0.972905
$768$	39.1918			1.41421
$769$	15.0000			0.540914			0.270457	−	0.962732i	$-0.412825\pi$
$769$	15.0000			0.540914			0.270457	+	0.962732i	$0.412825\pi$
$770$	−14.6969	−	14.6969i	−0.529641	−	0.529641i
$771$	31.8434			1.14681
$772$		−	18.0000i		−	0.647834i
$773$		−	22.0454i		−	0.792918i	−0.918052	−	0.396459i	$-0.870239\pi$
$773$		−	22.0454i		−	0.792918i	0.918052	−	0.396459i	$-0.129761\pi$
$774$	−7.34847	+	7.34847i	−0.264135	+	0.264135i
$775$	9.79796	+	20.0000i	0.351953	+	0.718421i
$776$	26.0000	+	26.0000i	0.933346	+	0.933346i
$777$	−36.0000			−1.29149
$778$	14.6969	+	14.6969i	0.526911	+	0.526911i
$779$			7.00000i			0.250801i
$780$	12.0000			0.429669
$781$			24.4949i			0.876496i
$782$	−18.0000	−	18.0000i	−0.643679	−	0.643679i
$783$		0			0
$784$	8.00000			0.285714
$785$	3.00000			0.107075
$786$	−24.4949	−	24.4949i	−0.873704	−	0.873704i
$787$	17.1464			0.611204			0.305602	−	0.952159i	$-0.401142\pi$
$787$	17.1464			0.611204			0.305602	+	0.952159i	$0.401142\pi$
$788$	−9.79796			−0.349038
$789$	6.00000			0.213606
$790$	−12.2474	+	12.2474i	−0.435745	+	0.435745i
$791$			3.00000i			0.106668i
$792$	−29.3939	−	29.3939i	−1.04447	−	1.04447i
$793$	−30.0000			−1.06533
$794$	17.0000	−	17.0000i	0.603307	−	0.603307i
$795$		−	24.0000i		−	0.851192i
$796$		0			0
$797$		−	4.89898i		−	0.173531i	−0.996229	−	0.0867654i	$-0.972347\pi$
$797$		−	4.89898i		−	0.173531i	0.996229	−	0.0867654i	$-0.0276530\pi$
$798$	−7.34847	+	7.34847i	−0.260133	+	0.260133i
$799$	−14.6969			−0.519940
$800$	−16.0000	+	16.0000i	−0.565685	+	0.565685i
$801$		−	7.34847i		−	0.259645i
$802$	12.2474	+	12.2474i	0.432472	+	0.432472i
$803$			48.0000i			1.69388i
$804$	−39.1918			−1.38219
$805$		−	7.34847i		−	0.259000i
$806$	−6.24745	+	18.2474i	−0.220057	+	0.642739i
$807$			24.0000i			0.844840i
$808$	−26.0000	−	26.0000i	−0.914677	−	0.914677i
$809$			34.2929i			1.20567i	0.797865	+	0.602836i	$0.205963\pi$
$809$			34.2929i			1.20567i	−0.797865	+	0.602836i	$0.794037\pi$
$810$	9.00000	−	9.00000i	0.316228	−	0.316228i
$811$		−	10.0000i		−	0.351147i	−0.984466	−	0.175574i	$-0.943822\pi$
$811$		−	10.0000i		−	0.351147i	0.984466	−	0.175574i	$-0.0561780\pi$
$812$			14.6969i			0.515761i
$813$	18.0000			0.631288
$814$	−24.0000	−	24.0000i	−0.841200	−	0.841200i
$815$			9.00000i			0.315256i
$816$		−	72.0000i		−	2.52050i
$817$			2.44949i			0.0856968i
$818$	−22.0454	−	22.0454i	−0.770800	−	0.770800i
$819$	22.0454			0.770329
$820$		−	14.0000i		−	0.488901i
$821$		−	36.7423i		−	1.28232i	−0.767409	−	0.641158i	$-0.778454\pi$
$821$		−	36.7423i		−	1.28232i	0.767409	−	0.641158i	$-0.221546\pi$
$822$	42.0000	+	42.0000i	1.46492	+	1.46492i
$823$	2.44949			0.0853838			0.0426919	−	0.999088i	$-0.486407\pi$
$823$	2.44949			0.0853838			0.0426919	+	0.999088i	$0.486407\pi$
$824$	2.00000	−	2.00000i	0.0696733	−	0.0696733i
$825$	48.0000			1.67115
$826$	−33.0000	+	33.0000i	−1.14822	+	1.14822i
$827$	17.1464			0.596240			0.298120	−	0.954528i	$-0.403640\pi$
$827$	17.1464			0.596240			0.298120	+	0.954528i	$0.403640\pi$
$828$		−	14.6969i		−	0.510754i
$829$		−	14.6969i		−	0.510446i	−0.966882	−	0.255223i	$-0.917851\pi$
$829$		−	14.6969i		−	0.510446i	0.966882	−	0.255223i	$-0.0821488\pi$
$830$	9.79796	−	9.79796i	0.340092	−	0.340092i
$831$		−	42.0000i		−	1.45696i
$832$	−19.5959			−0.679366
$833$		−	14.6969i		−	0.509219i
$834$		0			0
$835$	−19.5959			−0.678145
$836$	−9.79796			−0.338869
$837$		0			0
$838$	−1.00000	−	1.00000i	−0.0345444	−	0.0345444i
$839$			46.0000i			1.58810i	0.607855	+	0.794048i	$0.292030\pi$
$839$			46.0000i			1.58810i	−0.607855	+	0.794048i	$0.707970\pi$
$840$	14.6969	−	14.6969i	0.507093	−	0.507093i
$841$	23.0000			0.793103
$842$	33.0000	−	33.0000i	1.13726	−	1.13726i
$843$	−31.8434			−1.09674
$844$	30.0000			1.03264
$845$	7.00000			0.240807
$846$	−6.00000	−	6.00000i	−0.206284	−	0.206284i
$847$		−	39.0000i		−	1.34006i
$848$			39.1918i			1.34585i
$849$		−	14.6969i		−	0.504398i
$850$	29.3939	+	29.3939i	1.00820	+	1.00820i
$851$		−	12.0000i		−	0.411355i
$852$	−24.4949			−0.839181
$853$	−36.0000			−1.23262			−0.616308	−	0.787505i	$-0.711372\pi$
$853$	−36.0000			−1.23262			−0.616308	+	0.787505i	$0.711372\pi$
$854$	−36.7423	+	36.7423i	−1.25730	+	1.25730i
$855$			3.00000i			0.102598i
$856$	−14.0000	+	14.0000i	−0.478510	+	0.478510i
$857$	−32.0000			−1.09310			−0.546550	−	0.837427i	$-0.684059\pi$
$857$	−32.0000			−1.09310			−0.546550	+	0.837427i	$0.684059\pi$
$858$	29.3939	+	29.3939i	1.00349	+	1.00349i
$859$	48.9898			1.67151			0.835755	−	0.549102i	$-0.185030\pi$
$859$	48.9898			1.67151			0.835755	+	0.549102i	$0.185030\pi$
$860$		−	4.89898i		−	0.167054i
$861$		−	51.4393i		−	1.75305i
$862$	−20.0000	−	20.0000i	−0.681203	−	0.681203i
$863$	2.44949			0.0833816			0.0416908	−	0.999131i	$-0.486726\pi$
$863$	2.44949			0.0833816			0.0416908	+	0.999131i	$0.486726\pi$
$864$		0			0
$865$	−16.0000			−0.544016
$866$	22.0454	+	22.0454i	0.749133	+	0.749133i
$867$	−90.6311			−3.07799
$868$	14.6969	+	30.0000i	0.498847	+	1.01827i
$869$	−60.0000			−2.03536
$870$	6.00000	+	6.00000i	0.203419	+	0.203419i
$871$	19.5959			0.663982
$872$	10.0000	+	10.0000i	0.338643	+	0.338643i
$873$	39.0000			1.31995
$874$	−2.44949	−	2.44949i	−0.0828552	−	0.0828552i
$875$			27.0000i			0.912767i
$876$	−48.0000			−1.62177
$877$	−27.0000			−0.911725			−0.455863	−	0.890050i	$-0.650669\pi$
$877$	−27.0000			−0.911725			−0.455863	+	0.890050i	$0.650669\pi$
$878$	−31.0000	−	31.0000i	−1.04620	−	1.04620i
$879$	9.79796			0.330477
$880$	19.5959			0.660578
$881$			24.4949i			0.825254i	0.910900	+	0.412627i	$0.135389\pi$
$881$			24.4949i			0.825254i	−0.910900	+	0.412627i	$0.864611\pi$
$882$	6.00000	−	6.00000i	0.202031	−	0.202031i
$883$	39.1918			1.31891			0.659455	−	0.751744i	$-0.270787\pi$
$883$	39.1918			1.31891			0.659455	+	0.751744i	$0.270787\pi$
$884$			36.0000i			1.21081i
$885$			26.9444i			0.905726i
$886$	11.0000	+	11.0000i	0.369552	+	0.369552i
$887$		−	43.0000i		−	1.44380i	−0.691998	−	0.721899i	$-0.743269\pi$
$887$		−	43.0000i		−	1.44380i	0.691998	−	0.721899i	$-0.256731\pi$
$888$	24.0000	−	24.0000i	0.805387	−	0.805387i
$889$		−	14.6969i		−	0.492919i
$890$	2.44949	+	2.44949i	0.0821071	+	0.0821071i
$891$	44.0908			1.47710
$892$		−	29.3939i		−	0.984180i
$893$	−2.00000			−0.0669274
$894$	−48.9898	+	48.9898i	−1.63846	+	1.63846i
$895$	12.2474			0.409387
$896$	−24.0000	+	24.0000i	−0.801784	+	0.801784i
$897$			14.6969i			0.490716i
$898$	−9.79796	−	9.79796i	−0.326962	−	0.326962i
$899$	−12.2474	+	6.00000i	−0.408475	+	0.200111i
$900$			24.0000i			0.800000i
$901$	72.0000			2.39867
$902$	34.2929	−	34.2929i	1.14183	−	1.14183i
$903$		−	18.0000i		−	0.599002i
$904$	−2.00000	−	2.00000i	−0.0665190	−	0.0665190i
$905$			12.2474i			0.407119i
$906$	42.0000	−	42.0000i	1.39536	−	1.39536i
$907$			7.00000i			0.232431i	0.993224	+	0.116216i	$0.0370764\pi$
$907$			7.00000i			0.232431i	−0.993224	+	0.116216i	$0.962924\pi$
$908$	44.0000			1.46019
$909$	−39.0000			−1.29355
$910$	−7.34847	+	7.34847i	−0.243599	+	0.243599i
$911$	31.8434			1.05502			0.527509	−	0.849550i	$-0.323126\pi$
$911$	31.8434			1.05502			0.527509	+	0.849550i	$0.323126\pi$
$912$		−	9.79796i		−	0.324443i
$913$	48.0000			1.58857
$914$	4.89898	+	4.89898i	0.162044	+	0.162044i
$915$			30.0000i			0.991769i
$916$	19.5959			0.647467
$917$	30.0000			0.990687
$918$		0			0
$919$			46.0000i			1.51740i	0.651440	+	0.758700i	$0.274165\pi$
$919$			46.0000i			1.51740i	−0.651440	+	0.758700i	$0.725835\pi$
$920$	4.89898	+	4.89898i	0.161515	+	0.161515i
$921$		−	31.8434i		−	1.04927i
$922$	−24.4949	−	24.4949i	−0.806696	−	0.806696i
$923$	12.2474			0.403130
$924$	72.0000			2.36863
$925$			19.5959i			0.644310i
$926$	34.2929	−	34.2929i	1.12693	−	1.12693i
$927$		−	3.00000i		−	0.0985329i
$928$	−9.79796	−	9.79796i	−0.321634	−	0.321634i
$929$			9.79796i			0.321461i	0.986998	+	0.160730i	$0.0513849\pi$
$929$			9.79796i			0.321461i	−0.986998	+	0.160730i	$0.948615\pi$
$930$	18.2474	+	6.24745i	0.598357	+	0.204862i
$931$		−	2.00000i		−	0.0655474i
$932$			2.00000i			0.0655122i
$933$			12.2474i			0.400963i
$934$	13.0000	+	13.0000i	0.425373	+	0.425373i
$935$		−	36.0000i		−	1.17733i
$936$	−14.6969	+	14.6969i	−0.480384	+	0.480384i
$937$	−12.0000			−0.392023			−0.196011	−	0.980602i	$-0.562799\pi$
$937$	−12.0000			−0.392023			−0.196011	+	0.980602i	$0.562799\pi$
$938$	24.0000	−	24.0000i	0.783628	−	0.783628i
$939$			66.0000i			2.15383i
$940$	4.00000			0.130466
$941$		−	48.9898i		−	1.59702i	−0.601980	−	0.798511i	$-0.705621\pi$
$941$		−	48.9898i		−	1.59702i	0.601980	−	0.798511i	$-0.294379\pi$
$942$	−7.34847	+	7.34847i	−0.239426	+	0.239426i
$943$	17.1464			0.558365
$944$		−	44.0000i		−	1.43208i
$945$		0			0
$946$	12.0000	−	12.0000i	0.390154	−	0.390154i
$947$	−19.5959			−0.636782			−0.318391	−	0.947960i	$-0.603142\pi$
$947$	−19.5959			−0.636782			−0.318391	+	0.947960i	$0.603142\pi$
$948$		−	60.0000i		−	1.94871i
$949$	24.0000			0.779073
$950$	4.00000	+	4.00000i	0.129777	+	0.129777i
$951$	−41.6413			−1.35031
$952$	44.0908	+	44.0908i	1.42899	+	1.42899i
$953$			2.44949i			0.0793468i	0.999213	+	0.0396734i	$0.0126317\pi$
$953$			2.44949i			0.0793468i	−0.999213	+	0.0396734i	$0.987368\pi$
$954$	29.3939	+	29.3939i	0.951662	+	0.951662i
$955$		−	5.00000i		−	0.161796i
$956$			24.4949i			0.792222i
$957$			29.3939i			0.950169i
$958$	−11.0000	−	11.0000i	−0.355394	−	0.355394i
$959$	−51.4393			−1.66106
$960$			19.5959i			0.632456i
$961$	−19.0000	+	24.4949i	−0.612903	+	0.790158i
$962$	−12.0000	+	12.0000i	−0.386896	+	0.386896i
$963$			21.0000i			0.676716i
$964$	−48.9898			−1.57786
$965$	9.00000			0.289720
$966$	18.0000	+	18.0000i	0.579141	+	0.579141i
$967$	−44.0908			−1.41787			−0.708933	−	0.705276i	$-0.750823\pi$
$967$	−44.0908			−1.41787			−0.708933	+	0.705276i	$0.750823\pi$
$968$	26.0000	+	26.0000i	0.835672	+	0.835672i
$969$	−18.0000			−0.578243
$970$	−13.0000	+	13.0000i	−0.417405	+	0.417405i
$971$			50.0000i			1.60458i	0.596937	+	0.802288i	$0.296384\pi$
$971$			50.0000i			1.60458i	−0.596937	+	0.802288i	$0.703616\pi$
$972$			44.0908i			1.41421i
$973$		0			0
$974$	31.8434	−	31.8434i	1.02033	−	1.02033i
$975$		−	24.0000i		−	0.768615i
$976$		−	48.9898i		−	1.56813i
$977$	−47.0000			−1.50366			−0.751832	−	0.659355i	$-0.770829\pi$
$977$	−47.0000			−1.50366			−0.751832	+	0.659355i	$0.770829\pi$
$978$	−22.0454	−	22.0454i	−0.704934	−	0.704934i
$979$			12.0000i			0.383522i
$980$			4.00000i			0.127775i
$981$	15.0000			0.478913
$982$	29.3939	−	29.3939i	0.937996	−	0.937996i
$983$	−9.79796			−0.312506			−0.156253	−	0.987717i	$-0.549942\pi$
$983$	−9.79796			−0.312506			−0.156253	+	0.987717i	$0.549942\pi$
$984$	34.2929	+	34.2929i	1.09322	+	1.09322i
$985$		−	4.89898i		−	0.156094i
$986$	−18.0000	+	18.0000i	−0.573237	+	0.573237i
$987$	14.6969			0.467809
$988$			4.89898i			0.155857i
$989$	6.00000			0.190789
$990$	14.6969	−	14.6969i	0.467099	−	0.467099i
$991$	7.34847			0.233432			0.116716	−	0.993165i	$-0.462763\pi$
$991$	7.34847			0.233432			0.116716	+	0.993165i	$0.462763\pi$
$992$	−29.7980	−	10.2020i	−0.946086	−	0.323915i
$993$	−12.0000			−0.380808
$994$	15.0000	−	15.0000i	0.475771	−	0.475771i
$995$		0			0
$996$			48.0000i			1.52094i
$997$	23.0000			0.728417			0.364209	−	0.931317i	$-0.381339\pi$
$997$	23.0000			0.728417			0.364209	+	0.931317i	$0.381339\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	124.2.d.a.123.4	yes	4
3.2	odd	2		1116.2.g.d.991.2		4
4.3	odd	2	inner	124.2.d.a.123.1	✓	4
8.3	odd	2		1984.2.h.d.1983.4		4
8.5	even	2		1984.2.h.d.1983.1		4
12.11	even	2		1116.2.g.d.991.3		4
31.30	odd	2	inner	124.2.d.a.123.3	yes	4
93.92	even	2		1116.2.g.d.991.1		4
124.123	even	2	inner	124.2.d.a.123.2	yes	4
248.61	odd	2		1984.2.h.d.1983.3		4
248.123	even	2		1984.2.h.d.1983.2		4
372.371	odd	2		1116.2.g.d.991.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
124.2.d.a.123.1	✓	4	4.3	odd	2	inner
124.2.d.a.123.2	yes	4	124.123	even	2	inner
124.2.d.a.123.3	yes	4	31.30	odd	2	inner
124.2.d.a.123.4	yes	4	1.1	even	1	trivial
1116.2.g.d.991.1		4	93.92	even	2
1116.2.g.d.991.2		4	3.2	odd	2
1116.2.g.d.991.3		4	12.11	even	2
1116.2.g.d.991.4		4	372.371	odd	2
1984.2.h.d.1983.1		4	8.5	even	2
1984.2.h.d.1983.2		4	248.123	even	2
1984.2.h.d.1983.3		4	248.61	odd	2
1984.2.h.d.1983.4		4	8.3	odd	2

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:	\( N \)	\(=\)	\( 124 = 2^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	124.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.00000i) q^{2} +2.44949 q^{3} -2.00000i q^{4} +1.00000 q^{5} +(-2.44949 + 2.44949i) q^{6} -3.00000i q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.00000i) q^{2} +2.44949 q^{3} -2.00000i q^{4} +1.00000 q^{5} +(-2.44949 + 2.44949i) q^{6} -3.00000i q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000 q^{9} +(-1.00000 + 1.00000i) q^{10} -4.89898 q^{11} -4.89898i q^{12} +2.44949i q^{13} +(3.00000 + 3.00000i) q^{14} +2.44949 q^{15} -4.00000 q^{16} +7.34847i q^{17} +(-3.00000 + 3.00000i) q^{18} +1.00000i q^{19} -2.00000i q^{20} -7.34847i q^{21} +(4.89898 - 4.89898i) q^{22} +2.44949 q^{23} +(4.89898 + 4.89898i) q^{24} -4.00000 q^{25} +(-2.44949 - 2.44949i) q^{26} -6.00000 q^{28} -2.44949i q^{29} +(-2.44949 + 2.44949i) q^{30} +(-2.44949 - 5.00000i) q^{31} +(4.00000 - 4.00000i) q^{32} -12.0000 q^{33} +(-7.34847 - 7.34847i) q^{34} -3.00000i q^{35} -6.00000i q^{36} -4.89898i q^{37} +(-1.00000 - 1.00000i) q^{38} +6.00000i q^{39} +(2.00000 + 2.00000i) q^{40} +7.00000 q^{41} +(7.34847 + 7.34847i) q^{42} +2.44949 q^{43} +9.79796i q^{44} +3.00000 q^{45} +(-2.44949 + 2.44949i) q^{46} +2.00000i q^{47} -9.79796 q^{48} -2.00000 q^{49} +(4.00000 - 4.00000i) q^{50} +18.0000i q^{51} +4.89898 q^{52} -9.79796i q^{53} -4.89898 q^{55} +(6.00000 - 6.00000i) q^{56} +2.44949i q^{57} +(2.44949 + 2.44949i) q^{58} +11.0000i q^{59} -4.89898i q^{60} +12.2474i q^{61} +(7.44949 + 2.55051i) q^{62} -9.00000i q^{63} +8.00000i q^{64} +2.44949i q^{65} +(12.0000 - 12.0000i) q^{66} -8.00000i q^{67} +14.6969 q^{68} +6.00000 q^{69} +(3.00000 + 3.00000i) q^{70} -5.00000i q^{71} +(6.00000 + 6.00000i) q^{72} -9.79796i q^{73} +(4.89898 + 4.89898i) q^{74} -9.79796 q^{75} +2.00000 q^{76} +14.6969i q^{77} +(-6.00000 - 6.00000i) q^{78} +12.2474 q^{79} -4.00000 q^{80} -9.00000 q^{81} +(-7.00000 + 7.00000i) q^{82} -9.79796 q^{83} -14.6969 q^{84} +7.34847i q^{85} +(-2.44949 + 2.44949i) q^{86} -6.00000i q^{87} +(-9.79796 - 9.79796i) q^{88} -2.44949i q^{89} +(-3.00000 + 3.00000i) q^{90} +7.34847 q^{91} -4.89898i q^{92} +(-6.00000 - 12.2474i) q^{93} +(-2.00000 - 2.00000i) q^{94} +1.00000i q^{95} +(9.79796 - 9.79796i) q^{96} +13.0000 q^{97} +(2.00000 - 2.00000i) q^{98} -14.6969 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 4 q^{5} + 8 q^{8} + 12 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 + 4 * q^5 + 8 * q^8 + 12 * q^9	\( 4 q - 4 q^{2} + 4 q^{5} + 8 q^{8} + 12 q^{9} - 4 q^{10} + 12 q^{14} - 16 q^{16} - 12 q^{18} - 16 q^{25} - 24 q^{28} + 16 q^{32} - 48 q^{33} - 4 q^{38} + 8 q^{40} + 28 q^{41} + 12 q^{45} - 8 q^{49} + 16 q^{50} + 24 q^{56} + 20 q^{62} + 48 q^{66} + 24 q^{69} + 12 q^{70} + 24 q^{72} + 8 q^{76} - 24 q^{78} - 16 q^{80} - 36 q^{81} - 28 q^{82} - 12 q^{90} - 24 q^{93} - 8 q^{94} + 52 q^{97} + 8 q^{98}+O(q^{100}) \) 4 * q - 4 * q^2 + 4 * q^5 + 8 * q^8 + 12 * q^9 - 4 * q^10 + 12 * q^14 - 16 * q^16 - 12 * q^18 - 16 * q^25 - 24 * q^28 + 16 * q^32 - 48 * q^33 - 4 * q^38 + 8 * q^40 + 28 * q^41 + 12 * q^45 - 8 * q^49 + 16 * q^50 + 24 * q^56 + 20 * q^62 + 48 * q^66 + 24 * q^69 + 12 * q^70 + 24 * q^72 + 8 * q^76 - 24 * q^78 - 16 * q^80 - 36 * q^81 - 28 * q^82 - 12 * q^90 - 24 * q^93 - 8 * q^94 + 52 * q^97 + 8 * q^98

Introduction

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