LMFDB - Embedded newform 460.2.o.a.159.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(19,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 15]))

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

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

chi := DirichletCharacter("460.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.o (of order $22$, degree $10$, 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:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$4$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{22}]$

Embedding invariants

Embedding label			159.3
Character	$\chi$	$=$	460.159
Dual form			460.2.o.a.379.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.18971 + 0.764582i) q^{2} +(-0.412623 - 2.86986i) q^{3} +(0.830830 + 1.81926i) q^{4} +(-0.629973 + 2.14549i) q^{5} +(1.70334 - 3.72979i) q^{6} +(3.98826 + 3.45585i) q^{7} +(-0.402527 + 2.79964i) q^{8} +(-5.18734 + 1.52314i) q^{9} +O(q^{10})$	\(q+(1.18971 + 0.764582i) q^{2} +(-0.412623 - 2.86986i) q^{3} +(0.830830 + 1.81926i) q^{4} +(-0.629973 + 2.14549i) q^{5} +(1.70334 - 3.72979i) q^{6} +(3.98826 + 3.45585i) q^{7} +(-0.402527 + 2.79964i) q^{8} +(-5.18734 + 1.52314i) q^{9} +(-2.38989 + 2.07085i) q^{10} +(4.87821 - 3.13503i) q^{12} +(2.10260 + 7.16081i) q^{14} +(6.41720 + 0.922653i) q^{15} +(-2.61944 + 3.02300i) q^{16} +(-7.33601 - 2.15405i) q^{18} +(-4.42662 + 0.636451i) q^{20} +(8.27214 - 12.8717i) q^{21} +(3.15934 - 3.60813i) q^{23} +8.20065 q^{24} +(-4.20627 - 2.70320i) q^{25} +(2.89829 + 6.34638i) q^{27} +(-2.97353 + 10.1269i) q^{28} +(3.43833 - 7.52889i) q^{29} +(6.92917 + 6.00416i) q^{30} +(-5.42771 + 1.59372i) q^{32} +(-9.92699 + 6.37969i) q^{35} +(-7.08080 - 8.17168i) q^{36} +(-5.75302 - 2.62732i) q^{40} +(-4.29710 - 1.26174i) q^{41} +(19.6829 - 8.98889i) q^{42} +(12.7602 - 1.83464i) q^{43} -12.0889i q^{45} +(6.51741 - 1.87706i) q^{46} -6.82575 q^{47} +(9.75642 + 6.27007i) q^{48} +(2.96714 + 20.6369i) q^{49} +(-2.93743 - 6.43207i) q^{50} +(-1.40419 + 9.76634i) q^{54} +(-11.2805 + 9.77461i) q^{56} +(9.84707 - 6.32833i) q^{58} +(3.65305 + 12.4411i) q^{60} +(-12.7196 - 1.82881i) q^{61} +(-25.9522 - 11.8520i) q^{63} +(-7.67594 - 2.25386i) q^{64} +(3.48695 - 5.42579i) q^{67} +(-11.6584 - 7.57806i) q^{69} -16.6881 q^{70} +(-2.17620 - 15.1358i) q^{72} +(-6.02221 + 13.1868i) q^{75} +(-4.83564 - 7.52440i) q^{80} +(3.37299 - 2.16769i) q^{81} +(-4.14761 - 4.78660i) q^{82} +(-4.71849 - 16.0697i) q^{83} +(30.2898 + 4.35501i) q^{84} +(16.5837 + 7.57350i) q^{86} +(-23.0256 - 6.76092i) q^{87} +(-11.6848 + 1.68002i) q^{89} +(9.24298 - 14.3824i) q^{90} +(9.18901 + 2.74994i) q^{92} +(-8.12067 - 5.21884i) q^{94} +(6.81335 + 14.9192i) q^{96} +(-12.2485 + 26.8206i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 8 q^{4} - 8 q^{6} + 4 q^{9}+O(q^{10}) $ 40 * q - 8 * q^4 - 8 * q^6 + 4 * q^9	$ 40 q - 8 q^{4} - 8 q^{6} + 4 q^{9} - 16 q^{16} - 16 q^{24} + 20 q^{25} + 24 q^{29} + 8 q^{36} + 48 q^{41} - 4 q^{46} + 100 q^{49} - 276 q^{54} - 264 q^{56} - 32 q^{64} - 4 q^{69} - 40 q^{70} + 20 q^{81} + 352 q^{84} + 396 q^{86} - 56 q^{94} - 32 q^{96}+O(q^{100}) $ 40 * q - 8 * q^4 - 8 * q^6 + 4 * q^9 - 16 * q^16 - 16 * q^24 + 20 * q^25 + 24 * q^29 + 8 * q^36 + 48 * q^41 - 4 * q^46 + 100 * q^49 - 276 * q^54 - 264 * q^56 - 32 * q^64 - 4 * q^69 - 40 * q^70 + 20 * q^81 + 352 * q^84 + 396 * q^86 - 56 * q^94 - 32 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{13}{22}\right)$

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 $

$2$	1.18971	+	0.764582i	0.841254	+	0.540641i
$2$	1.18971	+	0.764582i	0.841254	+	0.540641i
$3$	−0.412623	−	2.86986i	−0.238228	−	1.65691i	−0.660784	−	0.750576i	$-0.729776\pi$
$3$	−0.412623	−	2.86986i	−0.238228	−	1.65691i	0.422556	−	0.906337i	$-0.361133\pi$
$4$	0.830830	+	1.81926i	0.415415	+	0.909632i
$5$	−0.629973	+	2.14549i	−0.281733	+	0.959493i
$5$	−0.629973	+	2.14549i	−0.281733	+	0.959493i
$6$	1.70334	−	3.72979i	0.695384	−	1.52268i
$7$	3.98826	+	3.45585i	1.50742	+	1.30619i	0.801784	+	0.597614i	$0.203885\pi$
$7$	3.98826	+	3.45585i	1.50742	+	1.30619i	0.705637	+	0.708573i	$0.250661\pi$
$8$	−0.402527	+	2.79964i	−0.142315	+	0.989821i
$9$	−5.18734	+	1.52314i	−1.72911	+	0.507714i
$10$	−2.38989	+	2.07085i	−0.755750	+	0.654861i
$11$		0			0		−0.540641	−	0.841254i	$-0.681818\pi$
$11$		0			0		0.540641	+	0.841254i	$0.318182\pi$
$12$	4.87821	−	3.13503i	1.40822	−	0.905006i
$13$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$13$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$14$	2.10260	+	7.16081i	0.561945	+	1.91381i
$15$	6.41720	+	0.922653i	1.65691	+	0.238228i
$16$	−2.61944	+	3.02300i	−0.654861	+	0.755750i
$17$		0			0		−0.909632	−	0.415415i	$-0.863636\pi$
$17$		0			0		0.909632	+	0.415415i	$0.136364\pi$
$18$	−7.33601	−	2.15405i	−1.72911	−	0.507714i
$19$		0			0		0.909632	−	0.415415i	$-0.136364\pi$
$19$		0			0		−0.909632	+	0.415415i	$0.863636\pi$
$20$	−4.42662	+	0.636451i	−0.989821	+	0.142315i
$21$	8.27214	−	12.8717i	1.80513	−	2.80884i
$22$		0			0
$23$	3.15934	−	3.60813i	0.658768	−	0.752346i
$23$	3.15934	−	3.60813i	0.658768	−	0.752346i
$24$	8.20065			1.67395
$25$	−4.20627	−	2.70320i	−0.841254	−	0.540641i
$26$		0			0
$27$	2.89829	+	6.34638i	0.557777	+	1.22136i
$28$	−2.97353	+	10.1269i	−0.561945	+	1.91381i
$29$	3.43833	−	7.52889i	0.638481	−	1.39808i	−0.262802	−	0.964850i	$-0.584647\pi$
$29$	3.43833	−	7.52889i	0.638481	−	1.39808i	0.901284	−	0.433230i	$-0.142626\pi$
$30$	6.92917	+	6.00416i	1.26509	+	1.09620i
$31$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$31$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$32$	−5.42771	+	1.59372i	−0.959493	+	0.281733i
$33$		0			0
$34$		0			0
$35$	−9.92699	+	6.37969i	−1.67797	+	1.07836i
$36$	−7.08080	−	8.17168i	−1.18013	−	1.36195i
$37$		0			0		−0.281733	−	0.959493i	$-0.590909\pi$
$37$		0			0		0.281733	+	0.959493i	$0.409091\pi$
$38$		0			0
$39$		0			0
$40$	−5.75302	−	2.62732i	−0.909632	−	0.415415i
$41$	−4.29710	−	1.26174i	−0.671095	−	0.197051i	−0.0716043	−	0.997433i	$-0.522812\pi$
$41$	−4.29710	−	1.26174i	−0.671095	−	0.197051i	−0.599490	+	0.800382i	$0.704630\pi$
$42$	19.6829	−	8.98889i	3.03714	−	1.38702i
$43$	12.7602	−	1.83464i	1.94591	−	0.279779i	0.946792	−	0.321845i	$-0.104303\pi$
$43$	12.7602	−	1.83464i	1.94591	−	0.279779i	0.999115	+	0.0420657i	$0.0133939\pi$
$44$		0			0
$45$		−	12.0889i		−	1.80211i
$46$	6.51741	−	1.87706i	0.960940	−	0.276757i
$47$	−6.82575			−0.995637			−0.497819	−	0.867281i	$-0.665866\pi$
$47$	−6.82575			−0.995637			−0.497819	+	0.867281i	$0.665866\pi$
$48$	9.75642	+	6.27007i	1.40822	+	0.905006i
$49$	2.96714	+	20.6369i	0.423877	+	2.94813i
$50$	−2.93743	−	6.43207i	−0.415415	−	0.909632i
$51$		0			0
$52$		0			0
$53$		0			0		−0.755750	−	0.654861i	$-0.772727\pi$
$53$		0			0		0.755750	+	0.654861i	$0.227273\pi$
$54$	−1.40419	+	9.76634i	−0.191086	+	1.32903i
$55$		0			0
$56$	−11.2805	+	9.77461i	−1.50742	+	1.30619i
$57$		0			0
$58$	9.84707	−	6.32833i	1.29298	−	0.830950i
$59$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$59$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$60$	3.65305	+	12.4411i	0.471607	+	1.60614i
$61$	−12.7196	−	1.82881i	−1.62858	−	0.234155i	−0.733381	−	0.679817i	$-0.762059\pi$
$61$	−12.7196	−	1.82881i	−1.62858	−	0.234155i	−0.895201	+	0.445663i	$0.852968\pi$
$62$		0			0
$63$	−25.9522	−	11.8520i	−3.26967	−	1.49321i
$64$	−7.67594	−	2.25386i	−0.959493	−	0.281733i
$65$		0			0
$66$		0			0
$67$	3.48695	−	5.42579i	0.425998	−	0.662866i	−0.560215	−	0.828347i	$-0.689281\pi$
$67$	3.48695	−	5.42579i	0.425998	−	0.662866i	0.986213	+	0.165481i	$0.0529178\pi$
$68$		0			0
$69$	−11.6584	−	7.57806i	−1.40351	−	0.912291i
$70$	−16.6881			−1.99460
$71$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$71$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$72$	−2.17620	−	15.1358i	−0.256467	−	1.78377i
$73$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$73$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$74$		0			0
$75$	−6.02221	+	13.1868i	−0.695384	+	1.52268i
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		0.755750	−	0.654861i	$-0.227273\pi$
$79$		0			0		−0.755750	+	0.654861i	$0.772727\pi$
$80$	−4.83564	−	7.52440i	−0.540641	−	0.841254i
$81$	3.37299	−	2.16769i	0.374776	−	0.240854i
$82$	−4.14761	−	4.78660i	−0.458027	−	0.528591i
$83$	−4.71849	−	16.0697i	−0.517922	−	1.76388i	−0.636862	−	0.770978i	$-0.719768\pi$
$83$	−4.71849	−	16.0697i	−0.517922	−	1.76388i	0.118940	−	0.992901i	$-0.462050\pi$
$84$	30.2898	+	4.35501i	3.30488	+	0.475171i
$85$		0			0
$86$	16.5837	+	7.57350i	1.78826	+	0.816672i
$87$	−23.0256	−	6.76092i	−2.46860	−	0.724846i
$88$		0			0
$89$	−11.6848	+	1.68002i	−1.23859	+	0.178082i	−0.730312	−	0.683114i	$-0.760625\pi$
$89$	−11.6848	+	1.68002i	−1.23859	+	0.178082i	−0.508274	+	0.861195i	$0.669716\pi$
$90$	9.24298	−	14.3824i	0.974296	−	1.51603i
$91$		0			0
$92$	9.18901	+	2.74994i	0.958020	+	0.286701i
$93$		0			0
$94$	−8.12067	−	5.21884i	−0.837583	−	0.538282i
$95$		0			0
$96$	6.81335	+	14.9192i	0.695384	+	1.52268i
$97$		0			0		0.281733	−	0.959493i	$-0.409091\pi$
$97$		0			0		−0.281733	+	0.959493i	$0.590909\pi$
$98$	−12.2485	+	26.8206i	−1.23729	+	2.70929i
$99$		0			0
$100$	1.42315	−	9.89821i	0.142315	−	0.989821i
$101$	10.9525	−	3.21595i	1.08982	−	0.319999i	0.313017	−	0.949748i	$-0.398660\pi$
$101$	10.9525	−	3.21595i	1.08982	−	0.319999i	0.776799	+	0.629749i	$0.216842\pi$
$102$		0			0
$103$	10.1407	+	15.7792i	0.999191	+	1.55477i	0.821121	+	0.570754i	$0.193349\pi$
$103$	10.1407	+	15.7792i	0.999191	+	1.55477i	0.178070	+	0.984018i	$0.443015\pi$
$104$		0			0
$105$	22.4049	+	25.8566i	2.18649	+	2.52335i
$106$		0			0
$107$	3.88303	+	0.558295i	0.375387	+	0.0539724i	0.327426	−	0.944877i	$-0.393819\pi$
$107$	3.88303	+	0.558295i	0.375387	+	0.0539724i	0.0479605	+	0.998849i	$0.484728\pi$
$108$	−9.13774	+	10.5455i	−0.879280	+	1.01474i
$109$	−2.39811	−	1.09518i	−0.229697	−	0.104899i	0.297242	−	0.954802i	$-0.403933\pi$
$109$	−2.39811	−	1.09518i	−0.229697	−	0.104899i	−0.526939	+	0.849903i	$0.676660\pi$
$110$		0			0
$111$		0			0
$112$	−20.8940	+	3.00411i	−1.97430	+	0.283862i
$113$		0			0		0.540641	−	0.841254i	$-0.318182\pi$
$113$		0			0		−0.540641	+	0.841254i	$0.681818\pi$
$114$		0			0
$115$	5.75090	+	9.05136i	0.536274	+	0.844044i
$116$	16.5537			1.53697
$117$		0			0
$118$		0			0
$119$		0			0
$120$	−5.16619	+	17.5944i	−0.471607	+	1.60614i
$121$	−4.56957	+	10.0060i	−0.415415	+	0.909632i
$122$	−13.7344	−	11.9010i	−1.24346	−	1.07746i
$123$	−1.84794	+	12.8527i	−0.166623	+	1.15889i
$124$		0			0
$125$	8.44954	−	7.32157i	0.755750	−	0.654861i
$126$	−21.8139	−	33.9430i	−1.94333	−	3.02389i
$127$	17.9245	−	11.5193i	1.59054	−	1.02218i	0.618971	−	0.785414i	$-0.287550\pi$
$127$	17.9245	−	11.5193i	1.59054	−	1.02218i	0.971567	−	0.236763i	$-0.0760864\pi$
$128$	−7.40890	−	8.55033i	−0.654861	−	0.755750i
$129$	−10.5303	−	35.8628i	−0.927140	−	3.15755i
$130$		0			0
$131$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$131$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$132$		0			0
$133$		0			0
$134$	8.29692	−	3.78908i	0.716745	−	0.327326i
$135$	−15.4419	+	2.22022i	−1.32903	+	0.191086i
$136$		0			0
$137$		0			0			−	1.00000i	$-0.5\pi$
$137$		0			0				1.00000i	$0.5\pi$
$138$	−8.07612	−	17.9295i	−0.687485	−	1.52626i
$139$		0			0		1.00000			$0$
$139$		0			0		−1.00000			$\pi$
$140$	−19.8540	−	12.7594i	−1.67797	−	1.07836i
$141$	2.81646	+	19.5889i	0.237189	+	1.64968i
$142$		0			0
$143$		0			0
$144$	8.98350	−	19.6711i	0.748625	−	1.63926i
$145$	13.9871	+	12.1199i	1.16157	+	1.00650i
$146$		0			0
$147$	58.0006	−	17.0305i	4.78381	−	1.40465i
$148$		0			0
$149$	1.33571	+	2.07840i	0.109425	+	0.170269i	0.891647	−	0.452731i	$-0.149550\pi$
$149$	1.33571	+	2.07840i	0.109425	+	0.170269i	−0.782222	+	0.623000i	$0.785914\pi$
$150$	−17.2471	+	11.0840i	−1.40822	+	0.905006i
$151$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$151$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.909632	−	0.415415i	$-0.136364\pi$
$157$		0			0		−0.909632	+	0.415415i	$0.863636\pi$
$158$		0			0
$159$		0			0
$160$		−	12.6491i		−	1.00000i
$161$	25.0694	−	3.47194i	1.97575	−	0.273628i
$162$	5.67026			0.445497
$163$	−21.3871	−	13.7447i	−1.67517	−	1.07657i	−0.888022	−	0.459802i	$-0.847921\pi$
$163$	−21.3871	−	13.7447i	−1.67517	−	1.07657i	−0.787148	−	0.616764i	$-0.788443\pi$
$164$	−1.27472	−	8.86586i	−0.0995388	−	0.692307i
$165$		0			0
$166$	6.67296	−	22.7260i	0.517922	−	1.76388i
$167$	7.73369	−	16.9344i	0.598451	−	1.31042i	−0.331748	−	0.943368i	$-0.607638\pi$
$167$	7.73369	−	16.9344i	0.598451	−	1.31042i	0.930199	−	0.367057i	$-0.119634\pi$
$168$	32.7063	+	28.3402i	2.52335	+	2.18649i
$169$	−1.85009	+	12.8677i	−0.142315	+	0.989821i
$170$		0			0
$171$		0			0
$172$	13.9392	+	21.6898i	1.06286	+	1.65383i
$173$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$173$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$174$	−22.2245	−	25.6485i	−1.68484	−	1.94441i
$175$	−7.43383	−	25.3173i	−0.561945	−	1.91381i
$176$		0			0
$177$		0			0
$178$	−15.1861	−	6.93524i	−1.13824	−	0.519818i
$179$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$179$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$180$	21.9930	−	10.0439i	1.63926	−	0.748625i
$181$	1.82035	−	0.261726i	0.135305	−	0.0194540i	−0.0743294	−	0.997234i	$-0.523682\pi$
$181$	1.82035	−	0.261726i	0.135305	−	0.0194540i	0.209635	+	0.977780i	$0.432773\pi$
$182$		0			0
$183$			37.2581i			2.75420i
$184$	8.82972	+	10.2974i	0.650936	+	0.759133i
$185$		0			0
$186$		0			0
$187$		0			0
$188$	−5.67103	−	12.4178i	−0.413603	−	0.905664i
$189$	−10.3730	+	35.3271i	−0.754522	+	2.56967i
$190$		0			0
$191$		0			0		−0.755750	−	0.654861i	$-0.772727\pi$
$191$		0			0		0.755750	+	0.654861i	$0.227273\pi$
$192$	−3.30099	+	22.9589i	−0.238228	+	1.65691i
$193$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$193$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$194$		0			0
$195$		0			0
$196$	−35.0788	+	22.5438i	−2.50563	+	1.61027i
$197$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$197$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$198$		0			0
$199$		0			0		−0.989821	−	0.142315i	$-0.954545\pi$
$199$		0			0		0.989821	+	0.142315i	$0.0454545\pi$
$200$	9.26113	−	10.6879i	0.654861	−	0.755750i
$201$	−17.0100	−	7.76823i	−1.19980	−	0.547928i
$202$	15.4892	+	4.54804i	1.08982	+	0.319999i
$203$	39.7316	−	18.1448i	2.78861	−	1.27352i
$204$		0			0
$205$	5.41412	−	8.42453i	0.378138	−	0.588395i
$206$			26.5261i			1.84816i
$207$	−10.8929	+	23.5287i	−0.757109	+	1.63536i
$208$		0			0
$209$		0			0
$210$	6.88588	+	47.8923i	0.475171	+	3.30488i
$211$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$211$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$212$		0			0
$213$		0			0
$214$	4.19283	+	3.63310i	0.286616	+	0.248354i
$215$	−4.10237	+	28.5326i	−0.279779	+	1.94591i
$216$	−18.9342	+	5.55958i	−1.28831	+	0.378282i
$217$		0			0
$218$	−2.01570	−	3.13649i	−0.136521	−	0.212430i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−9.96286	+	11.4978i	−0.667162	+	0.769946i	−0.983930	−	0.178557i	$-0.942857\pi$
$223$	−9.96286	+	11.4978i	−0.667162	+	0.769946i	0.316767	+	0.948503i	$0.397403\pi$
$224$	−27.1548	−	12.4012i	−1.81436	−	0.828588i
$225$	25.9367	+	7.61571i	1.72911	+	0.507714i
$226$		0			0
$227$	−29.7903	+	4.28320i	−1.97725	+	0.284286i	−0.981635	+	0.190767i	$0.938903\pi$
$227$	−29.7903	+	4.28320i	−1.97725	+	0.284286i	−0.995617	+	0.0935193i	$0.970188\pi$
$228$		0			0
$229$		−	30.1422i		−	1.99185i	−0.0901808	−	0.995925i	$-0.528744\pi$
$229$		−	30.1422i		−	1.99185i	0.0901808	−	0.995925i	$-0.471256\pi$
$230$	−0.0785855	+	15.1655i	−0.00518177	+	0.999987i
$231$		0			0
$232$	19.6941	+	12.6567i	1.29298	+	0.830950i
$233$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$233$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$234$		0			0
$235$	4.30004	−	14.6446i	0.280503	−	0.955307i
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$239$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$240$	−19.5987	+	16.9823i	−1.26509	+	1.09620i
$241$	6.69049	+	10.4106i	0.430972	+	0.670606i	0.987030	−	0.160538i	$-0.0513229\pi$
$241$	6.69049	+	10.4106i	0.430972	+	0.670606i	−0.556057	+	0.831144i	$0.687687\pi$
$242$	−13.0868	+	8.41040i	−0.841254	+	0.540641i
$243$	6.09389	+	7.03273i	0.390923	+	0.451150i
$244$	−7.24077	−	24.6598i	−0.463543	−	1.57868i
$245$	−46.1455	−	6.63472i	−2.94813	−	0.423877i
$246$	−12.0254	+	13.8781i	−0.766715	+	0.884836i
$247$		0			0
$248$		0			0
$249$	−44.1708	+	20.1721i	−2.79921	+	1.27836i
$250$	15.6505	−	2.25020i	0.989821	−	0.142315i
$251$		0			0		0.540641	−	0.841254i	$-0.318182\pi$
$251$		0			0		−0.540641	+	0.841254i	$0.681818\pi$
$252$		−	57.0609i		−	3.59450i
$253$		0			0
$254$	30.1324			1.89068
$255$		0			0
$256$	−2.27704	−	15.8371i	−0.142315	−	0.989821i
$257$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$257$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$258$	14.8921	−	50.7177i	0.927140	−	3.15755i
$259$		0			0
$260$		0			0
$261$	−6.36823	+	44.2920i	−0.394183	+	2.74161i
$262$		0			0
$263$	−1.75911	+	1.52428i	−0.108471	+	0.0939909i	−0.707408	−	0.706806i	$-0.750136\pi$
$263$	−1.75911	+	1.52428i	−0.108471	+	0.0939909i	0.598937	+	0.800796i	$0.295590\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	9.64284	+	32.8405i	0.590132	+	2.00981i
$268$	12.7680	+	1.83576i	0.779930	+	0.112137i
$269$	−12.2574	+	14.1458i	−0.747345	+	0.862482i	−0.994308	−	0.106543i	$-0.966022\pi$
$269$	−12.2574	+	14.1458i	−0.747345	+	0.862482i	0.246963	+	0.969025i	$0.420567\pi$
$270$	−20.0690	−	9.16521i	−1.22136	−	0.557777i
$271$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$271$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$	4.10033	−	27.5058i	0.246811	−	1.65566i
$277$		0			0		1.00000			$0$
$277$		0			0		−1.00000			$\pi$
$278$		0			0
$279$		0			0
$280$	−13.8649	−	30.3600i	−0.828588	−	1.81436i
$281$	−0.588529	+	2.00435i	−0.0351087	+	0.119569i	−0.975183	−	0.221401i	$-0.928937\pi$
$281$	−0.588529	+	2.00435i	−0.0351087	+	0.119569i	0.940074	+	0.340970i	$0.110755\pi$
$282$	−11.6265	+	25.4586i	−0.692351	+	1.51604i
$283$	2.08196	+	1.80403i	0.123760	+	0.107238i	0.714542	−	0.699593i	$-0.246635\pi$
$283$	2.08196	+	1.80403i	0.123760	+	0.107238i	−0.590782	+	0.806831i	$0.701181\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−12.7776	−	19.8823i	−0.754236	−	1.17361i
$288$	25.7279	−	16.5343i	1.51603	−	0.974296i
$289$	11.1326	+	12.8477i	0.654861	+	0.755750i
$290$	7.37398	+	25.1135i	0.433015	+	1.47471i
$291$		0			0
$292$		0			0
$293$		0			0		−0.909632	−	0.415415i	$-0.863636\pi$
$293$		0			0		0.909632	+	0.415415i	$0.136364\pi$
$294$	82.0253	+	24.0848i	4.78381	+	1.40465i
$295$		0			0
$296$		0			0
$297$		0			0
$298$			3.49395i			0.202399i
$299$		0			0
$300$	−28.9937			−1.67395
$301$	57.2311	+	36.7802i	3.29875	+	2.11997i
$302$		0			0
$303$	−13.7486	−	30.1052i	−0.789835	−	1.72950i
$304$		0			0
$305$	11.9367	−	26.1378i	0.683495	−	1.49664i
$306$		0			0
$307$	−4.13668	+	28.7713i	−0.236093	+	1.64206i	0.434813	+	0.900521i	$0.356814\pi$
$307$	−4.13668	+	28.7713i	−0.236093	+	1.64206i	−0.670906	+	0.741542i	$0.734095\pi$
$308$		0			0
$309$	41.0998	−	35.6132i	2.33809	−	2.02596i
$310$		0			0
$311$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$311$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$312$		0			0
$313$		0			0		−0.281733	−	0.959493i	$-0.590909\pi$
$313$		0			0		0.281733	+	0.959493i	$0.409091\pi$
$314$		0			0
$315$	41.7775	−	48.2138i	2.35390	−	2.71654i
$316$		0			0
$317$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$317$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$318$		0			0
$319$		0			0
$320$	9.67128	−	15.0488i	0.540641	−	0.841254i
$321$		−	11.3741i		−	0.634841i
$322$	32.4800	+	15.0370i	1.81004	+	0.837979i
$323$		0			0
$324$	6.74597	+	4.33537i	0.374776	+	0.240854i
$325$		0			0
$326$	−14.9356	−	32.7044i	−0.827207	−	1.81133i
$327$	−2.15349	+	7.33412i	−0.119088	+	0.405578i
$328$	5.26212	−	11.5224i	0.290552	−	0.636221i
$329$	−27.2229	−	23.5887i	−1.50084	−	1.30049i
$330$		0			0
$331$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$331$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$332$	25.3148	−	21.9354i	1.38933	−	1.20386i
$333$		0			0
$334$	22.1486	−	14.2340i	1.21192	−	0.778852i
$335$	9.44431	+	10.8993i	0.515998	+	0.595493i
$336$	17.2427	+	58.7234i	0.940668	+	3.20362i
$337$		0			0		−0.989821	−	0.142315i	$-0.954545\pi$
$337$		0			0		0.989821	+	0.142315i	$0.0454545\pi$
$338$	−12.0395	+	13.8943i	−0.654861	+	0.755750i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−39.5127	+	61.4829i	−2.13348	+	3.31976i
$344$			36.4623i			1.96592i
$345$	23.6032	−	20.2391i	1.27075	−	1.08963i
$346$		0			0
$347$	−20.8205	−	13.3805i	−1.11770	−	0.718303i	−0.154743	−	0.987955i	$-0.549455\pi$
$347$	−20.8205	−	13.3805i	−1.11770	−	0.718303i	−0.962958	+	0.269652i	$0.913091\pi$
$348$	−6.83044	−	47.5068i	−0.366150	−	2.54663i
$349$	−1.35114	−	2.95859i	−0.0723249	−	0.158370i	0.870016	−	0.493023i	$-0.164108\pi$
$349$	−1.35114	−	2.95859i	−0.0723249	−	0.158370i	−0.942341	+	0.334653i	$0.891381\pi$
$350$	10.5130	−	35.8041i	0.561945	−	1.91381i
$351$		0			0
$352$		0			0
$353$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$353$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$354$		0			0
$355$		0			0
$356$	−12.7645	−	19.8619i	−0.676516	−	1.05268i
$357$		0			0
$358$		0			0
$359$		0			0		−0.281733	−	0.959493i	$-0.590909\pi$
$359$		0			0		0.281733	+	0.959493i	$0.409091\pi$
$360$	33.8447	+	4.86613i	1.78377	+	0.256467i
$361$	12.4424	−	14.3592i	0.654861	−	0.755750i
$362$	2.36580	+	1.08042i	0.124344	+	0.0567858i
$363$	30.6012	+	8.98531i	1.60614	+	0.471607i
$364$		0			0
$365$		0			0
$366$	−28.4869	+	44.3265i	−1.48903	+	2.31698i
$367$		−	37.3451i		−	1.94940i	−0.223524	−	0.974698i	$-0.571756\pi$
$367$		−	37.3451i		−	1.94940i	0.223524	−	0.974698i	$-0.428244\pi$
$368$	2.63164	+	19.0020i	0.137184	+	0.990546i
$369$	24.2124			1.26045
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.281733	−	0.959493i	$-0.409091\pi$
$373$		0			0		−0.281733	+	0.959493i	$0.590909\pi$
$374$		0			0
$375$	−24.4983	−	21.2279i	−1.26509	−	1.09620i
$376$	2.74755	−	19.1096i	0.141694	−	0.985503i
$377$		0			0
$378$	−39.3513	+	34.0981i	−2.02401	+	1.75381i
$379$		0			0		−0.540641	−	0.841254i	$-0.681818\pi$
$379$		0			0		0.540641	+	0.841254i	$0.318182\pi$
$380$		0			0
$381$	−40.4549	−	46.6875i	−2.07257	−	2.39187i
$382$		0			0
$383$	−1.65238	−	0.237576i	−0.0844327	−	0.0121396i	0.0999690	−	0.994991i	$-0.468126\pi$
$383$	−1.65238	−	0.237576i	−0.0844327	−	0.0121396i	−0.184402	+	0.982851i	$0.559035\pi$
$384$	−21.4811	+	24.7906i	−1.09620	+	1.26509i
$385$		0			0
$386$		0			0
$387$	−63.3970	+	28.9524i	−3.22265	+	1.47173i
$388$		0			0
$389$	−21.2530	+	33.0703i	−1.07757	+	1.67673i	−0.469146	+	0.883120i	$0.655438\pi$
$389$	−21.2530	+	33.0703i	−1.07757	+	1.67673i	−0.608424	+	0.793612i	$0.708198\pi$
$390$		0			0
$391$		0			0
$392$	−58.9702			−2.97844
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$397$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$398$		0			0
$399$		0			0
$400$	19.1899	−	5.63465i	0.959493	−	0.281733i
$401$	−9.61705	+	8.33322i	−0.480252	+	0.416141i	−0.861052	−	0.508516i	$-0.830194\pi$
$401$	−9.61705	+	8.33322i	−0.480252	+	0.416141i	0.380800	+	0.924657i	$0.375649\pi$
$402$	−14.2976	−	22.2475i	−0.713100	−	1.10961i
$403$		0			0
$404$	14.9503	+	17.2536i	0.743807	+	0.858399i
$405$	2.52586	+	8.60230i	0.125511	+	0.427452i
$406$	61.1424	+	8.79095i	3.03445	+	0.436288i
$407$		0			0
$408$		0			0
$409$	−14.5627	−	4.27599i	−0.720079	−	0.211434i	−0.0988936	−	0.995098i	$-0.531530\pi$
$409$	−14.5627	−	4.27599i	−0.720079	−	0.211434i	−0.621185	+	0.783664i	$0.713349\pi$
$410$	12.8825	−	5.88323i	0.636221	−	0.290552i
$411$		0			0
$412$	−20.2814	+	31.5584i	−0.999191	+	1.55477i
$413$		0			0
$414$	−30.9490	+	19.6639i	−1.52106	+	0.966427i
$415$	37.4499			1.83835
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		0.281733	−	0.959493i	$-0.409091\pi$
$419$		0			0		−0.281733	+	0.959493i	$0.590909\pi$
$420$	−28.4254	+	62.2429i	−1.38702	+	3.03714i
$421$	24.4890	+	21.2199i	1.19352	+	1.03419i	0.998574	+	0.0533795i	$0.0169993\pi$
$421$	24.4890	+	21.2199i	1.19352	+	1.03419i	0.194948	+	0.980814i	$0.437546\pi$
$422$		0			0
$423$	35.4075	−	10.3966i	1.72157	−	0.505499i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−44.4091	−	51.2509i	−2.14911	−	2.48020i
$428$	2.21045	+	7.52810i	0.106846	+	0.363885i
$429$		0			0
$430$	−26.6961	+	30.8090i	−1.28740	+	1.48574i
$431$		0			0		−0.909632	−	0.415415i	$-0.863636\pi$
$431$		0			0		0.909632	+	0.415415i	$0.136364\pi$
$432$	−26.7770	−	7.86243i	−1.28831	−	0.378282i
$433$		0			0		0.909632	−	0.415415i	$-0.136364\pi$
$433$		0			0		−0.909632	+	0.415415i	$0.863636\pi$
$434$		0			0
$435$	29.0110	−	45.1420i	1.39097	−	2.16439i
$436$		−	5.27269i		−	0.252516i
$437$		0			0
$438$		0			0
$439$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$439$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$440$		0			0
$441$	−46.8245	−	102.531i	−2.22974	−	4.88244i
$442$		0			0
$443$	−3.49262	+	7.64778i	−0.165940	+	0.363357i	−0.974274	−	0.225367i	$-0.927642\pi$
$443$	−3.49262	+	7.64778i	−0.165940	+	0.363357i	0.808334	+	0.588724i	$0.200369\pi$
$444$		0			0
$445$	3.75664	−	26.1280i	0.178082	−	1.23859i
$446$	−20.6439	+	6.06160i	−0.977517	+	0.287025i
$447$	5.41357	−	4.69088i	0.256053	−	0.221871i
$448$	−22.8247	−	35.5159i	−1.07836	−	1.67797i
$449$	15.3075	−	9.83752i	0.722404	−	0.464261i	−0.127068	−	0.991894i	$-0.540557\pi$
$449$	15.3075	−	9.83752i	0.722404	−	0.464261i	0.849473	+	0.527633i	$0.176920\pi$
$450$	25.0344	+	28.8912i	1.18013	+	1.36195i
$451$		0			0
$452$		0			0
$453$		0			0
$454$	−38.7168	−	17.6814i	−1.81707	−	0.829827i
$455$		0			0
$456$		0			0
$457$		0			0		0.989821	−	0.142315i	$-0.0454545\pi$
$457$		0			0		−0.989821	+	0.142315i	$0.954545\pi$
$458$	23.0461	−	35.8605i	1.07688	−	1.67565i
$459$		0			0
$460$	−11.6888	+	17.9826i	−0.544993	+	0.838441i
$461$	−30.4970			−1.42039			−0.710194	−	0.704006i	$-0.751393\pi$
$461$	−30.4970			−1.42039			−0.710194	+	0.704006i	$0.751393\pi$
$462$		0			0
$463$	3.23532	+	22.5022i	0.150358	+	1.04576i	0.915620	+	0.402045i	$0.131700\pi$
$463$	3.23532	+	22.5022i	0.150358	+	1.04576i	−0.765262	+	0.643719i	$0.777390\pi$
$464$	13.7533	+	30.1156i	0.638481	+	1.39808i
$465$		0			0
$466$		0			0
$467$	21.5090	+	18.6377i	0.995318	+	0.862448i	0.990496	−	0.137540i	$-0.0439196\pi$
$467$	21.5090	+	18.6377i	0.995318	+	0.862448i	0.00482209	+	0.999988i	$0.498465\pi$
$468$		0			0
$469$	32.6576	−	9.58912i	1.50799	−	0.442785i
$470$	16.3128	−	14.1351i	0.752453	−	0.652004i
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		0.909632	−	0.415415i	$-0.136364\pi$
$479$		0			0		−0.909632	+	0.415415i	$0.863636\pi$
$480$	−36.3011	+	5.21932i	−1.65691	+	0.238228i
$481$		0			0
$482$			17.5010i			0.797151i
$483$	−20.3082	−	70.5130i	−0.924055	−	3.20845i
$484$	−22.0000			−1.00000
$485$		0			0
$486$	1.87289	+	13.0262i	0.0849558	+	0.590880i
$487$	17.3370	+	37.9628i	0.785617	+	1.72026i	0.688792	+	0.724959i	$0.258141\pi$
$487$	17.3370	+	37.9628i	0.785617	+	1.72026i	0.0968243	+	0.995301i	$0.469132\pi$
$488$	10.2400	−	34.8742i	0.463543	−	1.57868i
$489$	−30.6204	+	67.0494i	−1.38470	+	3.03208i
$490$	−49.8271	−	43.1754i	−2.25096	−	1.95047i
$491$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$491$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$492$	−24.9178	+	7.31652i	−1.12338	+	0.329854i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	−67.9738	−	9.77316i	−3.04598	−	0.437946i
$499$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$499$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$500$	20.3400	+	9.28896i	0.909632	+	0.415415i
$501$	−51.7905	−	15.2071i	−2.31383	−	0.679401i
$502$		0			0
$503$	15.5612	−	2.23736i	0.693839	−	0.0997589i	0.213632	−	0.976914i	$-0.431471\pi$
$503$	15.5612	−	2.23736i	0.693839	−	0.0997589i	0.480207	+	0.877155i	$0.340562\pi$
$504$	43.6277	−	67.8861i	1.94333	−	3.02389i
$505$			25.5245i			1.13582i
$506$		0			0
$507$	37.6918			1.67395
$508$	35.8489	+	23.0387i	1.59054	+	1.02218i
$509$	6.14408	+	42.7330i	0.272332	+	1.89411i	0.423976	+	0.905673i	$0.360634\pi$
$509$	6.14408	+	42.7330i	0.272332	+	1.89411i	−0.151644	+	0.988435i	$0.548457\pi$
$510$		0			0
$511$		0			0
$512$	9.39977	−	20.5826i	0.415415	−	0.909632i
$513$		0			0
$514$		0			0
$515$	−40.2425	+	11.8163i	−1.77330	+	0.520687i
$516$	56.4951	−	48.9533i	2.48706	−	2.15505i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	28.7016	+	4.12666i	1.25744	+	0.180792i	0.738637	−	0.674103i	$-0.235470\pi$
$521$	28.7016	+	4.12666i	1.25744	+	0.180792i	0.518801	+	0.854895i	$0.326379\pi$
$522$	−41.4412	+	47.8257i	−1.81383	+	2.09327i
$523$	22.2367	+	10.1551i	0.972341	+	0.444053i	0.837274	−	0.546783i	$-0.184148\pi$
$523$	22.2367	+	10.1551i	0.972341	+	0.444053i	0.135067	+	0.990837i	$0.456875\pi$
$524$		0			0
$525$	−69.5897	+	31.7805i	−3.03714	+	1.38702i
$526$	−3.25827	+	0.468468i	−0.142067	+	0.0204262i
$527$		0			0
$528$		0			0
$529$	−3.03713	−	22.7986i	−0.132049	−	0.991243i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$	−13.6370	+	46.4435i	−0.590132	+	2.00981i
$535$	−3.64402	+	7.97930i	−0.157545	+	0.344975i
$536$	13.7867	+	11.9462i	0.595493	+	0.515998i
$537$		0			0
$538$	−25.3983	+	7.45762i	−1.09500	+	0.321521i
$539$		0			0
$540$	−16.8688	−	26.2483i	−0.725917	−	1.12955i
$541$	−17.7940	+	11.4355i	−0.765023	+	0.491650i	−0.864032	−	0.503436i	$-0.832069\pi$
$541$	−17.7940	+	11.4355i	−0.765023	+	0.491650i	0.0990098	+	0.995086i	$0.468432\pi$
$542$		0			0
$543$	−1.50223	−	5.11614i	−0.0644670	−	0.219555i
$544$		0			0
$545$	3.86044	−	4.45518i	0.165363	−	0.190839i
$546$		0			0
$547$	42.1099	+	12.3646i	1.80049	+	0.528672i	0.997712	−	0.0676046i	$-0.0215356\pi$
$547$	42.1099	+	12.3646i	1.80049	+	0.528672i	0.802779	+	0.596277i	$0.203354\pi$
$548$		0			0
$549$	68.7666	−	9.88715i	2.93489	−	0.421973i
$550$		0			0
$551$		0			0
$552$	25.9087	−	29.5890i	1.10275	−	1.25939i
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$		0			0		0.281733	−	0.959493i	$-0.409091\pi$
$557$		0			0		−0.281733	+	0.959493i	$0.590909\pi$
$558$		0			0
$559$		0			0
$560$	6.71739	−	46.7205i	0.283862	−	1.97430i
$561$		0			0
$562$	−2.23267	+	1.93462i	−0.0941793	+	0.0816068i
$563$	16.2160	+	25.2325i	0.683422	+	1.06342i	0.993623	+	0.112754i	$0.0359672\pi$
$563$	16.2160	+	25.2325i	0.683422	+	1.06342i	−0.310201	+	0.950671i	$0.600396\pi$
$564$	−33.2974	+	21.3989i	−1.40207	+	0.901058i
$565$		0			0
$566$	1.09761	+	3.73810i	0.0461358	+	0.157124i
$567$	20.9435	+	3.01123i	0.879546	+	0.126460i
$568$		0			0
$569$	−36.4660	−	16.6535i	−1.52873	−	0.698149i	−0.539164	−	0.842201i	$-0.681260\pi$
$569$	−36.4660	−	16.6535i	−1.52873	−	0.698149i	−0.989570	+	0.144052i	$0.953987\pi$
$570$		0			0
$571$		0			0		0.909632	−	0.415415i	$-0.136364\pi$
$571$		0			0		−0.909632	+	0.415415i	$0.863636\pi$
$572$		0			0
$573$		0			0
$574$		−	33.4237i		−	1.39508i
$575$	−23.0425	+	6.63640i	−0.960940	+	0.276757i
$576$	43.2507			1.80211
$577$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$577$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$578$	3.42148	+	23.7969i	0.142315	+	0.989821i
$579$		0			0
$580$	−10.4284	+	35.5158i	−0.433015	+	1.47471i
$581$	36.7159	−	80.3966i	1.52323	−	3.33541i
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−32.8385	+	21.1040i	−1.35539	+	0.871057i	−0.998020	−	0.0629052i	$-0.979963\pi$
$587$	−32.8385	+	21.1040i	−1.35539	+	0.871057i	−0.357372	+	0.933962i	$0.616327\pi$
$588$	79.1717	+	91.3690i	3.26498	+	3.76799i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$593$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$594$		0			0
$595$		0			0
$596$	−2.67141	+	4.15680i	−0.109425	+	0.170269i
$597$		0			0
$598$		0			0
$599$		0			0		1.00000			$0$
$599$		0			0		−1.00000			$\pi$
$600$	−34.4941	−	22.1680i	−1.40822	−	0.905006i
$601$	0.255416	+	1.77646i	0.0104186	+	0.0724632i	0.994367	−	0.105988i	$-0.0338005\pi$
$601$	0.255416	+	1.77646i	0.0104186	+	0.0724632i	−0.983949	+	0.178451i	$0.942891\pi$
$602$	39.9671	+	87.5157i	1.62894	+	3.56687i
$603$	−9.82373	+	33.4566i	−0.400053	+	1.36246i
$604$		0			0
$605$	−18.5890	−	16.1074i	−0.755750	−	0.654861i
$606$	6.66102	−	46.3284i	0.270585	−	1.88196i
$607$	−4.80176	+	1.40992i	−0.194897	+	0.0572271i	−0.377725	−	0.925918i	$-0.623293\pi$
$607$	−4.80176	+	1.40992i	−0.194897	+	0.0572271i	0.182827	+	0.983145i	$0.441475\pi$
$608$		0			0
$609$	−68.4673	−	106.537i	−2.77443	−	4.31710i
$610$	34.1857	−	21.9698i	1.38414	−	0.889532i
$611$		0			0
$612$		0			0
$613$		0			0		−0.989821	−	0.142315i	$-0.954545\pi$
$613$		0			0		0.989821	+	0.142315i	$0.0454545\pi$
$614$	−26.9194	+	31.0667i	−1.08638	+	1.25375i
$615$	−26.4112	−	12.0616i	−1.06500	−	0.486370i
$616$		0			0
$617$		0			0		0.909632	−	0.415415i	$-0.136364\pi$
$617$		0			0		−0.909632	+	0.415415i	$0.863636\pi$
$618$	76.1261	−	10.9453i	3.06224	−	0.440284i
$619$		0			0		0.540641	−	0.841254i	$-0.318182\pi$
$619$		0			0		−0.540641	+	0.841254i	$0.681818\pi$
$620$		0			0
$621$	32.0552	+	9.59296i	1.28633	+	0.384952i
$622$		0			0
$623$	−52.4079	−	33.6805i	−2.09968	−	1.34938i
$624$		0			0
$625$	10.3854	+	22.7408i	0.415415	+	0.909632i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$	86.5667	−	25.4183i	3.44890	−	1.01269i
$631$		0			0		0.755750	−	0.654861i	$-0.227273\pi$
$631$		0			0		−0.755750	+	0.654861i	$0.772727\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	13.4227	+	45.7136i	0.532665	+	1.81409i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$	23.0121	−	10.5093i	0.909632	−	0.415415i
$641$	50.0668	−	7.19851i	1.97752	−	0.284324i	0.982167	−	0.188011i	$-0.0602042\pi$
$641$	50.0668	−	7.19851i	1.97752	−	0.284324i	0.995351	−	0.0963128i	$-0.0307049\pi$
$642$	8.69643	−	13.5319i	0.343221	−	0.534062i
$643$		−	9.93714i		−	0.391883i	−0.980616	−	0.195941i	$-0.937224\pi$
$643$		−	9.93714i		−	0.391883i	0.980616	−	0.195941i	$-0.0627762\pi$
$644$	27.1448	+	42.7233i	1.06965	+	1.68353i
$645$	83.5772			3.29085
$646$		0			0
$647$	−6.30952	−	43.8837i	−0.248053	−	1.72524i	−0.609443	−	0.792830i	$-0.708607\pi$
$647$	−6.30952	−	43.8837i	−0.248053	−	1.72524i	0.361390	−	0.932415i	$-0.382302\pi$
$648$	4.71102	+	10.3157i	0.185066	+	0.405239i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	7.23612	−	50.3283i	0.283388	−	1.97101i
$653$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$653$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$654$	−8.16957	+	7.07897i	−0.319455	+	0.276810i
$655$		0			0
$656$	15.0703	−	9.68507i	0.588395	−	0.378138i
$657$		0			0
$658$	−14.3518	−	48.8779i	−0.559493	−	1.90546i
$659$		0			0		−0.989821	−	0.142315i	$-0.954545\pi$
$659$		0			0		0.989821	+	0.142315i	$0.0454545\pi$
$660$		0			0
$661$	−26.9282	−	12.2977i	−1.04739	−	0.478325i	−0.184030	−	0.982921i	$-0.558914\pi$
$661$	−26.9282	−	12.2977i	−1.04739	−	0.478325i	−0.863356	+	0.504596i	$0.831642\pi$
$662$		0			0
$663$		0			0
$664$	46.8887	−	6.74158i	1.81963	−	0.261624i
$665$		0			0
$666$		0			0
$667$	−16.3023	−	36.1922i	−0.631228	−	1.40137i
$668$	37.2336			1.44061
$669$	37.1078	+	23.8477i	1.43467	+	0.922007i
$670$	2.90260	+	20.1880i	0.112137	+	0.779930i
$671$		0			0
$672$	−24.3849	+	83.0474i	−0.940668	+	3.20362i
$673$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$673$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$674$		0			0
$675$	4.96455	−	34.5292i	0.191086	−	1.32903i
$676$	−24.9468	+	7.32505i	−0.959493	+	0.281733i
$677$		0			0		0.755750	−	0.654861i	$-0.227273\pi$
$677$		0			0		−0.755750	+	0.654861i	$0.772727\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	24.5844	+	83.7266i	0.942074	+	3.20841i
$682$		0			0
$683$	−4.71532	+	5.44177i	−0.180427	+	0.208223i	−0.838757	−	0.544505i	$-0.816717\pi$
$683$	−4.71532	+	5.44177i	−0.180427	+	0.208223i	0.658331	+	0.752729i	$0.271263\pi$
$684$		0			0
$685$		0			0
$686$	−94.0174	+	42.9363i	−3.58960	+	1.63932i
$687$	−86.5037	+	12.4374i	−3.30032	+	0.474515i
$688$	−27.8784	+	43.3797i	−1.06286	+	1.65383i
$689$		0			0
$690$	43.5554	−	6.03213i	1.65812	−	0.229639i
$691$		0			0		1.00000			$0$
$691$		0			0		−1.00000			$\pi$
$692$		0			0
$693$		0			0
$694$	−14.5399	−	31.8379i	−0.551926	−	1.20855i
$695$		0			0
$696$	28.1965	−	61.7418i	1.06879	−	2.34032i
$697$		0			0
$698$	0.654612	−	4.55292i	0.0247774	−	0.172331i
$699$		0			0
$700$	39.8826	−	34.5585i	1.50742	−	1.30619i
$701$	18.5836	+	28.9167i	0.701895	+	1.09217i	0.990868	+	0.134832i	$0.0430496\pi$
$701$	18.5836	+	28.9167i	0.701895	+	1.09217i	−0.288974	+	0.957337i	$0.593314\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	−43.8021	−	6.29780i	−1.64968	−	0.237189i
$706$		0			0
$707$	54.7953	+	25.0242i	2.06079	+	0.941131i
$708$		0			0
$709$	24.4080	−	11.1468i	0.916661	−	0.418625i	0.0995021	−	0.995037i	$-0.468275\pi$
$709$	24.4080	−	11.1468i	0.916661	−	0.418625i	0.817159	+	0.576412i	$0.195548\pi$
$710$		0			0
$711$		0			0
$712$		−	33.3895i		−	1.25132i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$719$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$720$	36.5448	+	31.6663i	1.36195	+	1.18013i
$721$	−14.0869	+	97.9763i	−0.524622	+	3.64883i
$722$	25.7816	−	7.57017i	0.959493	−	0.281733i
$723$	27.1163	−	23.4964i	1.00847	−	0.873841i
$724$	1.98855	+	3.09424i	0.0739038	+	0.114997i
$725$	−34.8146	+	22.3740i	−1.29298	+	0.830950i
$726$	29.5366	+	34.0870i	1.09620	+	1.26509i
$727$	−14.8688	−	50.6386i	−0.551454	−	1.87808i	−0.472779	−	0.881181i	$-0.656749\pi$
$727$	−14.8688	−	50.6386i	−0.551454	−	1.87808i	−0.0786754	−	0.996900i	$-0.525069\pi$
$728$		0			0
$729$	25.5454	−	29.4810i	0.946126	−	1.09189i
$730$		0			0
$731$		0			0
$732$	−67.7824	+	30.9552i	−2.50531	+	1.14414i
$733$		0			0		0.989821	−	0.142315i	$-0.0454545\pi$
$733$		0			0		−0.989821	+	0.142315i	$0.954545\pi$
$734$	28.5534	−	44.4299i	1.05392	−	1.63994i
$735$			135.169i			4.98577i
$736$	−11.3976	+	24.6190i	−0.420123	+	0.907467i
$737$		0			0
$738$	28.8057	+	18.5123i	1.06035	+	0.681448i
$739$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$739$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−28.6751	−	24.8471i	−1.05199	−	0.911552i	−0.0557692	−	0.998444i	$-0.517761\pi$
$743$	−28.6751	−	24.8471i	−1.05199	−	0.911552i	−0.996218	+	0.0868918i	$0.972307\pi$
$744$		0			0
$745$	−5.30065	+	1.55641i	−0.194201	+	0.0570225i
$746$		0			0
$747$	48.9529	+	76.1722i	1.79109	+	2.78699i
$748$		0			0
$749$	13.5572	+	15.6458i	0.495368	+	0.571685i
$750$	−12.9155	−	43.9861i	−0.471607	−	1.60614i
$751$		0			0		−0.989821	−	0.142315i	$-0.954545\pi$
$751$		0			0		0.989821	+	0.142315i	$0.0454545\pi$
$752$	17.8797	−	20.6342i	0.652004	−	0.752453i
$753$		0			0
$754$		0			0
$755$		0			0
$756$	−72.8874	+	10.4796i	−2.65089	+	0.381140i
$757$		0			0		0.540641	−	0.841254i	$-0.318182\pi$
$757$		0			0		−0.540641	+	0.841254i	$0.681818\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−45.8842	−	29.4880i	−1.66330	−	1.06894i	−0.913106	−	0.407723i	$-0.866323\pi$
$761$	−45.8842	−	29.4880i	−1.66330	−	1.06894i	−0.750196	−	0.661216i	$-0.770041\pi$
$762$	−12.4333	−	86.4758i	−0.450412	−	3.13269i
$763$	−5.77950	−	12.6553i	−0.209232	−	0.458154i
$764$		0			0
$765$		0			0
$766$	−1.78421	−	1.54603i	−0.0644661	−	0.0558602i
$767$		0			0
$768$	−44.5108	+	13.0695i	−1.60614	+	0.471607i
$769$	7.22395	−	6.25959i	0.260502	−	0.225727i	−0.514810	−	0.857304i	$-0.672138\pi$
$769$	7.22395	−	6.25959i	0.260502	−	0.225727i	0.775313	+	0.631577i	$0.217592\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		0			0		−0.281733	−	0.959493i	$-0.590909\pi$
$773$		0			0		0.281733	+	0.959493i	$0.409091\pi$
$774$	−97.5606	−	14.0271i	−3.50674	−	0.504194i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	−50.5699	+	23.0945i	−1.81302	+	0.827978i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	57.7464			2.06369
$784$	−70.1575	−	45.0875i	−2.50563	−	1.61027i
$785$		0			0
$786$		0			0
$787$	−3.92732	+	13.3752i	−0.139994	+	0.476776i	−0.999404	−	0.0345107i	$-0.989013\pi$
$787$	−3.92732	+	13.3752i	−0.139994	+	0.476776i	0.859410	+	0.511286i	$0.170831\pi$
$788$		0			0
$789$	5.10030	+	4.41944i	0.181576	+	0.157336i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.989821	−	0.142315i	$-0.954545\pi$
$797$		0			0		0.989821	+	0.142315i	$0.0454545\pi$
$798$		0			0
$799$		0			0
$800$	27.1386	+	7.96860i	0.959493	+	0.281733i
$801$	58.0542	−	26.5124i	2.05124	−	0.936771i
$802$	−17.8129	+	2.56111i	−0.628997	+	0.0904361i
$803$		0			0
$804$		−	37.3998i		−	1.31899i
$805$	−8.34403	+	55.9734i	−0.294088	+	1.97280i
$806$		0			0
$807$	45.6540	+	29.3400i	1.60710	+	1.03282i
$808$	4.59481	+	31.9576i	0.161645	+	1.12426i
$809$	22.8889	+	50.1198i	0.804732	+	1.76212i	0.628564	+	0.777758i	$0.283643\pi$
$809$	22.8889	+	50.1198i	0.804732	+	1.76212i	0.176168	+	0.984360i	$0.443630\pi$
$810$	−3.57211	+	12.1655i	−0.125511	+	0.427452i
$811$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$811$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$812$	66.0205	+	57.2071i	2.31686	+	2.00757i
$813$		0			0
$814$		0			0
$815$	42.9624	−	37.2271i	1.50491	−	1.30401i
$816$		0			0
$817$		0			0
$818$	−14.0561	−	16.2216i	−0.491459	−	0.567174i
$819$		0			0
$820$	19.8247	+	2.85036i	0.692307	+	0.0995388i
$821$	−24.3844	+	28.1411i	−0.851022	+	0.982132i	−0.999977	−	0.00671205i	$-0.997863\pi$
$821$	−24.3844	+	28.1411i	−0.851022	+	0.982132i	0.148955	+	0.988844i	$0.452409\pi$
$822$		0			0
$823$	−46.1208	−	13.5423i	−1.60767	−	0.472054i	−0.650002	−	0.759933i	$-0.725232\pi$
$823$	−46.1208	−	13.5423i	−1.60767	−	0.472054i	−0.957667	+	0.287878i	$0.907050\pi$
$824$	−48.2580	+	22.0387i	−1.68115	+	0.767754i
$825$		0			0
$826$		0			0
$827$			47.4342i			1.64945i	0.565536	+	0.824724i	$0.308669\pi$
$827$			47.4342i			1.64945i	−0.565536	+	0.824724i	$0.691331\pi$
$828$	−51.8551	−	0.268705i	−1.80209	−	0.00933814i
$829$	−46.8116			−1.62584			−0.812918	−	0.582378i	$-0.802122\pi$
$829$	−46.8116			−1.62584			−0.812918	+	0.582378i	$0.802122\pi$
$830$	44.5547	+	28.6335i	1.54651	+	0.993885i
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$	31.4606	+	27.2608i	1.08874	+	0.943399i
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		−0.540641	−	0.841254i	$-0.681818\pi$
$839$		0			0		0.540641	+	0.841254i	$0.318182\pi$
$840$	−81.4078	+	52.3176i	−2.80884	+	1.80513i
$841$	−25.8711	−	29.8568i	−0.892107	−	1.02955i
$842$	12.9106	+	43.9694i	0.444928	+	1.51529i
$843$	5.99503	+	0.861955i	0.206480	+	0.0296873i
$844$		0			0
$845$	−26.4420	−	12.0757i	−0.909632	−	0.415415i
$846$	50.0737	+	14.7030i	1.72157	+	0.505499i
$847$	−52.8037	+	24.1146i	−1.81436	+	0.828588i
$848$		0			0
$849$	4.31824	−	6.71931i	0.148202	−	0.230606i
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$853$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$854$	−13.6486	−	94.9282i	−0.467046	−	3.24838i
$855$		0			0
$856$	−3.12605	+	10.6463i	−0.106846	+	0.363885i
$857$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$857$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$858$		0			0
$859$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$859$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$860$	−55.3167	+	16.2424i	−1.88628	+	0.553863i
$861$	−51.7870	+	44.8737i	−1.76490	+	1.52929i
$862$		0			0
$863$	25.9114	−	16.6523i	0.882035	−	0.566849i	−0.0193769	−	0.999812i	$-0.506168\pi$
$863$	25.9114	−	16.6523i	0.882035	−	0.566849i	0.901412	+	0.432963i	$0.142532\pi$
$864$	−25.8454	−	29.8272i	−0.879280	−	1.01474i
$865$		0			0
$866$		0			0
$867$	32.2776	−	37.2503i	1.09620	−	1.26509i
$868$		0			0
$869$		0			0
$870$	69.0294	−	31.5247i	2.34032	−	1.06879i
$871$		0			0
$872$	4.03141	−	6.27299i	0.136521	−	0.212430i
$873$		0			0
$874$		0			0
$875$	59.0012			1.99460
$876$		0			0
$877$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$877$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	2.72371	+	2.36011i	0.0917643	+	0.0795142i	0.699535	−	0.714598i	$-0.253391\pi$
$881$	2.72371	+	2.36011i	0.0917643	+	0.0795142i	−0.607771	+	0.794113i	$0.707936\pi$
$882$	22.6859	−	157.784i	0.763874	−	5.31286i
$883$	−33.0365	+	9.70038i	−1.11177	+	0.326444i	−0.785517	−	0.618840i	$-0.787603\pi$
$883$	−33.0365	+	9.70038i	−1.11177	+	0.326444i	−0.326249	+	0.945284i	$0.605785\pi$
$884$		0			0
$885$		0			0
$886$	−10.0026	+	6.42826i	−0.336043	+	0.215962i
$887$	18.7503	+	21.6390i	0.629572	+	0.726565i	0.977495	−	0.210958i	$-0.0676584\pi$
$887$	18.7503	+	21.6390i	0.629572	+	0.726565i	−0.347923	+	0.937523i	$0.613113\pi$
$888$		0			0
$889$	111.297	+	16.0020i	3.73277	+	0.536691i
$890$	24.4463	−	28.2125i	0.819442	−	0.945687i
$891$		0			0
$892$	−29.1949	−	8.57239i	−0.977517	−	0.287025i
$893$		0			0
$894$	10.0271	−	1.44169i	0.335358	−	0.0482172i
$895$		0			0
$896$		−	59.7050i		−	1.99460i
$897$		0			0
$898$	25.7331			0.858724
$899$		0			0
$900$	7.69402	+	53.5131i	0.256467	+	1.78377i
$901$		0			0
$902$		0			0
$903$	81.9390	−	179.421i	2.72676	−	5.97077i
$904$		0			0
$905$	−0.585238	+	4.07042i	−0.0194540	+	0.135305i
$906$		0			0
$907$	39.9331	−	34.6022i	1.32596	−	1.14895i	0.348617	−	0.937265i	$-0.386651\pi$
$907$	39.9331	−	34.6022i	1.32596	−	1.14895i	0.977339	−	0.211682i	$-0.0678940\pi$
$908$	−32.5430	−	50.6378i	−1.07998	−	1.68048i
$909$	−51.9161	+	33.3645i	−1.72195	+	1.10663i
$910$		0			0
$911$		0			0		−0.281733	−	0.959493i	$-0.590909\pi$
$911$		0			0		0.281733	+	0.959493i	$0.409091\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	−79.9370	−	23.4716i	−2.64264	−	0.775948i
$916$	54.8366	−	25.0430i	1.81185	−	0.827445i
$917$		0			0
$918$		0			0
$919$		0			0			−	1.00000i	$-0.5\pi$
$919$		0			0				1.00000i	$0.5\pi$
$920$	−27.6554	+	12.4570i	−0.911772	+	0.410696i
$921$	84.2763			2.77700
$922$	−36.2827	−	23.3175i	−1.19491	−	0.767919i
$923$		0			0
$924$		0			0
$925$		0			0
$926$	−13.3556	+	29.2448i	−0.438893	+	0.961042i
$927$	−76.6372	−	66.4065i	−2.51710	−	2.18108i
$928$	−6.66331	+	46.3444i	−0.218734	+	1.52133i
$929$	−19.8446	+	5.82689i	−0.651079	+	0.191174i	−0.590561	−	0.806993i	$-0.701093\pi$
$929$	−19.8446	+	5.82689i	−0.651079	+	0.191174i	−0.0605180	+	0.998167i	$0.519275\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$	11.3395	+	38.6188i	0.371040	+	1.26365i
$935$		0			0
$936$		0			0
$937$		0			0		−0.909632	−	0.415415i	$-0.863636\pi$
$937$		0			0		0.909632	+	0.415415i	$0.136364\pi$
$938$	46.1848	+	13.5611i	1.50799	+	0.442785i
$939$		0			0
$940$	30.2150	−	4.34426i	0.985503	−	0.141694i
$941$	30.6989	−	47.7685i	1.00076	−	1.55721i	0.181812	−	0.983333i	$-0.441804\pi$
$941$	30.6989	−	47.7685i	1.00076	−	1.55721i	0.818944	−	0.573874i	$-0.194560\pi$
$942$		0			0
$943$	−18.1285	+	11.5182i	−0.590346	+	0.375084i
$944$		0			0
$945$	−69.2592	−	44.5102i	−2.25300	−	1.44792i
$946$		0			0
$947$	−19.1210	−	41.8691i	−0.621349	−	1.36056i	−0.914534	−	0.404509i	$-0.867443\pi$
$947$	−19.1210	−	41.8691i	−0.621349	−	1.36056i	0.293185	−	0.956056i	$-0.405285\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$		0			0		0.755750	−	0.654861i	$-0.227273\pi$
$953$		0			0		−0.755750	+	0.654861i	$0.772727\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	−47.1785	−	21.5457i	−1.52268	−	0.695384i
$961$	−29.7443	−	8.73371i	−0.959493	−	0.281733i
$962$		0			0
$963$	−20.9930	+	3.01833i	−0.676489	+	0.0972644i
$964$	−13.3810	+	20.8212i	−0.430972	+	0.670606i
$965$		0			0
$966$	29.7520	−	99.4175i	0.957256	−	3.19870i
$967$	−17.0350			−0.547808			−0.273904	−	0.961757i	$-0.588315\pi$
$967$	−17.0350			−0.547808			−0.273904	+	0.961757i	$0.588315\pi$
$968$	−26.1737	−	16.8208i	−0.841254	−	0.540641i
$969$		0			0
$970$		0			0
$971$		0			0		0.281733	−	0.959493i	$-0.409091\pi$
$971$		0			0		−0.281733	+	0.959493i	$0.590909\pi$
$972$	−7.73140	+	16.9294i	−0.247985	+	0.543011i
$973$		0			0
$974$	−8.39959	+	58.4204i	−0.269140	+	1.87191i
$975$		0			0
$976$	38.8468	−	33.6610i	1.24346	−	1.07746i
$977$		0			0		−0.540641	−	0.841254i	$-0.681818\pi$
$977$		0			0		0.540641	+	0.841254i	$0.318182\pi$
$978$	−87.6942	+	56.3577i	−2.80415	+	1.80212i
$979$		0			0
$980$	−26.2688	−	89.4632i	−0.839125	−	2.85780i
$981$	14.1079	+	2.02841i	0.450431	+	0.0647622i
$982$		0			0
$983$	56.4672	+	25.7877i	1.80103	+	0.822501i	0.959188	+	0.282770i	$0.0912534\pi$
$983$	56.4672	+	25.7877i	1.80103	+	0.822501i	0.841838	+	0.539731i	$0.181474\pi$
$984$	−35.2390	−	10.3471i	−1.12338	−	0.329854i
$985$		0			0
$986$		0			0
$987$	−56.4635	+	87.8590i	−1.79725	+	2.79658i
$988$		0			0
$989$	33.6941	−	51.8365i	1.07141	−	1.64831i
$990$		0			0
$991$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$991$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$	−73.3969	−	63.5987i	−2.32567	−	2.01520i
$997$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$997$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.o.a.159.3	yes	40
4.3	odd	2	inner	460.2.o.a.159.2	✓	40
5.4	even	2	inner	460.2.o.a.159.2	✓	40
20.19	odd	2	CM	460.2.o.a.159.3	yes	40
23.11	odd	22	inner	460.2.o.a.379.3	yes	40
92.11	even	22	inner	460.2.o.a.379.2	yes	40
115.34	odd	22	inner	460.2.o.a.379.2	yes	40
460.379	even	22	inner	460.2.o.a.379.3	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.o.a.159.2	✓	40	4.3	odd	2	inner
460.2.o.a.159.2	✓	40	5.4	even	2	inner
460.2.o.a.159.3	yes	40	1.1	even	1	trivial
460.2.o.a.159.3	yes	40	20.19	odd	2	CM
460.2.o.a.379.2	yes	40	92.11	even	22	inner
460.2.o.a.379.2	yes	40	115.34	odd	22	inner
460.2.o.a.379.3	yes	40	23.11	odd	22	inner
460.2.o.a.379.3	yes	40	460.379	even	22	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:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.o (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(1.18971 + 0.764582i) q^{2} +(-0.412623 - 2.86986i) q^{3} +(0.830830 + 1.81926i) q^{4} +(-0.629973 + 2.14549i) q^{5} +(1.70334 - 3.72979i) q^{6} +(3.98826 + 3.45585i) q^{7} +(-0.402527 + 2.79964i) q^{8} +(-5.18734 + 1.52314i) q^{9} +O(q^{10})\)	\(q+(1.18971 + 0.764582i) q^{2} +(-0.412623 - 2.86986i) q^{3} +(0.830830 + 1.81926i) q^{4} +(-0.629973 + 2.14549i) q^{5} +(1.70334 - 3.72979i) q^{6} +(3.98826 + 3.45585i) q^{7} +(-0.402527 + 2.79964i) q^{8} +(-5.18734 + 1.52314i) q^{9} +(-2.38989 + 2.07085i) q^{10} +(4.87821 - 3.13503i) q^{12} +(2.10260 + 7.16081i) q^{14} +(6.41720 + 0.922653i) q^{15} +(-2.61944 + 3.02300i) q^{16} +(-7.33601 - 2.15405i) q^{18} +(-4.42662 + 0.636451i) q^{20} +(8.27214 - 12.8717i) q^{21} +(3.15934 - 3.60813i) q^{23} +8.20065 q^{24} +(-4.20627 - 2.70320i) q^{25} +(2.89829 + 6.34638i) q^{27} +(-2.97353 + 10.1269i) q^{28} +(3.43833 - 7.52889i) q^{29} +(6.92917 + 6.00416i) q^{30} +(-5.42771 + 1.59372i) q^{32} +(-9.92699 + 6.37969i) q^{35} +(-7.08080 - 8.17168i) q^{36} +(-5.75302 - 2.62732i) q^{40} +(-4.29710 - 1.26174i) q^{41} +(19.6829 - 8.98889i) q^{42} +(12.7602 - 1.83464i) q^{43} -12.0889i q^{45} +(6.51741 - 1.87706i) q^{46} -6.82575 q^{47} +(9.75642 + 6.27007i) q^{48} +(2.96714 + 20.6369i) q^{49} +(-2.93743 - 6.43207i) q^{50} +(-1.40419 + 9.76634i) q^{54} +(-11.2805 + 9.77461i) q^{56} +(9.84707 - 6.32833i) q^{58} +(3.65305 + 12.4411i) q^{60} +(-12.7196 - 1.82881i) q^{61} +(-25.9522 - 11.8520i) q^{63} +(-7.67594 - 2.25386i) q^{64} +(3.48695 - 5.42579i) q^{67} +(-11.6584 - 7.57806i) q^{69} -16.6881 q^{70} +(-2.17620 - 15.1358i) q^{72} +(-6.02221 + 13.1868i) q^{75} +(-4.83564 - 7.52440i) q^{80} +(3.37299 - 2.16769i) q^{81} +(-4.14761 - 4.78660i) q^{82} +(-4.71849 - 16.0697i) q^{83} +(30.2898 + 4.35501i) q^{84} +(16.5837 + 7.57350i) q^{86} +(-23.0256 - 6.76092i) q^{87} +(-11.6848 + 1.68002i) q^{89} +(9.24298 - 14.3824i) q^{90} +(9.18901 + 2.74994i) q^{92} +(-8.12067 - 5.21884i) q^{94} +(6.81335 + 14.9192i) q^{96} +(-12.2485 + 26.8206i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 8 q^{4} - 8 q^{6} + 4 q^{9}+O(q^{10}) \) 40 * q - 8 * q^4 - 8 * q^6 + 4 * q^9	\( 40 q - 8 q^{4} - 8 q^{6} + 4 q^{9} - 16 q^{16} - 16 q^{24} + 20 q^{25} + 24 q^{29} + 8 q^{36} + 48 q^{41} - 4 q^{46} + 100 q^{49} - 276 q^{54} - 264 q^{56} - 32 q^{64} - 4 q^{69} - 40 q^{70} + 20 q^{81} + 352 q^{84} + 396 q^{86} - 56 q^{94} - 32 q^{96}+O(q^{100}) \) 40 * q - 8 * q^4 - 8 * q^6 + 4 * q^9 - 16 * q^16 - 16 * q^24 + 20 * q^25 + 24 * q^29 + 8 * q^36 + 48 * q^41 - 4 * q^46 + 100 * q^49 - 276 * q^54 - 264 * q^56 - 32 * q^64 - 4 * q^69 - 40 * q^70 + 20 * q^81 + 352 * q^84 + 396 * q^86 - 56 * q^94 - 32 * q^96

Introduction

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