LMFDB - Embedded newform 720.2.t.b.181.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [720,2,Mod(181,720)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(720, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("720.181");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	720.t (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.74922894553$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.18939904.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 14x^{6} - 28x^{5} + 43x^{4} - 44x^{3} + 30x^{2} - 12x + 2 $ x^8 - 4x^7 + 14x^6 - 28x^5 + 43x^4 - 44x^3 + 30x^2 - 12*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 240)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			181.3
Root			$0.500000 - 1.44392i$ of defining polynomial
Character	$\chi$	$=$	720.181
Dual form			720.2.t.b.541.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.167452 + 1.40426i) q^{2} +(-1.94392 + 0.470294i) q^{4} +(-0.707107 - 0.707107i) q^{5} +1.41421i q^{7} +(-0.985930 - 2.65103i) q^{8} +O(q^{10})$	\(q+(0.167452 + 1.40426i) q^{2} +(-1.94392 + 0.470294i) q^{4} +(-0.707107 - 0.707107i) q^{5} +1.41421i q^{7} +(-0.985930 - 2.65103i) q^{8} +(0.874559 - 1.11137i) q^{10} +(-4.22274 - 4.22274i) q^{11} +(1.33490 - 1.33490i) q^{13} +(-1.98593 + 0.236813i) q^{14} +(3.55765 - 1.82843i) q^{16} +1.14343 q^{17} +(1.05941 - 1.05941i) q^{19} +(1.70711 + 1.04201i) q^{20} +(5.22274 - 6.63696i) q^{22} -7.77568i q^{23} +1.00000i q^{25} +(2.09809 + 1.65103i) q^{26} +(-0.665096 - 2.74912i) q^{28} +(-2.94059 + 2.94059i) q^{29} +0.389604 q^{31} +(3.16333 + 4.68971i) q^{32} +(0.191470 + 1.60568i) q^{34} +(1.00000 - 1.00000i) q^{35} +(-4.28216 - 4.28216i) q^{37} +(1.66510 + 1.31029i) q^{38} +(-1.17740 + 2.57172i) q^{40} -5.45844i q^{41} +(-4.91245 - 4.91245i) q^{43} +(10.1946 + 6.22274i) q^{44} +(10.9191 - 1.30205i) q^{46} +10.7324 q^{47} +5.00000 q^{49} +(-1.40426 + 0.167452i) q^{50} +(-1.96715 + 3.22274i) q^{52} +(0.863230 + 0.863230i) q^{53} +5.97186i q^{55} +(3.74912 - 1.39432i) q^{56} +(-4.62177 - 3.63696i) q^{58} +(-8.50961 - 8.50961i) q^{59} +(2.22746 - 2.22746i) q^{61} +(0.0652400 + 0.547108i) q^{62} +(-6.05588 + 5.22746i) q^{64} -1.88784 q^{65} +(2.94725 - 2.94725i) q^{67} +(-2.22274 + 0.537750i) q^{68} +(1.57172 + 1.23681i) q^{70} +3.27391i q^{71} +1.84138i q^{73} +(5.29623 - 6.73034i) q^{74} +(-1.56118 + 2.55765i) q^{76} +(5.97186 - 5.97186i) q^{77} -11.3861 q^{79} +(-3.80853 - 1.22274i) q^{80} +(7.66510 - 0.914027i) q^{82} +(-11.1153 + 11.1153i) q^{83} +(-0.808530 - 0.808530i) q^{85} +(6.07578 - 7.72098i) q^{86} +(-7.03127 + 15.3579i) q^{88} +18.6533i q^{89} +(1.88784 + 1.88784i) q^{91} +(3.65685 + 15.1153i) q^{92} +(1.79715 + 15.0711i) q^{94} -1.49824 q^{95} -5.44902 q^{97} +(0.837260 + 7.02132i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{4} + 12 q^{8}+O(q^{10}) $ 8 * q - 4 * q^4 + 12 * q^8	$ 8 q - 4 q^{4} + 12 q^{8} - 8 q^{11} + 8 q^{13} + 4 q^{14} - 8 q^{17} + 8 q^{19} + 8 q^{20} + 16 q^{22} + 20 q^{26} - 8 q^{28} - 24 q^{29} + 8 q^{31} + 16 q^{34} + 8 q^{35} - 8 q^{37} + 16 q^{38} - 4 q^{40} + 16 q^{44} + 24 q^{46} + 40 q^{49} - 4 q^{50} + 16 q^{52} + 16 q^{56} - 8 q^{59} - 16 q^{61} - 28 q^{62} + 8 q^{64} + 8 q^{65} + 8 q^{68} + 4 q^{70} + 36 q^{74} - 40 q^{76} + 8 q^{77} - 40 q^{79} - 16 q^{80} + 64 q^{82} - 32 q^{83} + 8 q^{85} - 16 q^{86} - 16 q^{88} - 8 q^{91} - 16 q^{92} + 32 q^{94} + 16 q^{95} - 48 q^{97}+O(q^{100}) $ 8 * q - 4 * q^4 + 12 * q^8 - 8 * q^11 + 8 * q^13 + 4 * q^14 - 8 * q^17 + 8 * q^19 + 8 * q^20 + 16 * q^22 + 20 * q^26 - 8 * q^28 - 24 * q^29 + 8 * q^31 + 16 * q^34 + 8 * q^35 - 8 * q^37 + 16 * q^38 - 4 * q^40 + 16 * q^44 + 24 * q^46 + 40 * q^49 - 4 * q^50 + 16 * q^52 + 16 * q^56 - 8 * q^59 - 16 * q^61 - 28 * q^62 + 8 * q^64 + 8 * q^65 + 8 * q^68 + 4 * q^70 + 36 * q^74 - 40 * q^76 + 8 * q^77 - 40 * q^79 - 16 * q^80 + 64 * q^82 - 32 * q^83 + 8 * q^85 - 16 * q^86 - 16 * q^88 - 8 * q^91 - 16 * q^92 + 32 * q^94 + 16 * q^95 - 48 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$.

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.167452	+	1.40426i	0.118406	+	0.992965i
$2$	0.167452	+	1.40426i	0.118406	+	0.992965i
$3$		0			0
$3$		0			0
$4$	−1.94392	+	0.470294i	−0.971960	+	0.235147i
$5$	−0.707107	−	0.707107i	−0.316228	−	0.316228i
$5$	−0.707107	−	0.707107i	−0.316228	−	0.316228i
$6$		0			0
$7$			1.41421i			0.534522i	0.963624	+	0.267261i	$0.0861187\pi$
$7$			1.41421i			0.534522i	−0.963624	+	0.267261i	$0.913881\pi$
$8$	−0.985930	−	2.65103i	−0.348579	−	0.937279i
$9$		0			0
$10$	0.874559	−	1.11137i	0.276560	−	0.351447i
$11$	−4.22274	−	4.22274i	−1.27321	−	1.27321i	−0.944397	−	0.328808i	$-0.893353\pi$
$11$	−4.22274	−	4.22274i	−1.27321	−	1.27321i	−0.328808	−	0.944397i	$-0.606647\pi$
$12$		0			0
$13$	1.33490	−	1.33490i	0.370236	−	0.370236i	−0.497327	−	0.867563i	$-0.665685\pi$
$13$	1.33490	−	1.33490i	0.370236	−	0.370236i	0.867563	+	0.497327i	$0.165685\pi$
$14$	−1.98593	+	0.236813i	−0.530762	+	0.0632909i
$15$		0			0
$16$	3.55765	−	1.82843i	0.889412	−	0.457107i
$17$	1.14343			0.277323			0.138662	−	0.990340i	$-0.455720\pi$
$17$	1.14343			0.277323			0.138662	+	0.990340i	$0.455720\pi$
$18$		0			0
$19$	1.05941	−	1.05941i	0.243046	−	0.243046i	−0.575063	−	0.818109i	$-0.695023\pi$
$19$	1.05941	−	1.05941i	0.243046	−	0.243046i	0.818109	+	0.575063i	$0.195023\pi$
$20$	1.70711	+	1.04201i	0.381721	+	0.233001i
$21$		0			0
$22$	5.22274	−	6.63696i	1.11349	−	1.41500i
$23$		−	7.77568i		−	1.62134i	−0.585503	−	0.810671i	$-0.699103\pi$
$23$		−	7.77568i		−	1.62134i	0.585503	−	0.810671i	$-0.300897\pi$
$24$		0			0
$25$			1.00000i			0.200000i
$26$	2.09809	+	1.65103i	0.411470	+	0.323793i
$27$		0			0
$28$	−0.665096	−	2.74912i	−0.125691	−	0.519534i
$29$	−2.94059	+	2.94059i	−0.546053	+	0.546053i	−0.925297	−	0.379243i	$-0.876184\pi$
$29$	−2.94059	+	2.94059i	−0.546053	+	0.546053i	0.379243	+	0.925297i	$0.376184\pi$
$30$		0			0
$31$	0.389604			0.0699750			0.0349875	−	0.999388i	$-0.488861\pi$
$31$	0.389604			0.0699750			0.0349875	+	0.999388i	$0.488861\pi$
$32$	3.16333	+	4.68971i	0.559203	+	0.829031i
$33$		0			0
$34$	0.191470	+	1.60568i	0.0328369	+	0.275373i
$35$	1.00000	−	1.00000i	0.169031	−	0.169031i
$36$		0			0
$37$	−4.28216	−	4.28216i	−0.703982	−	0.703982i	0.261281	−	0.965263i	$-0.415855\pi$
$37$	−4.28216	−	4.28216i	−0.703982	−	0.703982i	−0.965263	+	0.261281i	$0.915855\pi$
$38$	1.66510	+	1.31029i	0.270114	+	0.212558i
$39$		0			0
$40$	−1.17740	+	2.57172i	−0.186163	+	0.406624i
$41$		−	5.45844i		−	0.852465i	−0.904614	−	0.426233i	$-0.859841\pi$
$41$		−	5.45844i		−	0.852465i	0.904614	−	0.426233i	$-0.140159\pi$
$42$		0			0
$43$	−4.91245	−	4.91245i	−0.749141	−	0.749141i	0.225177	−	0.974318i	$-0.427704\pi$
$43$	−4.91245	−	4.91245i	−0.749141	−	0.749141i	−0.974318	+	0.225177i	$0.927704\pi$
$44$	10.1946	+	6.22274i	1.53689	+	0.938114i
$45$		0			0
$46$	10.9191	−	1.30205i	1.60994	−	0.191977i
$47$	10.7324			1.56547			0.782737	−	0.622352i	$-0.213823\pi$
$47$	10.7324			1.56547			0.782737	+	0.622352i	$0.213823\pi$
$48$		0			0
$49$	5.00000			0.714286
$50$	−1.40426	+	0.167452i	−0.198593	+	0.0236813i
$51$		0			0
$52$	−1.96715	+	3.22274i	−0.272794	+	0.446914i
$53$	0.863230	+	0.863230i	0.118574	+	0.118574i	0.763904	−	0.645330i	$-0.223280\pi$
$53$	0.863230	+	0.863230i	0.118574	+	0.118574i	−0.645330	+	0.763904i	$0.723280\pi$
$54$		0			0
$55$			5.97186i			0.805246i
$56$	3.74912	−	1.39432i	0.500997	−	0.186323i
$57$		0			0
$58$	−4.62177	−	3.63696i	−0.606868	−	0.477556i
$59$	−8.50961	−	8.50961i	−1.10786	−	1.10786i	−0.993432	−	0.114425i	$-0.963497\pi$
$59$	−8.50961	−	8.50961i	−1.10786	−	1.10786i	−0.114425	−	0.993432i	$-0.536503\pi$
$60$		0			0
$61$	2.22746	−	2.22746i	0.285196	−	0.285196i	−0.549981	−	0.835177i	$-0.685365\pi$
$61$	2.22746	−	2.22746i	0.285196	−	0.285196i	0.835177	+	0.549981i	$0.185365\pi$
$62$	0.0652400	+	0.547108i	0.00828549	+	0.0694827i
$63$		0			0
$64$	−6.05588	+	5.22746i	−0.756985	+	0.653432i
$65$	−1.88784			−0.234158
$66$		0			0
$67$	2.94725	−	2.94725i	0.360064	−	0.360064i	−0.503772	−	0.863836i	$-0.668055\pi$
$67$	2.94725	−	2.94725i	0.360064	−	0.360064i	0.863836	+	0.503772i	$0.168055\pi$
$68$	−2.22274	+	0.537750i	−0.269547	+	0.0652118i
$69$		0			0
$70$	1.57172	+	1.23681i	0.187856	+	0.147827i
$71$			3.27391i			0.388542i	0.980948	+	0.194271i	$0.0622341\pi$
$71$			3.27391i			0.388542i	−0.980948	+	0.194271i	$0.937766\pi$
$72$		0			0
$73$			1.84138i			0.215517i	0.994177	+	0.107759i	$0.0343674\pi$
$73$			1.84138i			0.215517i	−0.994177	+	0.107759i	$0.965633\pi$
$74$	5.29623	−	6.73034i	0.615674	−	0.782386i
$75$		0			0
$76$	−1.56118	+	2.55765i	−0.179079	+	0.293382i
$77$	5.97186	−	5.97186i	0.680557	−	0.680557i
$78$		0			0
$79$	−11.3861			−1.28103			−0.640517	−	0.767944i	$-0.721280\pi$
$79$	−11.3861			−1.28103			−0.640517	+	0.767944i	$0.721280\pi$
$80$	−3.80853	−	1.22274i	−0.425807	−	0.136707i
$81$		0			0
$82$	7.66510	−	0.914027i	0.846468	−	0.100937i
$83$	−11.1153	+	11.1153i	−1.22006	+	1.22006i	−0.252453	+	0.967609i	$0.581237\pi$
$83$	−11.1153	+	11.1153i	−1.22006	+	1.22006i	−0.967609	+	0.252453i	$0.918763\pi$
$84$		0			0
$85$	−0.808530	−	0.808530i	−0.0876974	−	0.0876974i
$86$	6.07578	−	7.72098i	0.655168	−	0.832575i
$87$		0			0
$88$	−7.03127	+	15.3579i	−0.749536	+	1.63716i
$89$			18.6533i			1.97725i	0.150407	+	0.988624i	$0.451942\pi$
$89$			18.6533i			1.97725i	−0.150407	+	0.988624i	$0.548058\pi$
$90$		0			0
$91$	1.88784	+	1.88784i	0.197899	+	0.197899i
$92$	3.65685	+	15.1153i	0.381253	+	1.57588i
$93$		0			0
$94$	1.79715	+	15.0711i	0.185362	+	1.55446i
$95$	−1.49824			−0.153716
$96$		0			0
$97$	−5.44902			−0.553264			−0.276632	−	0.960976i	$-0.589218\pi$
$97$	−5.44902			−0.553264			−0.276632	+	0.960976i	$0.589218\pi$
$98$	0.837260	+	7.02132i	0.0845760	+	0.709261i
$99$		0			0
$100$	−0.470294	−	1.94392i	−0.0470294	−	0.194392i
$101$	11.1899	+	11.1899i	1.11344	+	1.11344i	0.992683	+	0.120753i	$0.0385310\pi$
$101$	11.1899	+	11.1899i	1.11344	+	1.11344i	0.120753	+	0.992683i	$0.461469\pi$
$102$		0			0
$103$		−	18.2919i		−	1.80235i	−0.433455	−	0.901175i	$-0.642706\pi$
$103$		−	18.2919i		−	1.80235i	0.433455	−	0.901175i	$-0.357294\pi$
$104$	−4.85499	−	2.22274i	−0.476071	−	0.217958i
$105$		0			0
$106$	−1.06765	+	1.35675i	−0.103700	+	0.131780i
$107$	−6.99647	−	6.99647i	−0.676374	−	0.676374i	0.282804	−	0.959178i	$-0.408736\pi$
$107$	−6.99647	−	6.99647i	−0.676374	−	0.676374i	−0.959178	+	0.282804i	$0.908736\pi$
$108$		0			0
$109$	12.6729	−	12.6729i	1.21385	−	1.21385i	0.244097	−	0.969751i	$-0.421509\pi$
$109$	12.6729	−	12.6729i	1.21385	−	1.21385i	0.969751	−	0.244097i	$-0.0784915\pi$
$110$	−8.38607	+	1.00000i	−0.799581	+	0.0953463i
$111$		0			0
$112$	2.58579	+	5.03127i	0.244334	+	0.475411i
$113$	−17.8101			−1.67543			−0.837716	−	0.546106i	$-0.816110\pi$
$113$	−17.8101			−1.67543			−0.837716	+	0.546106i	$0.816110\pi$
$114$		0			0
$115$	−5.49824	+	5.49824i	−0.512713	+	0.512713i
$116$	4.33333	−	7.09921i	0.402339	−	0.659145i
$117$		0			0
$118$	10.5248	−	13.3747i	0.968886	−	1.23124i
$119$			1.61706i			0.148236i
$120$		0			0
$121$			24.6631i			2.24210i
$122$	3.50093	+	2.75495i	0.316959	+	0.249421i
$123$		0			0
$124$	−0.757359	+	0.183228i	−0.0680129	+	0.0164544i
$125$	0.707107	−	0.707107i	0.0632456	−	0.0632456i
$126$		0			0
$127$	−10.0442			−0.891281			−0.445641	−	0.895212i	$-0.647024\pi$
$127$	−10.0442			−0.891281			−0.445641	+	0.895212i	$0.647024\pi$
$128$	−8.35480	−	7.62872i	−0.738467	−	0.674290i
$129$		0			0
$130$	−0.316122	−	2.65103i	−0.0277258	−	0.232510i
$131$	−7.60215	+	7.60215i	−0.664203	+	0.664203i	−0.956368	−	0.292165i	$-0.905624\pi$
$131$	−7.60215	+	7.60215i	−0.664203	+	0.664203i	0.292165	+	0.956368i	$0.405624\pi$
$132$		0			0
$133$	1.49824	+	1.49824i	0.129913	+	0.129913i
$134$	4.63224	+	3.64520i	0.400165	+	0.314897i
$135$		0			0
$136$	−1.12735	−	3.03127i	−0.0966691	−	0.259930i
$137$		−	14.8003i		−	1.26447i	−0.774775	−	0.632237i	$-0.782137\pi$
$137$		−	14.8003i		−	1.26447i	0.774775	−	0.632237i	$-0.217863\pi$
$138$		0			0
$139$	−8.43606	−	8.43606i	−0.715537	−	0.715537i	0.252151	−	0.967688i	$-0.418862\pi$
$139$	−8.43606	−	8.43606i	−0.715537	−	0.715537i	−0.967688	+	0.252151i	$0.918862\pi$
$140$	−1.47363	+	2.41421i	−0.124544	+	0.204038i
$141$		0			0
$142$	−4.59744	+	0.548223i	−0.385809	+	0.0460059i
$143$	−11.2739			−0.942772
$144$		0			0
$145$	4.15862			0.345355
$146$	−2.58579	+	0.308343i	−0.214001	+	0.0255186i
$147$		0			0
$148$	10.3380	+	6.31029i	0.849781	+	0.518703i
$149$	−0.772545	−	0.772545i	−0.0632893	−	0.0632893i	0.674754	−	0.738043i	$-0.264250\pi$
$149$	−0.772545	−	0.772545i	−0.0632893	−	0.0632893i	−0.738043	+	0.674754i	$0.764250\pi$
$150$		0			0
$151$		−	2.90079i		−	0.236063i	−0.993010	−	0.118032i	$-0.962342\pi$
$151$		−	2.90079i		−	0.236063i	0.993010	−	0.118032i	$-0.0376584\pi$
$152$	−3.85304	−	1.76402i	−0.312523	−	0.143081i
$153$		0			0
$154$	9.38607	+	7.38607i	0.756351	+	0.595187i
$155$	−0.275492	−	0.275492i	−0.0221280	−	0.0221280i
$156$		0			0
$157$	2.60882	−	2.60882i	0.208206	−	0.208206i	−0.595298	−	0.803505i	$-0.702966\pi$
$157$	2.60882	−	2.60882i	0.208206	−	0.208206i	0.803505	+	0.595298i	$0.202966\pi$
$158$	−1.90662	−	15.9891i	−0.151683	−	1.27202i
$159$		0			0
$160$	1.07931	−	5.55294i	0.0853269	−	0.438998i
$161$	10.9965			0.866643
$162$		0			0
$163$	−1.42364	+	1.42364i	−0.111508	+	0.111508i	−0.760659	−	0.649151i	$-0.775124\pi$
$163$	−1.42364	+	1.42364i	−0.111508	+	0.111508i	0.649151	+	0.760659i	$0.275124\pi$
$164$	2.56707	+	10.6108i	0.200455	+	0.828562i
$165$		0			0
$166$	−17.4701	−	13.7475i	−1.35594	−	1.06702i
$167$			4.22117i			0.326644i	0.986573	+	0.163322i	$0.0522209\pi$
$167$			4.22117i			0.326644i	−0.986573	+	0.163322i	$0.947779\pi$
$168$		0			0
$169$			9.43606i			0.725851i
$170$	1.00000	−	1.27078i	0.0766965	−	0.0974644i
$171$		0			0
$172$	11.8597	+	7.23911i	0.904294	+	0.551977i
$173$	14.1582	−	14.1582i	1.07643	−	1.07643i	0.0796031	−	0.996827i	$-0.474635\pi$
$173$	14.1582	−	14.1582i	1.07643	−	1.07643i	0.996827	−	0.0796031i	$-0.0253653\pi$
$174$		0			0
$175$	−1.41421			−0.106904
$176$	−22.7440	−	7.30205i	−1.71439	−	0.550413i
$177$		0			0
$178$	−26.1942	+	3.12354i	−1.96334	+	0.234119i
$179$	11.8796	−	11.8796i	0.887923	−	0.887923i	−0.106401	−	0.994323i	$-0.533933\pi$
$179$	11.8796	−	11.8796i	0.887923	−	0.887923i	0.994323	+	0.106401i	$0.0339326\pi$
$180$		0			0
$181$	7.04646	+	7.04646i	0.523759	+	0.523759i	0.918705	−	0.394945i	$-0.129237\pi$
$181$	7.04646	+	7.04646i	0.523759	+	0.523759i	−0.394945	+	0.918705i	$0.629237\pi$
$182$	−2.33490	+	2.96715i	−0.173075	+	0.219940i
$183$		0			0
$184$	−20.6135	+	7.66628i	−1.51965	+	0.565166i
$185$			6.05588i			0.445237i
$186$		0			0
$187$	−4.82843	−	4.82843i	−0.353090	−	0.353090i
$188$	−20.8628	+	5.04736i	−1.52158	+	0.368117i
$189$		0			0
$190$	−0.250882	−	2.10392i	−0.0182009	−	0.152634i
$191$	15.3857			1.11327			0.556634	−	0.830758i	$-0.312092\pi$
$191$	15.3857			1.11327			0.556634	+	0.830758i	$0.312092\pi$
$192$		0			0
$193$	7.52099			0.541372			0.270686	−	0.962668i	$-0.412749\pi$
$193$	7.52099			0.541372			0.270686	+	0.962668i	$0.412749\pi$
$194$	−0.912449	−	7.65186i	−0.0655100	−	0.549372i
$195$		0			0
$196$	−9.71960	+	2.35147i	−0.694257	+	0.167962i
$197$	−9.66352	−	9.66352i	−0.688497	−	0.688497i	0.273403	−	0.961900i	$-0.411851\pi$
$197$	−9.66352	−	9.66352i	−0.688497	−	0.688497i	−0.961900	+	0.273403i	$0.911851\pi$
$198$		0			0
$199$			9.35570i			0.663208i	0.943419	+	0.331604i	$0.107590\pi$
$199$			9.35570i			0.663208i	−0.943419	+	0.331604i	$0.892410\pi$
$200$	2.65103	−	0.985930i	0.187456	−	0.0697158i
$201$		0			0
$202$	−13.8398	+	17.5873i	−0.973765	+	1.23744i
$203$	−4.15862	−	4.15862i	−0.291878	−	0.291878i
$204$		0			0
$205$	−3.85970	+	3.85970i	−0.269573	+	0.269573i
$206$	25.6866	−	3.06301i	1.78967	−	0.213410i
$207$		0			0
$208$	2.30834	−	7.18989i	0.160055	−	0.498529i
$209$	−8.94725			−0.618894
$210$		0			0
$211$	−0.0625461	+	0.0625461i	−0.00430585	+	0.00430585i	−0.709256	−	0.704951i	$-0.750969\pi$
$211$	−0.0625461	+	0.0625461i	−0.00430585	+	0.00430585i	0.704951	+	0.709256i	$0.250969\pi$
$212$	−2.08402	−	1.27208i	−0.143131	−	0.0873667i
$213$		0			0
$214$	8.65332	−	10.9965i	0.591529	−	0.751703i
$215$			6.94725i			0.473799i
$216$		0			0
$217$			0.550984i			0.0374032i
$218$	19.9183	+	15.6741i	1.34904	+	1.06158i
$219$		0			0
$220$	−2.80853	−	11.6088i	−0.189351	−	0.782666i
$221$	1.52637	−	1.52637i	0.102675	−	0.102675i
$222$		0			0
$223$	13.1203			0.878599			0.439300	−	0.898341i	$-0.355227\pi$
$223$	13.1203			0.878599			0.439300	+	0.898341i	$0.355227\pi$
$224$	−6.63224	+	4.47363i	−0.443136	+	0.298907i
$225$		0			0
$226$	−2.98233	−	25.0101i	−0.198382	−	1.66365i
$227$	−5.76235	+	5.76235i	−0.382461	+	0.382461i	−0.871988	−	0.489527i	$-0.837169\pi$
$227$	−5.76235	+	5.76235i	−0.382461	+	0.382461i	0.489527	+	0.871988i	$0.337169\pi$
$228$		0			0
$229$	5.12549	+	5.12549i	0.338702	+	0.338702i	0.855879	−	0.517177i	$-0.173017\pi$
$229$	5.12549	+	5.12549i	0.338702	+	0.338702i	−0.517177	+	0.855879i	$0.673017\pi$
$230$	−8.64167	−	6.80029i	−0.569815	−	0.448398i
$231$		0			0
$232$	10.6948	+	4.89636i	0.702147	+	0.321462i
$233$			13.2552i			0.868377i	0.900822	+	0.434188i	$0.142965\pi$
$233$			13.2552i			0.868377i	−0.900822	+	0.434188i	$0.857035\pi$
$234$		0			0
$235$	−7.58892	−	7.58892i	−0.495047	−	0.495047i
$236$	20.5440	+	12.5400i	1.33730	+	0.816283i
$237$		0			0
$238$	−2.27078	+	0.270780i	−0.147193	+	0.0175520i
$239$	18.8119			1.21684			0.608422	−	0.793614i	$-0.291803\pi$
$239$	18.8119			1.21684			0.608422	+	0.793614i	$0.291803\pi$
$240$		0			0
$241$	−2.66665			−0.171774			−0.0858871	−	0.996305i	$-0.527372\pi$
$241$	−2.66665			−0.171774			−0.0858871	+	0.996305i	$0.527372\pi$
$242$	−34.6336	+	4.12989i	−2.22633	+	0.265479i
$243$		0			0
$244$	−3.28244	+	5.37755i	−0.210136	+	0.344263i
$245$	−3.53553	−	3.53553i	−0.225877	−	0.225877i
$246$		0			0
$247$		−	2.82843i		−	0.179969i
$248$	−0.384123	−	1.03285i	−0.0243918	−	0.0655861i
$249$		0			0
$250$	1.11137	+	0.874559i	0.0702893	+	0.0553120i
$251$	7.77726	+	7.77726i	0.490896	+	0.490896i	0.908588	−	0.417692i	$-0.137161\pi$
$251$	7.77726	+	7.77726i	0.490896	+	0.490896i	−0.417692	+	0.908588i	$0.637161\pi$
$252$		0			0
$253$	−32.8347	+	32.8347i	−2.06430	+	2.06430i
$254$	−1.68193	−	14.1048i	−0.105533	−	0.885011i
$255$		0			0
$256$	9.31371	−	13.0098i	0.582107	−	0.813112i
$257$	5.83971			0.364271			0.182136	−	0.983273i	$-0.441699\pi$
$257$	5.83971			0.364271			0.182136	+	0.983273i	$0.441699\pi$
$258$		0			0
$259$	6.05588	−	6.05588i	0.376294	−	0.376294i
$260$	3.66981	−	0.887839i	0.227592	−	0.0550615i
$261$		0			0
$262$	−11.9484	−	9.40244i	−0.738177	−	0.580885i
$263$			10.0094i			0.617208i	0.951191	+	0.308604i	$0.0998617\pi$
$263$			10.0094i			0.617208i	−0.951191	+	0.308604i	$0.900138\pi$
$264$		0			0
$265$		−	1.22079i		−	0.0749926i
$266$	−1.85304	+	2.35480i	−0.113617	+	0.144382i
$267$		0			0
$268$	−4.34315	+	7.11529i	−0.265300	+	0.434636i
$269$	−1.82529	+	1.82529i	−0.111290	+	0.111290i	−0.760559	−	0.649269i	$-0.775075\pi$
$269$	−1.82529	+	1.82529i	−0.111290	+	0.111290i	0.649269	+	0.760559i	$0.275075\pi$
$270$		0			0
$271$	−5.44862			−0.330980			−0.165490	−	0.986211i	$-0.552921\pi$
$271$	−5.44862			−0.330980			−0.165490	+	0.986211i	$0.552921\pi$
$272$	4.06793	−	2.09069i	0.246655	−	0.126766i
$273$		0			0
$274$	20.7835	−	2.47834i	1.25558	−	0.149722i
$275$	4.22274	−	4.22274i	0.254641	−	0.254641i
$276$		0			0
$277$	10.5690	+	10.5690i	0.635031	+	0.635031i	0.949326	−	0.314294i	$-0.101768\pi$
$277$	10.5690	+	10.5690i	0.635031	+	0.635031i	−0.314294	+	0.949326i	$0.601768\pi$
$278$	10.4338	−	13.2591i	0.625780	−	0.795228i
$279$		0			0
$280$	−3.63696	−	1.66510i	−0.217350	−	0.0995085i
$281$			10.2376i			0.610727i	0.952236	+	0.305363i	$0.0987780\pi$
$281$			10.2376i			0.610727i	−0.952236	+	0.305363i	$0.901222\pi$
$282$		0			0
$283$	−9.88744	−	9.88744i	−0.587748	−	0.587748i	0.349273	−	0.937021i	$-0.386428\pi$
$283$	−9.88744	−	9.88744i	−0.587748	−	0.587748i	−0.937021	+	0.349273i	$0.886428\pi$
$284$	−1.53970	−	6.36423i	−0.0913645	−	0.377647i
$285$		0			0
$286$	−1.88784	−	15.8316i	−0.111630	−	0.936140i
$287$	7.71940			0.455662
$288$		0			0
$289$	−15.6926			−0.923092
$290$	0.696369	+	5.83980i	0.0408922	+	0.342925i
$291$		0			0
$292$	−0.865990	−	3.57950i	−0.0506782	−	0.209474i
$293$	−9.05235	−	9.05235i	−0.528844	−	0.528844i	0.391384	−	0.920228i	$-0.371997\pi$
$293$	−9.05235	−	9.05235i	−0.528844	−	0.528844i	−0.920228	+	0.391384i	$0.871997\pi$
$294$		0			0
$295$			12.0344i			0.700670i
$296$	−7.13020	+	15.5740i	−0.414434	+	0.905221i
$297$		0			0
$298$	0.955493	−	1.21422i	0.0553502	−	0.0703380i
$299$	−10.3798	−	10.3798i	−0.600278	−	0.600278i
$300$		0			0
$301$	6.94725	−	6.94725i	0.400433	−	0.400433i
$302$	4.07348	−	0.485744i	0.234403	−	0.0279514i
$303$		0			0
$304$	1.83196	−	5.70607i	0.105070	−	0.327266i
$305$	−3.15010			−0.180374
$306$		0			0
$307$	2.77215	−	2.77215i	0.158215	−	0.158215i	−0.623560	−	0.781775i	$-0.714314\pi$
$307$	2.77215	−	2.77215i	0.158215	−	0.158215i	0.781775	+	0.623560i	$0.214314\pi$
$308$	−8.80029	+	14.4173i	−0.501443	+	0.821505i
$309$		0			0
$310$	0.340732	−	0.432995i	0.0193523	−	0.0245925i
$311$			20.9441i			1.18763i	0.804601	+	0.593815i	$0.202379\pi$
$311$			20.9441i			1.18763i	−0.804601	+	0.593815i	$0.797621\pi$
$312$		0			0
$313$		−	10.1814i		−	0.575485i	−0.957708	−	0.287743i	$-0.907095\pi$
$313$		−	10.1814i		−	0.575485i	0.957708	−	0.287743i	$-0.0929047\pi$
$314$	4.10032	+	3.22662i	0.231395	+	0.182089i
$315$		0			0
$316$	22.1336	−	5.35480i	1.24511	−	0.301231i
$317$	14.7655	−	14.7655i	0.829312	−	0.829312i	−0.158109	−	0.987422i	$-0.550540\pi$
$317$	14.7655	−	14.7655i	0.829312	−	0.829312i	0.987422	+	0.158109i	$0.0505398\pi$
$318$		0			0
$319$	24.8347			1.39048
$320$	7.97852	+	0.585786i	0.446013	+	0.0327465i
$321$		0			0
$322$	1.84138	+	15.4420i	0.102616	+	0.860547i
$323$	1.21137	−	1.21137i	0.0674023	−	0.0674023i
$324$		0			0
$325$	1.33490	+	1.33490i	0.0740472	+	0.0740472i
$326$	−2.23756	−	1.76077i	−0.123927	−	0.0975202i
$327$		0			0
$328$	−14.4705	+	5.38164i	−0.798998	+	0.297151i
$329$			15.1778i			0.836781i
$330$		0			0
$331$	16.8815	+	16.8815i	0.927894	+	0.927894i	0.997570	−	0.0696758i	$-0.0221965\pi$
$331$	16.8815	+	16.8815i	0.927894	+	0.927894i	−0.0696758	+	0.997570i	$0.522196\pi$
$332$	16.3798	−	26.8347i	0.898957	−	1.47275i
$333$		0			0
$334$	−5.92763	+	0.706843i	−0.324346	+	0.0386767i
$335$	−4.16804			−0.227725
$336$		0			0
$337$	23.8343			1.29834			0.649169	−	0.760644i	$-0.275117\pi$
$337$	23.8343			1.29834			0.649169	+	0.760644i	$0.275117\pi$
$338$	−13.2507	+	1.58009i	−0.720745	+	0.0859454i
$339$		0			0
$340$	1.95196	+	1.19147i	0.105860	+	0.0646165i
$341$	−1.64520	−	1.64520i	−0.0890925	−	0.0890925i
$342$		0			0
$343$			16.9706i			0.916324i
$344$	−8.17970	+	17.8664i	−0.441020	+	0.963290i
$345$		0			0
$346$	22.2527	+	17.5111i	1.19631	+	0.941401i
$347$	4.38294	+	4.38294i	0.235289	+	0.235289i	0.814896	−	0.579607i	$-0.196794\pi$
$347$	4.38294	+	4.38294i	0.235289	+	0.235289i	−0.579607	+	0.814896i	$0.696794\pi$
$348$		0			0
$349$	17.4357	−	17.4357i	0.933310	−	0.933310i	−0.0646013	−	0.997911i	$-0.520578\pi$
$349$	17.4357	−	17.4357i	0.933310	−	0.933310i	0.997911	+	0.0646013i	$0.0205776\pi$
$350$	−0.236813	−	1.98593i	−0.0126582	−	0.106152i
$351$		0			0
$352$	6.44549	−	33.1614i	0.343546	−	1.76751i
$353$	31.5795			1.68081			0.840403	−	0.541961i	$-0.182318\pi$
$353$	31.5795			1.68081			0.840403	+	0.541961i	$0.182318\pi$
$354$		0			0
$355$	2.31501	−	2.31501i	0.122868	−	0.122868i
$356$	−8.77254	−	36.2606i	−0.464944	−	1.92181i
$357$		0			0
$358$	18.6714	+	14.6928i	0.986812	+	0.776541i
$359$		−	25.5310i		−	1.34747i	−0.738972	−	0.673737i	$-0.764688\pi$
$359$		−	25.5310i		−	1.34747i	0.738972	−	0.673737i	$-0.235312\pi$
$360$		0			0
$361$			16.7553i			0.881857i
$362$	−8.71515	+	11.0750i	−0.458058	+	0.582091i
$363$		0			0
$364$	−4.55765	−	2.78197i	−0.238886	−	0.145815i
$365$	1.30205	−	1.30205i	0.0681526	−	0.0681526i
$366$		0			0
$367$	13.9084			0.726010			0.363005	−	0.931787i	$-0.381751\pi$
$367$	13.9084			0.726010			0.363005	+	0.931787i	$0.381751\pi$
$368$	−14.2173	−	27.6631i	−0.741126	−	1.44204i
$369$		0			0
$370$	−8.50406	+	1.01407i	−0.442105	+	0.0527190i
$371$	−1.22079	+	1.22079i	−0.0633803	+	0.0633803i
$372$		0			0
$373$	2.88942	+	2.88942i	0.149608	+	0.149608i	0.777943	−	0.628335i	$-0.216263\pi$
$373$	2.88942	+	2.88942i	0.149608	+	0.149608i	−0.628335	+	0.777943i	$0.716263\pi$
$374$	5.97186	−	7.58892i	0.308798	−	0.392414i
$375$		0			0
$376$	−10.5814	−	28.4518i	−0.545692	−	1.46729i
$377$			7.85080i			0.404337i
$378$		0			0
$379$	−5.96687	−	5.96687i	−0.306497	−	0.306497i	0.537052	−	0.843549i	$-0.319538\pi$
$379$	−5.96687	−	5.96687i	−0.306497	−	0.306497i	−0.843549	+	0.537052i	$0.819538\pi$
$380$	2.91245	−	0.704611i	0.149405	−	0.0361458i
$381$		0			0
$382$	2.57636	+	21.6056i	0.131818	+	1.10544i
$383$	−13.8382			−0.707100			−0.353550	−	0.935416i	$-0.615026\pi$
$383$	−13.8382			−0.707100			−0.353550	+	0.935416i	$0.615026\pi$
$384$		0			0
$385$	−8.44549			−0.430422
$386$	1.25940	+	10.5615i	0.0641020	+	0.537564i
$387$		0			0
$388$	10.5925	−	2.56264i	0.537750	−	0.130098i
$389$	20.2560	+	20.2560i	1.02702	+	1.02702i	0.999625	+	0.0273936i	$0.00872075\pi$
$389$	20.2560	+	20.2560i	1.02702	+	1.02702i	0.0273936	+	0.999625i	$0.491279\pi$
$390$		0			0
$391$		−	8.89097i		−	0.449636i
$392$	−4.92965	−	13.2551i	−0.248985	−	0.669485i
$393$		0			0
$394$	11.9520	−	15.1883i	0.602131	−	0.765176i
$395$	8.05117	+	8.05117i	0.405098	+	0.405098i
$396$		0			0
$397$	21.0941	−	21.0941i	1.05868	−	1.05868i	0.0605152	−	0.998167i	$-0.480726\pi$
$397$	21.0941	−	21.0941i	1.05868	−	1.05868i	0.998167	−	0.0605152i	$-0.0192744\pi$
$398$	−13.1379	+	1.56663i	−0.658543	+	0.0785281i
$399$		0			0
$400$	1.82843	+	3.55765i	0.0914214	+	0.177882i
$401$	−4.98314			−0.248846			−0.124423	−	0.992229i	$-0.539708\pi$
$401$	−4.98314			−0.248846			−0.124423	+	0.992229i	$0.539708\pi$
$402$		0			0
$403$	0.520084	−	0.520084i	0.0259072	−	0.0259072i
$404$	−27.0148	−	16.4897i	−1.34404	−	0.820394i
$405$		0			0
$406$	5.14343	−	6.53617i	0.255264	−	0.324385i
$407$			36.1649i			1.79263i
$408$		0			0
$409$		−	33.7686i		−	1.66975i	−0.550439	−	0.834875i	$-0.685540\pi$
$409$		−	33.7686i		−	1.66975i	0.550439	−	0.834875i	$-0.314460\pi$
$410$	−6.06636	−	4.77373i	−0.299596	−	0.235758i
$411$		0			0
$412$	8.60255	+	35.5579i	0.423817	+	1.75181i
$413$	12.0344	−	12.0344i	0.592174	−	0.592174i
$414$		0			0
$415$	15.7194			0.771635
$416$	10.4830	+	2.03756i	0.513974	+	0.0998997i
$417$		0			0
$418$	−1.49824	−	12.5643i	−0.0732811	−	0.614541i
$419$	15.9453	−	15.9453i	0.778979	−	0.778979i	−0.200678	−	0.979657i	$-0.564315\pi$
$419$	15.9453	−	15.9453i	0.778979	−	0.778979i	0.979657	+	0.200678i	$0.0643146\pi$
$420$		0			0
$421$	−2.33295	−	2.33295i	−0.113701	−	0.113701i	0.647967	−	0.761668i	$-0.275619\pi$
$421$	−2.33295	−	2.33295i	−0.113701	−	0.113701i	−0.761668	+	0.647967i	$0.775619\pi$
$422$	−0.0983048	−	0.0773578i	−0.00478540	−	0.00376572i
$423$		0			0
$424$	1.43736	−	3.13953i	0.0698044	−	0.152469i
$425$			1.14343i			0.0554647i
$426$		0			0
$427$	3.15010	+	3.15010i	0.152444	+	0.152444i
$428$	16.8910	+	10.3102i	0.816456	+	0.498361i
$429$		0			0
$430$	−9.75578	+	1.16333i	−0.470466	+	0.0561008i
$431$	20.6400			0.994194			0.497097	−	0.867695i	$-0.334399\pi$
$431$	20.6400			0.994194			0.497097	+	0.867695i	$0.334399\pi$
$432$		0			0
$433$	1.07550			0.0516852			0.0258426	−	0.999666i	$-0.491773\pi$
$433$	1.07550			0.0516852			0.0258426	+	0.999666i	$0.491773\pi$
$434$	−0.773727	+	0.0922633i	−0.0371401	+	0.00442878i
$435$		0			0
$436$	−18.6752	+	30.5952i	−0.894379	+	1.46524i
$437$	−8.23765	−	8.23765i	−0.394060	−	0.394060i
$438$		0			0
$439$			4.24041i			0.202384i	0.994867	+	0.101192i	$0.0322656\pi$
$439$			4.24041i			0.202384i	−0.994867	+	0.101192i	$0.967734\pi$
$440$	15.8316	−	5.88784i	0.754740	−	0.280692i
$441$		0			0
$442$	2.39903	+	1.88784i	0.114110	+	0.0897954i
$443$	19.8969	+	19.8969i	0.945329	+	0.945329i	0.998581	−	0.0532524i	$-0.0169588\pi$
$443$	19.8969	+	19.8969i	0.945329	+	0.945329i	−0.0532524	+	0.998581i	$0.516959\pi$
$444$		0			0
$445$	13.1899	−	13.1899i	0.625261	−	0.625261i
$446$	2.19702	+	18.4244i	0.104032	+	0.872419i
$447$		0			0
$448$	−7.39274	−	8.56431i	−0.349274	−	0.404626i
$449$	−17.2441			−0.813800			−0.406900	−	0.913473i	$-0.633390\pi$
$449$	−17.2441			−0.813800			−0.406900	+	0.913473i	$0.633390\pi$
$450$		0			0
$451$	−23.0496	+	23.0496i	−1.08536	+	1.08536i
$452$	34.6214	−	8.37597i	1.62845	−	0.393973i
$453$		0			0
$454$	−9.05678	−	7.12695i	−0.425056	−	0.334484i
$455$		−	2.66981i		−	0.125163i
$456$		0			0
$457$		−	32.3141i		−	1.51159i	−0.654809	−	0.755795i	$-0.727251\pi$
$457$		−	32.3141i		−	1.51159i	0.654809	−	0.755795i	$-0.272749\pi$
$458$	−6.33927	+	8.05582i	−0.296215	+	0.376424i
$459$		0			0
$460$	8.10234	−	13.2739i	0.377774	−	0.618899i
$461$	−15.4884	+	15.4884i	−0.721367	+	0.721367i	−0.968884	−	0.247516i	$-0.920386\pi$
$461$	−15.4884	+	15.4884i	−0.721367	+	0.721367i	0.247516	+	0.968884i	$0.420386\pi$
$462$		0			0
$463$	27.2150			1.26479			0.632394	−	0.774647i	$-0.282072\pi$
$463$	27.2150			1.26479			0.632394	+	0.774647i	$0.282072\pi$
$464$	−5.08492	+	15.8382i	−0.236062	+	0.735271i
$465$		0			0
$466$	−18.6138	+	2.21961i	−0.862268	+	0.102821i
$467$	−7.60373	+	7.60373i	−0.351859	+	0.351859i	−0.860801	−	0.508942i	$-0.830037\pi$
$467$	−7.60373	+	7.60373i	−0.351859	+	0.351859i	0.508942	+	0.860801i	$0.330037\pi$
$468$		0			0
$469$	4.16804	+	4.16804i	0.192462	+	0.192462i
$470$	9.38607	−	11.9276i	0.432947	−	0.550181i
$471$		0			0
$472$	−14.1693	+	30.9491i	−0.652196	+	1.42455i
$473$			41.4880i			1.90762i
$474$		0			0
$475$	1.05941	+	1.05941i	0.0486092	+	0.0486092i
$476$	−0.760493	−	3.14343i	−0.0348571	−	0.144079i
$477$		0			0
$478$	3.15010	+	26.4170i	0.144082	+	1.20828i
$479$	−0.515092			−0.0235352			−0.0117676	−	0.999931i	$-0.503746\pi$
$479$	−0.515092			−0.0235352			−0.0117676	+	0.999931i	$0.503746\pi$
$480$		0			0
$481$	−11.4325			−0.521279
$482$	−0.446536	−	3.74469i	−0.0203392	−	0.170566i
$483$		0			0
$484$	−11.5989	−	47.9431i	−0.527223	−	2.17923i
$485$	3.85304	+	3.85304i	0.174957	+	0.174957i
$486$		0			0
$487$		−	18.2489i		−	0.826937i	−0.910518	−	0.413468i	$-0.864317\pi$
$487$		−	18.2489i		−	0.826937i	0.910518	−	0.413468i	$-0.135683\pi$
$488$	−8.10116	−	3.70893i	−0.366722	−	0.167895i
$489$		0			0
$490$	4.37279	−	5.55686i	0.197543	−	0.251033i
$491$	−26.5557	−	26.5557i	−1.19844	−	1.19844i	−0.974633	−	0.223807i	$-0.928151\pi$
$491$	−26.5557	−	26.5557i	−1.19844	−	1.19844i	−0.223807	−	0.974633i	$-0.571849\pi$
$492$		0			0
$493$	−3.36237	+	3.36237i	−0.151433	+	0.151433i
$494$	3.97186	−	0.473626i	0.178702	−	0.0213094i
$495$		0			0
$496$	1.38607	−	0.712363i	0.0622366	−	0.0319860i
$497$	−4.63001			−0.207684
$498$		0			0
$499$	−11.2247	+	11.2247i	−0.502486	+	0.502486i	−0.912210	−	0.409723i	$-0.865625\pi$
$499$	−11.2247	+	11.2247i	−0.502486	+	0.502486i	0.409723	+	0.912210i	$0.365625\pi$
$500$	−1.04201	+	1.70711i	−0.0466001	+	0.0763441i
$501$		0			0
$502$	−9.61901	+	12.2236i	−0.429317	+	0.545568i
$503$		−	27.3061i		−	1.21752i	−0.793355	−	0.608759i	$-0.791668\pi$
$503$		−	27.3061i		−	1.21752i	0.793355	−	0.608759i	$-0.208332\pi$
$504$		0			0
$505$		−	15.8249i		−	0.704199i
$506$	−51.6068	−	40.6104i	−2.29420	−	1.80535i
$507$		0			0
$508$	19.5252	−	4.72374i	0.866289	−	0.209582i
$509$	17.9387	−	17.9387i	0.795120	−	0.795120i	−0.187201	−	0.982322i	$-0.559942\pi$
$509$	17.9387	−	17.9387i	0.795120	−	0.795120i	0.982322	+	0.187201i	$0.0599417\pi$
$510$		0			0
$511$	−2.60411			−0.115199
$512$	19.8288	+	10.9004i	0.876317	+	0.481734i
$513$		0			0
$514$	0.977871	+	8.20050i	0.0431320	+	0.361708i
$515$	−12.9343	+	12.9343i	−0.569953	+	0.569953i
$516$		0			0
$517$	−45.3200	−	45.3200i	−1.99317	−	1.99317i
$518$	9.51813	+	7.48999i	0.418203	+	0.329091i
$519$		0			0
$520$	1.86128	+	5.00471i	0.0816224	+	0.219471i
$521$			11.7686i			0.515593i	0.966199	+	0.257796i	$0.0829963\pi$
$521$			11.7686i			0.515593i	−0.966199	+	0.257796i	$0.917004\pi$
$522$		0			0
$523$	2.02148	+	2.02148i	0.0883929	+	0.0883929i	0.749921	−	0.661528i	$-0.230092\pi$
$523$	2.02148	+	2.02148i	0.0883929	+	0.0883929i	−0.661528	+	0.749921i	$0.730092\pi$
$524$	11.2027	−	18.3532i	0.489394	−	0.801764i
$525$		0			0
$526$	−14.0559	+	1.67610i	−0.612866	+	0.0730813i
$527$	0.445487			0.0194057
$528$		0			0
$529$	−37.4612			−1.62875
$530$	1.71431	−	0.204424i	0.0744651	−	0.00887961i
$531$		0			0
$532$	−3.61706	−	2.20784i	−0.156819	−	0.0957219i
$533$	−7.28649	−	7.28649i	−0.315613	−	0.315613i
$534$		0			0
$535$			9.89450i			0.427777i
$536$	−10.7190	−	4.90746i	−0.462991	−	0.211970i
$537$		0			0
$538$	−2.86884	−	2.25755i	−0.123685	−	0.0973297i
$539$	−21.1137	−	21.1137i	−0.909432	−	0.909432i
$540$		0			0
$541$	−28.9598	+	28.9598i	−1.24508	+	1.24508i	−0.287213	+	0.957867i	$0.592729\pi$
$541$	−28.9598	+	28.9598i	−1.24508	+	1.24508i	−0.957867	+	0.287213i	$0.907271\pi$
$542$	−0.912382	−	7.65131i	−0.0391902	−	0.328652i
$543$		0			0
$544$	3.61706	+	5.36237i	0.155080	+	0.229910i
$545$	−17.9222			−0.767705
$546$		0			0
$547$	−11.3485	+	11.3485i	−0.485227	+	0.485227i	−0.906796	−	0.421569i	$-0.861480\pi$
$547$	−11.3485	+	11.3485i	−0.485227	+	0.485227i	0.421569	+	0.906796i	$0.361480\pi$
$548$	6.96049	+	28.7706i	0.297337	+	1.22902i
$549$		0			0
$550$	6.63696	+	5.22274i	0.283001	+	0.222699i
$551$			6.23059i			0.265432i
$552$		0			0
$553$		−	16.1023i		−	0.684741i
$554$	−13.0719	+	16.6115i	−0.555372	+	0.705756i
$555$		0			0
$556$	20.3665	+	12.4316i	0.863730	+	0.527217i
$557$	−18.8445	+	18.8445i	−0.798468	+	0.798468i	−0.982854	−	0.184386i	$-0.940970\pi$
$557$	−18.8445	+	18.8445i	−0.798468	+	0.798468i	0.184386	+	0.982854i	$0.440970\pi$
$558$		0			0
$559$	−13.1153			−0.554718
$560$	1.72922	−	5.38607i	0.0730729	−	0.227603i
$561$		0			0
$562$	−14.3764	+	1.71431i	−0.606431	+	0.0723140i
$563$	33.1082	−	33.1082i	1.39535	−	1.39535i	0.582553	−	0.812793i	$-0.302054\pi$
$563$	33.1082	−	33.1082i	1.39535	−	1.39535i	0.812793	−	0.582553i	$-0.197946\pi$
$564$		0			0
$565$	12.5936	+	12.5936i	0.529818	+	0.529818i
$566$	12.2289	−	15.5403i	0.514020	−	0.653206i
$567$		0			0
$568$	8.67923	−	3.22785i	0.364172	−	0.135438i
$569$		−	1.55688i		−	0.0652677i	−0.999467	−	0.0326339i	$-0.989610\pi$
$569$		−	1.55688i		−	0.0652677i	0.999467	−	0.0326339i	$-0.0103895\pi$
$570$		0			0
$571$	33.1614	+	33.1614i	1.38776	+	1.38776i	0.830008	+	0.557752i	$0.188336\pi$
$571$	33.1614	+	33.1614i	1.38776	+	1.38776i	0.557752	+	0.830008i	$0.311664\pi$
$572$	21.9156	−	5.30205i	0.916337	−	0.221690i
$573$		0			0
$574$	1.29263	+	10.8401i	0.0539533	+	0.452456i
$575$	7.77568			0.324268
$576$		0			0
$577$	−36.5706			−1.52245			−0.761227	−	0.648486i	$-0.775402\pi$
$577$	−36.5706			−1.52245			−0.761227	+	0.648486i	$0.775402\pi$
$578$	−2.62775	−	22.0365i	−0.109300	−	0.916598i
$579$		0			0
$580$	−8.08402	+	1.95577i	−0.335671	+	0.0812091i
$581$	−15.7194	−	15.7194i	−0.652151	−	0.652151i
$582$		0			0
$583$		−	7.29040i		−	0.301937i
$584$	4.88155	−	1.81547i	0.202000	−	0.0751248i
$585$		0			0
$586$	11.1961	−	14.2277i	0.462505	−	0.587742i
$587$	6.73235	+	6.73235i	0.277874	+	0.277874i	0.832260	−	0.554386i	$-0.187047\pi$
$587$	6.73235	+	6.73235i	0.277874	+	0.277874i	−0.554386	+	0.832260i	$0.687047\pi$
$588$		0			0
$589$	0.412751	−	0.412751i	0.0170071	−	0.0170071i
$590$	−16.8995	+	2.01519i	−0.695741	+	0.0829639i
$591$		0			0
$592$	−23.0640	−	7.40479i	−0.947925	−	0.304335i
$593$	−11.7154			−0.481092			−0.240546	−	0.970638i	$-0.577327\pi$
$593$	−11.7154			−0.481092			−0.240546	+	0.970638i	$0.577327\pi$
$594$		0			0
$595$	1.14343	−	1.14343i	0.0468762	−	0.0468762i
$596$	1.86509	+	1.13844i	0.0763970	+	0.0466324i
$597$		0			0
$598$	12.8379	−	16.3141i	0.524979	−	0.667132i
$599$		−	5.86233i		−	0.239528i	−0.992802	−	0.119764i	$-0.961786\pi$
$599$		−	5.86233i		−	0.239528i	0.992802	−	0.119764i	$-0.0382138\pi$
$600$		0			0
$601$		−	5.00353i		−	0.204098i	−0.994779	−	0.102049i	$-0.967460\pi$
$601$		−	5.00353i		−	0.204098i	0.994779	−	0.102049i	$-0.0325399\pi$
$602$	10.9191	+	8.59245i	0.445030	+	0.350202i
$603$		0			0
$604$	1.36423	+	5.63891i	0.0555095	+	0.229444i
$605$	17.4395	−	17.4395i	0.709015	−	0.709015i
$606$		0			0
$607$	22.7109			0.921806			0.460903	−	0.887450i	$-0.347526\pi$
$607$	22.7109			0.921806			0.460903	+	0.887450i	$0.347526\pi$
$608$	8.31960	+	1.61706i	0.337404	+	0.0655804i
$609$		0			0
$610$	−0.527490	−	4.42357i	−0.0213574	−	0.179105i
$611$	14.3267	−	14.3267i	0.579595	−	0.579595i
$612$		0			0
$613$	−7.25531	−	7.25531i	−0.293039	−	0.293039i	0.545240	−	0.838280i	$-0.316438\pi$
$613$	−7.25531	−	7.25531i	−0.293039	−	0.293039i	−0.838280	+	0.545240i	$0.816438\pi$
$614$	4.35703	+	3.42863i	0.175836	+	0.138368i
$615$		0			0
$616$	−21.7194	−	9.94372i	−0.875100	−	0.400644i
$617$		−	46.0710i		−	1.85475i	−0.374133	−	0.927375i	$-0.622060\pi$
$617$		−	46.0710i		−	1.85475i	0.374133	−	0.927375i	$-0.377940\pi$
$618$		0			0
$619$	−34.2931	−	34.2931i	−1.37836	−	1.37836i	−0.847396	−	0.530962i	$-0.821831\pi$
$619$	−34.2931	−	34.2931i	−1.37836	−	1.37836i	−0.530962	−	0.847396i	$-0.678169\pi$
$620$	0.665096	+	0.405972i	0.0267109	+	0.0163042i
$621$		0			0
$622$	−29.4111	+	3.50713i	−1.17928	+	0.140623i
$623$	−26.3798			−1.05688
$624$		0			0
$625$	−1.00000			−0.0400000
$626$	14.2973	−	1.70489i	0.571437	−	0.0681411i
$627$		0			0
$628$	−3.84442	+	6.29824i	−0.153409	+	0.251327i
$629$	−4.89636	−	4.89636i	−0.195231	−	0.195231i
$630$		0			0
$631$			25.9017i			1.03113i	0.856850	+	0.515566i	$0.172418\pi$
$631$			25.9017i			1.03113i	−0.856850	+	0.515566i	$0.827582\pi$
$632$	11.2259	+	30.1848i	0.446541	+	1.20069i
$633$		0			0
$634$	23.2072	+	18.2621i	0.921674	+	0.725282i
$635$	7.10234	+	7.10234i	0.281848	+	0.281848i
$636$		0			0
$637$	6.67452	−	6.67452i	0.264454	−	0.264454i
$638$	4.15862	+	34.8745i	0.164641	+	1.38069i
$639$		0			0
$640$	0.513421	+	11.3021i	0.0202947	+	0.446753i
$641$	15.3341			0.605660			0.302830	−	0.953045i	$-0.402069\pi$
$641$	15.3341			0.605660			0.302830	+	0.953045i	$0.402069\pi$
$642$		0			0
$643$	−16.7507	+	16.7507i	−0.660582	+	0.660582i	−0.955517	−	0.294935i	$-0.904702\pi$
$643$	−16.7507	+	16.7507i	−0.660582	+	0.660582i	0.294935	+	0.955517i	$0.404702\pi$
$644$	−21.3763	+	5.17157i	−0.842342	+	0.203789i
$645$		0			0
$646$	1.90393	+	1.49824i	0.0749090	+	0.0589473i
$647$			4.81900i			0.189455i	0.995503	+	0.0947273i	$0.0301979\pi$
$647$			4.81900i			0.189455i	−0.995503	+	0.0947273i	$0.969802\pi$
$648$		0			0
$649$			71.8678i			2.82106i
$650$	−1.65103	+	2.09809i	−0.0647586	+	0.0822939i
$651$		0			0
$652$	2.09791	−	3.43696i	0.0821605	−	0.134602i
$653$	−16.7842	+	16.7842i	−0.656817	+	0.656817i	−0.954625	−	0.297809i	$-0.903744\pi$
$653$	−16.7842	+	16.7842i	−0.656817	+	0.656817i	0.297809	+	0.954625i	$0.403744\pi$
$654$		0			0
$655$	10.7511			0.420079
$656$	−9.98036	−	19.4192i	−0.389668	−	0.758193i
$657$		0			0
$658$	−21.3137	+	2.54156i	−0.830895	+	0.0990803i
$659$	−16.4376	+	16.4376i	−0.640320	+	0.640320i	−0.950634	−	0.310314i	$-0.899566\pi$
$659$	−16.4376	+	16.4376i	−0.640320	+	0.640320i	0.310314	+	0.950634i	$0.399566\pi$
$660$		0			0
$661$	−17.5904	−	17.5904i	−0.684187	−	0.684187i	0.276754	−	0.960941i	$-0.410741\pi$
$661$	−17.5904	−	17.5904i	−0.684187	−	0.684187i	−0.960941	+	0.276754i	$0.910741\pi$
$662$	−20.8793	+	26.5330i	−0.811498	+	1.03123i
$663$		0			0
$664$	40.4258	+	18.5080i	1.56883	+	0.718251i
$665$		−	2.11882i		−	0.0821645i
$666$		0			0
$667$	22.8651	+	22.8651i	0.885339	+	0.885339i
$668$	−1.98519	−	8.20561i	−0.0768092	−	0.317484i
$669$		0			0
$670$	−0.697947	−	5.85304i	−0.0269640	−	0.226123i
$671$	−18.8119			−0.726227
$672$		0			0
$673$	27.0762			1.04371			0.521856	−	0.853033i	$-0.325240\pi$
$673$	27.0762			1.04371			0.521856	+	0.853033i	$0.325240\pi$
$674$	3.99110	+	33.4697i	0.153732	+	1.28920i
$675$		0			0
$676$	−4.43772	−	18.3429i	−0.170682	−	0.705498i
$677$	−16.9093	−	16.9093i	−0.649877	−	0.649877i	0.303086	−	0.952963i	$-0.401983\pi$
$677$	−16.9093	−	16.9093i	−0.649877	−	0.649877i	−0.952963	+	0.303086i	$0.901983\pi$
$678$		0			0
$679$		−	7.70607i		−	0.295732i
$680$	−1.34628	+	2.94059i	−0.0516275	+	0.112766i
$681$		0			0
$682$	2.03480	−	2.58579i	0.0779166	−	0.0990149i
$683$	14.0531	+	14.0531i	0.537728	+	0.537728i	0.922861	−	0.385133i	$-0.125845\pi$
$683$	14.0531	+	14.0531i	0.537728	+	0.537728i	−0.385133	+	0.922861i	$0.625845\pi$
$684$		0			0
$685$	−10.4654	+	10.4654i	−0.399862	+	0.399862i
$686$	−23.8312	+	2.84175i	−0.909878	+	0.108499i
$687$		0			0
$688$	−26.4588	−	8.49471i	−1.00873	−	0.323858i
$689$	2.30466			0.0878005
$690$		0			0
$691$	25.9737	−	25.9737i	0.988086	−	0.988086i	−0.0118439	−	0.999930i	$-0.503770\pi$
$691$	25.9737	−	25.9737i	0.988086	−	0.988086i	0.999930	+	0.0118439i	$0.00377011\pi$
$692$	−20.8639	+	34.1810i	−0.793127	+	1.29937i
$693$		0			0
$694$	−5.42088	+	6.88874i	−0.205774	+	0.261493i
$695$			11.9304i			0.452546i
$696$		0			0
$697$		−	6.24136i		−	0.236409i
$698$	27.4039	+	21.5647i	1.03725	+	0.816234i
$699$		0			0
$700$	2.74912	−	0.665096i	0.103907	−	0.0251383i
$701$	−20.8789	+	20.8789i	−0.788586	+	0.788586i	−0.981262	−	0.192676i	$-0.938283\pi$
$701$	−20.8789	+	20.8789i	−0.788586	+	0.788586i	0.192676	+	0.981262i	$0.438283\pi$
$702$		0			0
$703$	−9.07314			−0.342200
$704$	47.6466	+	3.49824i	1.79575	+	0.131845i
$705$		0			0
$706$	5.28805	+	44.3460i	0.199018	+	1.66898i
$707$	−15.8249	+	15.8249i	−0.595157	+	0.595157i
$708$		0			0
$709$	14.4580	+	14.4580i	0.542983	+	0.542983i	0.924402	−	0.381419i	$-0.124564\pi$
$709$	14.4580	+	14.4580i	0.542983	+	0.542983i	−0.381419	+	0.924402i	$0.624564\pi$
$710$	3.63853	+	2.86323i	0.136552	+	0.107455i
$711$		0			0
$712$	49.4505	−	18.3909i	1.85323	−	0.689227i
$713$		−	3.02944i		−	0.113453i
$714$		0			0
$715$	7.97186	+	7.97186i	0.298131	+	0.298131i
$716$	−17.5061	+	28.6799i	−0.654233	+	1.07182i
$717$		0			0
$718$	35.8522	−	4.27521i	1.33799	−	0.159549i
$719$	−3.53803			−0.131946			−0.0659731	−	0.997821i	$-0.521015\pi$
$719$	−3.53803			−0.131946			−0.0659731	+	0.997821i	$0.521015\pi$
$720$		0			0
$721$	25.8686			0.963397
$722$	−23.5289	+	2.80571i	−0.875654	+	0.104418i
$723$		0			0
$724$	−17.0117	−	10.3838i	−0.632233	−	0.385912i
$725$	−2.94059	−	2.94059i	−0.109211	−	0.109211i
$726$		0			0
$727$			23.6681i			0.877802i	0.898535	+	0.438901i	$0.144632\pi$
$727$			23.6681i			0.877802i	−0.898535	+	0.438901i	$0.855368\pi$
$728$	3.14343	−	6.86599i	0.116503	−	0.254471i
$729$		0			0
$730$	2.04646	+	1.61040i	0.0757428	+	0.0596034i
$731$	−5.61706	−	5.61706i	−0.207754	−	0.207754i
$732$		0			0
$733$	−20.3055	+	20.3055i	−0.750000	+	0.750000i	−0.974479	−	0.224479i	$-0.927932\pi$
$733$	−20.3055	+	20.3055i	−0.750000	+	0.750000i	0.224479	+	0.974479i	$0.427932\pi$
$734$	2.32898	+	19.5310i	0.0859643	+	0.720903i
$735$		0			0
$736$	36.4656	−	24.5970i	1.34414	−	0.906659i
$737$	−24.8910			−0.916871
$738$		0			0
$739$	4.63944	−	4.63944i	0.170664	−	0.170664i	−0.616607	−	0.787271i	$-0.711493\pi$
$739$	4.63944	−	4.63944i	0.170664	−	0.170664i	0.787271	+	0.616607i	$0.211493\pi$
$740$	−2.84804	−	11.7721i	−0.104696	−	0.432753i
$741$		0			0
$742$	−1.91874	−	1.50989i	−0.0704391	−	0.0554298i
$743$		−	27.3029i		−	1.00165i	−0.865549	−	0.500824i	$-0.833030\pi$
$743$		−	27.3029i		−	1.00165i	0.865549	−	0.500824i	$-0.166970\pi$
$744$		0			0
$745$			1.09254i			0.0400277i
$746$	−3.57367	+	4.54135i	−0.130841	+	0.166270i
$747$		0			0
$748$	11.6569	+	7.11529i	0.426217	+	0.260161i
$749$	9.89450	−	9.89450i	0.361537	−	0.361537i
$750$		0			0
$751$	−26.1582			−0.954527			−0.477264	−	0.878760i	$-0.658371\pi$
$751$	−26.1582			−0.954527			−0.477264	+	0.878760i	$0.658371\pi$
$752$	38.1819	−	19.6233i	1.39235	−	0.715589i
$753$		0			0
$754$	−11.0246	+	1.31463i	−0.401493	+	0.0478761i
$755$	−2.05117	+	2.05117i	−0.0746497	+	0.0746497i
$756$		0			0
$757$	−16.8559	−	16.8559i	−0.612638	−	0.612638i	0.330995	−	0.943633i	$-0.392616\pi$
$757$	−16.8559	−	16.8559i	−0.612638	−	0.612638i	−0.943633	+	0.330995i	$0.892616\pi$
$758$	7.37990	−	9.37823i	0.268050	−	0.340633i
$759$		0			0
$760$	1.47716	+	3.97186i	0.0535821	+	0.144075i
$761$		−	34.6337i		−	1.25547i	−0.778427	−	0.627735i	$-0.783982\pi$
$761$		−	34.6337i		−	1.25547i	0.778427	−	0.627735i	$-0.216018\pi$
$762$		0			0
$763$	17.9222	+	17.9222i	0.648829	+	0.648829i
$764$	−29.9085	+	7.23579i	−1.08205	+	0.261782i
$765$		0			0
$766$	−2.31724	−	19.4325i	−0.0837252	−	0.702126i
$767$	−22.7190			−0.820337
$768$		0			0
$769$	−8.79179			−0.317040			−0.158520	−	0.987356i	$-0.550672\pi$
$769$	−8.79179			−0.317040			−0.158520	+	0.987356i	$0.550672\pi$
$770$	−1.41421	−	11.8597i	−0.0509647	−	0.427394i
$771$		0			0
$772$	−14.6202	+	3.53707i	−0.526192	+	0.127302i
$773$	7.17118	+	7.17118i	0.257929	+	0.257929i	0.824211	−	0.566282i	$-0.191619\pi$
$773$	7.17118	+	7.17118i	0.257929	+	0.257929i	−0.566282	+	0.824211i	$0.691619\pi$
$774$		0			0
$775$			0.389604i			0.0139950i
$776$	5.37235	+	14.4455i	0.192856	+	0.518563i
$777$		0			0
$778$	−25.0528	+	31.8366i	−0.898188	+	1.14140i
$779$	−5.78274	−	5.78274i	−0.207188	−	0.207188i
$780$		0			0
$781$	13.8249	−	13.8249i	0.494694	−	0.494694i
$782$	12.4853	−	1.48881i	0.446473	−	0.0532398i
$783$		0			0
$784$	17.7882	−	9.14214i	0.635294	−	0.326505i
$785$	−3.68943			−0.131681
$786$		0			0
$787$	10.9687	−	10.9687i	0.390993	−	0.390993i	−0.484048	−	0.875041i	$-0.660834\pi$
$787$	10.9687	−	10.9687i	0.390993	−	0.390993i	0.875041	+	0.484048i	$0.160834\pi$
$788$	23.3298	+	14.2404i	0.831090	+	0.507294i
$789$		0			0
$790$	−9.95779	+	12.6542i	−0.354282	+	0.450215i
$791$		−	25.1873i		−	0.895556i
$792$		0			0
$793$		−	5.94688i		−	0.211180i
$794$	33.1540	+	26.0895i	1.17659	+	0.925880i
$795$		0			0
$796$	−4.39993	−	18.1867i	−0.155951	−	0.644612i
$797$	−1.13138	+	1.13138i	−0.0400756	+	0.0400756i	−0.726861	−	0.686785i	$-0.759021\pi$
$797$	−1.13138	+	1.13138i	−0.0400756	+	0.0400756i	0.686785	+	0.726861i	$0.259021\pi$
$798$		0			0
$799$	12.2717			0.434143
$800$	−4.68971	+	3.16333i	−0.165806	+	0.111841i
$801$		0			0
$802$	−0.834437	−	6.99765i	−0.0294650	−	0.247096i
$803$	7.77568	−	7.77568i	0.274398	−	0.274398i
$804$		0			0
$805$	−7.77568	−	7.77568i	−0.274057	−	0.274057i
$806$	0.817425	+	0.643247i	0.0287926	+	0.0226574i
$807$		0			0
$808$	18.6322	−	40.6972i	0.655480	−	1.43172i
$809$		−	20.1610i		−	0.708822i	−0.935090	−	0.354411i	$-0.884681\pi$
$809$		−	20.1610i		−	0.708822i	0.935090	−	0.354411i	$-0.115319\pi$
$810$		0			0
$811$	−28.0206	−	28.0206i	−0.983935	−	0.983935i	0.0159383	−	0.999873i	$-0.494926\pi$
$811$	−28.0206	−	28.0206i	−0.983935	−	0.983935i	−0.999873	+	0.0159383i	$0.994926\pi$
$812$	10.0398	+	6.12825i	0.352328	+	0.215059i
$813$		0			0
$814$	−50.7851	+	6.05588i	−1.78002	+	0.212259i
$815$	2.01333			0.0705238
$816$		0			0
$817$	−10.4086			−0.364151
$818$	47.4201	−	5.65462i	1.65800	−	0.197709i
$819$		0			0
$820$	5.68775	−	9.31814i	0.198625	−	0.325404i
$821$	−31.0657	−	31.0657i	−1.08420	−	1.08420i	−0.996113	−	0.0880869i	$-0.971925\pi$
$821$	−31.0657	−	31.0657i	−1.08420	−	1.08420i	−0.0880869	−	0.996113i	$-0.528075\pi$
$822$		0			0
$823$		−	18.5484i		−	0.646555i	−0.946304	−	0.323278i	$-0.895215\pi$
$823$		−	18.5484i		−	0.646555i	0.946304	−	0.323278i	$-0.104785\pi$
$824$	−48.4922	+	18.0345i	−1.68931	+	0.628262i
$825$		0			0
$826$	18.9147	+	14.8843i	0.658126	+	0.517891i
$827$	16.6080	+	16.6080i	0.577517	+	0.577517i	0.934218	−	0.356701i	$-0.116099\pi$
$827$	16.6080	+	16.6080i	0.577517	+	0.577517i	−0.356701	+	0.934218i	$0.616099\pi$
$828$		0			0
$829$	−19.0261	+	19.0261i	−0.660803	+	0.660803i	−0.955569	−	0.294767i	$-0.904758\pi$
$829$	−19.0261	+	19.0261i	−0.660803	+	0.660803i	0.294767	+	0.955569i	$0.404758\pi$
$830$	2.63224	+	22.0742i	0.0913666	+	0.766207i
$831$		0			0
$832$	−1.10587	+	15.0622i	−0.0383392	+	0.522187i
$833$	5.71717			0.198088
$834$		0			0
$835$	2.98481	−	2.98481i	0.103294	−	0.103294i
$836$	17.3927	−	4.20784i	0.601540	−	0.145531i
$837$		0			0
$838$	25.0615	+	19.7214i	0.865735	+	0.681263i
$839$			15.5569i			0.537083i	0.963268	+	0.268542i	$0.0865417\pi$
$839$			15.5569i			0.537083i	−0.963268	+	0.268542i	$0.913458\pi$
$840$		0			0
$841$			11.7059i			0.403651i
$842$	2.88543	−	3.66674i	0.0994383	−	0.126364i
$843$		0			0
$844$	0.0921695	−	0.151000i	0.00317261	−	0.00519762i
$845$	6.67230	−	6.67230i	0.229534	−	0.229534i
$846$		0			0
$847$	−34.8789			−1.19845
$848$	4.64942	+	1.49271i	0.159662	+	0.0512600i
$849$		0			0
$850$	−1.60568	+	0.191470i	−0.0550745	+	0.00656738i
$851$	−33.2967	+	33.2967i	−1.14139	+	1.14139i
$852$		0			0
$853$	−15.5124	−	15.5124i	−0.531133	−	0.531133i	0.389776	−	0.920910i	$-0.372552\pi$
$853$	−15.5124	−	15.5124i	−0.531133	−	0.531133i	−0.920910	+	0.389776i	$0.872552\pi$
$854$	−3.89608	+	4.95106i	−0.133321	+	0.169422i
$855$		0			0
$856$	−11.6498	+	25.4459i	−0.398182	+	0.869722i
$857$		−	27.0005i		−	0.922320i	−0.887317	−	0.461160i	$-0.847433\pi$
$857$		−	27.0005i		−	0.922320i	0.887317	−	0.461160i	$-0.152567\pi$
$858$		0			0
$859$	1.31020	+	1.31020i	0.0447035	+	0.0447035i	0.729105	−	0.684402i	$-0.239937\pi$
$859$	1.31020	+	1.31020i	0.0447035	+	0.0447035i	−0.684402	+	0.729105i	$0.739937\pi$
$860$	−3.26725	−	13.5049i	−0.111412	−	0.460513i
$861$		0			0
$862$	3.45621	+	28.9840i	0.117719	+	0.987200i
$863$	45.1917			1.53834			0.769172	−	0.639042i	$-0.220669\pi$
$863$	45.1917			1.53834			0.769172	+	0.639042i	$0.220669\pi$
$864$		0			0
$865$	−20.0228			−0.680794
$866$	0.180095	+	1.51029i	0.00611986	+	0.0513216i
$867$		0			0
$868$	−0.259124	−	1.07107i	−0.00879525	−	0.0363544i
$869$	48.0805	+	48.0805i	1.63102	+	1.63102i
$870$		0			0
$871$		−	7.86860i		−	0.266617i
$872$	−46.0909	−	21.1017i	−1.56084	−	0.714593i
$873$		0			0
$874$	10.1884	−	12.9473i	0.344629	−	0.437947i
$875$	1.00000	+	1.00000i	0.0338062	+	0.0338062i
$876$		0			0
$877$	−10.2259	+	10.2259i	−0.345303	+	0.345303i	−0.858357	−	0.513053i	$-0.828514\pi$
$877$	−10.2259	+	10.2259i	−0.345303	+	0.345303i	0.513053	+	0.858357i	$0.328514\pi$
$878$	−5.95466	+	0.710065i	−0.200960	+	0.0239635i
$879$		0			0
$880$	10.9191	+	21.2458i	0.368083	+	0.716195i
$881$	7.61942			0.256705			0.128352	−	0.991729i	$-0.459031\pi$
$881$	7.61942			0.256705			0.128352	+	0.991729i	$0.459031\pi$
$882$		0			0
$883$	−1.70424	+	1.70424i	−0.0573521	+	0.0573521i	−0.735201	−	0.677849i	$-0.762912\pi$
$883$	−1.70424	+	1.70424i	−0.0573521	+	0.0573521i	0.677849	+	0.735201i	$0.262912\pi$
$884$	−2.24930	+	3.68499i	−0.0756523	+	0.123940i
$885$		0			0
$886$	−24.6087	+	31.2722i	−0.826746	+	1.05061i
$887$			23.9647i			0.804655i	0.915496	+	0.402327i	$0.131799\pi$
$887$			23.9647i			0.804655i	−0.915496	+	0.402327i	$0.868201\pi$
$888$		0			0
$889$		−	14.2047i		−	0.476410i
$890$	20.7308	+	16.3134i	0.694897	+	0.546827i
$891$		0			0
$892$	−25.5048	+	6.17039i	−0.853963	+	0.206600i
$893$	11.3700	−	11.3700i	0.380482	−	0.380482i
$894$		0			0
$895$	−16.8003			−0.561572
$896$	10.7886	−	11.8155i	0.360423	−	0.394727i
$897$		0			0
$898$	−2.88756	−	24.2153i	−0.0963591	−	0.808075i
$899$	−1.14567	+	1.14567i	−0.0382101	+	0.0382101i
$900$		0			0
$901$	0.987046	+	0.987046i	0.0328833	+	0.0328833i
$902$	−36.2274	−	28.5080i	−1.20624	−	0.949214i
$903$		0			0
$904$	17.5595	+	47.2150i	0.584020	+	1.57035i
$905$		−	9.96520i		−	0.331254i
$906$		0			0
$907$	19.1197	+	19.1197i	0.634860	+	0.634860i	0.949283	−	0.314423i	$-0.101811\pi$
$907$	19.1197	+	19.1197i	0.634860	+	0.634860i	−0.314423	+	0.949283i	$0.601811\pi$
$908$	8.49155	−	13.9115i	0.281802	−	0.461671i
$909$		0			0
$910$	3.74912	−	0.447065i	0.124282	−	0.0148200i
$911$	−4.15918			−0.137800			−0.0688999	−	0.997624i	$-0.521949\pi$
$911$	−4.15918			−0.137800			−0.0688999	+	0.997624i	$0.521949\pi$
$912$		0			0
$913$	93.8741			3.10678
$914$	45.3775	−	5.41106i	1.50096	−	0.178982i
$915$		0			0
$916$	−12.3740	−	7.55305i	−0.408849	−	0.249560i
$917$	−10.7511	−	10.7511i	−0.355032	−	0.355032i
$918$		0			0
$919$			43.6229i			1.43899i	0.694499	+	0.719494i	$0.255626\pi$
$919$			43.6229i			1.43899i	−0.694499	+	0.719494i	$0.744374\pi$
$920$	19.9968	+	9.15509i	0.659276	+	0.301834i
$921$		0			0
$922$	−24.3434	−	19.1563i	−0.801707	−	0.630878i
$923$	4.37036	+	4.37036i	0.143852	+	0.143852i
$924$		0			0
$925$	4.28216	−	4.28216i	0.140796	−	0.140796i
$926$	4.55721	+	38.2171i	0.149759	+	1.25589i
$927$		0			0
$928$	−23.0925	−	4.48844i	−0.758050	−	0.147340i
$929$	−4.24392			−0.139238			−0.0696192	−	0.997574i	$-0.522178\pi$
$929$	−4.24392			−0.139238			−0.0696192	+	0.997574i	$0.522178\pi$
$930$		0			0
$931$	5.29706	−	5.29706i	0.173604	−	0.173604i
$932$	−6.23384	−	25.7670i	−0.204196	−	0.844027i
$933$		0			0
$934$	−11.9509	−	9.40439i	−0.391046	−	0.307721i
$935$			6.82843i			0.223313i
$936$		0			0
$937$			9.87491i			0.322599i	0.986905	+	0.161300i	$0.0515685\pi$
$937$			9.87491i			0.322599i	−0.986905	+	0.161300i	$0.948431\pi$
$938$	−5.15509	+	6.55098i	−0.168320	+	0.213897i
$939$		0			0
$940$	18.3213	+	11.1832i	0.597574	+	0.364757i
$941$	−26.0675	+	26.0675i	−0.849777	+	0.849777i	−0.990105	−	0.140328i	$-0.955184\pi$
$941$	−26.0675	+	26.0675i	−0.849777	+	0.849777i	0.140328	+	0.990105i	$0.455184\pi$
$942$		0			0
$943$	−42.4431			−1.38214
$944$	−45.8334	−	14.7150i	−1.49175	−	0.478932i
$945$		0			0
$946$	−58.2602	+	6.94725i	−1.89420	+	0.225875i
$947$	10.7355	−	10.7355i	0.348857	−	0.348857i	−0.510827	−	0.859684i	$-0.670661\pi$
$947$	10.7355	−	10.7355i	0.348857	−	0.348857i	0.859684	+	0.510827i	$0.170661\pi$
$948$		0			0
$949$	2.45807	+	2.45807i	0.0797922	+	0.0797922i
$950$	−1.31029	+	1.66510i	−0.0425116	+	0.0540228i
$951$		0			0
$952$	4.28687	−	1.59431i	0.138938	−	0.0516718i
$953$		−	34.0844i		−	1.10410i	−0.833811	−	0.552051i	$-0.813846\pi$
$953$		−	34.0844i		−	1.10410i	0.833811	−	0.552051i	$-0.186154\pi$
$954$		0			0
$955$	−10.8793	−	10.8793i	−0.352046	−	0.352046i
$956$	−36.5689	+	8.84714i	−1.18272	+	0.286137i
$957$		0			0
$958$	−0.0862532	−	0.723326i	−0.00278672	−	0.0233696i
$959$	20.9308			0.675890
$960$		0			0
$961$	−30.8482			−0.995104
$962$	−1.91440	−	16.0543i	−0.0617227	−	0.517612i
$963$		0			0
$964$	5.18376	−	1.25411i	0.166958	−	0.0403922i
$965$	−5.31814	−	5.31814i	−0.171197	−	0.171197i
$966$		0			0
$967$		−	9.41342i		−	0.302715i	−0.988479	−	0.151358i	$-0.951635\pi$
$967$		−	9.41342i		−	0.302715i	0.988479	−	0.151358i	$-0.0483645\pi$
$968$	65.3826	−	24.3161i	2.10148	−	0.781550i
$969$		0			0
$970$	−4.76549	+	6.05588i	−0.153011	+	0.194443i
$971$	6.84018	+	6.84018i	0.219512	+	0.219512i	0.808293	−	0.588781i	$-0.200392\pi$
$971$	6.84018	+	6.84018i	0.219512	+	0.219512i	−0.588781	+	0.808293i	$0.700392\pi$
$972$		0			0
$973$	11.9304	−	11.9304i	0.382471	−	0.382471i
$974$	25.6263	−	3.05582i	0.821120	−	0.0979147i
$975$		0			0
$976$	3.85176	−	11.9972i	0.123292	−	0.384022i
$977$	−5.38555			−0.172299			−0.0861494	−	0.996282i	$-0.527456\pi$
$977$	−5.38555			−0.172299			−0.0861494	+	0.996282i	$0.527456\pi$
$978$		0			0
$979$	78.7682	−	78.7682i	2.51744	−	2.51744i
$980$	8.53553	+	5.21005i	0.272658	+	0.166429i
$981$		0			0
$982$	32.8444	−	41.7380i	1.04811	−	1.33191i
$983$		−	9.31630i		−	0.297144i	−0.988902	−	0.148572i	$-0.952532\pi$
$983$		−	9.31630i		−	0.297144i	0.988902	−	0.148572i	$-0.0474677\pi$
$984$		0			0
$985$			13.6663i			0.435444i
$986$	−5.28469	−	4.15862i	−0.168299	−	0.132437i
$987$		0			0
$988$	1.33019	+	5.49824i	0.0423190	+	0.174922i
$989$	−38.1976	+	38.1976i	−1.21461	+	1.21461i
$990$		0			0
$991$	−1.25727			−0.0399384			−0.0199692	−	0.999801i	$-0.506357\pi$
$991$	−1.25727			−0.0399384			−0.0199692	+	0.999801i	$0.506357\pi$
$992$	1.23245	+	1.82713i	0.0391302	+	0.0580114i
$993$		0			0
$994$	−0.775305	−	6.50176i	−0.0245912	−	0.206223i
$995$	6.61548	−	6.61548i	0.209725	−	0.209725i
$996$		0			0
$997$	25.1661	+	25.1661i	0.797017	+	0.797017i	0.982624	−	0.185607i	$-0.0594250\pi$
$997$	25.1661	+	25.1661i	0.797017	+	0.797017i	−0.185607	+	0.982624i	$0.559425\pi$
$998$	−17.6420	−	13.8828i	−0.558449	−	0.439454i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.t.b.181.3		8
3.2	odd	2		240.2.s.b.181.2	yes	8
4.3	odd	2		2880.2.t.b.2161.2		8
12.11	even	2		960.2.s.b.241.3		8
16.3	odd	4		2880.2.t.b.721.2		8
16.13	even	4	inner	720.2.t.b.541.3		8
24.5	odd	2		1920.2.s.c.481.3		8
24.11	even	2		1920.2.s.d.481.2		8
48.5	odd	4		1920.2.s.c.1441.3		8
48.11	even	4		1920.2.s.d.1441.2		8
48.29	odd	4		240.2.s.b.61.2	✓	8
48.35	even	4		960.2.s.b.721.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.s.b.61.2	✓	8	48.29	odd	4
240.2.s.b.181.2	yes	8	3.2	odd	2
720.2.t.b.181.3		8	1.1	even	1	trivial
720.2.t.b.541.3		8	16.13	even	4	inner
960.2.s.b.241.3		8	12.11	even	2
960.2.s.b.721.3		8	48.35	even	4
1920.2.s.c.481.3		8	24.5	odd	2
1920.2.s.c.1441.3		8	48.5	odd	4
1920.2.s.d.481.2		8	24.11	even	2
1920.2.s.d.1441.2		8	48.11	even	4
2880.2.t.b.721.2		8	16.3	odd	4
2880.2.t.b.2161.2		8	4.3	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:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.t (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.167452 + 1.40426i) q^{2} +(-1.94392 + 0.470294i) q^{4} +(-0.707107 - 0.707107i) q^{5} +1.41421i q^{7} +(-0.985930 - 2.65103i) q^{8} +O(q^{10})\)	\(q+(0.167452 + 1.40426i) q^{2} +(-1.94392 + 0.470294i) q^{4} +(-0.707107 - 0.707107i) q^{5} +1.41421i q^{7} +(-0.985930 - 2.65103i) q^{8} +(0.874559 - 1.11137i) q^{10} +(-4.22274 - 4.22274i) q^{11} +(1.33490 - 1.33490i) q^{13} +(-1.98593 + 0.236813i) q^{14} +(3.55765 - 1.82843i) q^{16} +1.14343 q^{17} +(1.05941 - 1.05941i) q^{19} +(1.70711 + 1.04201i) q^{20} +(5.22274 - 6.63696i) q^{22} -7.77568i q^{23} +1.00000i q^{25} +(2.09809 + 1.65103i) q^{26} +(-0.665096 - 2.74912i) q^{28} +(-2.94059 + 2.94059i) q^{29} +0.389604 q^{31} +(3.16333 + 4.68971i) q^{32} +(0.191470 + 1.60568i) q^{34} +(1.00000 - 1.00000i) q^{35} +(-4.28216 - 4.28216i) q^{37} +(1.66510 + 1.31029i) q^{38} +(-1.17740 + 2.57172i) q^{40} -5.45844i q^{41} +(-4.91245 - 4.91245i) q^{43} +(10.1946 + 6.22274i) q^{44} +(10.9191 - 1.30205i) q^{46} +10.7324 q^{47} +5.00000 q^{49} +(-1.40426 + 0.167452i) q^{50} +(-1.96715 + 3.22274i) q^{52} +(0.863230 + 0.863230i) q^{53} +5.97186i q^{55} +(3.74912 - 1.39432i) q^{56} +(-4.62177 - 3.63696i) q^{58} +(-8.50961 - 8.50961i) q^{59} +(2.22746 - 2.22746i) q^{61} +(0.0652400 + 0.547108i) q^{62} +(-6.05588 + 5.22746i) q^{64} -1.88784 q^{65} +(2.94725 - 2.94725i) q^{67} +(-2.22274 + 0.537750i) q^{68} +(1.57172 + 1.23681i) q^{70} +3.27391i q^{71} +1.84138i q^{73} +(5.29623 - 6.73034i) q^{74} +(-1.56118 + 2.55765i) q^{76} +(5.97186 - 5.97186i) q^{77} -11.3861 q^{79} +(-3.80853 - 1.22274i) q^{80} +(7.66510 - 0.914027i) q^{82} +(-11.1153 + 11.1153i) q^{83} +(-0.808530 - 0.808530i) q^{85} +(6.07578 - 7.72098i) q^{86} +(-7.03127 + 15.3579i) q^{88} +18.6533i q^{89} +(1.88784 + 1.88784i) q^{91} +(3.65685 + 15.1153i) q^{92} +(1.79715 + 15.0711i) q^{94} -1.49824 q^{95} -5.44902 q^{97} +(0.837260 + 7.02132i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{4} + 12 q^{8}+O(q^{10}) \) 8 * q - 4 * q^4 + 12 * q^8	\( 8 q - 4 q^{4} + 12 q^{8} - 8 q^{11} + 8 q^{13} + 4 q^{14} - 8 q^{17} + 8 q^{19} + 8 q^{20} + 16 q^{22} + 20 q^{26} - 8 q^{28} - 24 q^{29} + 8 q^{31} + 16 q^{34} + 8 q^{35} - 8 q^{37} + 16 q^{38} - 4 q^{40} + 16 q^{44} + 24 q^{46} + 40 q^{49} - 4 q^{50} + 16 q^{52} + 16 q^{56} - 8 q^{59} - 16 q^{61} - 28 q^{62} + 8 q^{64} + 8 q^{65} + 8 q^{68} + 4 q^{70} + 36 q^{74} - 40 q^{76} + 8 q^{77} - 40 q^{79} - 16 q^{80} + 64 q^{82} - 32 q^{83} + 8 q^{85} - 16 q^{86} - 16 q^{88} - 8 q^{91} - 16 q^{92} + 32 q^{94} + 16 q^{95} - 48 q^{97}+O(q^{100}) \) 8 * q - 4 * q^4 + 12 * q^8 - 8 * q^11 + 8 * q^13 + 4 * q^14 - 8 * q^17 + 8 * q^19 + 8 * q^20 + 16 * q^22 + 20 * q^26 - 8 * q^28 - 24 * q^29 + 8 * q^31 + 16 * q^34 + 8 * q^35 - 8 * q^37 + 16 * q^38 - 4 * q^40 + 16 * q^44 + 24 * q^46 + 40 * q^49 - 4 * q^50 + 16 * q^52 + 16 * q^56 - 8 * q^59 - 16 * q^61 - 28 * q^62 + 8 * q^64 + 8 * q^65 + 8 * q^68 + 4 * q^70 + 36 * q^74 - 40 * q^76 + 8 * q^77 - 40 * q^79 - 16 * q^80 + 64 * q^82 - 32 * q^83 + 8 * q^85 - 16 * q^86 - 16 * q^88 - 8 * q^91 - 16 * q^92 + 32 * q^94 + 16 * q^95 - 48 * q^97

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