LMFDB - Embedded newform 240.3.bj.a.47.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [240,3,Mod(47,240)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(240, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 2, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("240.47");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	240.bj (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:	$6.53952634465$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			47.3
Root			$0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	240.47
Dual form			240.3.bj.a.143.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.507306 + 2.95680i) q^{3} +(3.53553 + 3.53553i) q^{5} +(8.66025 - 8.66025i) q^{7} +(-8.48528 + 3.00000i) q^{9} +O(q^{10})$	\(q+(0.507306 + 2.95680i) q^{3} +(3.53553 + 3.53553i) q^{5} +(8.66025 - 8.66025i) q^{7} +(-8.48528 + 3.00000i) q^{9} +17.1464 q^{11} +(4.00000 - 4.00000i) q^{13} +(-8.66025 + 12.2474i) q^{15} +(-15.5563 + 15.5563i) q^{17} -6.92820 q^{19} +(30.0000 + 21.2132i) q^{21} +(-4.89898 + 4.89898i) q^{23} +25.0000i q^{25} +(-13.1750 - 23.5673i) q^{27} -26.8701 q^{29} +3.46410i q^{31} +(8.69848 + 50.6985i) q^{33} +61.2372 q^{35} +(38.0000 + 38.0000i) q^{37} +(13.8564 + 9.79796i) q^{39} -62.2254i q^{41} +(-24.2487 - 24.2487i) q^{43} +(-40.6066 - 19.3934i) q^{45} +(9.79796 + 9.79796i) q^{47} -101.000i q^{49} +(-53.8888 - 38.1051i) q^{51} +(5.65685 + 5.65685i) q^{53} +(60.6218 + 60.6218i) q^{55} +(-3.51472 - 20.4853i) q^{57} -46.5403i q^{59} -42.0000 q^{61} +(-47.5039 + 99.4655i) q^{63} +28.2843 q^{65} +(-20.7846 + 20.7846i) q^{67} +(-16.9706 - 12.0000i) q^{69} +14.6969 q^{71} +(-37.0000 + 37.0000i) q^{73} +(-73.9199 + 12.6826i) q^{75} +(148.492 - 148.492i) q^{77} -72.7461 q^{79} +(63.0000 - 50.9117i) q^{81} +(93.0806 - 93.0806i) q^{83} -110.000 q^{85} +(-13.6313 - 79.4493i) q^{87} -87.6812 q^{89} -69.2820i q^{91} +(-10.2426 + 1.75736i) q^{93} +(-24.4949 - 24.4949i) q^{95} +(35.0000 + 35.0000i) q^{97} +(-145.492 + 51.4393i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q+O(q^{10}) $ 8 * q	$ 8 q + 32 q^{13} + 240 q^{21} - 168 q^{33} + 304 q^{37} - 240 q^{45} - 96 q^{57} - 336 q^{61} - 296 q^{73} + 504 q^{81} - 880 q^{85} - 48 q^{93} + 280 q^{97}+O(q^{100}) $ 8 * q + 32 * q^13 + 240 * q^21 - 168 * q^33 + 304 * q^37 - 240 * q^45 - 96 * q^57 - 336 * q^61 - 296 * q^73 + 504 * q^81 - 880 * q^85 - 48 * q^93 + 280 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$181$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

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			0
$2$		0			0
$3$	0.507306	+	2.95680i	0.169102	+	0.985599i
$3$	0.507306	+	2.95680i	0.169102	+	0.985599i
$4$		0			0
$5$	3.53553	+	3.53553i	0.707107	+	0.707107i
$5$	3.53553	+	3.53553i	0.707107	+	0.707107i
$6$		0			0
$7$	8.66025	−	8.66025i	1.23718	−	1.23718i	0.276030	−	0.961149i	$-0.410981\pi$
$7$	8.66025	−	8.66025i	1.23718	−	1.23718i	0.961149	−	0.276030i	$-0.0890190\pi$
$8$		0			0
$9$	−8.48528	+	3.00000i	−0.942809	+	0.333333i
$10$		0			0
$11$	17.1464			1.55877			0.779383	−	0.626548i	$-0.215533\pi$
$11$	17.1464			1.55877			0.779383	+	0.626548i	$0.215533\pi$
$12$		0			0
$13$	4.00000	−	4.00000i	0.307692	−	0.307692i	−0.536321	−	0.844014i	$-0.680187\pi$
$13$	4.00000	−	4.00000i	0.307692	−	0.307692i	0.844014	+	0.536321i	$0.180187\pi$
$14$		0			0
$15$	−8.66025	+	12.2474i	−0.577350	+	0.816497i
$16$		0			0
$17$	−15.5563	+	15.5563i	−0.915079	+	0.915079i	−0.996666	−	0.0815869i	$-0.974001\pi$
$17$	−15.5563	+	15.5563i	−0.915079	+	0.915079i	0.0815869	+	0.996666i	$0.474001\pi$
$18$		0			0
$19$	−6.92820			−0.364642			−0.182321	−	0.983239i	$-0.558361\pi$
$19$	−6.92820			−0.364642			−0.182321	+	0.983239i	$0.558361\pi$
$20$		0			0
$21$	30.0000	+	21.2132i	1.42857	+	1.01015i
$22$		0			0
$23$	−4.89898	+	4.89898i	−0.212999	+	0.212999i	−0.805540	−	0.592541i	$-0.798125\pi$
$23$	−4.89898	+	4.89898i	−0.212999	+	0.212999i	0.592541	+	0.805540i	$0.298125\pi$
$24$		0			0
$25$			25.0000i			1.00000i
$26$		0			0
$27$	−13.1750	−	23.5673i	−0.487964	−	0.872864i
$28$		0			0
$29$	−26.8701			−0.926554			−0.463277	−	0.886214i	$-0.653326\pi$
$29$	−26.8701			−0.926554			−0.463277	+	0.886214i	$0.653326\pi$
$30$		0			0
$31$			3.46410i			0.111745i	0.998438	+	0.0558726i	$0.0177941\pi$
$31$			3.46410i			0.111745i	−0.998438	+	0.0558726i	$0.982206\pi$
$32$		0			0
$33$	8.69848	+	50.6985i	0.263590	+	1.53632i
$34$		0			0
$35$	61.2372			1.74964
$36$		0			0
$37$	38.0000	+	38.0000i	1.02703	+	1.02703i	0.999624	+	0.0274025i	$0.00872359\pi$
$37$	38.0000	+	38.0000i	1.02703	+	1.02703i	0.0274025	+	0.999624i	$0.491276\pi$
$38$		0			0
$39$	13.8564	+	9.79796i	0.355292	+	0.251230i
$40$		0			0
$41$		−	62.2254i		−	1.51769i	−0.651270	−	0.758846i	$-0.725763\pi$
$41$		−	62.2254i		−	1.51769i	0.651270	−	0.758846i	$-0.274237\pi$
$42$		0			0
$43$	−24.2487	−	24.2487i	−0.563924	−	0.563924i	0.366496	−	0.930420i	$-0.380557\pi$
$43$	−24.2487	−	24.2487i	−0.563924	−	0.563924i	−0.930420	+	0.366496i	$0.880557\pi$
$44$		0			0
$45$	−40.6066	−	19.3934i	−0.902369	−	0.430964i
$46$		0			0
$47$	9.79796	+	9.79796i	0.208467	+	0.208467i	0.803616	−	0.595149i	$-0.202907\pi$
$47$	9.79796	+	9.79796i	0.208467	+	0.208467i	−0.595149	+	0.803616i	$0.702907\pi$
$48$		0			0
$49$		−	101.000i		−	2.06122i
$50$		0			0
$51$	−53.8888	−	38.1051i	−1.05664	−	0.747159i
$52$		0			0
$53$	5.65685	+	5.65685i	0.106733	+	0.106733i	0.758457	−	0.651724i	$-0.225954\pi$
$53$	5.65685	+	5.65685i	0.106733	+	0.106733i	−0.651724	+	0.758457i	$0.725954\pi$
$54$		0			0
$55$	60.6218	+	60.6218i	1.10221	+	1.10221i
$56$		0			0
$57$	−3.51472	−	20.4853i	−0.0616617	−	0.359391i
$58$		0			0
$59$		−	46.5403i		−	0.788819i	−0.918935	−	0.394409i	$-0.870949\pi$
$59$		−	46.5403i		−	0.788819i	0.918935	−	0.394409i	$-0.129051\pi$
$60$		0			0
$61$	−42.0000			−0.688525			−0.344262	−	0.938874i	$-0.611871\pi$
$61$	−42.0000			−0.688525			−0.344262	+	0.938874i	$0.611871\pi$
$62$		0			0
$63$	−47.5039	+	99.4655i	−0.754031	+	1.57882i
$64$		0			0
$65$	28.2843			0.435143
$66$		0			0
$67$	−20.7846	+	20.7846i	−0.310218	+	0.310218i	−0.844994	−	0.534776i	$-0.820396\pi$
$67$	−20.7846	+	20.7846i	−0.310218	+	0.310218i	0.534776	+	0.844994i	$0.320396\pi$
$68$		0			0
$69$	−16.9706	−	12.0000i	−0.245950	−	0.173913i
$70$		0			0
$71$	14.6969			0.206999			0.103500	−	0.994629i	$-0.466996\pi$
$71$	14.6969			0.206999			0.103500	+	0.994629i	$0.466996\pi$
$72$		0			0
$73$	−37.0000	+	37.0000i	−0.506849	+	0.506849i	−0.913558	−	0.406709i	$-0.866676\pi$
$73$	−37.0000	+	37.0000i	−0.506849	+	0.506849i	0.406709	+	0.913558i	$0.366676\pi$
$74$		0			0
$75$	−73.9199	+	12.6826i	−0.985599	+	0.169102i
$76$		0			0
$77$	148.492	−	148.492i	1.92847	−	1.92847i
$78$		0			0
$79$	−72.7461			−0.920837			−0.460419	−	0.887702i	$-0.652301\pi$
$79$	−72.7461			−0.920837			−0.460419	+	0.887702i	$0.652301\pi$
$80$		0			0
$81$	63.0000	−	50.9117i	0.777778	−	0.628539i
$82$		0			0
$83$	93.0806	−	93.0806i	1.12145	−	1.12145i	0.129930	−	0.991523i	$-0.458525\pi$
$83$	93.0806	−	93.0806i	1.12145	−	1.12145i	0.991523	−	0.129930i	$-0.0414753\pi$
$84$		0			0
$85$	−110.000			−1.29412
$86$		0			0
$87$	−13.6313	−	79.4493i	−0.156682	−	0.913210i
$88$		0			0
$89$	−87.6812			−0.985182			−0.492591	−	0.870261i	$-0.663950\pi$
$89$	−87.6812			−0.985182			−0.492591	+	0.870261i	$0.663950\pi$
$90$		0			0
$91$		−	69.2820i		−	0.761341i
$92$		0			0
$93$	−10.2426	+	1.75736i	−0.110136	+	0.0188963i
$94$		0			0
$95$	−24.4949	−	24.4949i	−0.257841	−	0.257841i
$96$		0			0
$97$	35.0000	+	35.0000i	0.360825	+	0.360825i	0.864117	−	0.503292i	$-0.167878\pi$
$97$	35.0000	+	35.0000i	0.360825	+	0.360825i	−0.503292	+	0.864117i	$0.667878\pi$
$98$		0			0
$99$	−145.492	+	51.4393i	−1.46962	+	0.519589i
$100$		0			0
$101$		−	49.4975i		−	0.490074i	−0.969514	−	0.245037i	$-0.921200\pi$
$101$		−	49.4975i		−	0.490074i	0.969514	−	0.245037i	$-0.0788001\pi$
$102$		0			0
$103$	43.3013	+	43.3013i	0.420401	+	0.420401i	0.885342	−	0.464941i	$-0.153924\pi$
$103$	43.3013	+	43.3013i	0.420401	+	0.420401i	−0.464941	+	0.885342i	$0.653924\pi$
$104$		0			0
$105$	31.0660	+	181.066i	0.295867	+	1.72444i
$106$		0			0
$107$	−53.8888	−	53.8888i	−0.503633	−	0.503633i	0.408932	−	0.912565i	$-0.365901\pi$
$107$	−53.8888	−	53.8888i	−0.503633	−	0.503633i	−0.912565	+	0.408932i	$0.865901\pi$
$108$		0			0
$109$		−	126.000i		−	1.15596i	−0.816050	−	0.577982i	$-0.803841\pi$
$109$		−	126.000i		−	1.15596i	0.816050	−	0.577982i	$-0.196159\pi$
$110$		0			0
$111$	−93.0806	+	131.636i	−0.838564	+	1.18591i
$112$		0			0
$113$	−46.6690	−	46.6690i	−0.413000	−	0.413000i	0.469782	−	0.882782i	$-0.344333\pi$
$113$	−46.6690	−	46.6690i	−0.413000	−	0.413000i	−0.882782	+	0.469782i	$0.844333\pi$
$114$		0			0
$115$	−34.6410			−0.301226
$116$		0			0
$117$	−21.9411	+	45.9411i	−0.187531	+	0.392659i
$118$		0			0
$119$			269.444i			2.26423i
$120$		0			0
$121$	173.000			1.42975
$122$		0			0
$123$	183.988	−	31.5673i	1.49584	−	0.256645i
$124$		0			0
$125$	−88.3883	+	88.3883i	−0.707107	+	0.707107i
$126$		0			0
$127$	32.9090	−	32.9090i	0.259126	−	0.259126i	−0.565573	−	0.824698i	$-0.691345\pi$
$127$	32.9090	−	32.9090i	0.259126	−	0.259126i	0.824698	+	0.565573i	$0.191345\pi$
$128$		0			0
$129$	59.3970	−	84.0000i	0.460442	−	0.651163i
$130$		0			0
$131$	7.34847			0.0560952			0.0280476	−	0.999607i	$-0.491071\pi$
$131$	7.34847			0.0560952			0.0280476	+	0.999607i	$0.491071\pi$
$132$		0			0
$133$	−60.0000	+	60.0000i	−0.451128	+	0.451128i
$134$		0			0
$135$	36.7423	−	129.904i	0.272166	−	0.962250i
$136$		0			0
$137$	−72.1249	+	72.1249i	−0.526459	+	0.526459i	−0.919515	−	0.393056i	$-0.871418\pi$
$137$	−72.1249	+	72.1249i	−0.526459	+	0.526459i	0.393056	+	0.919515i	$0.371418\pi$
$138$		0			0
$139$	69.2820			0.498432			0.249216	−	0.968448i	$-0.419827\pi$
$139$	69.2820			0.498432			0.249216	+	0.968448i	$0.419827\pi$
$140$		0			0
$141$	−24.0000	+	33.9411i	−0.170213	+	0.240717i
$142$		0			0
$143$	68.5857	−	68.5857i	0.479620	−	0.479620i
$144$		0			0
$145$	−95.0000	−	95.0000i	−0.655172	−	0.655172i
$146$		0			0
$147$	298.636	−	51.2379i	2.03154	−	0.348557i
$148$		0			0
$149$	−1.41421			−0.00949137			−0.00474568	−	0.999989i	$-0.501511\pi$
$149$	−1.41421			−0.00949137			−0.00474568	+	0.999989i	$0.501511\pi$
$150$		0			0
$151$		−	187.061i		−	1.23882i	−0.785069	−	0.619409i	$-0.787372\pi$
$151$		−	187.061i		−	1.23882i	0.785069	−	0.619409i	$-0.212628\pi$
$152$		0			0
$153$	85.3310	−	178.669i	0.557719	−	1.16777i
$154$		0			0
$155$	−12.2474	+	12.2474i	−0.0790158	+	0.0790158i
$156$		0			0
$157$	172.000	+	172.000i	1.09554	+	1.09554i	0.994925	+	0.100616i	$0.0320814\pi$
$157$	172.000	+	172.000i	1.09554	+	1.09554i	0.100616	+	0.994925i	$0.467919\pi$
$158$		0			0
$159$	−13.8564	+	19.5959i	−0.0871472	+	0.123245i
$160$		0			0
$161$			84.8528i			0.527036i
$162$		0			0
$163$	6.92820	+	6.92820i	0.0425043	+	0.0425043i	0.728039	−	0.685535i	$-0.240432\pi$
$163$	6.92820	+	6.92820i	0.0425043	+	0.0425043i	−0.685535	+	0.728039i	$0.740432\pi$
$164$		0			0
$165$	−148.492	+	210.000i	−0.899954	+	1.27273i
$166$		0			0
$167$	58.7878	+	58.7878i	0.352022	+	0.352022i	0.860862	−	0.508839i	$-0.169925\pi$
$167$	58.7878	+	58.7878i	0.352022	+	0.352022i	−0.508839	+	0.860862i	$0.669925\pi$
$168$		0			0
$169$			137.000i			0.810651i
$170$		0			0
$171$	58.7878	−	20.7846i	0.343788	−	0.121547i
$172$		0			0
$173$	207.889	+	207.889i	1.20167	+	1.20167i	0.973658	+	0.228015i	$0.0732236\pi$
$173$	207.889	+	207.889i	1.20167	+	1.20167i	0.228015	+	0.973658i	$0.426776\pi$
$174$		0			0
$175$	216.506	+	216.506i	1.23718	+	1.23718i
$176$		0			0
$177$	137.610	−	23.6102i	0.777459	−	0.133391i
$178$		0			0
$179$		−	85.7321i		−	0.478951i	−0.970902	−	0.239475i	$-0.923025\pi$
$179$		−	85.7321i		−	0.478951i	0.970902	−	0.239475i	$-0.0769754\pi$
$180$		0			0
$181$	150.000			0.828729			0.414365	−	0.910111i	$-0.364004\pi$
$181$	150.000			0.828729			0.414365	+	0.910111i	$0.364004\pi$
$182$		0			0
$183$	−21.3068	−	124.185i	−0.116431	−	0.678609i
$184$		0			0
$185$			268.701i			1.45244i
$186$		0			0
$187$	−266.736	+	266.736i	−1.42639	+	1.42639i
$188$		0			0
$189$	−318.198	−	90.0000i	−1.68359	−	0.476190i
$190$		0			0
$191$	−151.868			−0.795122			−0.397561	−	0.917576i	$-0.630143\pi$
$191$	−151.868			−0.795122			−0.397561	+	0.917576i	$0.630143\pi$
$192$		0			0
$193$	−131.000	+	131.000i	−0.678756	+	0.678756i	−0.959719	−	0.280962i	$-0.909346\pi$
$193$	−131.000	+	131.000i	−0.678756	+	0.678756i	0.280962	+	0.959719i	$0.409346\pi$
$194$		0			0
$195$	14.3488	+	83.6308i	0.0735835	+	0.428876i
$196$		0			0
$197$	−25.4558	+	25.4558i	−0.129217	+	0.129217i	−0.768758	−	0.639540i	$-0.779125\pi$
$197$	−25.4558	+	25.4558i	−0.129217	+	0.129217i	0.639540	+	0.768758i	$0.279125\pi$
$198$		0			0
$199$	−90.0666			−0.452596			−0.226298	−	0.974058i	$-0.572662\pi$
$199$	−90.0666			−0.452596			−0.226298	+	0.974058i	$0.572662\pi$
$200$		0			0
$201$	−72.0000	−	50.9117i	−0.358209	−	0.253292i
$202$		0			0
$203$	−232.702	+	232.702i	−1.14631	+	1.14631i
$204$		0			0
$205$	220.000	−	220.000i	1.07317	−	1.07317i
$206$		0			0
$207$	26.8723	−	56.2662i	0.129818	−	0.271817i
$208$		0			0
$209$	−118.794			−0.568392
$210$		0			0
$211$		−	374.123i		−	1.77309i	−0.462638	−	0.886547i	$-0.653097\pi$
$211$		−	374.123i		−	1.77309i	0.462638	−	0.886547i	$-0.346903\pi$
$212$		0			0
$213$	7.45584	+	43.4558i	0.0350040	+	0.204018i
$214$		0			0
$215$		−	171.464i		−	0.797508i
$216$		0			0
$217$	30.0000	+	30.0000i	0.138249	+	0.138249i
$218$		0			0
$219$	−128.172	−	90.6311i	−0.585259	−	0.413841i
$220$		0			0
$221$			124.451i			0.563126i
$222$		0			0
$223$	−202.650	−	202.650i	−0.908744	−	0.908744i	0.0874268	−	0.996171i	$-0.472136\pi$
$223$	−202.650	−	202.650i	−0.908744	−	0.908744i	−0.996171	+	0.0874268i	$0.972136\pi$
$224$		0			0
$225$	−75.0000	−	212.132i	−0.333333	−	0.942809i
$226$		0			0
$227$	71.0352	+	71.0352i	0.312930	+	0.312930i	0.846044	−	0.533113i	$-0.178978\pi$
$227$	71.0352	+	71.0352i	0.312930	+	0.312930i	−0.533113	+	0.846044i	$0.678978\pi$
$228$		0			0
$229$		−	130.000i		−	0.567686i	−0.958871	−	0.283843i	$-0.908391\pi$
$229$		−	130.000i		−	0.567686i	0.958871	−	0.283843i	$-0.0916094\pi$
$230$		0			0
$231$	514.393	+	363.731i	2.22681	+	1.57459i
$232$		0			0
$233$	−188.090	−	188.090i	−0.807255	−	0.807255i	0.176963	−	0.984218i	$-0.443373\pi$
$233$	−188.090	−	188.090i	−0.807255	−	0.807255i	−0.984218	+	0.176963i	$0.943373\pi$
$234$		0			0
$235$			69.2820i			0.294817i
$236$		0			0
$237$	−36.9045	−	215.095i	−0.155715	−	0.907576i
$238$		0			0
$239$		−	171.464i		−	0.717424i	−0.933448	−	0.358712i	$-0.883216\pi$
$239$		−	171.464i		−	0.717424i	0.933448	−	0.358712i	$-0.116784\pi$
$240$		0			0
$241$	−340.000			−1.41079			−0.705394	−	0.708815i	$-0.749230\pi$
$241$	−340.000			−1.41079			−0.705394	+	0.708815i	$0.749230\pi$
$242$		0			0
$243$	182.496	+	160.450i	0.751011	+	0.660289i
$244$		0			0
$245$	357.089	−	357.089i	1.45751	−	1.45751i
$246$		0			0
$247$	−27.7128	+	27.7128i	−0.112198	+	0.112198i
$248$		0			0
$249$	322.441	+	228.000i	1.29494	+	0.915663i
$250$		0			0
$251$	−467.853			−1.86395			−0.931977	−	0.362517i	$-0.881917\pi$
$251$	−467.853			−1.86395			−0.931977	+	0.362517i	$0.881917\pi$
$252$		0			0
$253$	−84.0000	+	84.0000i	−0.332016	+	0.332016i
$254$		0			0
$255$	−55.8037	−	325.248i	−0.218838	−	1.27548i
$256$		0			0
$257$	−156.978	+	156.978i	−0.610808	+	0.610808i	−0.943157	−	0.332348i	$-0.892159\pi$
$257$	−156.978	+	156.978i	−0.610808	+	0.610808i	0.332348	+	0.943157i	$0.392159\pi$
$258$		0			0
$259$	658.179			2.54123
$260$		0			0
$261$	228.000	−	80.6102i	0.873563	−	0.308851i
$262$		0			0
$263$	−274.343	+	274.343i	−1.04313	+	1.04313i	−0.0441017	+	0.999027i	$0.514043\pi$
$263$	−274.343	+	274.343i	−1.04313	+	1.04313i	−0.999027	+	0.0441017i	$0.985957\pi$
$264$		0			0
$265$			40.0000i			0.150943i
$266$		0			0
$267$	−44.4812	−	259.256i	−0.166596	−	0.970994i
$268$		0			0
$269$	315.370			1.17238			0.586189	−	0.810174i	$-0.300628\pi$
$269$	315.370			1.17238			0.586189	+	0.810174i	$0.300628\pi$
$270$		0			0
$271$			284.056i			1.04818i	0.851663	+	0.524089i	$0.175594\pi$
$271$			284.056i			1.04818i	−0.851663	+	0.524089i	$0.824406\pi$
$272$		0			0
$273$	204.853	−	35.1472i	0.750377	−	0.128744i
$274$		0			0
$275$			428.661i			1.55877i
$276$		0			0
$277$	−254.000	−	254.000i	−0.916968	−	0.916968i	0.0798402	−	0.996808i	$-0.474559\pi$
$277$	−254.000	−	254.000i	−0.916968	−	0.916968i	−0.996808	+	0.0798402i	$0.974559\pi$
$278$		0			0
$279$	−10.3923	−	29.3939i	−0.0372484	−	0.105354i
$280$		0			0
$281$		−	217.789i		−	0.775049i	−0.921859	−	0.387525i	$-0.873330\pi$
$281$		−	217.789i		−	0.775049i	0.921859	−	0.387525i	$-0.126670\pi$
$282$		0			0
$283$	−6.92820	−	6.92820i	−0.0244813	−	0.0244813i	0.694760	−	0.719241i	$-0.255510\pi$
$283$	−6.92820	−	6.92820i	−0.0244813	−	0.0244813i	−0.719241	+	0.694760i	$0.755510\pi$
$284$		0			0
$285$	60.0000	−	84.8528i	0.210526	−	0.297729i
$286$		0			0
$287$	−538.888	−	538.888i	−1.87766	−	1.87766i
$288$		0			0
$289$		−	195.000i		−	0.674740i
$290$		0			0
$291$	−85.7321	+	121.244i	−0.294612	+	0.416645i
$292$		0			0
$293$	42.4264	+	42.4264i	0.144800	+	0.144800i	0.775791	−	0.630991i	$-0.217351\pi$
$293$	42.4264	+	42.4264i	0.144800	+	0.144800i	−0.630991	+	0.775791i	$0.717351\pi$
$294$		0			0
$295$	164.545	−	164.545i	0.557779	−	0.557779i
$296$		0			0
$297$	−225.905	−	404.095i	−0.760621	−	1.36059i
$298$		0			0
$299$			39.1918i			0.131076i
$300$		0			0
$301$	−420.000			−1.39535
$302$		0			0
$303$	146.354	−	25.1104i	0.483016	−	0.0828725i
$304$		0			0
$305$	−148.492	−	148.492i	−0.486860	−	0.486860i
$306$		0			0
$307$	−176.669	+	176.669i	−0.575470	+	0.575470i	−0.933652	−	0.358182i	$-0.883397\pi$
$307$	−176.669	+	176.669i	−0.575470	+	0.575470i	0.358182	+	0.933652i	$0.383397\pi$
$308$		0			0
$309$	−106.066	+	150.000i	−0.343256	+	0.485437i
$310$		0			0
$311$	524.191			1.68550			0.842750	−	0.538304i	$-0.180935\pi$
$311$	524.191			1.68550			0.842750	+	0.538304i	$0.180935\pi$
$312$		0			0
$313$	257.000	−	257.000i	0.821086	−	0.821086i	−0.165178	−	0.986264i	$-0.552820\pi$
$313$	257.000	−	257.000i	0.821086	−	0.821086i	0.986264	+	0.165178i	$0.0528197\pi$
$314$		0			0
$315$	−519.615	+	183.712i	−1.64957	+	0.583212i
$316$		0			0
$317$	49.4975	−	49.4975i	0.156143	−	0.156143i	−0.624712	−	0.780855i	$-0.714784\pi$
$317$	49.4975	−	49.4975i	0.156143	−	0.156143i	0.780855	+	0.624712i	$0.214784\pi$
$318$		0			0
$319$	−460.726			−1.44428
$320$		0			0
$321$	132.000	−	186.676i	0.411215	−	0.581546i
$322$		0			0
$323$	107.778	−	107.778i	0.333677	−	0.333677i
$324$		0			0
$325$	100.000	+	100.000i	0.307692	+	0.307692i
$326$		0			0
$327$	372.556	−	63.9205i	1.13932	−	0.195476i
$328$		0			0
$329$	169.706			0.515823
$330$		0			0
$331$			346.410i			1.04656i	0.852162	+	0.523278i	$0.175291\pi$
$331$			346.410i			1.04656i	−0.852162	+	0.523278i	$0.824709\pi$
$332$		0			0
$333$	−436.441	−	208.441i	−1.31063	−	0.625948i
$334$		0			0
$335$	−146.969			−0.438715
$336$		0			0
$337$	115.000	+	115.000i	0.341246	+	0.341246i	0.856836	−	0.515589i	$-0.172427\pi$
$337$	115.000	+	115.000i	0.341246	+	0.341246i	−0.515589	+	0.856836i	$0.672427\pi$
$338$		0			0
$339$	114.315	−	161.666i	0.337213	−	0.476892i
$340$		0			0
$341$			59.3970i			0.174185i
$342$		0			0
$343$	−450.333	−	450.333i	−1.31292	−	1.31292i
$344$		0			0
$345$	−17.5736	−	102.426i	−0.0509380	−	0.296888i
$346$		0			0
$347$	169.015	+	169.015i	0.487074	+	0.487074i	0.907382	−	0.420307i	$-0.138078\pi$
$347$	169.015	+	169.015i	0.487074	+	0.487074i	−0.420307	+	0.907382i	$0.638078\pi$
$348$		0			0
$349$			642.000i			1.83954i	0.392456	+	0.919771i	$0.371626\pi$
$349$			642.000i			1.83954i	−0.392456	+	0.919771i	$0.628374\pi$
$350$		0			0
$351$	−146.969	−	41.5692i	−0.418716	−	0.118431i
$352$		0			0
$353$	329.512	+	329.512i	0.933461	+	0.933461i	0.997920	−	0.0644593i	$-0.0205323\pi$
$353$	329.512	+	329.512i	0.933461	+	0.933461i	−0.0644593	+	0.997920i	$0.520532\pi$
$354$		0			0
$355$	51.9615	+	51.9615i	0.146370	+	0.146370i
$356$		0			0
$357$	−796.690	+	136.690i	−2.23163	+	0.382886i
$358$		0			0
$359$		−	607.473i		−	1.69213i	−0.533082	−	0.846063i	$-0.678966\pi$
$359$		−	607.473i		−	1.69213i	0.533082	−	0.846063i	$-0.321034\pi$
$360$		0			0
$361$	−313.000			−0.867036
$362$		0			0
$363$	87.7639	+	511.526i	0.241774	+	1.40916i
$364$		0			0
$365$	−261.630			−0.716793
$366$		0			0
$367$	−244.219	+	244.219i	−0.665447	+	0.665447i	−0.956659	−	0.291211i	$-0.905942\pi$
$367$	−244.219	+	244.219i	−0.665447	+	0.665447i	0.291211	+	0.956659i	$0.405942\pi$
$368$		0			0
$369$	186.676	+	528.000i	0.505898	+	1.43089i
$370$		0			0
$371$	97.9796			0.264096
$372$		0			0
$373$	232.000	−	232.000i	0.621984	−	0.621984i	−0.324054	−	0.946038i	$-0.605046\pi$
$373$	232.000	−	232.000i	0.621984	−	0.621984i	0.946038	+	0.324054i	$0.105046\pi$
$374$		0			0
$375$	−306.186	−	216.506i	−0.816497	−	0.577350i
$376$		0			0
$377$	−107.480	+	107.480i	−0.285093	+	0.285093i
$378$		0			0
$379$	401.836			1.06025			0.530126	−	0.847919i	$-0.322144\pi$
$379$	401.836			1.06025			0.530126	+	0.847919i	$0.322144\pi$
$380$		0			0
$381$	114.000	+	80.6102i	0.299213	+	0.211575i
$382$		0			0
$383$	−29.3939	+	29.3939i	−0.0767464	+	0.0767464i	−0.744438	−	0.667692i	$-0.767283\pi$
$383$	−29.3939	+	29.3939i	−0.0767464	+	0.0767464i	0.667692	+	0.744438i	$0.267283\pi$
$384$		0			0
$385$	1050.00			2.72727
$386$		0			0
$387$	278.503	+	133.011i	0.719647	+	0.343698i
$388$		0			0
$389$	239.002			0.614401			0.307201	−	0.951645i	$-0.400608\pi$
$389$	239.002			0.614401			0.307201	+	0.951645i	$0.400608\pi$
$390$		0			0
$391$		−	152.420i		−	0.389822i
$392$		0			0
$393$	3.72792	+	21.7279i	0.00948581	+	0.0552873i
$394$		0			0
$395$	−257.196	−	257.196i	−0.651130	−	0.651130i
$396$		0			0
$397$	382.000	+	382.000i	0.962217	+	0.962217i	0.999312	−	0.0370951i	$-0.0118105\pi$
$397$	382.000	+	382.000i	0.962217	+	0.962217i	−0.0370951	+	0.999312i	$0.511810\pi$
$398$		0			0
$399$	−207.846	−	146.969i	−0.520918	−	0.368344i
$400$		0			0
$401$			659.024i			1.64345i	0.569884	+	0.821725i	$0.306988\pi$
$401$			659.024i			1.64345i	−0.569884	+	0.821725i	$0.693012\pi$
$402$		0			0
$403$	13.8564	+	13.8564i	0.0343831	+	0.0343831i
$404$		0			0
$405$	402.739	+	42.7386i	0.994416	+	0.105527i
$406$		0			0
$407$	651.564	+	651.564i	1.60090	+	1.60090i
$408$		0			0
$409$		−	240.000i		−	0.586797i	−0.955990	−	0.293399i	$-0.905214\pi$
$409$		−	240.000i		−	0.586797i	0.955990	−	0.293399i	$-0.0947863\pi$
$410$		0			0
$411$	−249.848	−	176.669i	−0.607903	−	0.429852i
$412$		0			0
$413$	−403.051	−	403.051i	−0.975910	−	0.975910i
$414$		0			0
$415$	658.179			1.58597
$416$		0			0
$417$	35.1472	+	204.853i	0.0842858	+	0.491254i
$418$		0			0
$419$			619.721i			1.47905i	0.673130	+	0.739524i	$0.264949\pi$
$419$			619.721i			1.47905i	−0.673130	+	0.739524i	$0.735051\pi$
$420$		0			0
$421$	−566.000			−1.34442			−0.672209	−	0.740361i	$-0.734654\pi$
$421$	−566.000			−1.34442			−0.672209	+	0.740361i	$0.734654\pi$
$422$		0			0
$423$	−112.532	−	53.7446i	−0.266034	−	0.127056i
$424$		0			0
$425$	−388.909	−	388.909i	−0.915079	−	0.915079i
$426$		0			0
$427$	−363.731	+	363.731i	−0.851828	+	0.851828i
$428$		0			0
$429$	237.588	+	168.000i	0.553818	+	0.391608i
$430$		0			0
$431$	666.261			1.54585			0.772925	−	0.634498i	$-0.218793\pi$
$431$	666.261			1.54585			0.772925	+	0.634498i	$0.218793\pi$
$432$		0			0
$433$	−289.000	+	289.000i	−0.667436	+	0.667436i	−0.957122	−	0.289685i	$-0.906449\pi$
$433$	−289.000	+	289.000i	−0.667436	+	0.667436i	0.289685	+	0.957122i	$0.406449\pi$
$434$		0			0
$435$	232.702	−	329.090i	0.534946	−	0.756528i
$436$		0			0
$437$	33.9411	−	33.9411i	0.0776685	−	0.0776685i
$438$		0			0
$439$	796.743			1.81491			0.907453	−	0.420154i	$-0.138024\pi$
$439$	796.743			1.81491			0.907453	+	0.420154i	$0.138024\pi$
$440$		0			0
$441$	303.000	+	857.013i	0.687075	+	1.94334i
$442$		0			0
$443$	453.156	−	453.156i	1.02292	−	1.02292i	0.0231936	−	0.999731i	$-0.492617\pi$
$443$	453.156	−	453.156i	1.02292	−	1.02292i	0.999731	−	0.0231936i	$-0.00738342\pi$
$444$		0			0
$445$	−310.000	−	310.000i	−0.696629	−	0.696629i
$446$		0			0
$447$	−0.717439	−	4.18154i	−0.00160501	−	0.00935468i
$448$		0			0
$449$	−709.935			−1.58115			−0.790574	−	0.612367i	$-0.790218\pi$
$449$	−709.935			−1.58115			−0.790574	+	0.612367i	$0.790218\pi$
$450$		0			0
$451$		−	1066.94i		−	2.36573i
$452$		0			0
$453$	553.103	−	94.8974i	1.22098	−	0.209487i
$454$		0			0
$455$	244.949	−	244.949i	0.538349	−	0.538349i
$456$		0			0
$457$	−259.000	−	259.000i	−0.566740	−	0.566740i	0.364474	−	0.931214i	$-0.381249\pi$
$457$	−259.000	−	259.000i	−0.566740	−	0.566740i	−0.931214	+	0.364474i	$0.881249\pi$
$458$		0			0
$459$	571.577	+	161.666i	1.24527	+	0.352214i
$460$		0			0
$461$			168.291i			0.365057i	0.983201	+	0.182529i	$0.0584282\pi$
$461$			168.291i			0.365057i	−0.983201	+	0.182529i	$0.941572\pi$
$462$		0			0
$463$	−185.329	−	185.329i	−0.400280	−	0.400280i	0.478052	−	0.878332i	$-0.341343\pi$
$463$	−185.329	−	185.329i	−0.400280	−	0.400280i	−0.878332	+	0.478052i	$0.841343\pi$
$464$		0			0
$465$	−42.4264	−	30.0000i	−0.0912396	−	0.0645161i
$466$		0			0
$467$	142.070	+	142.070i	0.304219	+	0.304219i	0.842662	−	0.538443i	$-0.180987\pi$
$467$	142.070	+	142.070i	0.304219	+	0.304219i	−0.538443	+	0.842662i	$0.680987\pi$
$468$		0			0
$469$			360.000i			0.767591i
$470$		0			0
$471$	−421.312	+	595.825i	−0.894506	+	1.26502i
$472$		0			0
$473$	−415.779	−	415.779i	−0.879025	−	0.879025i
$474$		0			0
$475$		−	173.205i		−	0.364642i
$476$		0			0
$477$	−64.9706	−	31.0294i	−0.136207	−	0.0650512i
$478$		0			0
$479$			700.554i			1.46253i	0.682091	+	0.731267i	$0.261071\pi$
$479$			700.554i			1.46253i	−0.682091	+	0.731267i	$0.738929\pi$
$480$		0			0
$481$	304.000			0.632017
$482$		0			0
$483$	−250.892	+	43.0463i	−0.519446	+	0.0891228i
$484$		0			0
$485$			247.487i			0.510283i
$486$		0			0
$487$	−126.440	+	126.440i	−0.259630	+	0.259630i	−0.824903	−	0.565274i	$-0.808771\pi$
$487$	−126.440	+	126.440i	−0.259630	+	0.259630i	0.565274	+	0.824903i	$0.308771\pi$
$488$		0			0
$489$	−16.9706	+	24.0000i	−0.0347046	+	0.0490798i
$490$		0			0
$491$	−355.176			−0.723373			−0.361686	−	0.932300i	$-0.617799\pi$
$491$	−355.176			−0.723373			−0.361686	+	0.932300i	$0.617799\pi$
$492$		0			0
$493$	418.000	−	418.000i	0.847870	−	0.847870i
$494$		0			0
$495$	−696.258	−	332.528i	−1.40658	−	0.671773i
$496$		0			0
$497$	127.279	−	127.279i	0.256095	−	0.256095i
$498$		0			0
$499$	−353.338			−0.708093			−0.354046	−	0.935228i	$-0.615195\pi$
$499$	−353.338			−0.708093			−0.354046	+	0.935228i	$0.615195\pi$
$500$		0			0
$501$	−144.000	+	203.647i	−0.287425	+	0.406481i
$502$		0			0
$503$	289.040	−	289.040i	0.574632	−	0.574632i	−0.358787	−	0.933419i	$-0.616810\pi$
$503$	289.040	−	289.040i	0.574632	−	0.574632i	0.933419	+	0.358787i	$0.116810\pi$
$504$		0			0
$505$	175.000	−	175.000i	0.346535	−	0.346535i
$506$		0			0
$507$	−405.081	+	69.5009i	−0.798976	+	0.137083i
$508$		0			0
$509$	866.913			1.70317			0.851584	−	0.524218i	$-0.175642\pi$
$509$	866.913			1.70317			0.851584	+	0.524218i	$0.175642\pi$
$510$		0			0
$511$			640.859i			1.25413i
$512$		0			0
$513$	91.2792	+	163.279i	0.177932	+	0.318283i
$514$		0			0
$515$			306.186i			0.594536i
$516$		0			0
$517$	168.000	+	168.000i	0.324952	+	0.324952i
$518$		0			0
$519$	−509.223	+	720.150i	−0.981162	+	1.38757i
$520$		0			0
$521$			19.7990i			0.0380019i	0.999819	+	0.0190009i	$0.00604855\pi$
$521$			19.7990i			0.0380019i	−0.999819	+	0.0190009i	$0.993951\pi$
$522$		0			0
$523$	138.564	+	138.564i	0.264941	+	0.264941i	0.827058	−	0.562117i	$-0.190013\pi$
$523$	138.564	+	138.564i	0.264941	+	0.264941i	−0.562117	+	0.827058i	$0.690013\pi$
$524$		0			0
$525$	−530.330	+	750.000i	−1.01015	+	1.42857i
$526$		0			0
$527$	−53.8888	−	53.8888i	−0.102256	−	0.102256i
$528$		0			0
$529$			481.000i			0.909263i
$530$		0			0
$531$	139.621	+	394.908i	0.262940	+	0.743705i
$532$		0			0
$533$	−248.902	−	248.902i	−0.466982	−	0.466982i
$534$		0			0
$535$		−	381.051i		−	0.712245i
$536$		0			0
$537$	253.492	−	43.4924i	0.472053	−	0.0809915i
$538$		0			0
$539$		−	1731.79i		−	3.21297i
$540$		0			0
$541$	186.000			0.343808			0.171904	−	0.985114i	$-0.445008\pi$
$541$	186.000			0.343808			0.171904	+	0.985114i	$0.445008\pi$
$542$		0			0
$543$	76.0959	+	443.519i	0.140140	+	0.816794i
$544$		0			0
$545$	445.477	−	445.477i	0.817389	−	0.817389i
$546$		0			0
$547$	79.6743	−	79.6743i	0.145657	−	0.145657i	−0.630518	−	0.776175i	$-0.717157\pi$
$547$	79.6743	−	79.6743i	0.145657	−	0.145657i	0.776175	+	0.630518i	$0.217157\pi$
$548$		0			0
$549$	356.382	−	126.000i	0.649147	−	0.229508i
$550$		0			0
$551$	186.161			0.337861
$552$		0			0
$553$	−630.000	+	630.000i	−1.13924	+	1.13924i
$554$		0			0
$555$	−794.493	+	136.313i	−1.43152	+	0.245610i
$556$		0			0
$557$	−489.318	+	489.318i	−0.878488	+	0.878488i	−0.993378	−	0.114890i	$-0.963348\pi$
$557$	−489.318	+	489.318i	−0.878488	+	0.878488i	0.114890	+	0.993378i	$0.463348\pi$
$558$		0			0
$559$	−193.990			−0.347030
$560$		0			0
$561$	−924.000	−	653.367i	−1.64706	−	1.16465i
$562$		0			0
$563$	467.853	−	467.853i	0.830999	−	0.830999i	−0.156654	−	0.987653i	$-0.550071\pi$
$563$	467.853	−	467.853i	0.830999	−	0.830999i	0.987653	+	0.156654i	$0.0500709\pi$
$564$		0			0
$565$		−	330.000i		−	0.584071i
$566$		0			0
$567$	104.688	−	986.504i	0.184635	−	1.73987i
$568$		0			0
$569$	777.817			1.36699			0.683495	−	0.729955i	$-0.260459\pi$
$569$	777.817			1.36699			0.683495	+	0.729955i	$0.260459\pi$
$570$		0			0
$571$		−	290.985i		−	0.509605i	−0.966993	−	0.254803i	$-0.917990\pi$
$571$		−	290.985i		−	0.509605i	0.966993	−	0.254803i	$-0.0820105\pi$
$572$		0			0
$573$	−77.0437	−	449.044i	−0.134457	−	0.783671i
$574$		0			0
$575$	−122.474	−	122.474i	−0.212999	−	0.212999i
$576$		0			0
$577$	−607.000	−	607.000i	−1.05199	−	1.05199i	−0.998572	−	0.0534210i	$-0.982987\pi$
$577$	−607.000	−	607.000i	−1.05199	−	1.05199i	−0.0534210	−	0.998572i	$-0.517013\pi$
$578$		0			0
$579$	−453.797	−	320.883i	−0.783760	−	0.554202i
$580$		0			0
$581$		−	1612.20i		−	2.77488i
$582$		0			0
$583$	96.9948	+	96.9948i	0.166372	+	0.166372i
$584$		0			0
$585$	−240.000	+	84.8528i	−0.410256	+	0.145048i
$586$		0			0
$587$	338.030	+	338.030i	0.575860	+	0.575860i	0.933760	−	0.357900i	$-0.116507\pi$
$587$	338.030	+	338.030i	0.575860	+	0.575860i	−0.357900	+	0.933760i	$0.616507\pi$
$588$		0			0
$589$		−	24.0000i		−	0.0407470i
$590$		0			0
$591$	−88.1816	−	62.3538i	−0.149207	−	0.105506i
$592$		0			0
$593$	241.831	+	241.831i	0.407809	+	0.407809i	0.880974	−	0.473165i	$-0.156889\pi$
$593$	241.831	+	241.831i	0.407809	+	0.407809i	−0.473165	+	0.880974i	$0.656889\pi$
$594$		0			0
$595$	−952.628	+	952.628i	−1.60106	+	1.60106i
$596$		0			0
$597$	−45.6913	−	266.309i	−0.0765349	−	0.446078i
$598$		0			0
$599$			313.535i			0.523430i	0.965145	+	0.261715i	$0.0842881\pi$
$599$			313.535i			0.523430i	−0.965145	+	0.261715i	$0.915712\pi$
$600$		0			0
$601$	30.0000			0.0499168			0.0249584	−	0.999688i	$-0.492055\pi$
$601$	30.0000			0.0499168			0.0249584	+	0.999688i	$0.492055\pi$
$602$		0			0
$603$	114.009	−	238.717i	0.189070	−	0.395882i
$604$		0			0
$605$	611.647	+	611.647i	1.01099	+	1.01099i
$606$		0			0
$607$	36.3731	−	36.3731i	0.0599227	−	0.0599227i	−0.676510	−	0.736433i	$-0.736509\pi$
$607$	36.3731	−	36.3731i	0.0599227	−	0.0599227i	0.736433	+	0.676510i	$0.236509\pi$
$608$		0			0
$609$	−806.102	−	570.000i	−1.32365	−	0.935961i
$610$		0			0
$611$	78.3837			0.128288
$612$		0			0
$613$	122.000	−	122.000i	0.199021	−	0.199021i	−0.600559	−	0.799580i	$-0.705055\pi$
$613$	122.000	−	122.000i	0.199021	−	0.199021i	0.799580	+	0.600559i	$0.205055\pi$
$614$		0			0
$615$	762.102	+	538.888i	1.23919	+	0.876240i
$616$		0			0
$617$	660.438	−	660.438i	1.07040	−	1.07040i	0.0730751	−	0.997326i	$-0.476719\pi$
$617$	660.438	−	660.438i	1.07040	−	1.07040i	0.997326	−	0.0730751i	$-0.0232813\pi$
$618$		0			0
$619$	−290.985			−0.470088			−0.235044	−	0.971985i	$-0.575523\pi$
$619$	−290.985			−0.470088			−0.235044	+	0.971985i	$0.575523\pi$
$620$		0			0
$621$	180.000	+	50.9117i	0.289855	+	0.0819834i
$622$		0			0
$623$	−759.342	+	759.342i	−1.21885	+	1.21885i
$624$		0			0
$625$	−625.000			−1.00000
$626$		0			0
$627$	−60.2649	−	351.249i	−0.0961162	−	0.560206i
$628$		0			0
$629$	−1182.28			−1.87962
$630$		0			0
$631$			620.074i			0.982685i	0.870966	+	0.491342i	$0.163494\pi$
$631$			620.074i			0.982685i	−0.870966	+	0.491342i	$0.836506\pi$
$632$		0			0
$633$	1106.21	−	189.795i	1.74756	−	0.299834i
$634$		0			0
$635$	232.702			0.366459
$636$		0			0
$637$	−404.000	−	404.000i	−0.634223	−	0.634223i
$638$		0			0
$639$	−124.708	+	44.0908i	−0.195161	+	0.0689997i
$640$		0			0
$641$		−	503.460i		−	0.785429i	−0.919660	−	0.392715i	$-0.871536\pi$
$641$		−	503.460i		−	0.785429i	0.919660	−	0.392715i	$-0.128464\pi$
$642$		0			0
$643$	665.108	+	665.108i	1.03438	+	1.03438i	0.999388	+	0.0349943i	$0.0111413\pi$
$643$	665.108	+	665.108i	1.03438	+	1.03438i	0.0349943	+	0.999388i	$0.488859\pi$
$644$		0			0
$645$	506.985	−	86.9848i	0.786023	−	0.134860i
$646$		0			0
$647$	−680.958	−	680.958i	−1.05249	−	1.05249i	−0.998544	−	0.0539414i	$-0.982822\pi$
$647$	−680.958	−	680.958i	−1.05249	−	1.05249i	−0.0539414	−	0.998544i	$-0.517178\pi$
$648$		0			0
$649$		−	798.000i		−	1.22958i
$650$		0			0
$651$	−73.4847	+	103.923i	−0.112880	+	0.159636i
$652$		0			0
$653$	117.380	+	117.380i	0.179755	+	0.179755i	0.791249	−	0.611494i	$-0.209431\pi$
$653$	117.380	+	117.380i	0.179755	+	0.179755i	−0.611494	+	0.791249i	$0.709431\pi$
$654$		0			0
$655$	25.9808	+	25.9808i	0.0396653	+	0.0396653i
$656$		0			0
$657$	202.955	−	424.955i	0.308912	−	0.646812i
$658$		0			0
$659$			276.792i			0.420019i	0.977699	+	0.210009i	$0.0673494\pi$
$659$			276.792i			0.420019i	−0.977699	+	0.210009i	$0.932651\pi$
$660$		0			0
$661$	582.000			0.880484			0.440242	−	0.897879i	$-0.354893\pi$
$661$	582.000			0.880484			0.440242	+	0.897879i	$0.354893\pi$
$662$		0			0
$663$	−367.976	+	63.1346i	−0.555016	+	0.0952257i
$664$		0			0
$665$	−424.264			−0.637991
$666$		0			0
$667$	131.636	−	131.636i	0.197355	−	0.197355i
$668$		0			0
$669$	496.389	−	702.000i	0.741986	−	1.04933i
$670$		0			0
$671$	−720.150			−1.07325
$672$		0			0
$673$	−443.000	+	443.000i	−0.658247	+	0.658247i	−0.954965	−	0.296718i	$-0.904108\pi$
$673$	−443.000	+	443.000i	−0.658247	+	0.658247i	0.296718	+	0.954965i	$0.404108\pi$
$674$		0			0
$675$	589.183	−	329.376i	0.872864	−	0.487964i
$676$		0			0
$677$	103.238	−	103.238i	0.152493	−	0.152493i	−0.626738	−	0.779230i	$-0.715610\pi$
$677$	103.238	−	103.238i	0.152493	−	0.152493i	0.779230	+	0.626738i	$0.215610\pi$
$678$		0			0
$679$	606.218			0.892810
$680$		0			0
$681$	−174.000	+	246.073i	−0.255507	+	0.361341i
$682$		0			0
$683$	−151.868	+	151.868i	−0.222355	+	0.222355i	−0.809489	−	0.587135i	$-0.800256\pi$
$683$	−151.868	+	151.868i	−0.222355	+	0.222355i	0.587135	+	0.809489i	$0.300256\pi$
$684$		0			0
$685$	−510.000			−0.744526
$686$		0			0
$687$	384.383	−	65.9498i	0.559510	−	0.0959968i
$688$		0			0
$689$	45.2548			0.0656819
$690$		0			0
$691$		−	949.164i		−	1.37361i	−0.726842	−	0.686805i	$-0.759013\pi$
$691$		−	949.164i		−	1.37361i	0.726842	−	0.686805i	$-0.240987\pi$
$692$		0			0
$693$	−814.523	+	1705.48i	−1.17536	+	2.46101i
$694$		0			0
$695$	244.949	+	244.949i	0.352445	+	0.352445i
$696$		0			0
$697$	968.000	+	968.000i	1.38881	+	1.38881i
$698$		0			0
$699$	460.726	−	651.564i	0.659121	−	0.932138i
$700$		0			0
$701$			620.840i			0.885649i	0.896608	+	0.442824i	$0.146023\pi$
$701$			620.840i			0.885649i	−0.896608	+	0.442824i	$0.853977\pi$
$702$		0			0
$703$	−263.272	−	263.272i	−0.374497	−	0.374497i
$704$		0			0
$705$	−204.853	+	35.1472i	−0.290571	+	0.0498542i
$706$		0			0
$707$	−428.661	−	428.661i	−0.606309	−	0.606309i
$708$		0			0
$709$		−	146.000i		−	0.205924i	−0.994685	−	0.102962i	$-0.967168\pi$
$709$		−	146.000i		−	0.205924i	0.994685	−	0.102962i	$-0.0328320\pi$
$710$		0			0
$711$	617.271	−	218.238i	0.868174	−	0.306946i
$712$		0			0
$713$	−16.9706	−	16.9706i	−0.0238016	−	0.0238016i
$714$		0			0
$715$	484.974			0.678286
$716$		0			0
$717$	506.985	−	86.9848i	0.707092	−	0.121318i
$718$		0			0
$719$			450.706i			0.626851i	0.949613	+	0.313426i	$0.101477\pi$
$719$			450.706i			0.626851i	−0.949613	+	0.313426i	$0.898523\pi$
$720$		0			0
$721$	750.000			1.04022
$722$		0			0
$723$	−172.484	−	1005.31i	−0.238567	−	1.39047i
$724$		0			0
$725$		−	671.751i		−	0.926554i
$726$		0			0
$727$	−355.070	+	355.070i	−0.488405	+	0.488405i	−0.907803	−	0.419398i	$-0.862241\pi$
$727$	−355.070	+	355.070i	−0.488405	+	0.488405i	0.419398	+	0.907803i	$0.362241\pi$
$728$		0			0
$729$	−381.838	+	621.000i	−0.523783	+	0.851852i
$730$		0			0
$731$	754.443			1.03207
$732$		0			0
$733$	−74.0000	+	74.0000i	−0.100955	+	0.100955i	−0.755780	−	0.654825i	$-0.772742\pi$
$733$	−74.0000	+	74.0000i	−0.100955	+	0.100955i	0.654825	+	0.755780i	$0.272742\pi$
$734$		0			0
$735$	1236.99	+	874.686i	1.68298	+	1.19005i
$736$		0			0
$737$	−356.382	+	356.382i	−0.483557	+	0.483557i
$738$		0			0
$739$	−124.708			−0.168752			−0.0843760	−	0.996434i	$-0.526890\pi$
$739$	−124.708			−0.168752			−0.0843760	+	0.996434i	$0.526890\pi$
$740$		0			0
$741$	−96.0000	−	67.8823i	−0.129555	−	0.0916090i
$742$		0			0
$743$	−641.766	+	641.766i	−0.863750	+	0.863750i	−0.991771	−	0.128021i	$-0.959137\pi$
$743$	−641.766	+	641.766i	−0.863750	+	0.863750i	0.128021	+	0.991771i	$0.459137\pi$
$744$		0			0
$745$	−5.00000	−	5.00000i	−0.00671141	−	0.00671141i
$746$		0			0
$747$	−510.573	+	1069.06i	−0.683498	+	1.43113i
$748$		0			0
$749$	−933.381			−1.24617
$750$		0			0
$751$		−	142.028i		−	0.189119i	−0.995519	−	0.0945594i	$-0.969856\pi$
$751$		−	142.028i		−	0.189119i	0.995519	−	0.0945594i	$-0.0301442\pi$
$752$		0			0
$753$	−237.344	−	1383.34i	−0.315198	−	1.83711i
$754$		0			0
$755$	661.362	−	661.362i	0.875976	−	0.875976i
$756$		0			0
$757$	506.000	+	506.000i	0.668428	+	0.668428i	0.957352	−	0.288924i	$-0.0932975\pi$
$757$	506.000	+	506.000i	0.668428	+	0.668428i	−0.288924	+	0.957352i	$0.593297\pi$
$758$		0			0
$759$	−290.985	−	205.757i	−0.383379	−	0.271090i
$760$		0			0
$761$			647.710i			0.851130i	0.904928	+	0.425565i	$0.139925\pi$
$761$			647.710i			0.851130i	−0.904928	+	0.425565i	$0.860075\pi$
$762$		0			0
$763$	−1091.19	−	1091.19i	−1.43013	−	1.43013i
$764$		0			0
$765$	933.381	−	330.000i	1.22011	−	0.431373i
$766$		0			0
$767$	−186.161	−	186.161i	−0.242713	−	0.242713i
$768$		0			0
$769$		−	486.000i		−	0.631990i	−0.948761	−	0.315995i	$-0.897662\pi$
$769$		−	486.000i		−	0.631990i	0.948761	−	0.315995i	$-0.102338\pi$
$770$		0			0
$771$	−543.787	−	384.515i	−0.705301	−	0.498723i
$772$		0			0
$773$	651.952	+	651.952i	0.843406	+	0.843406i	0.989300	−	0.145895i	$-0.0466060\pi$
$773$	651.952	+	651.952i	0.843406	+	0.843406i	−0.145895	+	0.989300i	$0.546606\pi$
$774$		0			0
$775$	−86.6025			−0.111745
$776$		0			0
$777$	333.898	+	1946.10i	0.429728	+	2.50464i
$778$		0			0
$779$			431.110i			0.553415i
$780$		0			0
$781$	252.000			0.322663
$782$		0			0
$783$	354.014	+	633.255i	0.452125	+	0.808755i
$784$		0			0
$785$			1216.22i			1.54933i
$786$		0			0
$787$	478.046	−	478.046i	0.607428	−	0.607428i	−0.334845	−	0.942273i	$-0.608684\pi$
$787$	478.046	−	478.046i	0.607428	−	0.607428i	0.942273	+	0.334845i	$0.108684\pi$
$788$		0			0
$789$	−950.352	−	672.000i	−1.20450	−	0.851711i
$790$		0			0
$791$	−808.332			−1.02191
$792$		0			0
$793$	−168.000	+	168.000i	−0.211854	+	0.211854i
$794$		0			0
$795$	−118.272	+	20.2922i	−0.148770	+	0.0255248i
$796$		0			0
$797$	−275.772	+	275.772i	−0.346012	+	0.346012i	−0.858622	−	0.512610i	$-0.828679\pi$
$797$	−275.772	+	275.772i	−0.346012	+	0.346012i	0.512610	+	0.858622i	$0.328679\pi$
$798$		0			0
$799$	−304.841			−0.381528
$800$		0			0
$801$	744.000	−	263.044i	0.928839	−	0.328394i
$802$		0			0
$803$	−634.418	+	634.418i	−0.790060	+	0.790060i
$804$		0			0
$805$	−300.000	+	300.000i	−0.372671	+	0.372671i
$806$		0			0
$807$	159.989	+	932.484i	0.198251	+	1.15549i
$808$		0			0
$809$	−497.803			−0.615331			−0.307666	−	0.951495i	$-0.599548\pi$
$809$	−497.803			−0.615331			−0.307666	+	0.951495i	$0.599548\pi$
$810$		0			0
$811$			242.487i			0.298998i	0.988762	+	0.149499i	$0.0477660\pi$
$811$			242.487i			0.298998i	−0.988762	+	0.149499i	$0.952234\pi$
$812$		0			0
$813$	−839.897	+	144.103i	−1.03308	+	0.177249i
$814$		0			0
$815$			48.9898i			0.0601102i
$816$		0			0
$817$	168.000	+	168.000i	0.205630	+	0.205630i
$818$		0			0
$819$	207.846	+	587.878i	0.253780	+	0.717799i
$820$		0			0
$821$			1169.55i			1.42455i	0.701901	+	0.712274i	$0.252335\pi$
$821$			1169.55i			1.42455i	−0.701901	+	0.712274i	$0.747665\pi$
$822$		0			0
$823$	691.088	+	691.088i	0.839718	+	0.839718i	0.988822	−	0.149103i	$-0.0476387\pi$
$823$	691.088	+	691.088i	0.839718	+	0.839718i	−0.149103	+	0.988822i	$0.547639\pi$
$824$		0			0
$825$	−1267.46	+	217.462i	−1.53632	+	0.263590i
$826$		0			0
$827$	−242.499	−	242.499i	−0.293228	−	0.293228i	0.545126	−	0.838354i	$-0.316482\pi$
$827$	−242.499	−	242.499i	−0.293228	−	0.293228i	−0.838354	+	0.545126i	$0.816482\pi$
$828$		0			0
$829$		−	822.000i		−	0.991556i	−0.868449	−	0.495778i	$-0.834883\pi$
$829$		−	822.000i		−	0.991556i	0.868449	−	0.495778i	$-0.165117\pi$
$830$		0			0
$831$	622.170	−	879.882i	0.748701	−	1.05882i
$832$		0			0
$833$	1571.19	+	1571.19i	1.88618	+	1.88618i
$834$		0			0
$835$			415.692i			0.497835i
$836$		0			0
$837$	81.6396	−	45.6396i	0.0975384	−	0.0545276i
$838$		0			0
$839$		−	264.545i		−	0.315310i	−0.987494	−	0.157655i	$-0.949607\pi$
$839$		−	264.545i		−	0.315310i	0.987494	−	0.157655i	$-0.0503934\pi$
$840$		0			0
$841$	−119.000			−0.141498
$842$		0			0
$843$	643.957	−	110.486i	0.763888	−	0.131062i
$844$		0			0
$845$	−484.368	+	484.368i	−0.573217	+	0.573217i
$846$		0			0
$847$	1498.22	−	1498.22i	1.76886	−	1.76886i
$848$		0			0
$849$	16.9706	−	24.0000i	0.0199889	−	0.0282686i
$850$		0			0
$851$	−372.322			−0.437512
$852$		0			0
$853$	−266.000	+	266.000i	−0.311841	+	0.311841i	−0.845622	−	0.533782i	$-0.820770\pi$
$853$	−266.000	+	266.000i	−0.311841	+	0.311841i	0.533782	+	0.845622i	$0.320770\pi$
$854$		0			0
$855$	281.331	+	134.361i	0.329042	+	0.157148i
$856$		0			0
$857$	900.854	−	900.854i	1.05117	−	1.05117i	0.0525535	−	0.998618i	$-0.483264\pi$
$857$	900.854	−	900.854i	1.05117	−	1.05117i	0.998618	−	0.0525535i	$-0.0167360\pi$
$858$		0			0
$859$	−1344.07			−1.56469			−0.782347	−	0.622843i	$-0.785977\pi$
$859$	−1344.07			−1.56469			−0.782347	+	0.622843i	$0.785977\pi$
$860$		0			0
$861$	1320.00	−	1866.76i	1.53310	−	2.16813i
$862$		0			0
$863$	1023.89	−	1023.89i	1.18643	−	1.18643i	0.208379	−	0.978048i	$-0.433181\pi$
$863$	1023.89	−	1023.89i	1.18643	−	1.18643i	0.978048	−	0.208379i	$-0.0668188\pi$
$864$		0			0
$865$			1470.00i			1.69942i
$866$		0			0
$867$	576.575	−	98.9247i	0.665023	−	0.114100i
$868$		0			0
$869$	−1247.34			−1.43537
$870$		0			0
$871$			166.277i			0.190903i
$872$		0			0
$873$	−401.985	−	191.985i	−0.460464	−	0.219914i
$874$		0			0
$875$			1530.93i			1.74964i
$876$		0			0
$877$	−40.0000	−	40.0000i	−0.0456100	−	0.0456100i	0.683934	−	0.729544i	$-0.260268\pi$
$877$	−40.0000	−	40.0000i	−0.0456100	−	0.0456100i	−0.729544	+	0.683934i	$0.760268\pi$
$878$		0			0
$879$	−103.923	+	146.969i	−0.118229	+	0.167201i
$880$		0			0
$881$		−	659.024i		−	0.748040i	−0.927421	−	0.374020i	$-0.877979\pi$
$881$		−	659.024i		−	0.748040i	0.927421	−	0.374020i	$-0.122021\pi$
$882$		0			0
$883$	935.307	+	935.307i	1.05924	+	1.05924i	0.998131	+	0.0611071i	$0.0194631\pi$
$883$	935.307	+	935.307i	1.05924	+	1.05924i	0.0611071	+	0.998131i	$0.480537\pi$
$884$		0			0
$885$	570.000	+	403.051i	0.644068	+	0.455425i
$886$		0			0
$887$	690.756	+	690.756i	0.778755	+	0.778755i	0.979619	−	0.200864i	$-0.0643748\pi$
$887$	690.756	+	690.756i	0.778755	+	0.778755i	−0.200864	+	0.979619i	$0.564375\pi$
$888$		0			0
$889$		−	570.000i		−	0.641170i
$890$		0			0
$891$	1080.22	−	872.954i	1.21237	−	0.979746i
$892$		0			0
$893$	−67.8823	−	67.8823i	−0.0760160	−	0.0760160i
$894$		0			0
$895$	303.109	−	303.109i	0.338669	−	0.338669i
$896$		0			0
$897$	−115.882	+	19.8823i	−0.129189	+	0.0221653i
$898$		0			0
$899$		−	93.0806i		−	0.103538i
$900$		0			0
$901$	−176.000			−0.195339
$902$		0			0
$903$	−213.068	−	1241.85i	−0.235956	−	1.37525i
$904$		0			0
$905$	530.330	+	530.330i	0.586000	+	0.586000i
$906$		0			0
$907$	1008.05	−	1008.05i	1.11142	−	1.11142i	0.118456	−	0.992959i	$-0.462206\pi$
$907$	1008.05	−	1008.05i	1.11142	−	1.11142i	0.992959	−	0.118456i	$-0.0377944\pi$
$908$		0			0
$909$	148.492	+	420.000i	0.163358	+	0.462046i
$910$		0			0
$911$	29.3939			0.0322655			0.0161328	−	0.999870i	$-0.494865\pi$
$911$	29.3939			0.0322655			0.0161328	+	0.999870i	$0.494865\pi$
$912$		0			0
$913$	1596.00	−	1596.00i	1.74808	−	1.74808i
$914$		0			0
$915$	363.731	−	514.393i	0.397520	−	0.562178i
$916$		0			0
$917$	63.6396	−	63.6396i	0.0693998	−	0.0693998i
$918$		0			0
$919$	−322.161			−0.350557			−0.175278	−	0.984519i	$-0.556083\pi$
$919$	−322.161			−0.350557			−0.175278	+	0.984519i	$0.556083\pi$
$920$		0			0
$921$	−612.000	−	432.749i	−0.664495	−	0.469869i
$922$		0			0
$923$	58.7878	−	58.7878i	0.0636920	−	0.0636920i
$924$		0			0
$925$	−950.000	+	950.000i	−1.02703	+	1.02703i
$926$		0			0
$927$	−497.327	−	237.520i	−0.536491	−	0.256224i
$928$		0			0
$929$	1411.39			1.51925			0.759626	−	0.650360i	$-0.225382\pi$
$929$	1411.39			1.51925			0.759626	+	0.650360i	$0.225382\pi$
$930$		0			0
$931$			699.749i			0.751610i
$932$		0			0
$933$	265.925	+	1549.93i	0.285022	+	1.66123i
$934$		0			0
$935$	−1886.11			−2.01723
$936$		0			0
$937$	−425.000	−	425.000i	−0.453575	−	0.453575i	0.442964	−	0.896539i	$-0.353927\pi$
$937$	−425.000	−	425.000i	−0.453575	−	0.453575i	−0.896539	+	0.442964i	$0.853927\pi$
$938$		0			0
$939$	890.274	+	629.519i	0.948109	+	0.670414i
$940$		0			0
$941$			272.943i			0.290057i	0.989428	+	0.145028i	$0.0463273\pi$
$941$			272.943i			0.290057i	−0.989428	+	0.145028i	$0.953673\pi$
$942$		0			0
$943$	304.841	+	304.841i	0.323267	+	0.323267i
$944$		0			0
$945$	−806.802	−	1443.20i	−0.853759	−	1.52719i
$946$		0			0
$947$	−1124.32	−	1124.32i	−1.18724	−	1.18724i	−0.977828	−	0.209412i	$-0.932845\pi$
$947$	−1124.32	−	1124.32i	−1.18724	−	1.18724i	−0.209412	−	0.977828i	$-0.567155\pi$
$948$		0			0
$949$			296.000i			0.311907i
$950$		0			0
$951$	171.464	+	121.244i	0.180299	+	0.127491i
$952$		0			0
$953$	−1090.36	−	1090.36i	−1.14413	−	1.14413i	−0.987686	−	0.156446i	$-0.949996\pi$
$953$	−1090.36	−	1090.36i	−1.14413	−	1.14413i	−0.156446	−	0.987686i	$-0.550004\pi$
$954$		0			0
$955$	−536.936	−	536.936i	−0.562236	−	0.562236i
$956$		0			0
$957$	−233.729	−	1362.27i	−0.244231	−	1.42348i
$958$		0			0
$959$			1249.24i			1.30265i
$960$		0			0
$961$	949.000			0.987513
$962$		0			0
$963$	618.928	+	295.595i	0.642708	+	0.306952i
$964$		0			0
$965$	−926.310			−0.959907
$966$		0			0
$967$	−420.888	+	420.888i	−0.435252	+	0.435252i	−0.890410	−	0.455159i	$-0.849583\pi$
$967$	−420.888	+	420.888i	−0.435252	+	0.435252i	0.455159	+	0.890410i	$0.349583\pi$
$968$		0			0
$969$	373.352	+	264.000i	0.385297	+	0.272446i
$970$		0			0
$971$	−1599.52			−1.64729			−0.823644	−	0.567107i	$-0.808063\pi$
$971$	−1599.52			−1.64729			−0.823644	+	0.567107i	$0.808063\pi$
$972$		0			0
$973$	600.000	−	600.000i	0.616650	−	0.616650i
$974$		0			0
$975$	−244.949	+	346.410i	−0.251230	+	0.355292i
$976$		0			0
$977$	−601.041	+	601.041i	−0.615190	+	0.615190i	−0.944294	−	0.329104i	$-0.893253\pi$
$977$	−601.041	+	601.041i	−0.615190	+	0.615190i	0.329104	+	0.944294i	$0.393253\pi$
$978$		0			0
$979$	−1503.42			−1.53567
$980$		0			0
$981$	378.000	+	1069.15i	0.385321	+	1.08985i
$982$		0			0
$983$	484.999	−	484.999i	0.493387	−	0.493387i	−0.415985	−	0.909371i	$-0.636563\pi$
$983$	484.999	−	484.999i	0.493387	−	0.493387i	0.909371	+	0.415985i	$0.136563\pi$
$984$		0			0
$985$	−180.000			−0.182741
$986$		0			0
$987$	86.0927	+	501.785i	0.0872266	+	0.508394i
$988$		0			0
$989$	237.588			0.240230
$990$		0			0
$991$			741.318i			0.748050i	0.927419	+	0.374025i	$0.122023\pi$
$991$			741.318i			0.748050i	−0.927419	+	0.374025i	$0.877977\pi$
$992$		0			0
$993$	−1024.26	+	175.736i	−1.03148	+	0.176975i
$994$		0			0
$995$	−318.434	−	318.434i	−0.320034	−	0.320034i
$996$		0			0
$997$	1052.00	+	1052.00i	1.05517	+	1.05517i	0.998387	+	0.0567787i	$0.0180829\pi$
$997$	1052.00	+	1052.00i	1.05517	+	1.05517i	0.0567787	+	0.998387i	$0.481917\pi$
$998$		0			0
$999$	394.908	−	1396.21i	0.395303	−	1.39761i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.3.bj.a.47.3	yes	8
3.2	odd	2	inner	240.3.bj.a.47.4	yes	8
4.3	odd	2	inner	240.3.bj.a.47.2	yes	8
5.3	odd	4	inner	240.3.bj.a.143.1	yes	8
12.11	even	2	inner	240.3.bj.a.47.1	✓	8
15.8	even	4	inner	240.3.bj.a.143.2	yes	8
20.3	even	4	inner	240.3.bj.a.143.4	yes	8
60.23	odd	4	inner	240.3.bj.a.143.3	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.3.bj.a.47.1	✓	8	12.11	even	2	inner
240.3.bj.a.47.2	yes	8	4.3	odd	2	inner
240.3.bj.a.47.3	yes	8	1.1	even	1	trivial
240.3.bj.a.47.4	yes	8	3.2	odd	2	inner
240.3.bj.a.143.1	yes	8	5.3	odd	4	inner
240.3.bj.a.143.2	yes	8	15.8	even	4	inner
240.3.bj.a.143.3	yes	8	60.23	odd	4	inner
240.3.bj.a.143.4	yes	8	20.3	even	4	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:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	240.bj (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.507306 + 2.95680i) q^{3} +(3.53553 + 3.53553i) q^{5} +(8.66025 - 8.66025i) q^{7} +(-8.48528 + 3.00000i) q^{9} +O(q^{10})\)	\(q+(0.507306 + 2.95680i) q^{3} +(3.53553 + 3.53553i) q^{5} +(8.66025 - 8.66025i) q^{7} +(-8.48528 + 3.00000i) q^{9} +17.1464 q^{11} +(4.00000 - 4.00000i) q^{13} +(-8.66025 + 12.2474i) q^{15} +(-15.5563 + 15.5563i) q^{17} -6.92820 q^{19} +(30.0000 + 21.2132i) q^{21} +(-4.89898 + 4.89898i) q^{23} +25.0000i q^{25} +(-13.1750 - 23.5673i) q^{27} -26.8701 q^{29} +3.46410i q^{31} +(8.69848 + 50.6985i) q^{33} +61.2372 q^{35} +(38.0000 + 38.0000i) q^{37} +(13.8564 + 9.79796i) q^{39} -62.2254i q^{41} +(-24.2487 - 24.2487i) q^{43} +(-40.6066 - 19.3934i) q^{45} +(9.79796 + 9.79796i) q^{47} -101.000i q^{49} +(-53.8888 - 38.1051i) q^{51} +(5.65685 + 5.65685i) q^{53} +(60.6218 + 60.6218i) q^{55} +(-3.51472 - 20.4853i) q^{57} -46.5403i q^{59} -42.0000 q^{61} +(-47.5039 + 99.4655i) q^{63} +28.2843 q^{65} +(-20.7846 + 20.7846i) q^{67} +(-16.9706 - 12.0000i) q^{69} +14.6969 q^{71} +(-37.0000 + 37.0000i) q^{73} +(-73.9199 + 12.6826i) q^{75} +(148.492 - 148.492i) q^{77} -72.7461 q^{79} +(63.0000 - 50.9117i) q^{81} +(93.0806 - 93.0806i) q^{83} -110.000 q^{85} +(-13.6313 - 79.4493i) q^{87} -87.6812 q^{89} -69.2820i q^{91} +(-10.2426 + 1.75736i) q^{93} +(-24.4949 - 24.4949i) q^{95} +(35.0000 + 35.0000i) q^{97} +(-145.492 + 51.4393i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q+O(q^{10}) \) 8 * q	\( 8 q + 32 q^{13} + 240 q^{21} - 168 q^{33} + 304 q^{37} - 240 q^{45} - 96 q^{57} - 336 q^{61} - 296 q^{73} + 504 q^{81} - 880 q^{85} - 48 q^{93} + 280 q^{97}+O(q^{100}) \) 8 * q + 32 * q^13 + 240 * q^21 - 168 * q^33 + 304 * q^37 - 240 * q^45 - 96 * q^57 - 336 * q^61 - 296 * q^73 + 504 * q^81 - 880 * q^85 - 48 * q^93 + 280 * q^97

Introduction

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