LMFDB - Embedded newform 588.2.e.b.491.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [588,2,Mod(491,588)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(588, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("588.491");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 588 = 2^{2} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	588.e (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.69520363885$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.3317760000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 8x^{6} + 13x^{4} + 12x^{2} + 36 $ x^8 - 8x^6 + 13x^4 + 12*x^2 + 36
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			491.4
Root			$2.15988 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	588.491
Dual form			588.2.e.b.491.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 + 1.11803i) q^{2} +(1.58114 - 0.707107i) q^{3} +(-0.500000 - 1.93649i) q^{4} -2.44949i q^{5} +(-0.578737 + 2.38014i) q^{6} +(2.59808 + 1.11803i) q^{8} +(2.00000 - 2.23607i) q^{9} +(2.73861 + 2.12132i) q^{10} +3.46410 q^{11} +(-2.15988 - 2.70831i) q^{12} -5.47723 q^{13} +(-1.73205 - 3.87298i) q^{15} +(-3.50000 + 1.93649i) q^{16} -4.89898i q^{17} +(0.767949 + 4.17256i) q^{18} +4.24264i q^{19} +(-4.74342 + 1.22474i) q^{20} +(-3.00000 + 3.87298i) q^{22} +(4.89849 - 0.0693504i) q^{24} -1.00000 q^{25} +(4.74342 - 6.12372i) q^{26} +(1.58114 - 4.94975i) q^{27} -4.47214i q^{29} +(5.83013 + 1.41761i) q^{30} -8.48528i q^{31} +(0.866025 - 5.59017i) q^{32} +(5.47723 - 2.44949i) q^{33} +(5.47723 + 4.24264i) q^{34} +(-5.33013 - 2.75495i) q^{36} -2.00000 q^{37} +(-4.74342 - 3.67423i) q^{38} +(-8.66025 + 3.87298i) q^{39} +(2.73861 - 6.36396i) q^{40} +7.74597i q^{43} +(-1.73205 - 6.70820i) q^{44} +(-5.47723 - 4.89898i) q^{45} +(-4.16468 + 5.53674i) q^{48} +(0.866025 - 1.11803i) q^{50} +(-3.46410 - 7.74597i) q^{51} +(2.73861 + 10.6066i) q^{52} +4.47214i q^{53} +(4.16468 + 6.05437i) q^{54} -8.48528i q^{55} +(3.00000 + 6.70820i) q^{57} +(5.00000 + 3.87298i) q^{58} +9.48683 q^{59} +(-6.63397 + 5.29059i) q^{60} +5.47723 q^{61} +(9.48683 + 7.34847i) q^{62} +(5.50000 + 5.80948i) q^{64} +13.4164i q^{65} +(-2.00480 + 8.24504i) q^{66} -7.74597i q^{67} +(-9.48683 + 2.44949i) q^{68} +3.46410 q^{71} +(7.69615 - 3.57341i) q^{72} -10.9545 q^{73} +(1.73205 - 2.23607i) q^{74} +(-1.58114 + 0.707107i) q^{75} +(8.21584 - 2.12132i) q^{76} +(3.16987 - 13.0366i) q^{78} +15.4919i q^{79} +(4.74342 + 8.57321i) q^{80} +(-1.00000 - 8.94427i) q^{81} +9.48683 q^{83} -12.0000 q^{85} +(-8.66025 - 6.70820i) q^{86} +(-3.16228 - 7.07107i) q^{87} +(9.00000 + 3.87298i) q^{88} +9.79796i q^{89} +(10.2206 - 1.88108i) q^{90} +(-6.00000 - 13.4164i) q^{93} +10.3923 q^{95} +(-2.58354 - 9.45121i) q^{96} +(6.92820 - 7.74597i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{4} + 16 q^{9} - 28 q^{16} + 20 q^{18} - 24 q^{22} - 8 q^{25} + 12 q^{30} - 8 q^{36} - 16 q^{37} + 24 q^{57} + 40 q^{58} - 60 q^{60} + 44 q^{64} + 20 q^{72} + 60 q^{78} - 8 q^{81} - 96 q^{85}+ \cdots - 48 q^{93}+O(q^{100}) $ 8 * q - 4 * q^4 + 16 * q^9 - 28 * q^16 + 20 * q^18 - 24 * q^22 - 8 * q^25 + 12 * q^30 - 8 * q^36 - 16 * q^37 + 24 * q^57 + 40 * q^58 - 60 * q^60 + 44 * q^64 + 20 * q^72 + 60 * q^78 - 8 * q^81 - 96 * q^85 + 72 * q^88 - 48 * q^93

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$493$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.866025	+	1.11803i	−0.612372	+	0.790569i
$2$	−0.866025	+	1.11803i	−0.612372	+	0.790569i
$3$	1.58114	−	0.707107i	0.912871	−	0.408248i
$3$	1.58114	−	0.707107i	0.912871	−	0.408248i
$4$	−0.500000	−	1.93649i	−0.250000	−	0.968246i
$5$		−	2.44949i		−	1.09545i	−0.836660	−	0.547723i	$-0.815495\pi$
$5$		−	2.44949i		−	1.09545i	0.836660	−	0.547723i	$-0.184505\pi$
$6$	−0.578737	+	2.38014i	−0.236268	+	0.971688i
$7$		0			0
$7$		0			0
$8$	2.59808	+	1.11803i	0.918559	+	0.395285i
$9$	2.00000	−	2.23607i	0.666667	−	0.745356i
$10$	2.73861	+	2.12132i	0.866025	+	0.670820i
$11$	3.46410			1.04447			0.522233	−	0.852803i	$-0.325099\pi$
$11$	3.46410			1.04447			0.522233	+	0.852803i	$0.325099\pi$
$12$	−2.15988	−	2.70831i	−0.623502	−	0.781821i
$13$	−5.47723			−1.51911			−0.759555	−	0.650444i	$-0.774583\pi$
$13$	−5.47723			−1.51911			−0.759555	+	0.650444i	$0.774583\pi$
$14$		0			0
$15$	−1.73205	−	3.87298i	−0.447214	−	1.00000i
$16$	−3.50000	+	1.93649i	−0.875000	+	0.484123i
$17$		−	4.89898i		−	1.18818i	−0.804400	−	0.594089i	$-0.797513\pi$
$17$		−	4.89898i		−	1.18818i	0.804400	−	0.594089i	$-0.202487\pi$
$18$	0.767949	+	4.17256i	0.181007	+	0.983482i
$19$			4.24264i			0.973329i	0.873589	+	0.486664i	$0.161786\pi$
$19$			4.24264i			0.973329i	−0.873589	+	0.486664i	$0.838214\pi$
$20$	−4.74342	+	1.22474i	−1.06066	+	0.273861i
$21$		0			0
$22$	−3.00000	+	3.87298i	−0.639602	+	0.825723i
$23$		0			0			−	1.00000i	$-0.5\pi$
$23$		0			0				1.00000i	$0.5\pi$
$24$	4.89849	−	0.0693504i	0.999900	−	0.0141561i
$25$	−1.00000			−0.200000
$26$	4.74342	−	6.12372i	0.930261	−	1.20096i
$27$	1.58114	−	4.94975i	0.304290	−	0.952579i
$28$		0			0
$29$		−	4.47214i		−	0.830455i	−0.909718	−	0.415227i	$-0.863702\pi$
$29$		−	4.47214i		−	0.830455i	0.909718	−	0.415227i	$-0.136298\pi$
$30$	5.83013	+	1.41761i	1.06443	+	0.258819i
$31$		−	8.48528i		−	1.52400i	−0.647576	−	0.762001i	$-0.724217\pi$
$31$		−	8.48528i		−	1.52400i	0.647576	−	0.762001i	$-0.275783\pi$
$32$	0.866025	−	5.59017i	0.153093	−	0.988212i
$33$	5.47723	−	2.44949i	0.953463	−	0.426401i
$34$	5.47723	+	4.24264i	0.939336	+	0.727607i
$35$		0			0
$36$	−5.33013	−	2.75495i	−0.888355	−	0.459158i
$37$	−2.00000			−0.328798			−0.164399	−	0.986394i	$-0.552568\pi$
$37$	−2.00000			−0.328798			−0.164399	+	0.986394i	$0.552568\pi$
$38$	−4.74342	−	3.67423i	−0.769484	−	0.596040i
$39$	−8.66025	+	3.87298i	−1.38675	+	0.620174i
$40$	2.73861	−	6.36396i	0.433013	−	1.00623i
$41$		0			0		1.00000			$0$
$41$		0			0		−1.00000			$\pi$
$42$		0			0
$43$			7.74597i			1.18125i	0.806947	+	0.590624i	$0.201119\pi$
$43$			7.74597i			1.18125i	−0.806947	+	0.590624i	$0.798881\pi$
$44$	−1.73205	−	6.70820i	−0.261116	−	1.01130i
$45$	−5.47723	−	4.89898i	−0.816497	−	0.730297i
$46$		0			0
$47$		0			0			−	1.00000i	$-0.5\pi$
$47$		0			0				1.00000i	$0.5\pi$
$48$	−4.16468	+	5.53674i	−0.601120	+	0.799159i
$49$		0			0
$50$	0.866025	−	1.11803i	0.122474	−	0.158114i
$51$	−3.46410	−	7.74597i	−0.485071	−	1.08465i
$52$	2.73861	+	10.6066i	0.379777	+	1.47087i
$53$			4.47214i			0.614295i	0.951662	+	0.307148i	$0.0993745\pi$
$53$			4.47214i			0.614295i	−0.951662	+	0.307148i	$0.900625\pi$
$54$	4.16468	+	6.05437i	0.566741	+	0.823896i
$55$		−	8.48528i		−	1.14416i
$56$		0			0
$57$	3.00000	+	6.70820i	0.397360	+	0.888523i
$58$	5.00000	+	3.87298i	0.656532	+	0.508548i
$59$	9.48683			1.23508			0.617540	−	0.786539i	$-0.288129\pi$
$59$	9.48683			1.23508			0.617540	+	0.786539i	$0.288129\pi$
$60$	−6.63397	+	5.29059i	−0.856442	+	0.683013i
$61$	5.47723			0.701287			0.350643	−	0.936509i	$-0.385963\pi$
$61$	5.47723			0.701287			0.350643	+	0.936509i	$0.385963\pi$
$62$	9.48683	+	7.34847i	1.20483	+	0.933257i
$63$		0			0
$64$	5.50000	+	5.80948i	0.687500	+	0.726184i
$65$			13.4164i			1.66410i
$66$	−2.00480	+	8.24504i	−0.246774	+	1.01489i
$67$		−	7.74597i		−	0.946320i	−0.880976	−	0.473160i	$-0.843113\pi$
$67$		−	7.74597i		−	0.946320i	0.880976	−	0.473160i	$-0.156887\pi$
$68$	−9.48683	+	2.44949i	−1.15045	+	0.297044i
$69$		0			0
$70$		0			0
$71$	3.46410			0.411113			0.205557	−	0.978645i	$-0.434100\pi$
$71$	3.46410			0.411113			0.205557	+	0.978645i	$0.434100\pi$
$72$	7.69615	−	3.57341i	0.907000	−	0.421130i
$73$	−10.9545			−1.28212			−0.641061	−	0.767490i	$-0.721505\pi$
$73$	−10.9545			−1.28212			−0.641061	+	0.767490i	$0.721505\pi$
$74$	1.73205	−	2.23607i	0.201347	−	0.259938i
$75$	−1.58114	+	0.707107i	−0.182574	+	0.0816497i
$76$	8.21584	−	2.12132i	0.942421	−	0.243332i
$77$		0			0
$78$	3.16987	−	13.0366i	0.358917	−	1.47610i
$79$			15.4919i			1.74298i	0.490414	+	0.871489i	$0.336845\pi$
$79$			15.4919i			1.74298i	−0.490414	+	0.871489i	$0.663155\pi$
$80$	4.74342	+	8.57321i	0.530330	+	0.958514i
$81$	−1.00000	−	8.94427i	−0.111111	−	0.993808i
$82$		0			0
$83$	9.48683			1.04132			0.520658	−	0.853766i	$-0.325687\pi$
$83$	9.48683			1.04132			0.520658	+	0.853766i	$0.325687\pi$
$84$		0			0
$85$	−12.0000			−1.30158
$86$	−8.66025	−	6.70820i	−0.933859	−	0.723364i
$87$	−3.16228	−	7.07107i	−0.339032	−	0.758098i
$88$	9.00000	+	3.87298i	0.959403	+	0.412861i
$89$			9.79796i			1.03858i	0.854598	+	0.519291i	$0.173804\pi$
$89$			9.79796i			1.03858i	−0.854598	+	0.519291i	$0.826196\pi$
$90$	10.2206	−	1.88108i	1.07735	−	0.198284i
$91$		0			0
$92$		0			0
$93$	−6.00000	−	13.4164i	−0.622171	−	1.39122i
$94$		0			0
$95$	10.3923			1.06623
$96$	−2.58354	−	9.45121i	−0.263682	−	0.964610i
$97$		0			0			−	1.00000i	$-0.5\pi$
$97$		0			0				1.00000i	$0.5\pi$
$98$		0			0
$99$	6.92820	−	7.74597i	0.696311	−	0.778499i
$100$	0.500000	+	1.93649i	0.0500000	+	0.193649i
$101$			7.34847i			0.731200i	0.930772	+	0.365600i	$0.119136\pi$
$101$			7.34847i			0.731200i	−0.930772	+	0.365600i	$0.880864\pi$
$102$	11.6603	+	2.83522i	1.15454	+	0.280729i
$103$		0			0		1.00000			$0$
$103$		0			0		−1.00000			$\pi$
$104$	−14.2302	−	6.12372i	−1.39539	−	0.600481i
$105$		0			0
$106$	−5.00000	−	3.87298i	−0.485643	−	0.376177i
$107$	17.3205			1.67444			0.837218	−	0.546869i	$-0.184180\pi$
$107$	17.3205			1.67444			0.837218	+	0.546869i	$0.184180\pi$
$108$	−10.3757	−	0.586988i	−0.998404	−	0.0564830i
$109$	10.0000			0.957826			0.478913	−	0.877862i	$-0.341031\pi$
$109$	10.0000			0.957826			0.478913	+	0.877862i	$0.341031\pi$
$110$	9.48683	+	7.34847i	0.904534	+	0.700649i
$111$	−3.16228	+	1.41421i	−0.300150	+	0.134231i
$112$		0			0
$113$			4.47214i			0.420703i	0.977626	+	0.210352i	$0.0674609\pi$
$113$			4.47214i			0.420703i	−0.977626	+	0.210352i	$0.932539\pi$
$114$	−10.0981	−	2.45537i	−0.945771	−	0.229967i
$115$		0			0
$116$	−8.66025	+	2.23607i	−0.804084	+	0.207614i
$117$	−10.9545	+	12.2474i	−1.01274	+	1.13228i
$118$	−8.21584	+	10.6066i	−0.756329	+	0.976417i
$119$		0			0
$120$	−0.169873	−	11.9988i	−0.0155072	−	1.09534i
$121$	1.00000			0.0909091
$122$	−4.74342	+	6.12372i	−0.429449	+	0.554416i
$123$		0			0
$124$	−16.4317	+	4.24264i	−1.47561	+	0.381000i
$125$		−	9.79796i		−	0.876356i
$126$		0			0
$127$			7.74597i			0.687343i	0.939090	+	0.343672i	$0.111671\pi$
$127$			7.74597i			0.687343i	−0.939090	+	0.343672i	$0.888329\pi$
$128$	−11.2583	+	1.11803i	−0.995105	+	0.0988212i
$129$	5.47723	+	12.2474i	0.482243	+	1.07833i
$130$	−15.0000	−	11.6190i	−1.31559	−	1.01905i
$131$	−9.48683			−0.828868			−0.414434	−	0.910079i	$-0.636021\pi$
$131$	−9.48683			−0.828868			−0.414434	+	0.910079i	$0.636021\pi$
$132$	−7.48203	−	9.38186i	−0.651227	−	0.816586i
$133$		0			0
$134$	8.66025	+	6.70820i	0.748132	+	0.579501i
$135$	−12.1244	−	3.87298i	−1.04350	−	0.333333i
$136$	5.47723	−	12.7279i	0.469668	−	1.09141i
$137$			8.94427i			0.764161i	0.924129	+	0.382080i	$0.124792\pi$
$137$			8.94427i			0.764161i	−0.924129	+	0.382080i	$0.875208\pi$
$138$		0			0
$139$			4.24264i			0.359856i	0.983680	+	0.179928i	$0.0575865\pi$
$139$			4.24264i			0.359856i	−0.983680	+	0.179928i	$0.942414\pi$
$140$		0			0
$141$		0			0
$142$	−3.00000	+	3.87298i	−0.251754	+	0.325014i
$143$	−18.9737			−1.58666
$144$	−2.66987	+	11.6992i	−0.222489	+	0.974935i
$145$	−10.9545			−0.909718
$146$	9.48683	−	12.2474i	0.785136	−	1.01361i
$147$		0			0
$148$	1.00000	+	3.87298i	0.0821995	+	0.318357i
$149$			4.47214i			0.366372i	0.983078	+	0.183186i	$0.0586410\pi$
$149$			4.47214i			0.366372i	−0.983078	+	0.183186i	$0.941359\pi$
$150$	0.578737	−	2.38014i	0.0472537	−	0.194338i
$151$			7.74597i			0.630358i	0.949032	+	0.315179i	$0.102065\pi$
$151$			7.74597i			0.630358i	−0.949032	+	0.315179i	$0.897935\pi$
$152$	−4.74342	+	11.0227i	−0.384742	+	0.894059i
$153$	−10.9545	−	9.79796i	−0.885615	−	0.792118i
$154$		0			0
$155$	−20.7846			−1.66946
$156$	11.8301	+	14.8340i	0.947168	+	1.18767i
$157$	5.47723			0.437130			0.218565	−	0.975822i	$-0.429862\pi$
$157$	5.47723			0.437130			0.218565	+	0.975822i	$0.429862\pi$
$158$	−17.3205	−	13.4164i	−1.37795	−	1.06735i
$159$	3.16228	+	7.07107i	0.250785	+	0.560772i
$160$	−13.6931	−	2.12132i	−1.08253	−	0.167705i
$161$		0			0
$162$	10.8660	+	6.62793i	0.853716	+	0.520740i
$163$		−	7.74597i		−	0.606711i	−0.952877	−	0.303355i	$-0.901893\pi$
$163$		−	7.74597i		−	0.606711i	0.952877	−	0.303355i	$-0.0981070\pi$
$164$		0			0
$165$	−6.00000	−	13.4164i	−0.467099	−	1.04447i
$166$	−8.21584	+	10.6066i	−0.637673	+	0.823232i
$167$	−18.9737			−1.46823			−0.734113	−	0.679027i	$-0.762402\pi$
$167$	−18.9737			−1.46823			−0.734113	+	0.679027i	$0.762402\pi$
$168$		0			0
$169$	17.0000			1.30769
$170$	10.3923	−	13.4164i	0.797053	−	1.02899i
$171$	9.48683	+	8.48528i	0.725476	+	0.648886i
$172$	15.0000	−	3.87298i	1.14374	−	0.295312i
$173$		−	2.44949i		−	0.186231i	−0.995655	−	0.0931156i	$-0.970317\pi$
$173$		−	2.44949i		−	0.186231i	0.995655	−	0.0931156i	$-0.0296826\pi$
$174$	10.6443	+	2.58819i	0.806943	+	0.196210i
$175$		0			0
$176$	−12.1244	+	6.70820i	−0.913908	+	0.505650i
$177$	15.0000	−	6.70820i	1.12747	−	0.504219i
$178$	−10.9545	−	8.48528i	−0.821071	−	0.635999i
$179$	−10.3923			−0.776757			−0.388379	−	0.921500i	$-0.626965\pi$
$179$	−10.3923			−0.776757			−0.388379	+	0.921500i	$0.626965\pi$
$180$	−6.74822	+	13.0561i	−0.502983	+	0.973144i
$181$	16.4317			1.22136			0.610678	−	0.791879i	$-0.290897\pi$
$181$	16.4317			1.22136			0.610678	+	0.791879i	$0.290897\pi$
$182$		0			0
$183$	8.66025	−	3.87298i	0.640184	−	0.286299i
$184$		0			0
$185$			4.89898i			0.360180i
$186$	20.1962	+	4.91075i	1.48085	+	0.360073i
$187$		−	16.9706i		−	1.24101i
$188$		0			0
$189$		0			0
$190$	−9.00000	+	11.6190i	−0.652929	+	0.842927i
$191$	3.46410			0.250654			0.125327	−	0.992116i	$-0.460002\pi$
$191$	3.46410			0.250654			0.125327	+	0.992116i	$0.460002\pi$
$192$	12.8042	+	5.29650i	0.924062	+	0.382242i
$193$	−16.0000			−1.15171			−0.575853	−	0.817554i	$-0.695330\pi$
$193$	−16.0000			−1.15171			−0.575853	+	0.817554i	$0.695330\pi$
$194$		0			0
$195$	9.48683	+	21.2132i	0.679366	+	1.51911i
$196$		0			0
$197$		−	22.3607i		−	1.59313i	−0.604551	−	0.796566i	$-0.706648\pi$
$197$		−	22.3607i		−	1.59313i	0.604551	−	0.796566i	$-0.293352\pi$
$198$	2.66025	+	14.4542i	0.189056	+	1.02721i
$199$			16.9706i			1.20301i	0.798869	+	0.601506i	$0.205432\pi$
$199$			16.9706i			1.20301i	−0.798869	+	0.601506i	$0.794568\pi$
$200$	−2.59808	−	1.11803i	−0.183712	−	0.0790569i
$201$	−5.47723	−	12.2474i	−0.386334	−	0.863868i
$202$	−8.21584	−	6.36396i	−0.578064	−	0.447767i
$203$		0			0
$204$	−13.2679	+	10.5812i	−0.928942	+	0.740831i
$205$		0			0
$206$		0			0
$207$		0			0
$208$	19.1703	−	10.6066i	1.32922	−	0.735436i
$209$			14.6969i			1.01661i
$210$		0			0
$211$		−	7.74597i		−	0.533254i	−0.963800	−	0.266627i	$-0.914091\pi$
$211$		−	7.74597i		−	0.533254i	0.963800	−	0.266627i	$-0.0859092\pi$
$212$	8.66025	−	2.23607i	0.594789	−	0.153574i
$213$	5.47723	−	2.44949i	0.375293	−	0.167836i
$214$	−15.0000	+	19.3649i	−1.02538	+	1.32376i
$215$	18.9737			1.29399
$216$	9.64191	−	11.0921i	0.656049	−	0.754719i
$217$		0			0
$218$	−8.66025	+	11.1803i	−0.586546	+	0.757228i
$219$	−17.3205	+	7.74597i	−1.17041	+	0.523424i
$220$	−16.4317	+	4.24264i	−1.10782	+	0.286039i
$221$			26.8328i			1.80497i
$222$	1.15747	−	4.76028i	0.0776846	−	0.319489i
$223$			8.48528i			0.568216i	0.958792	+	0.284108i	$0.0916975\pi$
$223$			8.48528i			0.568216i	−0.958792	+	0.284108i	$0.908302\pi$
$224$		0			0
$225$	−2.00000	+	2.23607i	−0.133333	+	0.149071i
$226$	−5.00000	−	3.87298i	−0.332595	−	0.257627i
$227$	9.48683			0.629663			0.314832	−	0.949148i	$-0.398052\pi$
$227$	9.48683			0.629663			0.314832	+	0.949148i	$0.398052\pi$
$228$	11.4904	−	9.16358i	0.760969	−	0.606873i
$229$	5.47723			0.361945			0.180973	−	0.983488i	$-0.442075\pi$
$229$	5.47723			0.361945			0.180973	+	0.983488i	$0.442075\pi$
$230$		0			0
$231$		0			0
$232$	5.00000	−	11.6190i	0.328266	−	0.762821i
$233$			8.94427i			0.585959i	0.956119	+	0.292979i	$0.0946467\pi$
$233$			8.94427i			0.585959i	−0.956119	+	0.292979i	$0.905353\pi$
$234$	−4.20623	−	22.8541i	−0.274970	−	1.49402i
$235$		0			0
$236$	−4.74342	−	18.3712i	−0.308770	−	1.19586i
$237$	10.9545	+	24.4949i	0.711568	+	1.59111i
$238$		0			0
$239$	−6.92820			−0.448148			−0.224074	−	0.974572i	$-0.571936\pi$
$239$	−6.92820			−0.448148			−0.224074	+	0.974572i	$0.571936\pi$
$240$	13.5622	+	10.2013i	0.875435	+	0.658494i
$241$	21.9089			1.41128			0.705638	−	0.708572i	$-0.250660\pi$
$241$	21.9089			1.41128			0.705638	+	0.708572i	$0.250660\pi$
$242$	−0.866025	+	1.11803i	−0.0556702	+	0.0718699i
$243$	−7.90569	−	13.4350i	−0.507151	−	0.861858i
$244$	−2.73861	−	10.6066i	−0.175322	−	0.679018i
$245$		0			0
$246$		0			0
$247$		−	23.2379i		−	1.47859i
$248$	9.48683	−	22.0454i	0.602414	−	1.39988i
$249$	15.0000	−	6.70820i	0.950586	−	0.425115i
$250$	10.9545	+	8.48528i	0.692820	+	0.536656i
$251$	9.48683			0.598804			0.299402	−	0.954127i	$-0.403213\pi$
$251$	9.48683			0.598804			0.299402	+	0.954127i	$0.403213\pi$
$252$		0			0
$253$		0			0
$254$	−8.66025	−	6.70820i	−0.543393	−	0.420910i
$255$	−18.9737	+	8.48528i	−1.18818	+	0.531369i
$256$	8.50000	−	13.5554i	0.531250	−	0.847215i
$257$		−	4.89898i		−	0.305590i	−0.988258	−	0.152795i	$-0.951173\pi$
$257$		−	4.89898i		−	0.305590i	0.988258	−	0.152795i	$-0.0488274\pi$
$258$	−18.4365	−	4.48288i	−1.14781	−	0.279092i
$259$		0			0
$260$	25.9808	−	6.70820i	1.61126	−	0.416025i
$261$	−10.0000	−	8.94427i	−0.618984	−	0.553637i
$262$	8.21584	−	10.6066i	0.507576	−	0.655278i
$263$	3.46410			0.213606			0.106803	−	0.994280i	$-0.465939\pi$
$263$	3.46410			0.213606			0.106803	+	0.994280i	$0.465939\pi$
$264$	16.9689	−	0.240237i	1.04436	−	0.0147855i
$265$	10.9545			0.672927
$266$		0			0
$267$	6.92820	+	15.4919i	0.423999	+	0.948091i
$268$	−15.0000	+	3.87298i	−0.916271	+	0.236580i
$269$		−	2.44949i		−	0.149348i	−0.997208	−	0.0746740i	$-0.976208\pi$
$269$		−	2.44949i		−	0.149348i	0.997208	−	0.0746740i	$-0.0237916\pi$
$270$	14.8301	−	10.2013i	0.902533	−	0.620834i
$271$			8.48528i			0.515444i	0.966219	+	0.257722i	$0.0829719\pi$
$271$			8.48528i			0.515444i	−0.966219	+	0.257722i	$0.917028\pi$
$272$	9.48683	+	17.1464i	0.575224	+	1.03965i
$273$		0			0
$274$	−10.0000	−	7.74597i	−0.604122	−	0.467951i
$275$	−3.46410			−0.208893
$276$		0			0
$277$	2.00000			0.120168			0.0600842	−	0.998193i	$-0.480863\pi$
$277$	2.00000			0.120168			0.0600842	+	0.998193i	$0.480863\pi$
$278$	−4.74342	−	3.67423i	−0.284491	−	0.220366i
$279$	−18.9737	−	16.9706i	−1.13592	−	1.01600i
$280$		0			0
$281$			8.94427i			0.533571i	0.963756	+	0.266785i	$0.0859614\pi$
$281$			8.94427i			0.533571i	−0.963756	+	0.266785i	$0.914039\pi$
$282$		0			0
$283$			29.6985i			1.76539i	0.469945	+	0.882696i	$0.344274\pi$
$283$			29.6985i			1.76539i	−0.469945	+	0.882696i	$0.655726\pi$
$284$	−1.73205	−	6.70820i	−0.102778	−	0.398059i
$285$	16.4317	−	7.34847i	0.973329	−	0.435286i
$286$	16.4317	−	21.2132i	0.971625	−	1.25436i
$287$		0			0
$288$	−10.7679	−	13.1168i	−0.634507	−	0.772917i
$289$	−7.00000			−0.411765
$290$	9.48683	−	12.2474i	0.557086	−	0.719195i
$291$		0			0
$292$	5.47723	+	21.2132i	0.320530	+	1.24141i
$293$			2.44949i			0.143101i	0.997437	+	0.0715504i	$0.0227947\pi$
$293$			2.44949i			0.143101i	−0.997437	+	0.0715504i	$0.977205\pi$
$294$		0			0
$295$		−	23.2379i		−	1.35296i
$296$	−5.19615	−	2.23607i	−0.302020	−	0.129969i
$297$	5.47723	−	17.1464i	0.317821	−	0.994937i
$298$	−5.00000	−	3.87298i	−0.289642	−	0.224356i
$299$		0			0
$300$	2.15988	+	2.70831i	0.124700	+	0.156364i
$301$		0			0
$302$	−8.66025	−	6.70820i	−0.498342	−	0.386014i
$303$	5.19615	+	11.6190i	0.298511	+	0.667491i
$304$	−8.21584	−	14.8492i	−0.471211	−	0.851662i
$305$		−	13.4164i		−	0.768221i
$306$	20.4413	−	3.76217i	1.16855	−	0.215069i
$307$			21.2132i			1.21070i	0.795959	+	0.605351i	$0.206967\pi$
$307$			21.2132i			1.21070i	−0.795959	+	0.605351i	$0.793033\pi$
$308$		0			0
$309$		0			0
$310$	18.0000	−	23.2379i	1.02233	−	1.31982i
$311$	−18.9737			−1.07590			−0.537949	−	0.842977i	$-0.680801\pi$
$311$	−18.9737			−1.07590			−0.537949	+	0.842977i	$0.680801\pi$
$312$	−26.8301	+	0.379848i	−1.51896	+	0.0215046i
$313$	10.9545			0.619182			0.309591	−	0.950870i	$-0.399808\pi$
$313$	10.9545			0.619182			0.309591	+	0.950870i	$0.399808\pi$
$314$	−4.74342	+	6.12372i	−0.267686	+	0.345582i
$315$		0			0
$316$	30.0000	−	7.74597i	1.68763	−	0.435745i
$317$			4.47214i			0.251180i	0.992082	+	0.125590i	$0.0400824\pi$
$317$			4.47214i			0.251180i	−0.992082	+	0.125590i	$0.959918\pi$
$318$	−10.6443	−	2.58819i	−0.596903	−	0.145139i
$319$		−	15.4919i		−	0.867382i
$320$	14.2302	−	13.4722i	0.795495	−	0.753119i
$321$	27.3861	−	12.2474i	1.52854	−	0.683586i
$322$		0			0
$323$	20.7846			1.15649
$324$	−16.8205	+	6.40863i	−0.934473	+	0.356035i
$325$	5.47723			0.303822
$326$	8.66025	+	6.70820i	0.479647	+	0.371533i
$327$	15.8114	−	7.07107i	0.874372	−	0.391031i
$328$		0			0
$329$		0			0
$330$	20.1962	+	4.91075i	1.11176	+	0.270328i
$331$			23.2379i			1.27727i	0.769510	+	0.638635i	$0.220501\pi$
$331$			23.2379i			1.27727i	−0.769510	+	0.638635i	$0.779499\pi$
$332$	−4.74342	−	18.3712i	−0.260329	−	1.00825i
$333$	−4.00000	+	4.47214i	−0.219199	+	0.245072i
$334$	16.4317	−	21.2132i	0.899101	−	1.16073i
$335$	−18.9737			−1.03664
$336$		0			0
$337$	−8.00000			−0.435788			−0.217894	−	0.975972i	$-0.569919\pi$
$337$	−8.00000			−0.435788			−0.217894	+	0.975972i	$0.569919\pi$
$338$	−14.7224	+	19.0066i	−0.800795	+	1.03382i
$339$	3.16228	+	7.07107i	0.171751	+	0.384048i
$340$	6.00000	+	23.2379i	0.325396	+	1.26025i
$341$		−	29.3939i		−	1.59177i
$342$	−17.7027	+	3.25813i	−0.957251	+	0.176180i
$343$		0			0
$344$	−8.66025	+	20.1246i	−0.466930	+	1.08505i
$345$		0			0
$346$	2.73861	+	2.12132i	0.147229	+	0.114043i
$347$	24.2487			1.30174			0.650870	−	0.759190i	$-0.274404\pi$
$347$	24.2487			1.30174			0.650870	+	0.759190i	$0.274404\pi$
$348$	−12.1119	+	9.65926i	−0.649267	+	0.517791i
$349$	−16.4317			−0.879567			−0.439784	−	0.898104i	$-0.644945\pi$
$349$	−16.4317			−0.879567			−0.439784	+	0.898104i	$0.644945\pi$
$350$		0			0
$351$	−8.66025	+	27.1109i	−0.462250	+	1.44707i
$352$	3.00000	−	19.3649i	0.159901	−	1.03215i
$353$		−	14.6969i		−	0.782239i	−0.920340	−	0.391120i	$-0.872088\pi$
$353$		−	14.6969i		−	0.782239i	0.920340	−	0.391120i	$-0.127912\pi$
$354$	−5.49038	+	22.5800i	−0.291810	+	1.20011i
$355$		−	8.48528i		−	0.450352i
$356$	18.9737	−	4.89898i	1.00560	−	0.259645i
$357$		0			0
$358$	9.00000	−	11.6190i	0.475665	−	0.614081i
$359$	27.7128			1.46263			0.731313	−	0.682042i	$-0.238908\pi$
$359$	27.7128			1.46263			0.731313	+	0.682042i	$0.238908\pi$
$360$	−8.75302	−	18.8516i	−0.461325	−	0.993569i
$361$	1.00000			0.0526316
$362$	−14.2302	+	18.3712i	−0.747925	+	0.965567i
$363$	1.58114	−	0.707107i	0.0829883	−	0.0371135i
$364$		0			0
$365$			26.8328i			1.40449i
$366$	−3.16987	+	13.0366i	−0.165692	+	0.681432i
$367$		−	25.4558i		−	1.32878i	−0.747384	−	0.664392i	$-0.768691\pi$
$367$		−	25.4558i		−	1.32878i	0.747384	−	0.664392i	$-0.231309\pi$
$368$		0			0
$369$		0			0
$370$	−5.47723	−	4.24264i	−0.284747	−	0.220564i
$371$		0			0
$372$	−22.9808	+	18.3272i	−1.19150	+	0.950219i
$373$	26.0000			1.34623			0.673114	−	0.739538i	$-0.264956\pi$
$373$	26.0000			1.34623			0.673114	+	0.739538i	$0.264956\pi$
$374$	18.9737	+	14.6969i	0.981105	+	0.759961i
$375$	−6.92820	−	15.4919i	−0.357771	−	0.800000i
$376$		0			0
$377$			24.4949i			1.26155i
$378$		0			0
$379$		−	7.74597i		−	0.397884i	−0.980011	−	0.198942i	$-0.936250\pi$
$379$		−	7.74597i		−	0.397884i	0.980011	−	0.198942i	$-0.0637505\pi$
$380$	−5.19615	−	20.1246i	−0.266557	−	1.03237i
$381$	5.47723	+	12.2474i	0.280607	+	0.627456i
$382$	−3.00000	+	3.87298i	−0.153493	+	0.198159i
$383$		0			0			−	1.00000i	$-0.5\pi$
$383$		0			0				1.00000i	$0.5\pi$
$384$	−17.0104	+	9.72861i	−0.868059	+	0.496461i
$385$		0			0
$386$	13.8564	−	17.8885i	0.705273	−	0.910503i
$387$	17.3205	+	15.4919i	0.880451	+	0.787499i
$388$		0			0
$389$		−	31.3050i		−	1.58722i	−0.608424	−	0.793612i	$-0.708198\pi$
$389$		−	31.3050i		−	1.58722i	0.608424	−	0.793612i	$-0.291802\pi$
$390$	−31.9329	−	7.76457i	−1.61699	−	0.393174i
$391$		0			0
$392$		0			0
$393$	−15.0000	+	6.70820i	−0.756650	+	0.338384i
$394$	25.0000	+	19.3649i	1.25948	+	0.975590i
$395$	37.9473			1.90934
$396$	−18.4641	−	9.54342i	−0.927856	−	0.479575i
$397$	−38.3406			−1.92426			−0.962129	−	0.272594i	$-0.912119\pi$
$397$	−38.3406			−1.92426			−0.962129	+	0.272594i	$0.912119\pi$
$398$	−18.9737	−	14.6969i	−0.951064	−	0.736691i
$399$		0			0
$400$	3.50000	−	1.93649i	0.175000	−	0.0968246i
$401$		−	4.47214i		−	0.223328i	−0.993746	−	0.111664i	$-0.964382\pi$
$401$		−	4.47214i		−	0.223328i	0.993746	−	0.111664i	$-0.0356180\pi$
$402$	18.4365	+	4.48288i	0.919528	+	0.223586i
$403$			46.4758i			2.31512i
$404$	14.2302	−	3.67423i	0.707981	−	0.182800i
$405$	−21.9089	+	2.44949i	−1.08866	+	0.121716i
$406$		0			0
$407$	−6.92820			−0.343418
$408$	−0.339746	−	23.9976i	−0.0168199	−	1.18806i
$409$	10.9545			0.541663			0.270831	−	0.962627i	$-0.412701\pi$
$409$	10.9545			0.541663			0.270831	+	0.962627i	$0.412701\pi$
$410$		0			0
$411$	6.32456	+	14.1421i	0.311967	+	0.697580i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		−	23.2379i		−	1.14070i
$416$	−4.74342	+	30.6186i	−0.232565	+	1.50120i
$417$	3.00000	+	6.70820i	0.146911	+	0.328502i
$418$	−16.4317	−	12.7279i	−0.803700	−	0.622543i
$419$	28.4605			1.39039			0.695193	−	0.718823i	$-0.255319\pi$
$419$	28.4605			1.39039			0.695193	+	0.718823i	$0.255319\pi$
$420$		0			0
$421$	−10.0000			−0.487370			−0.243685	−	0.969854i	$-0.578356\pi$
$421$	−10.0000			−0.487370			−0.243685	+	0.969854i	$0.578356\pi$
$422$	8.66025	+	6.70820i	0.421575	+	0.326550i
$423$		0			0
$424$	−5.00000	+	11.6190i	−0.242821	+	0.564266i
$425$			4.89898i			0.237635i
$426$	−2.00480	+	8.24504i	−0.0971331	+	0.399474i
$427$		0			0
$428$	−8.66025	−	33.5410i	−0.418609	−	1.62127i
$429$	−30.0000	+	13.4164i	−1.44841	+	0.647750i
$430$	−16.4317	+	21.2132i	−0.792406	+	1.02299i
$431$	−20.7846			−1.00116			−0.500580	−	0.865690i	$-0.666880\pi$
$431$	−20.7846			−1.00116			−0.500580	+	0.865690i	$0.666880\pi$
$432$	4.05116	+	20.3860i	0.194911	+	0.980821i
$433$	−21.9089			−1.05287			−0.526437	−	0.850214i	$-0.676473\pi$
$433$	−21.9089			−1.05287			−0.526437	+	0.850214i	$0.676473\pi$
$434$		0			0
$435$	−17.3205	+	7.74597i	−0.830455	+	0.371391i
$436$	−5.00000	−	19.3649i	−0.239457	−	0.927411i
$437$		0			0
$438$	6.33975	−	26.0731i	0.302925	−	1.24582i
$439$			16.9706i			0.809961i	0.914325	+	0.404980i	$0.132722\pi$
$439$			16.9706i			0.809961i	−0.914325	+	0.404980i	$0.867278\pi$
$440$	9.48683	−	22.0454i	0.452267	−	1.05097i
$441$		0			0
$442$	−30.0000	−	23.2379i	−1.42695	−	1.10531i
$443$	−31.1769			−1.48126			−0.740630	−	0.671913i	$-0.765473\pi$
$443$	−31.1769			−1.48126			−0.740630	+	0.671913i	$0.765473\pi$
$444$	4.31975	+	5.41662i	0.205006	+	0.257061i
$445$	24.0000			1.13771
$446$	−9.48683	−	7.34847i	−0.449215	−	0.347960i
$447$	3.16228	+	7.07107i	0.149571	+	0.334450i
$448$		0			0
$449$		−	35.7771i		−	1.68843i	−0.536009	−	0.844213i	$-0.680069\pi$
$449$		−	35.7771i		−	1.68843i	0.536009	−	0.844213i	$-0.319931\pi$
$450$	−0.767949	−	4.17256i	−0.0362015	−	0.196696i
$451$		0			0
$452$	8.66025	−	2.23607i	0.407344	−	0.105176i
$453$	5.47723	+	12.2474i	0.257343	+	0.575435i
$454$	−8.21584	+	10.6066i	−0.385588	+	0.497792i
$455$		0			0
$456$	0.294229	+	20.7825i	0.0137785	+	0.973231i
$457$	−28.0000			−1.30978			−0.654892	−	0.755722i	$-0.727286\pi$
$457$	−28.0000			−1.30978			−0.654892	+	0.755722i	$0.727286\pi$
$458$	−4.74342	+	6.12372i	−0.221645	+	0.286143i
$459$	−24.2487	−	7.74597i	−1.13183	−	0.361551i
$460$		0			0
$461$		−	36.7423i		−	1.71126i	−0.517587	−	0.855631i	$-0.673169\pi$
$461$		−	36.7423i		−	1.71126i	0.517587	−	0.855631i	$-0.326831\pi$
$462$		0			0
$463$			15.4919i			0.719971i	0.932958	+	0.359986i	$0.117218\pi$
$463$			15.4919i			0.719971i	−0.932958	+	0.359986i	$0.882782\pi$
$464$	8.66025	+	15.6525i	0.402042	+	0.726648i
$465$	−32.8634	+	14.6969i	−1.52400	+	0.681554i
$466$	−10.0000	−	7.74597i	−0.463241	−	0.358825i
$467$	−28.4605			−1.31699			−0.658497	−	0.752583i	$-0.728808\pi$
$467$	−28.4605			−1.31699			−0.658497	+	0.752583i	$0.728808\pi$
$468$	29.1943	+	15.0895i	1.34951	+	0.697511i
$469$		0			0
$470$		0			0
$471$	8.66025	−	3.87298i	0.399043	−	0.178458i
$472$	24.6475	+	10.6066i	1.13449	+	0.488208i
$473$			26.8328i			1.23377i
$474$	−36.8730	−	8.96575i	−1.69363	−	0.411811i
$475$		−	4.24264i		−	0.194666i
$476$		0			0
$477$	10.0000	+	8.94427i	0.457869	+	0.409530i
$478$	6.00000	−	7.74597i	0.274434	−	0.354292i
$479$	−37.9473			−1.73386			−0.866929	−	0.498432i	$-0.833909\pi$
$479$	−37.9473			−1.73386			−0.866929	+	0.498432i	$0.833909\pi$
$480$	−23.1506	+	6.32836i	−1.05668	+	0.288849i
$481$	10.9545			0.499480
$482$	−18.9737	+	24.4949i	−0.864227	+	1.11571i
$483$		0			0
$484$	−0.500000	−	1.93649i	−0.0227273	−	0.0880223i
$485$		0			0
$486$	21.8674	+	2.79624i	0.991923	+	0.126840i
$487$		−	7.74597i		−	0.351003i	−0.984479	−	0.175502i	$-0.943845\pi$
$487$		−	7.74597i		−	0.351003i	0.984479	−	0.175502i	$-0.0561547\pi$
$488$	14.2302	+	6.12372i	0.644173	+	0.277208i
$489$	−5.47723	−	12.2474i	−0.247689	−	0.553849i
$490$		0			0
$491$	31.1769			1.40699			0.703497	−	0.710698i	$-0.251621\pi$
$491$	31.1769			1.40699			0.703497	+	0.710698i	$0.251621\pi$
$492$		0			0
$493$	−21.9089			−0.986727
$494$	25.9808	+	20.1246i	1.16893	+	0.905449i
$495$	−18.9737	−	16.9706i	−0.852803	−	0.762770i
$496$	16.4317	+	29.6985i	0.737804	+	1.33350i
$497$		0			0
$498$	−5.49038	+	22.5800i	−0.246030	+	1.01183i
$499$		−	23.2379i		−	1.04027i	−0.854084	−	0.520136i	$-0.825881\pi$
$499$		−	23.2379i		−	1.04027i	0.854084	−	0.520136i	$-0.174119\pi$
$500$	−18.9737	+	4.89898i	−0.848528	+	0.219089i
$501$	−30.0000	+	13.4164i	−1.34030	+	0.599401i
$502$	−8.21584	+	10.6066i	−0.366691	+	0.473396i
$503$	−18.9737			−0.845994			−0.422997	−	0.906131i	$-0.639022\pi$
$503$	−18.9737			−0.845994			−0.422997	+	0.906131i	$0.639022\pi$
$504$		0			0
$505$	18.0000			0.800989
$506$		0			0
$507$	26.8794	−	12.0208i	1.19375	−	0.533863i
$508$	15.0000	−	3.87298i	0.665517	−	0.171836i
$509$			36.7423i			1.62858i	0.580461	+	0.814288i	$0.302872\pi$
$509$			36.7423i			1.62858i	−0.580461	+	0.814288i	$0.697128\pi$
$510$	6.94484	−	28.5617i	0.307523	−	1.26473i
$511$		0			0
$512$	7.79423	+	21.2426i	0.344459	+	0.938801i
$513$	21.0000	+	6.70820i	0.927173	+	0.296174i
$514$	5.47723	+	4.24264i	0.241590	+	0.187135i
$515$		0			0
$516$	20.9785	−	16.7303i	0.923526	−	0.736512i
$517$		0			0
$518$		0			0
$519$	−1.73205	−	3.87298i	−0.0760286	−	0.170005i
$520$	−15.0000	+	34.8569i	−0.657794	+	1.52857i
$521$			29.3939i			1.28777i	0.765123	+	0.643885i	$0.222678\pi$
$521$			29.3939i			1.28777i	−0.765123	+	0.643885i	$0.777322\pi$
$522$	18.6603	−	3.43437i	0.816737	−	0.150318i
$523$			21.2132i			0.927589i	0.885943	+	0.463794i	$0.153512\pi$
$523$			21.2132i			0.927589i	−0.885943	+	0.463794i	$0.846488\pi$
$524$	4.74342	+	18.3712i	0.207217	+	0.802548i
$525$		0			0
$526$	−3.00000	+	3.87298i	−0.130806	+	0.168870i
$527$	−41.5692			−1.81078
$528$	−14.4269	+	19.1798i	−0.627849	+	0.834694i
$529$	−23.0000			−1.00000
$530$	−9.48683	+	12.2474i	−0.412082	+	0.531995i
$531$	18.9737	−	21.2132i	0.823387	−	0.920575i
$532$		0			0
$533$		0			0
$534$	−23.3205	−	5.67044i	−1.00918	−	0.245384i
$535$		−	42.4264i		−	1.83425i
$536$	8.66025	−	20.1246i	0.374066	−	0.869251i
$537$	−16.4317	+	7.34847i	−0.709079	+	0.317110i
$538$	2.73861	+	2.12132i	0.118070	+	0.0914566i
$539$		0			0
$540$	−1.43782	+	25.4152i	−0.0618740	+	1.09370i
$541$	38.0000			1.63375			0.816874	−	0.576816i	$-0.195705\pi$
$541$	38.0000			1.63375			0.816874	+	0.576816i	$0.195705\pi$
$542$	−9.48683	−	7.34847i	−0.407494	−	0.315644i
$543$	25.9808	−	11.6190i	1.11494	−	0.498617i
$544$	−27.3861	−	4.24264i	−1.17417	−	0.181902i
$545$		−	24.4949i		−	1.04925i
$546$		0			0
$547$		−	38.7298i		−	1.65597i	−0.560752	−	0.827984i	$-0.689488\pi$
$547$		−	38.7298i		−	1.65597i	0.560752	−	0.827984i	$-0.310512\pi$
$548$	17.3205	−	4.47214i	0.739895	−	0.191040i
$549$	10.9545	−	12.2474i	0.467525	−	0.522708i
$550$	3.00000	−	3.87298i	0.127920	−	0.165145i
$551$	18.9737			0.808305
$552$		0			0
$553$		0			0
$554$	−1.73205	+	2.23607i	−0.0735878	+	0.0950014i
$555$	3.46410	+	7.74597i	0.147043	+	0.328798i
$556$	8.21584	−	2.12132i	0.348429	−	0.0899640i
$557$		−	22.3607i		−	0.947452i	−0.880672	−	0.473726i	$-0.842909\pi$
$557$		−	22.3607i		−	0.947452i	0.880672	−	0.473726i	$-0.157091\pi$
$558$	35.4053	−	6.51626i	1.49883	−	0.275855i
$559$		−	42.4264i		−	1.79445i
$560$		0			0
$561$	−12.0000	−	26.8328i	−0.506640	−	1.13288i
$562$	−10.0000	−	7.74597i	−0.421825	−	0.326744i
$563$	9.48683			0.399822			0.199911	−	0.979814i	$-0.435935\pi$
$563$	9.48683			0.399822			0.199911	+	0.979814i	$0.435935\pi$
$564$		0			0
$565$	10.9545			0.460857
$566$	−33.2039	−	25.7196i	−1.39566	−	1.08108i
$567$		0			0
$568$	9.00000	+	3.87298i	0.377632	+	0.162507i
$569$		−	31.3050i		−	1.31237i	−0.754599	−	0.656186i	$-0.772169\pi$
$569$		−	31.3050i		−	1.31237i	0.754599	−	0.656186i	$-0.227831\pi$
$570$	−6.01441	+	24.7351i	−0.251916	+	1.03604i
$571$		−	23.2379i		−	0.972476i	−0.873826	−	0.486238i	$-0.838369\pi$
$571$		−	23.2379i		−	0.972476i	0.873826	−	0.486238i	$-0.161631\pi$
$572$	9.48683	+	36.7423i	0.396664	+	1.53627i
$573$	5.47723	−	2.44949i	0.228814	−	0.102329i
$574$		0			0
$575$		0			0
$576$	23.9904	−	0.679424i	0.999599	−	0.0283093i
$577$	−43.8178			−1.82416			−0.912080	−	0.410013i	$-0.865524\pi$
$577$	−43.8178			−1.82416			−0.912080	+	0.410013i	$0.865524\pi$
$578$	6.06218	−	7.82624i	0.252153	−	0.325529i
$579$	−25.2982	+	11.3137i	−1.05136	+	0.470182i
$580$	5.47723	+	21.2132i	0.227429	+	0.880830i
$581$		0			0
$582$		0			0
$583$			15.4919i			0.641610i
$584$	−28.4605	−	12.2474i	−1.17770	−	0.506803i
$585$	30.0000	+	26.8328i	1.24035	+	1.10940i
$586$	−2.73861	−	2.12132i	−0.113131	−	0.0876309i
$587$	9.48683			0.391564			0.195782	−	0.980647i	$-0.437276\pi$
$587$	9.48683			0.391564			0.195782	+	0.980647i	$0.437276\pi$
$588$		0			0
$589$	36.0000			1.48335
$590$	25.9808	+	20.1246i	1.06961	+	0.828517i
$591$	−15.8114	−	35.3553i	−0.650394	−	1.45432i
$592$	7.00000	−	3.87298i	0.287698	−	0.159179i
$593$			34.2929i			1.40824i	0.710082	+	0.704119i	$0.248658\pi$
$593$			34.2929i			1.40824i	−0.710082	+	0.704119i	$0.751342\pi$
$594$	14.4269	+	20.9730i	0.591942	+	0.860531i
$595$		0			0
$596$	8.66025	−	2.23607i	0.354738	−	0.0915929i
$597$	12.0000	+	26.8328i	0.491127	+	1.09819i
$598$		0			0
$599$	24.2487			0.990775			0.495388	−	0.868672i	$-0.335026\pi$
$599$	24.2487			0.990775			0.495388	+	0.868672i	$0.335026\pi$
$600$	−4.89849	+	0.0693504i	−0.199980	+	0.00283122i
$601$	10.9545			0.446841			0.223421	−	0.974722i	$-0.428278\pi$
$601$	10.9545			0.446841			0.223421	+	0.974722i	$0.428278\pi$
$602$		0			0
$603$	−17.3205	−	15.4919i	−0.705346	−	0.630880i
$604$	15.0000	−	3.87298i	0.610341	−	0.157589i
$605$		−	2.44949i		−	0.0995859i
$606$	−17.4904	−	4.25283i	−0.710498	−	0.172759i
$607$		−	25.4558i		−	1.03322i	−0.856221	−	0.516610i	$-0.827194\pi$
$607$		−	25.4558i		−	1.03322i	0.856221	−	0.516610i	$-0.172806\pi$
$608$	23.7171	+	3.67423i	0.961855	+	0.149010i
$609$		0			0
$610$	15.0000	+	11.6190i	0.607332	+	0.470438i
$611$		0			0
$612$	−13.4964	+	26.1122i	−0.545561	+	1.05552i
$613$	−14.0000			−0.565455			−0.282727	−	0.959200i	$-0.591239\pi$
$613$	−14.0000			−0.565455			−0.282727	+	0.959200i	$0.591239\pi$
$614$	−23.7171	−	18.3712i	−0.957144	−	0.741400i
$615$		0			0
$616$		0			0
$617$			22.3607i			0.900207i	0.892976	+	0.450104i	$0.148613\pi$
$617$			22.3607i			0.900207i	−0.892976	+	0.450104i	$0.851387\pi$
$618$		0			0
$619$			4.24264i			0.170526i	0.996358	+	0.0852631i	$0.0271731\pi$
$619$			4.24264i			0.170526i	−0.996358	+	0.0852631i	$0.972827\pi$
$620$	10.3923	+	40.2492i	0.417365	+	1.61645i
$621$		0			0
$622$	16.4317	−	21.2132i	0.658850	−	0.850572i
$623$		0			0
$624$	22.8109	−	30.3260i	0.913166	−	1.21401i
$625$	−29.0000			−1.16000
$626$	−9.48683	+	12.2474i	−0.379170	+	0.489506i
$627$	10.3923	+	23.2379i	0.415029	+	0.928032i
$628$	−2.73861	−	10.6066i	−0.109283	−	0.423249i
$629$			9.79796i			0.390670i
$630$		0			0
$631$		0			0		1.00000			$0$
$631$		0			0		−1.00000			$\pi$
$632$	−17.3205	+	40.2492i	−0.688973	+	1.60103i
$633$	−5.47723	−	12.2474i	−0.217700	−	0.486792i
$634$	−5.00000	−	3.87298i	−0.198575	−	0.153816i
$635$	18.9737			0.752947
$636$	12.1119	−	9.65926i	0.480269	−	0.383015i
$637$		0			0
$638$	17.3205	+	13.4164i	0.685725	+	0.531161i
$639$	6.92820	−	7.74597i	0.274075	−	0.306426i
$640$	2.73861	+	27.5772i	0.108253	+	1.09008i
$641$		−	31.3050i		−	1.23647i	−0.785993	−	0.618236i	$-0.787848\pi$
$641$		−	31.3050i		−	1.23647i	0.785993	−	0.618236i	$-0.212152\pi$
$642$	−10.0240	+	41.2252i	−0.395616	+	1.62703i
$643$		−	21.2132i		−	0.836567i	−0.908317	−	0.418284i	$-0.862632\pi$
$643$		−	21.2132i		−	0.836567i	0.908317	−	0.418284i	$-0.137368\pi$
$644$		0			0
$645$	30.0000	−	13.4164i	1.18125	−	0.528271i
$646$	−18.0000	+	23.2379i	−0.708201	+	0.914283i
$647$	18.9737			0.745932			0.372966	−	0.927845i	$-0.378341\pi$
$647$	18.9737			0.745932			0.372966	+	0.927845i	$0.378341\pi$
$648$	7.40192	−	24.3559i	0.290775	−	0.956791i
$649$	32.8634			1.29000
$650$	−4.74342	+	6.12372i	−0.186052	+	0.240192i
$651$		0			0
$652$	−15.0000	+	3.87298i	−0.587445	+	0.151678i
$653$		−	31.3050i		−	1.22506i	−0.790448	−	0.612529i	$-0.790152\pi$
$653$		−	31.3050i		−	1.22506i	0.790448	−	0.612529i	$-0.209848\pi$
$654$	−5.78737	+	23.8014i	−0.226304	+	0.930708i
$655$			23.2379i			0.907980i
$656$		0			0
$657$	−21.9089	+	24.4949i	−0.854748	+	0.955637i
$658$		0			0
$659$	−24.2487			−0.944596			−0.472298	−	0.881439i	$-0.656575\pi$
$659$	−24.2487			−0.944596			−0.472298	+	0.881439i	$0.656575\pi$
$660$	−22.9808	+	18.3272i	−0.894525	+	0.713384i
$661$	−38.3406			−1.49128			−0.745638	−	0.666351i	$-0.767855\pi$
$661$	−38.3406			−1.49128			−0.745638	+	0.666351i	$0.767855\pi$
$662$	−25.9808	−	20.1246i	−1.00977	−	0.782165i
$663$	18.9737	+	42.4264i	0.736876	+	1.64771i
$664$	24.6475	+	10.6066i	0.956509	+	0.411616i
$665$		0			0
$666$	−1.53590	−	8.34512i	−0.0595149	−	0.323367i
$667$		0			0
$668$	9.48683	+	36.7423i	0.367057	+	1.42160i
$669$	6.00000	+	13.4164i	0.231973	+	0.518708i
$670$	16.4317	−	21.2132i	0.634811	−	0.819538i
$671$	18.9737			0.732470
$672$		0			0
$673$	−26.0000			−1.00223			−0.501113	−	0.865382i	$-0.667076\pi$
$673$	−26.0000			−1.00223			−0.501113	+	0.865382i	$0.667076\pi$
$674$	6.92820	−	8.94427i	0.266864	−	0.344520i
$675$	−1.58114	+	4.94975i	−0.0608581	+	0.190516i
$676$	−8.50000	−	32.9204i	−0.326923	−	1.26617i
$677$			7.34847i			0.282425i	0.989979	+	0.141212i	$0.0451000\pi$
$677$			7.34847i			0.282425i	−0.989979	+	0.141212i	$0.954900\pi$
$678$	−10.6443	−	2.58819i	−0.408792	−	0.0993989i
$679$		0			0
$680$	−31.1769	−	13.4164i	−1.19558	−	0.514496i
$681$	15.0000	−	6.70820i	0.574801	−	0.257059i
$682$	32.8634	+	25.4558i	1.25840	+	0.974755i
$683$	−38.1051			−1.45805			−0.729026	−	0.684486i	$-0.760027\pi$
$683$	−38.1051			−1.45805			−0.729026	+	0.684486i	$0.760027\pi$
$684$	11.6883	−	22.6138i	0.446912	−	0.864661i
$685$	21.9089			0.837096
$686$		0			0
$687$	8.66025	−	3.87298i	0.330409	−	0.147764i
$688$	−15.0000	−	27.1109i	−0.571870	−	1.03359i
$689$		−	24.4949i		−	0.933181i
$690$		0			0
$691$		−	12.7279i		−	0.484193i	−0.970252	−	0.242096i	$-0.922165\pi$
$691$		−	12.7279i		−	0.484193i	0.970252	−	0.242096i	$-0.0778351\pi$
$692$	−4.74342	+	1.22474i	−0.180318	+	0.0465578i
$693$		0			0
$694$	−21.0000	+	27.1109i	−0.797149	+	1.02912i
$695$	10.3923			0.394203
$696$	−0.310144	−	21.9067i	−0.0117560	−	0.830372i
$697$		0			0
$698$	14.2302	−	18.3712i	0.538623	−	0.695359i
$699$	6.32456	+	14.1421i	0.239217	+	0.534905i
$700$		0			0
$701$			22.3607i			0.844551i	0.906467	+	0.422276i	$0.138769\pi$
$701$			22.3607i			0.844551i	−0.906467	+	0.422276i	$0.861231\pi$
$702$	−22.8109	−	33.1612i	−0.860942	−	1.25159i
$703$		−	8.48528i		−	0.320028i
$704$	19.0526	+	20.1246i	0.718070	+	0.758475i
$705$		0			0
$706$	16.4317	+	12.7279i	0.618414	+	0.479022i
$707$		0			0
$708$	−20.4904	−	25.6933i	−0.770076	−	0.965612i
$709$	10.0000			0.375558			0.187779	−	0.982211i	$-0.439871\pi$
$709$	10.0000			0.375558			0.187779	+	0.982211i	$0.439871\pi$
$710$	9.48683	+	7.34847i	0.356034	+	0.275783i
$711$	34.6410	+	30.9839i	1.29914	+	1.16199i
$712$	−10.9545	+	25.4558i	−0.410535	+	0.953998i
$713$		0			0
$714$		0			0
$715$			46.4758i			1.73810i
$716$	5.19615	+	20.1246i	0.194189	+	0.752092i
$717$	−10.9545	+	4.89898i	−0.409101	+	0.182956i
$718$	−24.0000	+	30.9839i	−0.895672	+	1.15631i
$719$	−37.9473			−1.41520			−0.707598	−	0.706615i	$-0.750221\pi$
$719$	−37.9473			−1.41520			−0.707598	+	0.706615i	$0.750221\pi$
$720$	28.6571	+	6.53983i	1.06799	+	0.243725i
$721$		0			0
$722$	−0.866025	+	1.11803i	−0.0322301	+	0.0416089i
$723$	34.6410	−	15.4919i	1.28831	−	0.576151i
$724$	−8.21584	−	31.8198i	−0.305339	−	1.18257i
$725$			4.47214i			0.166091i
$726$	−0.578737	+	2.38014i	−0.0214789	+	0.0883353i
$727$		−	16.9706i		−	0.629403i	−0.949191	−	0.314702i	$-0.898096\pi$
$727$		−	16.9706i		−	0.629403i	0.949191	−	0.314702i	$-0.101904\pi$
$728$		0			0
$729$	−22.0000	−	15.6525i	−0.814815	−	0.579721i
$730$	−30.0000	−	23.2379i	−1.11035	−	0.860073i
$731$	37.9473			1.40353
$732$	−11.8301	−	14.8340i	−0.437254	−	0.548281i
$733$	16.4317			0.606918			0.303459	−	0.952845i	$-0.401858\pi$
$733$	16.4317			0.606918			0.303459	+	0.952845i	$0.401858\pi$
$734$	28.4605	+	22.0454i	1.05050	+	0.813711i
$735$		0			0
$736$		0			0
$737$		−	26.8328i		−	0.988399i
$738$		0			0
$739$		−	38.7298i		−	1.42470i	−0.701824	−	0.712350i	$-0.747631\pi$
$739$		−	38.7298i		−	1.42470i	0.701824	−	0.712350i	$-0.252369\pi$
$740$	9.48683	−	2.44949i	0.348743	−	0.0900450i
$741$	−16.4317	−	36.7423i	−0.603633	−	1.34976i
$742$		0			0
$743$	13.8564			0.508342			0.254171	−	0.967159i	$-0.418197\pi$
$743$	13.8564			0.508342			0.254171	+	0.967159i	$0.418197\pi$
$744$	−0.588457	−	41.5651i	−0.0215739	−	1.52385i
$745$	10.9545			0.401340
$746$	−22.5167	+	29.0689i	−0.824394	+	1.06429i
$747$	18.9737	−	21.2132i	0.694210	−	0.776151i
$748$	−32.8634	+	8.48528i	−1.20160	+	0.310253i
$749$		0			0
$750$	23.3205	+	5.67044i	0.851545	+	0.207055i
$751$			7.74597i			0.282654i	0.989963	+	0.141327i	$0.0451370\pi$
$751$			7.74597i			0.282654i	−0.989963	+	0.141327i	$0.954863\pi$
$752$		0			0
$753$	15.0000	−	6.70820i	0.546630	−	0.244461i
$754$	−27.3861	−	21.2132i	−0.997344	−	0.772539i
$755$	18.9737			0.690522
$756$		0			0
$757$	−38.0000			−1.38113			−0.690567	−	0.723269i	$-0.742639\pi$
$757$	−38.0000			−1.38113			−0.690567	+	0.723269i	$0.742639\pi$
$758$	8.66025	+	6.70820i	0.314555	+	0.243653i
$759$		0			0
$760$	27.0000	+	11.6190i	0.979393	+	0.421464i
$761$		−	48.9898i		−	1.77588i	−0.459961	−	0.887939i	$-0.652136\pi$
$761$		−	48.9898i		−	1.77588i	0.459961	−	0.887939i	$-0.347864\pi$
$762$	−18.4365	−	4.48288i	−0.667883	−	0.162398i
$763$		0			0
$764$	−1.73205	−	6.70820i	−0.0626634	−	0.242694i
$765$	−24.0000	+	26.8328i	−0.867722	+	0.970143i
$766$		0			0
$767$	−51.9615			−1.87622
$768$	3.85454	−	27.4434i	0.139089	−	0.990280i
$769$	−21.9089			−0.790055			−0.395028	−	0.918669i	$-0.629265\pi$
$769$	−21.9089			−0.790055			−0.395028	+	0.918669i	$0.629265\pi$
$770$		0			0
$771$	−3.46410	−	7.74597i	−0.124757	−	0.278964i
$772$	8.00000	+	30.9839i	0.287926	+	1.11513i
$773$		−	2.44949i		−	0.0881020i	−0.999029	−	0.0440510i	$-0.985974\pi$
$773$		−	2.44949i		−	0.0881020i	0.999029	−	0.0440510i	$-0.0140264\pi$
$774$	−32.3205	+	5.94851i	−1.16174	+	0.213815i
$775$			8.48528i			0.304800i
$776$		0			0
$777$		0			0
$778$	35.0000	+	27.1109i	1.25481	+	0.971972i
$779$		0			0
$780$	36.3358	−	28.9778i	1.30103	−	1.03757i
$781$	12.0000			0.429394
$782$		0			0
$783$	−22.1359	−	7.07107i	−0.791074	−	0.252699i
$784$		0			0
$785$		−	13.4164i		−	0.478852i
$786$	5.49038	−	22.5800i	0.195835	−	0.805401i
$787$		−	21.2132i		−	0.756169i	−0.925771	−	0.378085i	$-0.876583\pi$
$787$		−	21.2132i		−	0.756169i	0.925771	−	0.378085i	$-0.123417\pi$
$788$	−43.3013	+	11.1803i	−1.54254	+	0.398283i
$789$	5.47723	−	2.44949i	0.194994	−	0.0872041i
$790$	−32.8634	+	42.4264i	−1.16923	+	1.50946i
$791$		0			0
$792$	26.6603	−	12.3786i	0.947331	−	0.439856i
$793$	−30.0000			−1.06533
$794$	33.2039	−	42.8661i	1.17836	−	1.52126i
$795$	17.3205	−	7.74597i	0.614295	−	0.274721i
$796$	32.8634	−	8.48528i	1.16481	−	0.300753i
$797$			41.6413i			1.47501i	0.675341	+	0.737506i	$0.263997\pi$
$797$			41.6413i			1.47501i	−0.675341	+	0.737506i	$0.736003\pi$
$798$		0			0
$799$		0			0
$800$	−0.866025	+	5.59017i	−0.0306186	+	0.197642i
$801$	21.9089	+	19.5959i	0.774113	+	0.692388i
$802$	5.00000	+	3.87298i	0.176556	+	0.136760i
$803$	−37.9473			−1.33913
$804$	−20.9785	+	16.7303i	−0.739854	+	0.590033i
$805$		0			0
$806$	−51.9615	−	40.2492i	−1.83027	−	1.41772i
$807$	−1.73205	−	3.87298i	−0.0609711	−	0.136335i
$808$	−8.21584	+	19.0919i	−0.289032	+	0.671650i
$809$		−	22.3607i		−	0.786160i	−0.919504	−	0.393080i	$-0.871410\pi$
$809$		−	22.3607i		−	0.786160i	0.919504	−	0.393080i	$-0.128590\pi$
$810$	16.2351	−	26.6162i	0.570442	−	0.935199i
$811$			12.7279i			0.446938i	0.974711	+	0.223469i	$0.0717381\pi$
$811$			12.7279i			0.446938i	−0.974711	+	0.223469i	$0.928262\pi$
$812$		0			0
$813$	6.00000	+	13.4164i	0.210429	+	0.470534i
$814$	6.00000	−	7.74597i	0.210300	−	0.271496i
$815$	−18.9737			−0.664619
$816$	27.1244	+	20.4027i	0.949542	+	0.714237i
$817$	−32.8634			−1.14974
$818$	−9.48683	+	12.2474i	−0.331699	+	0.428222i
$819$		0			0
$820$		0			0
$821$			31.3050i			1.09255i	0.837606	+	0.546275i	$0.183955\pi$
$821$			31.3050i			1.09255i	−0.837606	+	0.546275i	$0.816045\pi$
$822$	−21.2886	−	5.17638i	−0.742526	−	0.180547i
$823$		0			0		1.00000			$0$
$823$		0			0		−1.00000			$\pi$
$824$		0			0
$825$	−5.47723	+	2.44949i	−0.190693	+	0.0852803i
$826$		0			0
$827$	−17.3205			−0.602293			−0.301147	−	0.953578i	$-0.597369\pi$
$827$	−17.3205			−0.602293			−0.301147	+	0.953578i	$0.597369\pi$
$828$		0			0
$829$	49.2950			1.71209			0.856044	−	0.516904i	$-0.172915\pi$
$829$	49.2950			1.71209			0.856044	+	0.516904i	$0.172915\pi$
$830$	25.9808	+	20.1246i	0.901805	+	0.698535i
$831$	3.16228	−	1.41421i	0.109698	−	0.0490585i
$832$	−30.1247	−	31.8198i	−1.04439	−	1.10315i
$833$		0			0
$834$	−10.0981	−	2.45537i	−0.349668	−	0.0850226i
$835$			46.4758i			1.60836i
$836$	28.4605	−	7.34847i	0.984327	−	0.254152i
$837$	−42.0000	−	13.4164i	−1.45173	−	0.463739i
$838$	−24.6475	+	31.8198i	−0.851434	+	1.09920i
$839$	−18.9737			−0.655044			−0.327522	−	0.944844i	$-0.606214\pi$
$839$	−18.9737			−0.655044			−0.327522	+	0.944844i	$0.606214\pi$
$840$		0			0
$841$	9.00000			0.310345
$842$	8.66025	−	11.1803i	0.298452	−	0.385300i
$843$	6.32456	+	14.1421i	0.217829	+	0.487081i
$844$	−15.0000	+	3.87298i	−0.516321	+	0.133314i
$845$		−	41.6413i		−	1.43251i
$846$		0			0
$847$		0			0
$848$	−8.66025	−	15.6525i	−0.297394	−	0.537508i
$849$	21.0000	+	46.9574i	0.720718	+	1.61157i
$850$	−5.47723	−	4.24264i	−0.187867	−	0.145521i
$851$		0			0
$852$	−7.48203	−	9.38186i	−0.256330	−	0.321417i
$853$	−16.4317			−0.562610			−0.281305	−	0.959618i	$-0.590767\pi$
$853$	−16.4317			−0.562610			−0.281305	+	0.959618i	$0.590767\pi$
$854$		0			0
$855$	20.7846	−	23.2379i	0.710819	−	0.794719i
$856$	45.0000	+	19.3649i	1.53807	+	0.661879i
$857$		−	19.5959i		−	0.669384i	−0.942328	−	0.334692i	$-0.891368\pi$
$857$		−	19.5959i		−	0.669384i	0.942328	−	0.334692i	$-0.108632\pi$
$858$	10.9808	−	45.1600i	0.374877	−	1.54174i
$859$			46.6690i			1.59233i	0.605081	+	0.796164i	$0.293141\pi$
$859$			46.6690i			1.59233i	−0.605081	+	0.796164i	$0.706859\pi$
$860$	−9.48683	−	36.7423i	−0.323498	−	1.25290i
$861$		0			0
$862$	18.0000	−	23.2379i	0.613082	−	0.791486i
$863$	−17.3205			−0.589597			−0.294798	−	0.955559i	$-0.595253\pi$
$863$	−17.3205			−0.589597			−0.294798	+	0.955559i	$0.595253\pi$
$864$	−26.3006	−	13.1254i	−0.894765	−	0.446537i
$865$	−6.00000			−0.204006
$866$	18.9737	−	24.4949i	0.644751	−	0.832370i
$867$	−11.0680	+	4.94975i	−0.375888	+	0.168102i
$868$		0			0
$869$			53.6656i			1.82048i
$870$	6.33975	−	26.0731i	0.214938	−	0.883962i
$871$			42.4264i			1.43756i
$872$	25.9808	+	11.1803i	0.879820	+	0.378614i
$873$		0			0
$874$		0			0
$875$		0			0
$876$	23.6603	+	29.6680i	0.799406	+	1.00239i
$877$	22.0000			0.742887			0.371444	−	0.928456i	$-0.378863\pi$
$877$	22.0000			0.742887			0.371444	+	0.928456i	$0.378863\pi$
$878$	−18.9737	−	14.6969i	−0.640330	−	0.495998i
$879$	1.73205	+	3.87298i	0.0584206	+	0.130632i
$880$	16.4317	+	29.6985i	0.553912	+	1.00114i
$881$		−	44.0908i		−	1.48546i	−0.669593	−	0.742729i	$-0.733531\pi$
$881$		−	44.0908i		−	1.48546i	0.669593	−	0.742729i	$-0.266469\pi$
$882$		0			0
$883$			54.2218i			1.82471i	0.409403	+	0.912354i	$0.365737\pi$
$883$			54.2218i			1.82471i	−0.409403	+	0.912354i	$0.634263\pi$
$884$	51.9615	−	13.4164i	1.74766	−	0.451243i
$885$	−16.4317	−	36.7423i	−0.552345	−	1.23508i
$886$	27.0000	−	34.8569i	0.907083	−	1.17104i
$887$	56.9210			1.91122			0.955610	−	0.294634i	$-0.0951979\pi$
$887$	56.9210			1.91122			0.955610	+	0.294634i	$0.0951979\pi$
$888$	−9.79698	+	0.138701i	−0.328765	+	0.00465449i
$889$		0			0
$890$	−20.7846	+	26.8328i	−0.696702	+	0.899438i
$891$	−3.46410	−	30.9839i	−0.116052	−	1.03800i
$892$	16.4317	−	4.24264i	0.550173	−	0.142054i
$893$		0			0
$894$	−10.6443	−	2.58819i	−0.355999	−	0.0865620i
$895$			25.4558i			0.850895i
$896$		0			0
$897$		0			0
$898$	40.0000	+	30.9839i	1.33482	+	1.03395i
$899$	−37.9473			−1.26561
$900$	5.33013	+	2.75495i	0.177671	+	0.0918316i
$901$	21.9089			0.729891
$902$		0			0
$903$		0			0
$904$	−5.00000	+	11.6190i	−0.166298	+	0.386441i
$905$		−	40.2492i		−	1.33793i
$906$	−18.4365	−	4.48288i	−0.612511	−	0.148934i
$907$			7.74597i			0.257201i	0.991697	+	0.128600i	$0.0410484\pi$
$907$			7.74597i			0.257201i	−0.991697	+	0.128600i	$0.958952\pi$
$908$	−4.74342	−	18.3712i	−0.157416	−	0.609669i
$909$	16.4317	+	14.6969i	0.545004	+	0.487467i
$910$		0			0
$911$	20.7846			0.688625			0.344312	−	0.938855i	$-0.388112\pi$
$911$	20.7846			0.688625			0.344312	+	0.938855i	$0.388112\pi$
$912$	−23.4904	−	17.6692i	−0.777844	−	0.585087i
$913$	32.8634			1.08762
$914$	24.2487	−	31.3050i	0.802076	−	1.03548i
$915$	−9.48683	−	21.2132i	−0.313625	−	0.701287i
$916$	−2.73861	−	10.6066i	−0.0904863	−	0.350452i
$917$		0			0
$918$	29.6603	−	20.4027i	0.978934	−	0.673389i
$919$			30.9839i			1.02206i	0.859562	+	0.511032i	$0.170737\pi$
$919$			30.9839i			1.02206i	−0.859562	+	0.511032i	$0.829263\pi$
$920$		0			0
$921$	15.0000	+	33.5410i	0.494267	+	1.10521i
$922$	41.0792	+	31.8198i	1.35287	+	1.04793i
$923$	−18.9737			−0.624526
$924$		0			0
$925$	2.00000			0.0657596
$926$	−17.3205	−	13.4164i	−0.569187	−	0.440891i
$927$		0			0
$928$	−25.0000	−	3.87298i	−0.820665	−	0.127137i
$929$		−	24.4949i		−	0.803652i	−0.915716	−	0.401826i	$-0.868376\pi$
$929$		−	24.4949i		−	0.803652i	0.915716	−	0.401826i	$-0.131624\pi$
$930$	12.0288	−	49.4703i	0.394441	−	1.62219i
$931$		0			0
$932$	17.3205	−	4.47214i	0.567352	−	0.146490i
$933$	−30.0000	+	13.4164i	−0.982156	+	0.439233i
$934$	24.6475	−	31.8198i	0.806491	−	1.04118i
$935$	−41.5692			−1.35946
$936$	−42.1536	+	19.5724i	−1.37783	+	0.639742i
$937$	−10.9545			−0.357866			−0.178933	−	0.983861i	$-0.557265\pi$
$937$	−10.9545			−0.357866			−0.178933	+	0.983861i	$0.557265\pi$
$938$		0			0
$939$	17.3205	−	7.74597i	0.565233	−	0.252780i
$940$		0			0
$941$		−	12.2474i		−	0.399255i	−0.979872	−	0.199628i	$-0.936027\pi$
$941$		−	12.2474i		−	0.399255i	0.979872	−	0.199628i	$-0.0639733\pi$
$942$	−3.16987	+	13.0366i	−0.103280	+	0.424754i
$943$		0			0
$944$	−33.2039	+	18.3712i	−1.08070	+	0.597931i
$945$		0			0
$946$	−30.0000	−	23.2379i	−0.975384	−	0.755529i
$947$	−10.3923			−0.337705			−0.168852	−	0.985641i	$-0.554006\pi$
$947$	−10.3923			−0.337705			−0.168852	+	0.985641i	$0.554006\pi$
$948$	41.9569	−	33.4607i	1.36270	−	1.08675i
$949$	60.0000			1.94768
$950$	4.74342	+	3.67423i	0.153897	+	0.119208i
$951$	3.16228	+	7.07107i	0.102544	+	0.229295i
$952$		0			0
$953$		−	8.94427i		−	0.289733i	−0.989451	−	0.144867i	$-0.953725\pi$
$953$		−	8.94427i		−	0.289733i	0.989451	−	0.144867i	$-0.0462753\pi$
$954$	−18.6603	+	3.43437i	−0.604148	+	0.111192i
$955$		−	8.48528i		−	0.274577i
$956$	3.46410	+	13.4164i	0.112037	+	0.433918i
$957$	−10.9545	−	24.4949i	−0.354107	−	0.791808i
$958$	32.8634	−	42.4264i	1.06177	−	1.37073i
$959$		0			0
$960$	12.9737	−	31.3637i	0.418725	−	1.01226i
$961$	−41.0000			−1.32258
$962$	−9.48683	+	12.2474i	−0.305868	+	0.394874i
$963$	34.6410	−	38.7298i	1.11629	−	1.24805i
$964$	−10.9545	−	42.4264i	−0.352819	−	1.36646i
$965$			39.1918i			1.26163i
$966$		0			0
$967$			23.2379i			0.747280i	0.927574	+	0.373640i	$0.121891\pi$
$967$			23.2379i			0.747280i	−0.927574	+	0.373640i	$0.878109\pi$
$968$	2.59808	+	1.11803i	0.0835053	+	0.0359350i
$969$	32.8634	−	14.6969i	1.05572	−	0.472134i
$970$		0			0
$971$	47.4342			1.52223			0.761117	−	0.648614i	$-0.224651\pi$
$971$	47.4342			1.52223			0.761117	+	0.648614i	$0.224651\pi$
$972$	−22.0640	+	22.0268i	−0.707702	+	0.706511i
$973$		0			0
$974$	8.66025	+	6.70820i	0.277492	+	0.214945i
$975$	8.66025	−	3.87298i	0.277350	−	0.124035i
$976$	−19.1703	+	10.6066i	−0.613626	+	0.339509i
$977$			35.7771i			1.14461i	0.820041	+	0.572305i	$0.193951\pi$
$977$			35.7771i			1.14461i	−0.820041	+	0.572305i	$0.806049\pi$
$978$	18.4365	+	4.48288i	0.589534	+	0.143347i
$979$			33.9411i			1.08476i
$980$		0			0
$981$	20.0000	−	22.3607i	0.638551	−	0.713922i
$982$	−27.0000	+	34.8569i	−0.861605	+	1.11233i
$983$	18.9737			0.605166			0.302583	−	0.953123i	$-0.402151\pi$
$983$	18.9737			0.605166			0.302583	+	0.953123i	$0.402151\pi$
$984$		0			0
$985$	−54.7723			−1.74519
$986$	18.9737	−	24.4949i	0.604245	−	0.780076i
$987$		0			0
$988$	−45.0000	+	11.6190i	−1.43164	+	0.369648i
$989$		0			0
$990$	35.4053	−	6.51626i	1.12526	−	0.207100i
$991$		−	15.4919i		−	0.492117i	−0.969255	−	0.246059i	$-0.920864\pi$
$991$		−	15.4919i		−	0.492117i	0.969255	−	0.246059i	$-0.0791356\pi$
$992$	−47.4342	−	7.34847i	−1.50604	−	0.233314i
$993$	16.4317	+	36.7423i	0.521443	+	1.16598i
$994$		0			0
$995$	41.5692			1.31783
$996$	−20.4904	−	25.6933i	−0.649263	−	0.814123i
$997$	5.47723			0.173465			0.0867327	−	0.996232i	$-0.472357\pi$
$997$	5.47723			0.173465			0.0867327	+	0.996232i	$0.472357\pi$
$998$	25.9808	+	20.1246i	0.822407	+	0.637033i
$999$	−3.16228	+	9.89949i	−0.100050	+	0.313206i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.2.e.b.491.4	yes	8
3.2	odd	2	inner	588.2.e.b.491.5	yes	8
4.3	odd	2	inner	588.2.e.b.491.7	yes	8
7.2	even	3		588.2.n.c.263.7		16
7.3	odd	6		588.2.n.c.275.4		16
7.4	even	3		588.2.n.c.275.3		16
7.5	odd	6		588.2.n.c.263.8		16
7.6	odd	2	inner	588.2.e.b.491.3	yes	8
12.11	even	2	inner	588.2.e.b.491.2	yes	8
21.2	odd	6		588.2.n.c.263.2		16
21.5	even	6		588.2.n.c.263.1		16
21.11	odd	6		588.2.n.c.275.6		16
21.17	even	6		588.2.n.c.275.5		16
21.20	even	2	inner	588.2.e.b.491.6	yes	8
28.3	even	6		588.2.n.c.275.1		16
28.11	odd	6		588.2.n.c.275.2		16
28.19	even	6		588.2.n.c.263.5		16
28.23	odd	6		588.2.n.c.263.6		16
28.27	even	2	inner	588.2.e.b.491.8	yes	8
84.11	even	6		588.2.n.c.275.7		16
84.23	even	6		588.2.n.c.263.3		16
84.47	odd	6		588.2.n.c.263.4		16
84.59	odd	6		588.2.n.c.275.8		16
84.83	odd	2	inner	588.2.e.b.491.1	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
588.2.e.b.491.1	✓	8	84.83	odd	2	inner
588.2.e.b.491.2	yes	8	12.11	even	2	inner
588.2.e.b.491.3	yes	8	7.6	odd	2	inner
588.2.e.b.491.4	yes	8	1.1	even	1	trivial
588.2.e.b.491.5	yes	8	3.2	odd	2	inner
588.2.e.b.491.6	yes	8	21.20	even	2	inner
588.2.e.b.491.7	yes	8	4.3	odd	2	inner
588.2.e.b.491.8	yes	8	28.27	even	2	inner
588.2.n.c.263.1		16	21.5	even	6
588.2.n.c.263.2		16	21.2	odd	6
588.2.n.c.263.3		16	84.23	even	6
588.2.n.c.263.4		16	84.47	odd	6
588.2.n.c.263.5		16	28.19	even	6
588.2.n.c.263.6		16	28.23	odd	6
588.2.n.c.263.7		16	7.2	even	3
588.2.n.c.263.8		16	7.5	odd	6
588.2.n.c.275.1		16	28.3	even	6
588.2.n.c.275.2		16	28.11	odd	6
588.2.n.c.275.3		16	7.4	even	3
588.2.n.c.275.4		16	7.3	odd	6
588.2.n.c.275.5		16	21.17	even	6
588.2.n.c.275.6		16	21.11	odd	6
588.2.n.c.275.7		16	84.11	even	6
588.2.n.c.275.8		16	84.59	odd	6

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:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	588.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 1.11803i) q^{2} +(1.58114 - 0.707107i) q^{3} +(-0.500000 - 1.93649i) q^{4} -2.44949i q^{5} +(-0.578737 + 2.38014i) q^{6} +(2.59808 + 1.11803i) q^{8} +(2.00000 - 2.23607i) q^{9} +(2.73861 + 2.12132i) q^{10} +3.46410 q^{11} +(-2.15988 - 2.70831i) q^{12} -5.47723 q^{13} +(-1.73205 - 3.87298i) q^{15} +(-3.50000 + 1.93649i) q^{16} -4.89898i q^{17} +(0.767949 + 4.17256i) q^{18} +4.24264i q^{19} +(-4.74342 + 1.22474i) q^{20} +(-3.00000 + 3.87298i) q^{22} +(4.89849 - 0.0693504i) q^{24} -1.00000 q^{25} +(4.74342 - 6.12372i) q^{26} +(1.58114 - 4.94975i) q^{27} -4.47214i q^{29} +(5.83013 + 1.41761i) q^{30} -8.48528i q^{31} +(0.866025 - 5.59017i) q^{32} +(5.47723 - 2.44949i) q^{33} +(5.47723 + 4.24264i) q^{34} +(-5.33013 - 2.75495i) q^{36} -2.00000 q^{37} +(-4.74342 - 3.67423i) q^{38} +(-8.66025 + 3.87298i) q^{39} +(2.73861 - 6.36396i) q^{40} +7.74597i q^{43} +(-1.73205 - 6.70820i) q^{44} +(-5.47723 - 4.89898i) q^{45} +(-4.16468 + 5.53674i) q^{48} +(0.866025 - 1.11803i) q^{50} +(-3.46410 - 7.74597i) q^{51} +(2.73861 + 10.6066i) q^{52} +4.47214i q^{53} +(4.16468 + 6.05437i) q^{54} -8.48528i q^{55} +(3.00000 + 6.70820i) q^{57} +(5.00000 + 3.87298i) q^{58} +9.48683 q^{59} +(-6.63397 + 5.29059i) q^{60} +5.47723 q^{61} +(9.48683 + 7.34847i) q^{62} +(5.50000 + 5.80948i) q^{64} +13.4164i q^{65} +(-2.00480 + 8.24504i) q^{66} -7.74597i q^{67} +(-9.48683 + 2.44949i) q^{68} +3.46410 q^{71} +(7.69615 - 3.57341i) q^{72} -10.9545 q^{73} +(1.73205 - 2.23607i) q^{74} +(-1.58114 + 0.707107i) q^{75} +(8.21584 - 2.12132i) q^{76} +(3.16987 - 13.0366i) q^{78} +15.4919i q^{79} +(4.74342 + 8.57321i) q^{80} +(-1.00000 - 8.94427i) q^{81} +9.48683 q^{83} -12.0000 q^{85} +(-8.66025 - 6.70820i) q^{86} +(-3.16228 - 7.07107i) q^{87} +(9.00000 + 3.87298i) q^{88} +9.79796i q^{89} +(10.2206 - 1.88108i) q^{90} +(-6.00000 - 13.4164i) q^{93} +10.3923 q^{95} +(-2.58354 - 9.45121i) q^{96} +(6.92820 - 7.74597i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{4} + 16 q^{9} - 28 q^{16} + 20 q^{18} - 24 q^{22} - 8 q^{25} + 12 q^{30} - 8 q^{36} - 16 q^{37} + 24 q^{57} + 40 q^{58} - 60 q^{60} + 44 q^{64} + 20 q^{72} + 60 q^{78} - 8 q^{81} - 96 q^{85}+ \cdots - 48 q^{93}+O(q^{100}) \) 8 * q - 4 * q^4 + 16 * q^9 - 28 * q^16 + 20 * q^18 - 24 * q^22 - 8 * q^25 + 12 * q^30 - 8 * q^36 - 16 * q^37 + 24 * q^57 + 40 * q^58 - 60 * q^60 + 44 * q^64 + 20 * q^72 + 60 * q^78 - 8 * q^81 - 96 * q^85 + 72 * q^88 - 48 * q^93

Introduction

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