LMFDB - Embedded newform 588.2.e.b.491.5

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			491.5
Root			$0.578737 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	588.491
Dual form			588.2.e.b.491.7

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 1.11803i) q^{2} +(-1.58114 - 0.707107i) q^{3} +(-0.500000 - 1.93649i) q^{4} +2.44949i q^{5} +(-2.15988 + 1.15539i) q^{6} +(-2.59808 - 1.11803i) q^{8} +(2.00000 + 2.23607i) q^{9} +(2.73861 + 2.12132i) q^{10} -3.46410 q^{11} +(-0.578737 + 3.41542i) q^{12} -5.47723 q^{13} +(1.73205 - 3.87298i) q^{15} +(-3.50000 + 1.93649i) q^{16} +4.89898i q^{17} +(4.23205 - 0.299576i) q^{18} +4.24264i q^{19} +(4.74342 - 1.22474i) q^{20} +(-3.00000 + 3.87298i) q^{22} +(3.31735 + 3.60488i) q^{24} -1.00000 q^{25} +(-4.74342 + 6.12372i) q^{26} +(-1.58114 - 4.94975i) q^{27} +4.47214i q^{29} +(-2.83013 - 5.29059i) q^{30} -8.48528i q^{31} +(-0.866025 + 5.59017i) q^{32} +(5.47723 + 2.44949i) q^{33} +(5.47723 + 4.24264i) q^{34} +(3.33013 - 4.99102i) q^{36} -2.00000 q^{37} +(4.74342 + 3.67423i) q^{38} +(8.66025 + 3.87298i) q^{39} +(2.73861 - 6.36396i) q^{40} +7.74597i q^{43} +(1.73205 + 6.70820i) q^{44} +(-5.47723 + 4.89898i) q^{45} +(6.90329 - 0.586988i) q^{48} +(-0.866025 + 1.11803i) q^{50} +(3.46410 - 7.74597i) q^{51} +(2.73861 + 10.6066i) q^{52} -4.47214i q^{53} +(-6.90329 - 2.51884i) q^{54} -8.48528i q^{55} +(3.00000 - 6.70820i) q^{57} +(5.00000 + 3.87298i) q^{58} -9.48683 q^{59} +(-8.36603 - 1.41761i) q^{60} +5.47723 q^{61} +(-9.48683 - 7.34847i) q^{62} +(5.50000 + 5.80948i) q^{64} -13.4164i q^{65} +(7.48203 - 4.00240i) q^{66} -7.74597i q^{67} +(9.48683 - 2.44949i) q^{68} -3.46410 q^{71} +(-2.69615 - 8.04554i) q^{72} -10.9545 q^{73} +(-1.73205 + 2.23607i) q^{74} +(1.58114 + 0.707107i) q^{75} +(8.21584 - 2.12132i) q^{76} +(11.8301 - 6.32836i) q^{78} +15.4919i q^{79} +(-4.74342 - 8.57321i) q^{80} +(-1.00000 + 8.94427i) q^{81} -9.48683 q^{83} -12.0000 q^{85} +(8.66025 + 6.70820i) q^{86} +(3.16228 - 7.07107i) q^{87} +(9.00000 + 3.87298i) q^{88} -9.79796i q^{89} +(0.733809 + 10.3664i) q^{90} +(-6.00000 + 13.4164i) q^{93} -10.3923 q^{95} +(5.32215 - 8.22646i) q^{96} +(-6.92820 - 7.74597i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$8 q - 4 q^{4} + 16 q^{9} - 28 q^{16} + 20 q^{18} - 24 q^{22} - 8 q^{25} + 12 q^{30} - 8 q^{36} - 16 q^{37} + 24 q^{57} + 40 q^{58} - 60 q^{60} + 44 q^{64} + 20 q^{72} + 60 q^{78} - 8 q^{81} - 96 q^{85}+ \cdots - 48 q^{93}+O(q^{100})$ 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	$0.184505\pi$
$5$			2.44949i			1.09545i	−0.836660	+	0.547723i	$0.815495\pi$
$6$	−2.15988	+	1.15539i	−0.881766	+	0.471688i
$7$		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	$-0.674901\pi$
$11$	−3.46410			−1.04447			−0.522233	+	0.852803i	$0.674901\pi$
$12$	−0.578737	+	3.41542i	−0.167067	+	0.985946i
$13$	−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	$0.202487\pi$
$17$			4.89898i			1.18818i	−0.804400	+	0.594089i	$0.797513\pi$
$18$	4.23205	−	0.299576i	0.997504	−	0.0706108i
$19$			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	$0.5\pi$
$24$	3.31735	+	3.60488i	0.677151	+	0.735844i
$25$	−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	$0.136298\pi$
$29$			4.47214i			0.830455i	−0.909718	+	0.415227i	$0.863702\pi$
$30$	−2.83013	−	5.29059i	−0.516708	−	0.965926i
$31$		−	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
$36$	3.33013	−	4.99102i	0.555021	−	0.831836i
$37$	−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	$0.5\pi$
$48$	6.90329	−	0.586988i	0.996404	−	0.0847245i
$49$		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	$-0.900625\pi$
$53$		−	4.47214i		−	0.614295i	0.951662	−	0.307148i	$-0.0993745\pi$
$54$	−6.90329	−	2.51884i	−0.939419	−	0.342771i
$55$		−	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	$-0.711871\pi$
$59$	−9.48683			−1.23508			−0.617540	+	0.786539i	$0.711871\pi$
$60$	−8.36603	−	1.41761i	−1.08005	−	0.183013i
$61$	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
$66$	7.48203	−	4.00240i	0.920974	−	0.492662i
$67$		−	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	$-0.565900\pi$
$71$	−3.46410			−0.411113			−0.205557	+	0.978645i	$0.565900\pi$
$72$	−2.69615	−	8.04554i	−0.317745	−	0.948176i
$73$	−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
$78$	11.8301	−	6.32836i	1.33950	−	0.716545i
$79$			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	$-0.674313\pi$
$83$	−9.48683			−1.04132			−0.520658	+	0.853766i	$0.674313\pi$
$84$		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	$-0.826196\pi$
$89$		−	9.79796i		−	1.03858i	0.854598	−	0.519291i	$-0.173804\pi$
$90$	0.733809	+	10.3664i	0.0773503	+	1.09271i
$91$		0			0
$92$		0			0
$93$	−6.00000	+	13.4164i	−0.622171	+	1.39122i
$94$		0			0
$95$	−10.3923			−1.06623
$96$	5.32215	−	8.22646i	0.543190	−	0.839610i
$97$		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	$-0.880864\pi$
$101$		−	7.34847i		−	0.731200i	0.930772	−	0.365600i	$-0.119136\pi$
$102$	−5.66025	−	10.5812i	−0.560449	−	1.04769i
$103$		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	$-0.815820\pi$
$107$	−17.3205			−1.67444			−0.837218	+	0.546869i	$0.815820\pi$
$108$	−8.79458	+	5.53674i	−0.846258	+	0.532773i
$109$	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	$-0.932539\pi$
$113$		−	4.47214i		−	0.420703i	0.977626	−	0.210352i	$-0.0674609\pi$
$114$	−4.90192	−	9.16358i	−0.459107	−	0.858248i
$115$		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
$120$	−8.83013	+	8.12581i	−0.806077	+	0.741782i
$121$	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	$-0.363979\pi$
$131$	9.48683			0.828868			0.414434	+	0.910079i	$0.363979\pi$
$132$	2.00480	−	11.8313i	0.174496	−	1.02979i
$133$		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	$-0.875208\pi$
$137$		−	8.94427i		−	0.764161i	0.924129	−	0.382080i	$-0.124792\pi$
$138$		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
$144$	−11.3301	−	3.95325i	−0.944177	−	0.329438i
$145$	−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	$-0.941359\pi$
$149$		−	4.47214i		−	0.366372i	0.983078	−	0.183186i	$-0.0586410\pi$
$150$	2.15988	−	1.15539i	0.176353	−	0.0943376i
$151$			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
$156$	3.16987	−	18.7070i	0.253793	−	1.49776i
$157$	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
$162$	9.13397	+	8.86400i	0.717633	+	0.696422i
$163$		−	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	$-0.237598\pi$
$167$	18.9737			1.46823			0.734113	+	0.679027i	$0.237598\pi$
$168$		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	$0.0296826\pi$
$173$			2.44949i			0.186231i	−0.995655	+	0.0931156i	$0.970317\pi$
$174$	−5.16708	−	9.65926i	−0.391715	−	0.732266i
$175$		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	$-0.373035\pi$
$179$	10.3923			0.776757			0.388379	+	0.921500i	$0.373035\pi$
$180$	12.2254	+	8.15711i	0.911231	+	0.607995i
$181$	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
$186$	9.80385	+	18.3272i	0.718853	+	1.34381i
$187$		−	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	$-0.539998\pi$
$191$	−3.46410			−0.250654			−0.125327	+	0.992116i	$0.539998\pi$
$192$	−4.58834	−	13.0747i	−0.331135	−	0.943583i
$193$	−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	$0.293352\pi$
$197$			22.3607i			1.59313i	−0.604551	+	0.796566i	$0.706648\pi$
$198$	−14.6603	+	1.03776i	−1.04186	+	0.0737506i
$199$			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
$204$	−16.7321	−	2.83522i	−1.17148	−	0.198505i
$205$		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
$216$	−1.42607	+	14.6276i	−0.0970316	+	0.995281i
$217$		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
$222$	4.31975	−	2.31079i	0.289923	−	0.155090i
$223$			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	$-0.601948\pi$
$227$	−9.48683			−0.629663			−0.314832	+	0.949148i	$0.601948\pi$
$228$	−14.4904	−	2.45537i	−0.959649	−	0.162611i
$229$	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	$-0.905353\pi$
$233$		−	8.94427i		−	0.585959i	0.956119	−	0.292979i	$-0.0946467\pi$
$234$	−23.1799	+	1.64085i	−1.51532	+	0.107266i
$235$		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	$-0.428064\pi$
$239$	6.92820			0.448148			0.224074	+	0.974572i	$0.428064\pi$
$240$	1.43782	+	16.9095i	0.0928110	+	1.09151i
$241$	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	$-0.596787\pi$
$251$	−9.48683			−0.598804			−0.299402	+	0.954127i	$0.596787\pi$
$252$		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	$0.0488274\pi$
$257$			4.89898i			0.305590i	−0.988258	+	0.152795i	$0.951173\pi$
$258$	−8.94965	−	16.7303i	−0.557181	−	1.04158i
$259$		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	$-0.534061\pi$
$263$	−3.46410			−0.213606			−0.106803	+	0.994280i	$0.534061\pi$
$264$	−11.4916	−	12.4877i	−0.707261	−	0.768564i
$265$	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	$0.0237916\pi$
$269$			2.44949i			0.149348i	−0.997208	+	0.0746740i	$0.976208\pi$
$270$	6.16987	−	16.9095i	0.375487	−	1.02908i
$271$			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	$-0.914039\pi$
$281$		−	8.94427i		−	0.533571i	0.963756	−	0.266785i	$-0.0859614\pi$
$282$		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
$288$	−14.2321	+	9.24385i	−0.838632	+	0.544699i
$289$	−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	$-0.977205\pi$
$293$		−	2.44949i		−	0.143101i	0.997437	−	0.0715504i	$-0.0227947\pi$
$294$		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
$300$	0.578737	−	3.41542i	0.0334134	−	0.197189i
$301$		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
$306$	1.46762	+	20.7327i	0.0838981	+	1.18521i
$307$			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	$-0.319199\pi$
$311$	18.9737			1.07590			0.537949	+	0.842977i	$0.319199\pi$
$312$	−18.1699	−	19.7448i	−1.02867	−	1.11783i
$313$	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	$-0.959918\pi$
$317$		−	4.47214i		−	0.251180i	0.992082	−	0.125590i	$-0.0400824\pi$
$318$	5.16708	+	9.65926i	0.289756	+	0.541664i
$319$		−	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
$324$	17.8205	−	2.53564i	0.990028	−	0.140869i
$325$	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
$330$	9.80385	+	18.3272i	0.539684	+	1.00888i
$331$			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
$342$	1.27099	+	17.9551i	0.0687275	+	0.970899i
$343$		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	$-0.725596\pi$
$347$	−24.2487			−1.30174			−0.650870	+	0.759190i	$0.725596\pi$
$348$	−15.2742	−	2.58819i	−0.818783	−	0.138742i
$349$	−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	$0.127912\pi$
$353$			14.6969i			0.782239i	−0.920340	+	0.391120i	$0.872088\pi$
$354$	20.4904	−	10.9610i	1.08905	−	0.582572i
$355$		−	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	$-0.761092\pi$
$359$	−27.7128			−1.46263			−0.731313	+	0.682042i	$0.761092\pi$
$360$	19.7075	−	6.60420i	1.03868	−	0.348072i
$361$	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
$366$	−11.8301	+	6.32836i	−0.618371	+	0.330788i
$367$		−	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
$372$	28.9808	+	4.91075i	1.50258	+	0.254610i
$373$	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	$0.5\pi$
$384$	−18.5916	−	6.19307i	−0.948746	−	0.316039i
$385$		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	$0.291802\pi$
$389$			31.3050i			1.58722i	−0.608424	+	0.793612i	$0.708198\pi$
$390$	15.5012	+	28.9778i	0.784936	+	1.46735i
$391$		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
$396$	−11.5359	+	17.2894i	−0.579701	+	0.868825i
$397$	−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	$0.0356180\pi$
$401$			4.47214i			0.223328i	−0.993746	+	0.111664i	$0.964382\pi$
$402$	8.94965	+	16.7303i	0.446368	+	0.834433i
$403$			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
$408$	−17.6603	+	16.2516i	−0.874313	+	0.804575i
$409$	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	$-0.744681\pi$
$419$	−28.4605			−1.39039			−0.695193	+	0.718823i	$0.744681\pi$
$420$		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
$426$	7.48203	−	4.00240i	0.362506	−	0.193917i
$427$		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	$-0.333120\pi$
$431$	20.7846			1.00116			0.500580	+	0.865690i	$0.333120\pi$
$432$	15.1191	+	14.2623i	0.727420	+	0.686193i
$433$	−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
$438$	23.6603	−	12.6567i	1.13053	−	0.604761i
$439$			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	$-0.234527\pi$
$443$	31.1769			1.48126			0.740630	+	0.671913i	$0.234527\pi$
$444$	1.15747	−	6.83083i	0.0549313	−	0.324177i
$445$	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	$0.319931\pi$
$449$			35.7771i			1.68843i	−0.536009	+	0.844213i	$0.680069\pi$
$450$	−4.23205	+	0.299576i	−0.199501	+	0.0141222i
$451$		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
$456$	−15.2942	+	14.0743i	−0.716218	+	0.659091i
$457$	−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	$0.326831\pi$
$461$			36.7423i			1.71126i	−0.517587	+	0.855631i	$0.673169\pi$
$462$		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	$-0.271192\pi$
$467$	28.4605			1.31699			0.658497	+	0.752583i	$0.271192\pi$
$468$	−18.2399	+	27.3369i	−0.843138	+	1.26365i
$469$		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
$474$	−17.8993	−	33.4607i	−0.822142	−	1.53690i
$475$		−	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	$-0.166091\pi$
$479$	37.9473			1.73386			0.866929	+	0.498432i	$0.166091\pi$
$480$	20.1506	+	13.0366i	0.919746	+	0.595035i
$481$	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
$486$	−8.17429	−	20.4739i	−0.370793	−	0.928715i
$487$		−	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	$-0.748379\pi$
$491$	−31.1769			−1.40699			−0.703497	+	0.710698i	$0.748379\pi$
$492$		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
$498$	20.4904	−	10.9610i	0.918196	−	0.491176i
$499$		−	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	$-0.360978\pi$
$503$	18.9737			0.845994			0.422997	+	0.906131i	$0.360978\pi$
$504$		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	$-0.697128\pi$
$509$		−	36.7423i		−	1.62858i	0.580461	−	0.814288i	$-0.302872\pi$
$510$	25.9185	−	13.8647i	1.14769	−	0.613941i
$511$		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
$516$	−26.4557	−	4.48288i	−1.16465	−	0.197348i
$517$		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	$-0.777322\pi$
$521$		−	29.3939i		−	1.28777i	0.765123	−	0.643885i	$-0.222678\pi$
$522$	1.33975	+	18.9263i	0.0586391	+	0.828382i
$523$			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
$528$	−23.9137	+	2.03339i	−1.04071	+	0.0884918i
$529$	−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
$534$	11.3205	+	21.1624i	0.489886	+	0.915786i
$535$		−	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
$540$	−13.5622	−	21.5422i	−0.583623	−	0.927030i
$541$	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	$0.157091\pi$
$557$			22.3607i			0.947452i	−0.880672	+	0.473726i	$0.842909\pi$
$558$	−2.54199	−	35.9101i	−0.107611	−	1.52020i
$559$		−	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	$-0.564065\pi$
$563$	−9.48683			−0.399822			−0.199911	+	0.979814i	$0.564065\pi$
$564$		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	$0.227831\pi$
$569$			31.3050i			1.31237i	−0.754599	+	0.656186i	$0.772169\pi$
$570$	22.4461	−	12.0072i	0.940163	−	0.502927i
$571$		−	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
$576$	−1.99038	+	23.9173i	−0.0829325	+	0.996555i
$577$	−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	$-0.562724\pi$
$587$	−9.48683			−0.391564			−0.195782	+	0.980647i	$0.562724\pi$
$588$		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	$-0.751342\pi$
$593$		−	34.2929i		−	1.40824i	0.710082	−	0.704119i	$-0.248658\pi$
$594$	23.9137	+	8.72552i	0.981191	+	0.358012i
$595$		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	$-0.664974\pi$
$599$	−24.2487			−0.990775			−0.495388	+	0.868672i	$0.664974\pi$
$600$	−3.31735	−	3.60488i	−0.135430	−	0.147169i
$601$	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
$606$	8.49038	+	15.8718i	0.344898	+	0.644747i
$607$		−	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
$612$	24.4509	+	16.3142i	0.988369	+	0.659463i
$613$	−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	$-0.851387\pi$
$617$		−	22.3607i		−	0.900207i	0.892976	−	0.450104i	$-0.148613\pi$
$618$		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
$624$	−37.8109	+	3.21507i	−1.51365	+	0.128706i
$625$	−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
$636$	15.2742	+	2.58819i	0.605662	+	0.102628i
$637$		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	$0.212152\pi$
$641$			31.3050i			1.23647i	−0.785993	+	0.618236i	$0.787848\pi$
$642$	37.4101	−	20.0120i	1.47646	−	0.789811i
$643$		−	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	$-0.621659\pi$
$647$	−18.9737			−0.745932			−0.372966	+	0.927845i	$0.621659\pi$
$648$	12.5981	−	22.1199i	0.494899	−	0.868950i
$649$	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	$0.209848\pi$
$653$			31.3050i			1.22506i	−0.790448	+	0.612529i	$0.790152\pi$
$654$	−21.5988	+	11.5539i	−0.844578	+	0.451795i
$655$			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	$-0.343425\pi$
$659$	24.2487			0.944596			0.472298	+	0.881439i	$0.343425\pi$
$660$	28.9808	+	4.91075i	1.12807	+	0.191151i
$661$	−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
$666$	−8.46410	+	0.599153i	−0.327977	+	0.0232167i
$667$		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	$-0.954900\pi$
$677$		−	7.34847i		−	0.282425i	0.989979	−	0.141212i	$-0.0451000\pi$
$678$	5.16708	+	9.65926i	0.198441	+	0.370962i
$679$		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	$-0.239973\pi$
$683$	38.1051			1.45805			0.729026	+	0.684486i	$0.239973\pi$
$684$	21.1751	+	14.1285i	0.809650	+	0.540218i
$685$	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
$696$	−16.1215	+	14.8356i	−0.611085	+	0.562343i
$697$		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	$-0.861231\pi$
$701$		−	22.3607i		−	0.844551i	0.906467	−	0.422276i	$-0.138769\pi$
$702$	37.8109	+	13.7963i	1.42708	+	0.520706i
$703$		−	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
$708$	5.49038	−	32.4015i	0.206341	−	1.21772i
$709$	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	$-0.249779\pi$
$719$	37.9473			1.41520			0.707598	+	0.706615i	$0.249779\pi$
$720$	9.68346	−	27.7530i	0.360881	−	1.03429i
$721$		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
$726$	−2.15988	+	1.15539i	−0.0801605	+	0.0428807i
$727$		−	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
$732$	−3.16987	+	18.7070i	−0.117162	+	0.691431i
$733$	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	$-0.581803\pi$
$743$	−13.8564			−0.508342			−0.254171	+	0.967159i	$0.581803\pi$
$744$	30.5885	−	28.1486i	1.12143	−	1.03198i
$745$	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
$750$	−11.3205	−	21.1624i	−0.413367	−	0.772741i
$751$			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	$0.347864\pi$
$761$			48.9898i			1.77588i	−0.459961	+	0.887939i	$0.652136\pi$
$762$	−8.94965	−	16.7303i	−0.324212	−	0.606076i
$763$		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
$768$	−23.0248	+	15.4226i	−0.830837	+	0.556516i
$769$	−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	$0.0140264\pi$
$773$			2.44949i			0.0881020i	−0.999029	+	0.0440510i	$0.985974\pi$
$774$	2.32051	+	32.7813i	0.0834089	+	1.17830i
$775$			8.48528i			0.304800i
$776$		0			0
$777$		0			0
$778$	35.0000	+	27.1109i	1.25481	+	0.971972i
$779$		0			0
$780$	45.8226	+	7.76457i	1.64071	+	0.278016i
$781$	12.0000			0.429394
$782$		0			0
$783$	22.1359	−	7.07107i	0.791074	−	0.252699i
$784$		0			0
$785$			13.4164i			0.478852i
$786$	−20.4904	+	10.9610i	−0.730868	+	0.390967i
$787$		−	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
$792$	9.33975	+	27.8706i	0.331873	+	0.990338i
$793$	−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	$-0.736003\pi$
$797$		−	41.6413i		−	1.47501i	0.675341	−	0.737506i	$-0.263997\pi$
$798$		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
$804$	26.4557	+	4.48288i	0.933020	+	0.158099i
$805$		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	$0.128590\pi$
$809$			22.3607i			0.786160i	−0.919504	+	0.393080i	$0.871410\pi$
$810$	−21.7123	+	22.3736i	−0.762892	+	0.786127i
$811$			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
$816$	2.87564	+	33.8191i	0.100668	+	1.18390i
$817$	−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	$-0.816045\pi$
$821$		−	31.3050i		−	1.09255i	0.837606	−	0.546275i	$-0.183955\pi$
$822$	10.3342	+	19.3185i	0.360445	+	0.673811i
$823$		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	$-0.402631\pi$
$827$	17.3205			0.602293			0.301147	+	0.953578i	$0.402631\pi$
$828$		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
$834$	−4.90192	−	9.16358i	−0.169740	−	0.317309i
$835$			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	$-0.393786\pi$
$839$	18.9737			0.655044			0.327522	+	0.944844i	$0.393786\pi$
$840$		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
$852$	2.00480	−	11.8313i	0.0686834	−	0.405335i
$853$	−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	$0.108632\pi$
$857$			19.5959i			0.669384i	−0.942328	+	0.334692i	$0.891368\pi$
$858$	−40.9808	+	21.9221i	−1.39906	+	0.748407i
$859$			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	$-0.404747\pi$
$863$	17.3205			0.589597			0.294798	+	0.955559i	$0.404747\pi$
$864$	29.0392	−	4.55223i	0.987935	−	0.154870i
$865$	−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
$870$	23.6603	−	12.6567i	0.802158	−	0.429103i
$871$			42.4264i			1.43756i
$872$	−25.9808	−	11.1803i	−0.879820	−	0.378614i
$873$		0			0
$874$		0			0
$875$		0			0
$876$	6.33975	−	37.4140i	0.214200	−	1.26410i
$877$	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	$0.266469\pi$
$881$			44.0908i			1.48546i	−0.669593	+	0.742729i	$0.733531\pi$
$882$		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	$-0.904802\pi$
$887$	−56.9210			−1.91122			−0.955610	+	0.294634i	$0.904802\pi$
$888$	−6.63470	−	7.20977i	−0.222646	−	0.241944i
$889$		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
$894$	5.16708	+	9.65926i	0.172813	+	0.323054i
$895$			25.4558i			0.850895i
$896$		0			0
$897$		0			0
$898$	40.0000	+	30.9839i	1.33482	+	1.03395i
$899$	37.9473			1.26561
$900$	−3.33013	+	4.99102i	−0.111004	+	0.166367i
$901$	21.9089			0.729891
$902$		0			0
$903$		0			0
$904$	−5.00000	+	11.6190i	−0.166298	+	0.386441i
$905$			40.2492i			1.33793i
$906$	−8.94965	−	16.7303i	−0.297332	−	0.555828i
$907$			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	$-0.611888\pi$
$911$	−20.7846			−0.688625			−0.344312	+	0.938855i	$0.611888\pi$
$912$	2.49038	+	29.2882i	0.0824648	+	0.969829i
$913$	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
$918$	12.3397	−	33.8191i	0.407272	−	1.11620i
$919$			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	$0.131624\pi$
$929$			24.4949i			0.803652i	−0.915716	+	0.401826i	$0.868376\pi$
$930$	−44.8922	+	24.0144i	−1.47207	+	0.787464i
$931$		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
$936$	14.7674	+	44.0673i	0.482689	+	1.44038i
$937$	−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	$0.0639733\pi$
$941$			12.2474i			0.399255i	−0.979872	+	0.199628i	$0.936027\pi$
$942$	−11.8301	+	6.32836i	−0.385446	+	0.206189i
$943$		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	$-0.445994\pi$
$947$	10.3923			0.337705			0.168852	+	0.985641i	$0.445994\pi$
$948$	−52.9114	−	8.96575i	−1.71848	−	0.291194i
$949$	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	$0.0462753\pi$
$953$			8.94427i			0.289733i	−0.989451	+	0.144867i	$0.953725\pi$
$954$	−1.33975	−	18.9263i	−0.0433759	−	0.612762i
$955$		−	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
$960$	32.0263	−	11.2391i	1.03364	−	0.362740i
$961$	−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	$-0.775349\pi$
$971$	−47.4342			−1.52223			−0.761117	+	0.648614i	$0.775349\pi$
$972$	−29.9697	−	8.59180i	−0.961278	−	0.275582i
$973$		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	$-0.806049\pi$
$977$		−	35.7771i		−	1.14461i	0.820041	−	0.572305i	$-0.193951\pi$
$978$	8.94965	+	16.7303i	0.286178	+	0.534977i
$979$			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	$-0.597849\pi$
$983$	−18.9737			−0.605166			−0.302583	+	0.953123i	$0.597849\pi$
$984$		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
$990$	−2.54199	−	35.9101i	−0.0807897	−	1.14130i
$991$		−	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
$996$	5.49038	−	32.4015i	0.173969	−	1.02668i
$997$	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

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

)

Twists

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

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	588.2.e.b.491.5

Level	$588$
Weight	$2$
Character	588.491
Analytic conductor	$4.695$
Analytic rank	$0$
Dimension	$8$
Inner twists	$8$