LMFDB - Embedded newform 567.2.o.c.188.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(188,567)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(567, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 3]))

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

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

chi := DirichletCharacter("567.188");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.o (of order $6$, degree $2$, not 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:	$4.52751779461$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 5x^{2} + 25 $ x^4 - 5*x^2 + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 189)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			188.2
Root			$1.93649 + 1.11803i$ of defining polynomial
Character	$\chi$	$=$	567.188
Dual form			567.2.o.c.377.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.93649 + 1.11803i) q^{2} +(1.50000 + 2.59808i) q^{4} +(1.93649 + 3.35410i) q^{5} +(-0.500000 - 2.59808i) q^{7} +2.23607i q^{8} +O(q^{10})$	\(q+(1.93649 + 1.11803i) q^{2} +(1.50000 + 2.59808i) q^{4} +(1.93649 + 3.35410i) q^{5} +(-0.500000 - 2.59808i) q^{7} +2.23607i q^{8} +8.66025i q^{10} +(1.93649 + 1.11803i) q^{11} +(-3.00000 + 1.73205i) q^{13} +(1.93649 - 5.59017i) q^{14} +(0.500000 - 0.866025i) q^{16} -5.19615i q^{19} +(-5.80948 + 10.0623i) q^{20} +(2.50000 + 4.33013i) q^{22} +(-1.93649 + 1.11803i) q^{23} +(-5.00000 + 8.66025i) q^{25} -7.74597 q^{26} +(6.00000 - 5.19615i) q^{28} +(-3.87298 - 2.23607i) q^{29} +(1.50000 - 0.866025i) q^{31} +(5.80948 - 3.35410i) q^{32} +(7.74597 - 6.70820i) q^{35} -1.00000 q^{37} +(5.80948 - 10.0623i) q^{38} +(-7.50000 + 4.33013i) q^{40} +(1.93649 + 3.35410i) q^{41} +(-1.00000 + 1.73205i) q^{43} +6.70820i q^{44} -5.00000 q^{46} +(3.87298 - 6.70820i) q^{47} +(-6.50000 + 2.59808i) q^{49} +(-19.3649 + 11.1803i) q^{50} +(-9.00000 - 5.19615i) q^{52} -8.94427i q^{53} +8.66025i q^{55} +(5.80948 - 1.11803i) q^{56} +(-5.00000 - 8.66025i) q^{58} +(-3.87298 - 6.70820i) q^{59} +(6.00000 + 3.46410i) q^{61} +3.87298 q^{62} +13.0000 q^{64} +(-11.6190 - 6.70820i) q^{65} +(5.00000 + 8.66025i) q^{67} +(22.5000 - 4.33013i) q^{70} +11.1803i q^{71} -10.3923i q^{73} +(-1.93649 - 1.11803i) q^{74} +(13.5000 - 7.79423i) q^{76} +(1.93649 - 5.59017i) q^{77} +(-1.00000 + 1.73205i) q^{79} +3.87298 q^{80} +8.66025i q^{82} +(3.87298 - 6.70820i) q^{83} +(-3.87298 + 2.23607i) q^{86} +(-2.50000 + 4.33013i) q^{88} +11.6190 q^{89} +(6.00000 + 6.92820i) q^{91} +(-5.80948 - 3.35410i) q^{92} +(15.0000 - 8.66025i) q^{94} +(17.4284 - 10.0623i) q^{95} +(-12.0000 - 6.92820i) q^{97} +(-15.4919 - 2.23607i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 6 q^{4} - 2 q^{7}+O(q^{10}) $ 4 * q + 6 * q^4 - 2 * q^7	$ 4 q + 6 q^{4} - 2 q^{7} - 12 q^{13} + 2 q^{16} + 10 q^{22} - 20 q^{25} + 24 q^{28} + 6 q^{31} - 4 q^{37} - 30 q^{40} - 4 q^{43} - 20 q^{46} - 26 q^{49} - 36 q^{52} - 20 q^{58} + 24 q^{61} + 52 q^{64} + 20 q^{67} + 90 q^{70} + 54 q^{76} - 4 q^{79} - 10 q^{88} + 24 q^{91} + 60 q^{94} - 48 q^{97}+O(q^{100}) $ 4 * q + 6 * q^4 - 2 * q^7 - 12 * q^13 + 2 * q^16 + 10 * q^22 - 20 * q^25 + 24 * q^28 + 6 * q^31 - 4 * q^37 - 30 * q^40 - 4 * q^43 - 20 * q^46 - 26 * q^49 - 36 * q^52 - 20 * q^58 + 24 * q^61 + 52 * q^64 + 20 * q^67 + 90 * q^70 + 54 * q^76 - 4 * q^79 - 10 * q^88 + 24 * q^91 + 60 * q^94 - 48 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	1.93649	+	1.11803i	1.36931	+	0.790569i	0.990839	−	0.135045i	$-0.0431180\pi$
$2$	1.93649	+	1.11803i	1.36931	+	0.790569i	0.378467	+	0.925615i	$0.376451\pi$
$3$		0			0
$3$		0			0
$4$	1.50000	+	2.59808i	0.750000	+	1.29904i
$5$	1.93649	+	3.35410i	0.866025	+	1.50000i	0.866025	+	0.500000i	$0.166667\pi$
$5$	1.93649	+	3.35410i	0.866025	+	1.50000i			1.00000i	$0.5\pi$
$6$		0			0
$7$	−0.500000	−	2.59808i	−0.188982	−	0.981981i
$7$	−0.500000	−	2.59808i	−0.188982	−	0.981981i
$8$			2.23607i			0.790569i
$9$		0			0
$10$			8.66025i			2.73861i
$11$	1.93649	+	1.11803i	0.583874	+	0.337100i	0.762672	−	0.646786i	$-0.223887\pi$
$11$	1.93649	+	1.11803i	0.583874	+	0.337100i	−0.178797	+	0.983886i	$0.557221\pi$
$12$		0			0
$13$	−3.00000	+	1.73205i	−0.832050	+	0.480384i	−0.854554	−	0.519362i	$-0.826170\pi$
$13$	−3.00000	+	1.73205i	−0.832050	+	0.480384i	0.0225039	+	0.999747i	$0.492836\pi$
$14$	1.93649	−	5.59017i	0.517549	−	1.49404i
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$		0			0			−	1.00000i	$-0.5\pi$
$17$		0			0				1.00000i	$0.5\pi$
$18$		0			0
$19$		−	5.19615i		−	1.19208i	−0.802955	−	0.596040i	$-0.796740\pi$
$19$		−	5.19615i		−	1.19208i	0.802955	−	0.596040i	$-0.203260\pi$
$20$	−5.80948	+	10.0623i	−1.29904	+	2.25000i
$21$		0			0
$22$	2.50000	+	4.33013i	0.533002	+	0.923186i
$23$	−1.93649	+	1.11803i	−0.403786	+	0.233126i	−0.688116	−	0.725600i	$-0.741562\pi$
$23$	−1.93649	+	1.11803i	−0.403786	+	0.233126i	0.284330	+	0.958726i	$0.408229\pi$
$24$		0			0
$25$	−5.00000	+	8.66025i	−1.00000	+	1.73205i
$26$	−7.74597			−1.51911
$27$		0			0
$28$	6.00000	−	5.19615i	1.13389	−	0.981981i
$29$	−3.87298	−	2.23607i	−0.719195	−	0.415227i	0.0952614	−	0.995452i	$-0.469631\pi$
$29$	−3.87298	−	2.23607i	−0.719195	−	0.415227i	−0.814456	+	0.580225i	$0.802965\pi$
$30$		0			0
$31$	1.50000	−	0.866025i	0.269408	−	0.155543i	−0.359211	−	0.933257i	$-0.616954\pi$
$31$	1.50000	−	0.866025i	0.269408	−	0.155543i	0.628619	+	0.777714i	$0.283621\pi$
$32$	5.80948	−	3.35410i	1.02698	−	0.592927i
$33$		0			0
$34$		0			0
$35$	7.74597	−	6.70820i	1.30931	−	1.13389i
$36$		0			0
$37$	−1.00000			−0.164399			−0.0821995	−	0.996616i	$-0.526194\pi$
$37$	−1.00000			−0.164399			−0.0821995	+	0.996616i	$0.526194\pi$
$38$	5.80948	−	10.0623i	0.942421	−	1.63232i
$39$		0			0
$40$	−7.50000	+	4.33013i	−1.18585	+	0.684653i
$41$	1.93649	+	3.35410i	0.302429	+	0.523823i	0.976686	−	0.214675i	$-0.0688691\pi$
$41$	1.93649	+	3.35410i	0.302429	+	0.523823i	−0.674256	+	0.738497i	$0.735536\pi$
$42$		0			0
$43$	−1.00000	+	1.73205i	−0.152499	+	0.264135i	−0.932145	−	0.362084i	$-0.882065\pi$
$43$	−1.00000	+	1.73205i	−0.152499	+	0.264135i	0.779647	+	0.626219i	$0.215399\pi$
$44$			6.70820i			1.01130i
$45$		0			0
$46$	−5.00000			−0.737210
$47$	3.87298	−	6.70820i	0.564933	−	0.978492i	−0.432123	−	0.901815i	$-0.642235\pi$
$47$	3.87298	−	6.70820i	0.564933	−	0.978492i	0.997056	−	0.0766776i	$-0.0244312\pi$
$48$		0			0
$49$	−6.50000	+	2.59808i	−0.928571	+	0.371154i
$50$	−19.3649	+	11.1803i	−2.73861	+	1.58114i
$51$		0			0
$52$	−9.00000	−	5.19615i	−1.24808	−	0.720577i
$53$		−	8.94427i		−	1.22859i	−0.789076	−	0.614295i	$-0.789440\pi$
$53$		−	8.94427i		−	1.22859i	0.789076	−	0.614295i	$-0.210560\pi$
$54$		0			0
$55$			8.66025i			1.16775i
$56$	5.80948	−	1.11803i	0.776324	−	0.149404i
$57$		0			0
$58$	−5.00000	−	8.66025i	−0.656532	−	1.13715i
$59$	−3.87298	−	6.70820i	−0.504219	−	0.873334i	−0.999988	−	0.00487911i	$-0.998447\pi$
$59$	−3.87298	−	6.70820i	−0.504219	−	0.873334i	0.495769	−	0.868455i	$-0.334886\pi$
$60$		0			0
$61$	6.00000	+	3.46410i	0.768221	+	0.443533i	0.832240	−	0.554416i	$-0.187058\pi$
$61$	6.00000	+	3.46410i	0.768221	+	0.443533i	−0.0640184	+	0.997949i	$0.520392\pi$
$62$	3.87298			0.491869
$63$		0			0
$64$	13.0000			1.62500
$65$	−11.6190	−	6.70820i	−1.44115	−	0.832050i
$66$		0			0
$67$	5.00000	+	8.66025i	0.610847	+	1.05802i	0.991098	+	0.133135i	$0.0425044\pi$
$67$	5.00000	+	8.66025i	0.610847	+	1.05802i	−0.380251	+	0.924883i	$0.624162\pi$
$68$		0			0
$69$		0			0
$70$	22.5000	−	4.33013i	2.68926	−	0.517549i
$71$			11.1803i			1.32686i	0.748237	+	0.663431i	$0.230900\pi$
$71$			11.1803i			1.32686i	−0.748237	+	0.663431i	$0.769100\pi$
$72$		0			0
$73$		−	10.3923i		−	1.21633i	−0.793812	−	0.608164i	$-0.791906\pi$
$73$		−	10.3923i		−	1.21633i	0.793812	−	0.608164i	$-0.208094\pi$
$74$	−1.93649	−	1.11803i	−0.225113	−	0.129969i
$75$		0			0
$76$	13.5000	−	7.79423i	1.54856	−	0.894059i
$77$	1.93649	−	5.59017i	0.220684	−	0.637059i
$78$		0			0
$79$	−1.00000	+	1.73205i	−0.112509	+	0.194871i	−0.916781	−	0.399390i	$-0.869222\pi$
$79$	−1.00000	+	1.73205i	−0.112509	+	0.194871i	0.804272	+	0.594261i	$0.202555\pi$
$80$	3.87298			0.433013
$81$		0			0
$82$			8.66025i			0.956365i
$83$	3.87298	−	6.70820i	0.425115	−	0.736321i	−0.571316	−	0.820730i	$-0.693567\pi$
$83$	3.87298	−	6.70820i	0.425115	−	0.736321i	0.996431	+	0.0844091i	$0.0269003\pi$
$84$		0			0
$85$		0			0
$86$	−3.87298	+	2.23607i	−0.417635	+	0.241121i
$87$		0			0
$88$	−2.50000	+	4.33013i	−0.266501	+	0.461593i
$89$	11.6190			1.23161			0.615803	−	0.787900i	$-0.288832\pi$
$89$	11.6190			1.23161			0.615803	+	0.787900i	$0.288832\pi$
$90$		0			0
$91$	6.00000	+	6.92820i	0.628971	+	0.726273i
$92$	−5.80948	−	3.35410i	−0.605680	−	0.349689i
$93$		0			0
$94$	15.0000	−	8.66025i	1.54713	−	0.893237i
$95$	17.4284	−	10.0623i	1.78812	−	1.03237i
$96$		0			0
$97$	−12.0000	−	6.92820i	−1.21842	−	0.703452i	−0.253837	−	0.967247i	$-0.581693\pi$
$97$	−12.0000	−	6.92820i	−1.21842	−	0.703452i	−0.964579	+	0.263795i	$0.915026\pi$
$98$	−15.4919	−	2.23607i	−1.56492	−	0.225877i
$99$		0			0
$100$	−30.0000			−3.00000
$101$	−7.74597	+	13.4164i	−0.770752	+	1.33498i	0.166399	+	0.986059i	$0.446786\pi$
$101$	−7.74597	+	13.4164i	−0.770752	+	1.33498i	−0.937151	+	0.348924i	$0.886547\pi$
$102$		0			0
$103$	1.50000	−	0.866025i	0.147799	−	0.0853320i	−0.424277	−	0.905533i	$-0.639472\pi$
$103$	1.50000	−	0.866025i	0.147799	−	0.0853320i	0.572076	+	0.820201i	$0.306138\pi$
$104$	−3.87298	−	6.70820i	−0.379777	−	0.657794i
$105$		0			0
$106$	10.0000	−	17.3205i	0.971286	−	1.68232i
$107$		−	8.94427i		−	0.864675i	−0.901712	−	0.432338i	$-0.857689\pi$
$107$		−	8.94427i		−	0.864675i	0.901712	−	0.432338i	$-0.142311\pi$
$108$		0			0
$109$	−7.00000			−0.670478			−0.335239	−	0.942133i	$-0.608817\pi$
$109$	−7.00000			−0.670478			−0.335239	+	0.942133i	$0.608817\pi$
$110$	−9.68246	+	16.7705i	−0.923186	+	1.59901i
$111$		0			0
$112$	−2.50000	−	0.866025i	−0.236228	−	0.0818317i
$113$	−7.74597	+	4.47214i	−0.728679	+	0.420703i	−0.817939	−	0.575305i	$-0.804883\pi$
$113$	−7.74597	+	4.47214i	−0.728679	+	0.420703i	0.0892596	+	0.996008i	$0.471550\pi$
$114$		0			0
$115$	−7.50000	−	4.33013i	−0.699379	−	0.403786i
$116$		−	13.4164i		−	1.24568i
$117$		0			0
$118$		−	17.3205i		−	1.59448i
$119$		0			0
$120$		0			0
$121$	−3.00000	−	5.19615i	−0.272727	−	0.472377i
$122$	7.74597	+	13.4164i	0.701287	+	1.21466i
$123$		0			0
$124$	4.50000	+	2.59808i	0.404112	+	0.233314i
$125$	−19.3649			−1.73205
$126$		0			0
$127$	−10.0000			−0.887357			−0.443678	−	0.896186i	$-0.646327\pi$
$127$	−10.0000			−0.887357			−0.443678	+	0.896186i	$0.646327\pi$
$128$	13.5554	+	7.82624i	1.19814	+	0.691748i
$129$		0			0
$130$	−15.0000	−	25.9808i	−1.31559	−	2.27866i
$131$	−3.87298	−	6.70820i	−0.338384	−	0.586098i	0.645745	−	0.763553i	$-0.276547\pi$
$131$	−3.87298	−	6.70820i	−0.338384	−	0.586098i	−0.984129	+	0.177455i	$0.943214\pi$
$132$		0			0
$133$	−13.5000	+	2.59808i	−1.17060	+	0.225282i
$134$			22.3607i			1.93167i
$135$		0			0
$136$		0			0
$137$	19.3649	+	11.1803i	1.65446	+	0.955201i	0.975207	+	0.221293i	$0.0710278\pi$
$137$	19.3649	+	11.1803i	1.65446	+	0.955201i	0.679249	+	0.733908i	$0.262306\pi$
$138$		0			0
$139$	−3.00000	+	1.73205i	−0.254457	+	0.146911i	−0.621803	−	0.783174i	$-0.713600\pi$
$139$	−3.00000	+	1.73205i	−0.254457	+	0.146911i	0.367347	+	0.930084i	$0.380266\pi$
$140$	29.0474	+	10.0623i	2.45495	+	0.850420i
$141$		0			0
$142$	−12.5000	+	21.6506i	−1.04898	+	1.81688i
$143$	−7.74597			−0.647750
$144$		0			0
$145$		−	17.3205i		−	1.43839i
$146$	11.6190	−	20.1246i	0.961591	−	1.66552i
$147$		0			0
$148$	−1.50000	−	2.59808i	−0.123299	−	0.213561i
$149$	−7.74597	+	4.47214i	−0.634574	+	0.366372i	−0.782521	−	0.622624i	$-0.786067\pi$
$149$	−7.74597	+	4.47214i	−0.634574	+	0.366372i	0.147947	+	0.988995i	$0.452733\pi$
$150$		0			0
$151$	8.00000	−	13.8564i	0.651031	−	1.12762i	−0.331842	−	0.943335i	$-0.607670\pi$
$151$	8.00000	−	13.8564i	0.651031	−	1.12762i	0.982873	−	0.184284i	$-0.0589965\pi$
$152$	11.6190			0.942421
$153$		0			0
$154$	10.0000	−	8.66025i	0.805823	−	0.697863i
$155$	5.80948	+	3.35410i	0.466628	+	0.269408i
$156$		0			0
$157$	−3.00000	+	1.73205i	−0.239426	+	0.138233i	−0.614913	−	0.788595i	$-0.710809\pi$
$157$	−3.00000	+	1.73205i	−0.239426	+	0.138233i	0.375487	+	0.926828i	$0.377476\pi$
$158$	−3.87298	+	2.23607i	−0.308118	+	0.177892i
$159$		0			0
$160$	22.5000	+	12.9904i	1.77878	+	1.02698i
$161$	3.87298	+	4.47214i	0.305234	+	0.352454i
$162$		0			0
$163$	−10.0000			−0.783260			−0.391630	−	0.920123i	$-0.628089\pi$
$163$	−10.0000			−0.783260			−0.391630	+	0.920123i	$0.628089\pi$
$164$	−5.80948	+	10.0623i	−0.453644	+	0.785734i
$165$		0			0
$166$	15.0000	−	8.66025i	1.16423	−	0.672166i
$167$	7.74597	+	13.4164i	0.599401	+	1.03819i	0.992910	+	0.118872i	$0.0379278\pi$
$167$	7.74597	+	13.4164i	0.599401	+	1.03819i	−0.393509	+	0.919321i	$0.628739\pi$
$168$		0			0
$169$	−0.500000	+	0.866025i	−0.0384615	+	0.0666173i
$170$		0			0
$171$		0			0
$172$	−6.00000			−0.457496
$173$	−1.93649	+	3.35410i	−0.147229	+	0.255008i	−0.930202	−	0.367047i	$-0.880369\pi$
$173$	−1.93649	+	3.35410i	−0.147229	+	0.255008i	0.782973	+	0.622055i	$0.213702\pi$
$174$		0			0
$175$	25.0000	+	8.66025i	1.88982	+	0.654654i
$176$	1.93649	−	1.11803i	0.145969	−	0.0842750i
$177$		0			0
$178$	22.5000	+	12.9904i	1.68645	+	0.973670i
$179$			17.8885i			1.33705i	0.743689	+	0.668526i	$0.233075\pi$
$179$			17.8885i			1.33705i	−0.743689	+	0.668526i	$0.766925\pi$
$180$		0			0
$181$		0			0		1.00000			$0$
$181$		0			0		−1.00000			$\pi$
$182$	3.87298	+	20.1246i	0.287085	+	1.49174i
$183$		0			0
$184$	−2.50000	−	4.33013i	−0.184302	−	0.319221i
$185$	−1.93649	−	3.35410i	−0.142374	−	0.246598i
$186$		0			0
$187$		0			0
$188$	23.2379			1.69480
$189$		0			0
$190$	45.0000			3.26464
$191$	1.93649	+	1.11803i	0.140120	+	0.0808981i	0.568421	−	0.822738i	$-0.307554\pi$
$191$	1.93649	+	1.11803i	0.140120	+	0.0808981i	−0.428301	+	0.903636i	$0.640888\pi$
$192$		0			0
$193$	−1.00000	−	1.73205i	−0.0719816	−	0.124676i	0.827788	−	0.561041i	$-0.189599\pi$
$193$	−1.00000	−	1.73205i	−0.0719816	−	0.124676i	−0.899770	+	0.436365i	$0.856266\pi$
$194$	−15.4919	−	26.8328i	−1.11226	−	1.92648i
$195$		0			0
$196$	−16.5000	−	12.9904i	−1.17857	−	0.927884i
$197$		−	8.94427i		−	0.637253i	−0.947880	−	0.318626i	$-0.896778\pi$
$197$		−	8.94427i		−	0.637253i	0.947880	−	0.318626i	$-0.103222\pi$
$198$		0			0
$199$			25.9808i			1.84173i	0.389885	+	0.920864i	$0.372515\pi$
$199$			25.9808i			1.84173i	−0.389885	+	0.920864i	$0.627485\pi$
$200$	−19.3649	−	11.1803i	−1.36931	−	0.790569i
$201$		0			0
$202$	−30.0000	+	17.3205i	−2.11079	+	1.21867i
$203$	−3.87298	+	11.1803i	−0.271830	+	0.784706i
$204$		0			0
$205$	−7.50000	+	12.9904i	−0.523823	+	0.907288i
$206$	3.87298			0.269844
$207$		0			0
$208$			3.46410i			0.240192i
$209$	5.80948	−	10.0623i	0.401850	−	0.696024i
$210$		0			0
$211$	−4.00000	−	6.92820i	−0.275371	−	0.476957i	0.694857	−	0.719148i	$-0.255467\pi$
$211$	−4.00000	−	6.92820i	−0.275371	−	0.476957i	−0.970229	+	0.242190i	$0.922134\pi$
$212$	23.2379	−	13.4164i	1.59599	−	0.921443i
$213$		0			0
$214$	10.0000	−	17.3205i	0.683586	−	1.18401i
$215$	−7.74597			−0.528271
$216$		0			0
$217$	−3.00000	−	3.46410i	−0.203653	−	0.235159i
$218$	−13.5554	−	7.82624i	−0.918090	−	0.530060i
$219$		0			0
$220$	−22.5000	+	12.9904i	−1.51695	+	0.875811i
$221$		0			0
$222$		0			0
$223$	1.50000	+	0.866025i	0.100447	+	0.0579934i	0.549382	−	0.835571i	$-0.314863\pi$
$223$	1.50000	+	0.866025i	0.100447	+	0.0579934i	−0.448935	+	0.893565i	$0.648196\pi$
$224$	−11.6190	−	13.4164i	−0.776324	−	0.896421i
$225$		0			0
$226$	−20.0000			−1.33038
$227$	−7.74597	+	13.4164i	−0.514118	+	0.890478i	0.485748	+	0.874099i	$0.338547\pi$
$227$	−7.74597	+	13.4164i	−0.514118	+	0.890478i	−0.999866	+	0.0163794i	$0.994786\pi$
$228$		0			0
$229$	−12.0000	+	6.92820i	−0.792982	+	0.457829i	−0.841011	−	0.541017i	$-0.818039\pi$
$229$	−12.0000	+	6.92820i	−0.792982	+	0.457829i	0.0480291	+	0.998846i	$0.484706\pi$
$230$	−9.68246	−	16.7705i	−0.638442	−	1.10581i
$231$		0			0
$232$	5.00000	−	8.66025i	0.328266	−	0.568574i
$233$			17.8885i			1.17192i	0.810341	+	0.585959i	$0.199282\pi$
$233$			17.8885i			1.17192i	−0.810341	+	0.585959i	$0.800718\pi$
$234$		0			0
$235$	30.0000			1.95698
$236$	11.6190	−	20.1246i	0.756329	−	1.31000i
$237$		0			0
$238$		0			0
$239$	−7.74597	+	4.47214i	−0.501045	+	0.289278i	−0.729145	−	0.684359i	$-0.760082\pi$
$239$	−7.74597	+	4.47214i	−0.501045	+	0.289278i	0.228100	+	0.973638i	$0.426749\pi$
$240$		0			0
$241$	15.0000	+	8.66025i	0.966235	+	0.557856i	0.898086	−	0.439819i	$-0.144957\pi$
$241$	15.0000	+	8.66025i	0.966235	+	0.557856i	0.0681486	+	0.997675i	$0.478291\pi$
$242$		−	13.4164i		−	0.862439i
$243$		0			0
$244$			20.7846i			1.33060i
$245$	−21.3014	−	16.7705i	−1.36090	−	1.07143i
$246$		0			0
$247$	9.00000	+	15.5885i	0.572656	+	0.991870i
$248$	1.93649	+	3.35410i	0.122967	+	0.212986i
$249$		0			0
$250$	−37.5000	−	21.6506i	−2.37171	−	1.36931i
$251$		0			0			−	1.00000i	$-0.5\pi$
$251$		0			0				1.00000i	$0.5\pi$
$252$		0			0
$253$	−5.00000			−0.314347
$254$	−19.3649	−	11.1803i	−1.21506	−	0.701517i
$255$		0			0
$256$	4.50000	+	7.79423i	0.281250	+	0.487139i
$257$	13.5554	+	23.4787i	0.845565	+	1.46456i	0.885129	+	0.465345i	$0.154070\pi$
$257$	13.5554	+	23.4787i	0.845565	+	1.46456i	−0.0395642	+	0.999217i	$0.512597\pi$
$258$		0			0
$259$	0.500000	+	2.59808i	0.0310685	+	0.161437i
$260$		−	40.2492i		−	2.49615i
$261$		0			0
$262$		−	17.3205i		−	1.07006i
$263$	1.93649	+	1.11803i	0.119409	+	0.0689409i	0.558515	−	0.829494i	$-0.311371\pi$
$263$	1.93649	+	1.11803i	0.119409	+	0.0689409i	−0.439106	+	0.898435i	$0.644705\pi$
$264$		0			0
$265$	30.0000	−	17.3205i	1.84289	−	1.06399i
$266$	−29.0474	−	10.0623i	−1.78101	−	0.616960i
$267$		0			0
$268$	−15.0000	+	25.9808i	−0.916271	+	1.58703i
$269$	−11.6190			−0.708420			−0.354210	−	0.935166i	$-0.615250\pi$
$269$	−11.6190			−0.708420			−0.354210	+	0.935166i	$0.615250\pi$
$270$		0			0
$271$			10.3923i			0.631288i	0.948878	+	0.315644i	$0.102220\pi$
$271$			10.3923i			0.631288i	−0.948878	+	0.315644i	$0.897780\pi$
$272$		0			0
$273$		0			0
$274$	25.0000	+	43.3013i	1.51031	+	2.61593i
$275$	−19.3649	+	11.1803i	−1.16775	+	0.674200i
$276$		0			0
$277$	−5.50000	+	9.52628i	−0.330463	+	0.572379i	−0.982603	−	0.185720i	$-0.940538\pi$
$277$	−5.50000	+	9.52628i	−0.330463	+	0.572379i	0.652140	+	0.758099i	$0.273872\pi$
$278$	−7.74597			−0.464572
$279$		0			0
$280$	15.0000	+	17.3205i	0.896421	+	1.03510i
$281$	19.3649	+	11.1803i	1.15521	+	0.666963i	0.950152	−	0.311786i	$-0.100927\pi$
$281$	19.3649	+	11.1803i	1.15521	+	0.666963i	0.205062	+	0.978749i	$0.434260\pi$
$282$		0			0
$283$	−21.0000	+	12.1244i	−1.24832	+	0.720718i	−0.970774	−	0.239994i	$-0.922854\pi$
$283$	−21.0000	+	12.1244i	−1.24832	+	0.720718i	−0.277546	+	0.960712i	$0.589521\pi$
$284$	−29.0474	+	16.7705i	−1.72364	+	0.995147i
$285$		0			0
$286$	−15.0000	−	8.66025i	−0.886969	−	0.512092i
$287$	7.74597	−	6.70820i	0.457230	−	0.395973i
$288$		0			0
$289$	−17.0000			−1.00000
$290$	19.3649	−	33.5410i	1.13715	−	1.96960i
$291$		0			0
$292$	27.0000	−	15.5885i	1.58006	−	0.912245i
$293$	−15.4919	−	26.8328i	−0.905048	−	1.56759i	−0.820852	−	0.571141i	$-0.806501\pi$
$293$	−15.4919	−	26.8328i	−0.905048	−	1.56759i	−0.0841962	−	0.996449i	$-0.526832\pi$
$294$		0			0
$295$	15.0000	−	25.9808i	0.873334	−	1.51266i
$296$		−	2.23607i		−	0.129969i
$297$		0			0
$298$	−20.0000			−1.15857
$299$	3.87298	−	6.70820i	0.223980	−	0.387945i
$300$		0			0
$301$	5.00000	+	1.73205i	0.288195	+	0.0998337i
$302$	30.9839	−	17.8885i	1.78292	−	1.02937i
$303$		0			0
$304$	−4.50000	−	2.59808i	−0.258093	−	0.149010i
$305$			26.8328i			1.53644i
$306$		0			0
$307$		−	5.19615i		−	0.296560i	−0.988945	−	0.148280i	$-0.952626\pi$
$307$		−	5.19615i		−	0.296560i	0.988945	−	0.148280i	$-0.0473737\pi$
$308$	17.4284	−	3.35410i	0.993077	−	0.191118i
$309$		0			0
$310$	7.50000	+	12.9904i	0.425971	+	0.737804i
$311$	−3.87298	−	6.70820i	−0.219617	−	0.380387i	0.735074	−	0.677987i	$-0.237147\pi$
$311$	−3.87298	−	6.70820i	−0.219617	−	0.380387i	−0.954691	+	0.297599i	$0.903814\pi$
$312$		0			0
$313$	−3.00000	−	1.73205i	−0.169570	−	0.0979013i	0.412813	−	0.910816i	$-0.364546\pi$
$313$	−3.00000	−	1.73205i	−0.169570	−	0.0979013i	−0.582383	+	0.812914i	$0.697880\pi$
$314$	−7.74597			−0.437130
$315$		0			0
$316$	−6.00000			−0.337526
$317$	−3.87298	−	2.23607i	−0.217528	−	0.125590i	0.387277	−	0.921963i	$-0.373416\pi$
$317$	−3.87298	−	2.23607i	−0.217528	−	0.125590i	−0.604805	+	0.796373i	$0.706749\pi$
$318$		0			0
$319$	−5.00000	−	8.66025i	−0.279946	−	0.484881i
$320$	25.1744	+	43.6033i	1.40729	+	2.43750i
$321$		0			0
$322$	2.50000	+	12.9904i	0.139320	+	0.723926i
$323$		0			0
$324$		0			0
$325$		−	34.6410i		−	1.92154i
$326$	−19.3649	−	11.1803i	−1.07252	−	0.619222i
$327$		0			0
$328$	−7.50000	+	4.33013i	−0.414118	+	0.239091i
$329$	−19.3649	−	6.70820i	−1.06762	−	0.369835i
$330$		0			0
$331$	2.00000	−	3.46410i	0.109930	−	0.190404i	−0.805812	−	0.592172i	$-0.798271\pi$
$331$	2.00000	−	3.46410i	0.109930	−	0.190404i	0.915742	+	0.401768i	$0.131604\pi$
$332$	23.2379			1.27535
$333$		0			0
$334$			34.6410i			1.89547i
$335$	−19.3649	+	33.5410i	−1.05802	+	1.83254i
$336$		0			0
$337$	−17.5000	−	30.3109i	−0.953286	−	1.65114i	−0.738243	−	0.674535i	$-0.764344\pi$
$337$	−17.5000	−	30.3109i	−0.953286	−	1.65114i	−0.215043	−	0.976605i	$-0.568989\pi$
$338$	−1.93649	+	1.11803i	−0.105331	+	0.0608130i
$339$		0			0
$340$		0			0
$341$	3.87298			0.209734
$342$		0			0
$343$	10.0000	+	15.5885i	0.539949	+	0.841698i
$344$	−3.87298	−	2.23607i	−0.208817	−	0.120561i
$345$		0			0
$346$	−7.50000	+	4.33013i	−0.403202	+	0.232789i
$347$	9.68246	−	5.59017i	0.519782	−	0.300096i	−0.217064	−	0.976157i	$-0.569648\pi$
$347$	9.68246	−	5.59017i	0.519782	−	0.300096i	0.736845	+	0.676061i	$0.236315\pi$
$348$		0			0
$349$	−12.0000	−	6.92820i	−0.642345	−	0.370858i	0.143172	−	0.989698i	$-0.454270\pi$
$349$	−12.0000	−	6.92820i	−0.642345	−	0.370858i	−0.785517	+	0.618840i	$0.787603\pi$
$350$	38.7298	+	44.7214i	2.07020	+	2.39046i
$351$		0			0
$352$	15.0000			0.799503
$353$	9.68246	−	16.7705i	0.515345	−	0.892604i	−0.484496	−	0.874793i	$-0.660997\pi$
$353$	9.68246	−	16.7705i	0.515345	−	0.892604i	0.999841	−	0.0178108i	$-0.00566964\pi$
$354$		0			0
$355$	−37.5000	+	21.6506i	−1.99029	+	1.14910i
$356$	17.4284	+	30.1869i	0.923705	+	1.59990i
$357$		0			0
$358$	−20.0000	+	34.6410i	−1.05703	+	1.83083i
$359$		−	8.94427i		−	0.472061i	−0.971746	−	0.236030i	$-0.924154\pi$
$359$		−	8.94427i		−	0.472061i	0.971746	−	0.236030i	$-0.0758465\pi$
$360$		0			0
$361$	−8.00000			−0.421053
$362$		0			0
$363$		0			0
$364$	−9.00000	+	25.9808i	−0.471728	+	1.36176i
$365$	34.8569	−	20.1246i	1.82449	−	1.05337i
$366$		0			0
$367$	1.50000	+	0.866025i	0.0782994	+	0.0452062i	0.538639	−	0.842537i	$-0.318939\pi$
$367$	1.50000	+	0.866025i	0.0782994	+	0.0452062i	−0.460339	+	0.887743i	$0.652272\pi$
$368$			2.23607i			0.116563i
$369$		0			0
$370$		−	8.66025i		−	0.450225i
$371$	−23.2379	+	4.47214i	−1.20645	+	0.232182i
$372$		0			0
$373$	−8.50000	−	14.7224i	−0.440113	−	0.762299i	0.557584	−	0.830120i	$-0.311728\pi$
$373$	−8.50000	−	14.7224i	−0.440113	−	0.762299i	−0.997697	+	0.0678218i	$0.978395\pi$
$374$		0			0
$375$		0			0
$376$	15.0000	+	8.66025i	0.773566	+	0.446619i
$377$	15.4919			0.797875
$378$		0			0
$379$	26.0000			1.33553			0.667765	−	0.744372i	$-0.267251\pi$
$379$	26.0000			1.33553			0.667765	+	0.744372i	$0.267251\pi$
$380$	52.2853	+	30.1869i	2.68218	+	1.54856i
$381$		0			0
$382$	2.50000	+	4.33013i	0.127911	+	0.221549i
$383$	−15.4919	−	26.8328i	−0.791601	−	1.37109i	−0.924975	−	0.380027i	$-0.875915\pi$
$383$	−15.4919	−	26.8328i	−0.791601	−	1.37109i	0.133375	−	0.991066i	$-0.457419\pi$
$384$		0			0
$385$	22.5000	−	4.33013i	1.14671	−	0.220684i
$386$		−	4.47214i		−	0.227626i
$387$		0			0
$388$		−	41.5692i		−	2.11036i
$389$	30.9839	+	17.8885i	1.57094	+	0.906985i	0.996053	+	0.0887551i	$0.0282889\pi$
$389$	30.9839	+	17.8885i	1.57094	+	0.906985i	0.574891	+	0.818230i	$0.305044\pi$
$390$		0			0
$391$		0			0
$392$	−5.80948	−	14.5344i	−0.293423	−	0.734100i
$393$		0			0
$394$	10.0000	−	17.3205i	0.503793	−	0.872595i
$395$	−7.74597			−0.389742
$396$		0			0
$397$			20.7846i			1.04315i	0.853206	+	0.521575i	$0.174655\pi$
$397$			20.7846i			1.04315i	−0.853206	+	0.521575i	$0.825345\pi$
$398$	−29.0474	+	50.3115i	−1.45601	+	2.52189i
$399$		0			0
$400$	5.00000	+	8.66025i	0.250000	+	0.433013i
$401$	27.1109	−	15.6525i	1.35385	−	0.781647i	0.365066	−	0.930982i	$-0.381046\pi$
$401$	27.1109	−	15.6525i	1.35385	−	0.781647i	0.988787	+	0.149334i	$0.0477130\pi$
$402$		0			0
$403$	−3.00000	+	5.19615i	−0.149441	+	0.258839i
$404$	−46.4758			−2.31226
$405$		0			0
$406$	−20.0000	+	17.3205i	−0.992583	+	0.859602i
$407$	−1.93649	−	1.11803i	−0.0959883	−	0.0554189i
$408$		0			0
$409$	15.0000	−	8.66025i	0.741702	−	0.428222i	−0.0809857	−	0.996715i	$-0.525807\pi$
$409$	15.0000	−	8.66025i	0.741702	−	0.428222i	0.822688	+	0.568493i	$0.192473\pi$
$410$	−29.0474	+	16.7705i	−1.43455	+	0.828236i
$411$		0			0
$412$	4.50000	+	2.59808i	0.221699	+	0.127998i
$413$	−15.4919	+	13.4164i	−0.762308	+	0.660178i
$414$		0			0
$415$	30.0000			1.47264
$416$	−11.6190	+	20.1246i	−0.569666	+	0.986690i
$417$		0			0
$418$	22.5000	−	12.9904i	1.10051	−	0.635380i
$419$	7.74597	+	13.4164i	0.378415	+	0.655434i	0.990832	−	0.135101i	$-0.0431358\pi$
$419$	7.74597	+	13.4164i	0.378415	+	0.655434i	−0.612417	+	0.790535i	$0.709802\pi$
$420$		0			0
$421$	−5.50000	+	9.52628i	−0.268054	+	0.464282i	−0.968359	−	0.249561i	$-0.919714\pi$
$421$	−5.50000	+	9.52628i	−0.268054	+	0.464282i	0.700306	+	0.713843i	$0.253047\pi$
$422$		−	17.8885i		−	0.870801i
$423$		0			0
$424$	20.0000			0.971286
$425$		0			0
$426$		0			0
$427$	6.00000	−	17.3205i	0.290360	−	0.838198i
$428$	23.2379	−	13.4164i	1.12325	−	0.648507i
$429$		0			0
$430$	−15.0000	−	8.66025i	−0.723364	−	0.417635i
$431$		−	2.23607i		−	0.107708i	−0.998549	−	0.0538538i	$-0.982850\pi$
$431$		−	2.23607i		−	0.107708i	0.998549	−	0.0538538i	$-0.0171505\pi$
$432$		0			0
$433$		−	10.3923i		−	0.499422i	−0.968320	−	0.249711i	$-0.919664\pi$
$433$		−	10.3923i		−	0.499422i	0.968320	−	0.249711i	$-0.0803357\pi$
$434$	−1.93649	−	10.0623i	−0.0929546	−	0.483006i
$435$		0			0
$436$	−10.5000	−	18.1865i	−0.502859	−	0.870977i
$437$	5.80948	+	10.0623i	0.277905	+	0.481345i
$438$		0			0
$439$	33.0000	+	19.0526i	1.57500	+	0.909329i	0.995541	+	0.0943306i	$0.0300711\pi$
$439$	33.0000	+	19.0526i	1.57500	+	0.909329i	0.579463	+	0.814998i	$0.303262\pi$
$440$	−19.3649			−0.923186
$441$		0			0
$442$		0			0
$443$	−21.3014	−	12.2984i	−1.01206	−	0.584313i	−0.100266	−	0.994961i	$-0.531969\pi$
$443$	−21.3014	−	12.2984i	−1.01206	−	0.584313i	−0.911794	+	0.410647i	$0.865303\pi$
$444$		0			0
$445$	22.5000	+	38.9711i	1.06660	+	1.84741i
$446$	1.93649	+	3.35410i	0.0916955	+	0.158821i
$447$		0			0
$448$	−6.50000	−	33.7750i	−0.307096	−	1.59572i
$449$		−	8.94427i		−	0.422106i	−0.977475	−	0.211053i	$-0.932311\pi$
$449$		−	8.94427i		−	0.422106i	0.977475	−	0.211053i	$-0.0676893\pi$
$450$		0			0
$451$			8.66025i			0.407795i
$452$	−23.2379	−	13.4164i	−1.09302	−	0.631055i
$453$		0			0
$454$	−30.0000	+	17.3205i	−1.40797	+	0.812892i
$455$	−11.6190	+	33.5410i	−0.544705	+	1.57243i
$456$		0			0
$457$	12.5000	−	21.6506i	0.584725	−	1.01277i	−0.410184	−	0.912003i	$-0.634536\pi$
$457$	12.5000	−	21.6506i	0.584725	−	1.01277i	0.994910	−	0.100771i	$-0.0321310\pi$
$458$	−30.9839			−1.44778
$459$		0			0
$460$		−	25.9808i		−	1.21136i
$461$	−1.93649	+	3.35410i	−0.0901914	+	0.156216i	−0.907592	−	0.419854i	$-0.862081\pi$
$461$	−1.93649	+	3.35410i	−0.0901914	+	0.156216i	0.817400	+	0.576070i	$0.195415\pi$
$462$		0			0
$463$	−4.00000	−	6.92820i	−0.185896	−	0.321981i	0.757982	−	0.652275i	$-0.226185\pi$
$463$	−4.00000	−	6.92820i	−0.185896	−	0.321981i	−0.943878	+	0.330294i	$0.892852\pi$
$464$	−3.87298	+	2.23607i	−0.179799	+	0.103807i
$465$		0			0
$466$	−20.0000	+	34.6410i	−0.926482	+	1.60471i
$467$	−23.2379			−1.07532			−0.537661	−	0.843161i	$-0.680692\pi$
$467$	−23.2379			−1.07532			−0.537661	+	0.843161i	$0.680692\pi$
$468$		0			0
$469$	20.0000	−	17.3205i	0.923514	−	0.799787i
$470$	58.0948	+	33.5410i	2.67971	+	1.54713i
$471$		0			0
$472$	15.0000	−	8.66025i	0.690431	−	0.398621i
$473$	−3.87298	+	2.23607i	−0.178080	+	0.102815i
$474$		0			0
$475$	45.0000	+	25.9808i	2.06474	+	1.19208i
$476$		0			0
$477$		0			0
$478$	−20.0000			−0.914779
$479$	15.4919	−	26.8328i	0.707845	−	1.22602i	−0.257811	−	0.966195i	$-0.583001\pi$
$479$	15.4919	−	26.8328i	0.707845	−	1.22602i	0.965655	−	0.259827i	$-0.0836656\pi$
$480$		0			0
$481$	3.00000	−	1.73205i	0.136788	−	0.0789747i
$482$	19.3649	+	33.5410i	0.882048	+	1.52775i
$483$		0			0
$484$	9.00000	−	15.5885i	0.409091	−	0.708566i
$485$		−	53.6656i		−	2.43683i
$486$		0			0
$487$	−10.0000			−0.453143			−0.226572	−	0.973995i	$-0.572752\pi$
$487$	−10.0000			−0.453143			−0.226572	+	0.973995i	$0.572752\pi$
$488$	−7.74597	+	13.4164i	−0.350643	+	0.607332i
$489$		0			0
$490$	−22.5000	−	56.2917i	−1.01645	−	2.54300i
$491$	32.9204	−	19.0066i	1.48567	−	0.857755i	0.485808	−	0.874066i	$-0.338525\pi$
$491$	32.9204	−	19.0066i	1.48567	−	0.857755i	0.999867	+	0.0163107i	$0.00519209\pi$
$492$		0			0
$493$		0			0
$494$			40.2492i			1.81090i
$495$		0			0
$496$		−	1.73205i		−	0.0777714i
$497$	29.0474	−	5.59017i	1.30295	−	0.250753i
$498$		0			0
$499$	−19.0000	−	32.9090i	−0.850557	−	1.47321i	−0.880707	−	0.473662i	$-0.842932\pi$
$499$	−19.0000	−	32.9090i	−0.850557	−	1.47321i	0.0301498	−	0.999545i	$-0.490402\pi$
$500$	−29.0474	−	50.3115i	−1.29904	−	2.25000i
$501$		0			0
$502$		0			0
$503$	23.2379			1.03613			0.518063	−	0.855342i	$-0.326653\pi$
$503$	23.2379			1.03613			0.518063	+	0.855342i	$0.326653\pi$
$504$		0			0
$505$	−60.0000			−2.66996
$506$	−9.68246	−	5.59017i	−0.430438	−	0.248513i
$507$		0			0
$508$	−15.0000	−	25.9808i	−0.665517	−	1.15271i
$509$	7.74597	+	13.4164i	0.343334	+	0.594672i	0.985050	−	0.172271i	$-0.0551104\pi$
$509$	7.74597	+	13.4164i	0.343334	+	0.594672i	−0.641716	+	0.766943i	$0.721777\pi$
$510$		0			0
$511$	−27.0000	+	5.19615i	−1.19441	+	0.229864i
$512$		−	11.1803i		−	0.494106i
$513$		0			0
$514$			60.6218i			2.67391i
$515$	5.80948	+	3.35410i	0.255996	+	0.147799i
$516$		0			0
$517$	15.0000	−	8.66025i	0.659699	−	0.380878i
$518$	−1.93649	+	5.59017i	−0.0850846	+	0.245618i
$519$		0			0
$520$	15.0000	−	25.9808i	0.657794	−	1.13933i
$521$	34.8569			1.52711			0.763553	−	0.645745i	$-0.223453\pi$
$521$	34.8569			1.52711			0.763553	+	0.645745i	$0.223453\pi$
$522$		0			0
$523$		−	15.5885i		−	0.681636i	−0.940129	−	0.340818i	$-0.889296\pi$
$523$		−	15.5885i		−	0.681636i	0.940129	−	0.340818i	$-0.110704\pi$
$524$	11.6190	−	20.1246i	0.507576	−	0.879148i
$525$		0			0
$526$	2.50000	+	4.33013i	0.109005	+	0.188803i
$527$		0			0
$528$		0			0
$529$	−9.00000	+	15.5885i	−0.391304	+	0.677759i
$530$	77.4597			3.36463
$531$		0			0
$532$	−27.0000	−	31.1769i	−1.17060	−	1.35169i
$533$	−11.6190	−	6.70820i	−0.503273	−	0.290565i
$534$		0			0
$535$	30.0000	−	17.3205i	1.29701	−	0.748831i
$536$	−19.3649	+	11.1803i	−0.836437	+	0.482917i
$537$		0			0
$538$	−22.5000	−	12.9904i	−0.970044	−	0.560055i
$539$	−15.4919	−	2.23607i	−0.667285	−	0.0963143i
$540$		0			0
$541$	−1.00000			−0.0429934			−0.0214967	−	0.999769i	$-0.506843\pi$
$541$	−1.00000			−0.0429934			−0.0214967	+	0.999769i	$0.506843\pi$
$542$	−11.6190	+	20.1246i	−0.499077	+	0.864426i
$543$		0			0
$544$		0			0
$545$	−13.5554	−	23.4787i	−0.580651	−	1.00572i
$546$		0			0
$547$	8.00000	−	13.8564i	0.342055	−	0.592457i	−0.642759	−	0.766068i	$-0.722210\pi$
$547$	8.00000	−	13.8564i	0.342055	−	0.592457i	0.984814	+	0.173611i	$0.0555436\pi$
$548$			67.0820i			2.86560i
$549$		0			0
$550$	−50.0000			−2.13201
$551$	−11.6190	+	20.1246i	−0.494984	+	0.857337i
$552$		0			0
$553$	5.00000	+	1.73205i	0.212622	+	0.0736543i
$554$	−21.3014	+	12.2984i	−0.905010	+	0.522508i
$555$		0			0
$556$	−9.00000	−	5.19615i	−0.381685	−	0.220366i
$557$		−	8.94427i		−	0.378981i	−0.981883	−	0.189490i	$-0.939316\pi$
$557$		−	8.94427i		−	0.378981i	0.981883	−	0.189490i	$-0.0606836\pi$
$558$		0			0
$559$		−	6.92820i		−	0.293032i
$560$	−1.93649	−	10.0623i	−0.0818317	−	0.425210i
$561$		0			0
$562$	25.0000	+	43.3013i	1.05456	+	1.82655i
$563$	19.3649	+	33.5410i	0.816134	+	1.41359i	0.908511	+	0.417861i	$0.137220\pi$
$563$	19.3649	+	33.5410i	0.816134	+	1.41359i	−0.0923769	+	0.995724i	$0.529446\pi$
$564$		0			0
$565$	−30.0000	−	17.3205i	−1.26211	−	0.728679i
$566$	−54.2218			−2.27911
$567$		0			0
$568$	−25.0000			−1.04898
$569$	−15.4919	−	8.94427i	−0.649456	−	0.374963i	0.138792	−	0.990322i	$-0.455678\pi$
$569$	−15.4919	−	8.94427i	−0.649456	−	0.374963i	−0.788248	+	0.615358i	$0.789011\pi$
$570$		0			0
$571$	8.00000	+	13.8564i	0.334790	+	0.579873i	0.983444	−	0.181210i	$-0.0580014\pi$
$571$	8.00000	+	13.8564i	0.334790	+	0.579873i	−0.648655	+	0.761083i	$0.724668\pi$
$572$	−11.6190	−	20.1246i	−0.485813	−	0.841452i
$573$		0			0
$574$	22.5000	−	4.33013i	0.939132	−	0.180736i
$575$		−	22.3607i		−	0.932505i
$576$		0			0
$577$			20.7846i			0.865275i	0.901568	+	0.432637i	$0.142417\pi$
$577$			20.7846i			0.865275i	−0.901568	+	0.432637i	$0.857583\pi$
$578$	−32.9204	−	19.0066i	−1.36931	−	0.790569i
$579$		0			0
$580$	45.0000	−	25.9808i	1.86852	−	1.07879i
$581$	−19.3649	−	6.70820i	−0.803392	−	0.278303i
$582$		0			0
$583$	10.0000	−	17.3205i	0.414158	−	0.717342i
$584$	23.2379			0.961591
$585$		0			0
$586$		−	69.2820i		−	2.86201i
$587$	15.4919	−	26.8328i	0.639421	−	1.10751i	−0.346140	−	0.938183i	$-0.612508\pi$
$587$	15.4919	−	26.8328i	0.639421	−	1.10751i	0.985560	−	0.169326i	$-0.0541590\pi$
$588$		0			0
$589$	−4.50000	−	7.79423i	−0.185419	−	0.321156i
$590$	58.0948	−	33.5410i	2.39172	−	1.38086i
$591$		0			0
$592$	−0.500000	+	0.866025i	−0.0205499	+	0.0355934i
$593$	34.8569			1.43140			0.715700	−	0.698408i	$-0.246108\pi$
$593$	34.8569			1.43140			0.715700	+	0.698408i	$0.246108\pi$
$594$		0			0
$595$		0			0
$596$	−23.2379	−	13.4164i	−0.951861	−	0.549557i
$597$		0			0
$598$	15.0000	−	8.66025i	0.613396	−	0.354144i
$599$	−25.1744	+	14.5344i	−1.02860	+	0.593861i	−0.916583	−	0.399845i	$-0.869064\pi$
$599$	−25.1744	+	14.5344i	−1.02860	+	0.593861i	−0.112015	+	0.993707i	$0.535731\pi$
$600$		0			0
$601$	−21.0000	−	12.1244i	−0.856608	−	0.494563i	0.00626702	−	0.999980i	$-0.498005\pi$
$601$	−21.0000	−	12.1244i	−0.856608	−	0.494563i	−0.862875	+	0.505418i	$0.831338\pi$
$602$	7.74597	+	8.94427i	0.315702	+	0.364541i
$603$		0			0
$604$	48.0000			1.95309
$605$	11.6190	−	20.1246i	0.472377	−	0.818182i
$606$		0			0
$607$	33.0000	−	19.0526i	1.33943	−	0.773320i	0.352706	−	0.935734i	$-0.385262\pi$
$607$	33.0000	−	19.0526i	1.33943	−	0.773320i	0.986723	+	0.162415i	$0.0519282\pi$
$608$	−17.4284	−	30.1869i	−0.706816	−	1.22424i
$609$		0			0
$610$	−30.0000	+	51.9615i	−1.21466	+	2.10386i
$611$			26.8328i			1.08554i
$612$		0			0
$613$	17.0000			0.686624			0.343312	−	0.939222i	$-0.388451\pi$
$613$	17.0000			0.686624			0.343312	+	0.939222i	$0.388451\pi$
$614$	5.80948	−	10.0623i	0.234451	−	0.406082i
$615$		0			0
$616$	12.5000	+	4.33013i	0.503639	+	0.174466i
$617$	−19.3649	+	11.1803i	−0.779602	+	0.450104i	−0.836289	−	0.548288i	$-0.815280\pi$
$617$	−19.3649	+	11.1803i	−0.779602	+	0.450104i	0.0566871	+	0.998392i	$0.481946\pi$
$618$		0			0
$619$	19.5000	+	11.2583i	0.783771	+	0.452510i	0.837765	−	0.546031i	$-0.183862\pi$
$619$	19.5000	+	11.2583i	0.783771	+	0.452510i	−0.0539940	+	0.998541i	$0.517195\pi$
$620$			20.1246i			0.808224i
$621$		0			0
$622$		−	17.3205i		−	0.694489i
$623$	−5.80948	−	30.1869i	−0.232752	−	1.20941i
$624$		0			0
$625$	−12.5000	−	21.6506i	−0.500000	−	0.866025i
$626$	−3.87298	−	6.70820i	−0.154796	−	0.268114i
$627$		0			0
$628$	−9.00000	−	5.19615i	−0.359139	−	0.207349i
$629$		0			0
$630$		0			0
$631$	2.00000			0.0796187			0.0398094	−	0.999207i	$-0.487325\pi$
$631$	2.00000			0.0796187			0.0398094	+	0.999207i	$0.487325\pi$
$632$	−3.87298	−	2.23607i	−0.154059	−	0.0889460i
$633$		0			0
$634$	−5.00000	−	8.66025i	−0.198575	−	0.343943i
$635$	−19.3649	−	33.5410i	−0.768473	−	1.33103i
$636$		0			0
$637$	15.0000	−	19.0526i	0.594322	−	0.754890i
$638$		−	22.3607i		−	0.885268i
$639$		0			0
$640$			60.6218i			2.39629i
$641$	−15.4919	−	8.94427i	−0.611895	−	0.353278i	0.161812	−	0.986822i	$-0.448266\pi$
$641$	−15.4919	−	8.94427i	−0.611895	−	0.353278i	−0.773707	+	0.633544i	$0.781600\pi$
$642$		0			0
$643$	−34.5000	+	19.9186i	−1.36055	+	0.785512i	−0.989697	−	0.143180i	$-0.954267\pi$
$643$	−34.5000	+	19.9186i	−1.36055	+	0.785512i	−0.370851	+	0.928693i	$0.620934\pi$
$644$	−5.80948	+	16.7705i	−0.228925	+	0.660851i
$645$		0			0
$646$		0			0
$647$	23.2379			0.913576			0.456788	−	0.889576i	$-0.349000\pi$
$647$	23.2379			0.913576			0.456788	+	0.889576i	$0.349000\pi$
$648$		0			0
$649$		−	17.3205i		−	0.679889i
$650$	38.7298	−	67.0820i	1.51911	−	2.63117i
$651$		0			0
$652$	−15.0000	−	25.9808i	−0.587445	−	1.01749i
$653$	−42.6028	+	24.5967i	−1.66718	+	0.962545i	−0.698028	+	0.716071i	$0.745939\pi$
$653$	−42.6028	+	24.5967i	−1.66718	+	0.962545i	−0.969149	+	0.246474i	$0.920728\pi$
$654$		0			0
$655$	15.0000	−	25.9808i	0.586098	−	1.01515i
$656$	3.87298			0.151215
$657$		0			0
$658$	−30.0000	−	34.6410i	−1.16952	−	1.35045i
$659$	1.93649	+	1.11803i	0.0754350	+	0.0435524i	0.537243	−	0.843427i	$-0.319466\pi$
$659$	1.93649	+	1.11803i	0.0754350	+	0.0435524i	−0.461808	+	0.886980i	$0.652799\pi$
$660$		0			0
$661$	−39.0000	+	22.5167i	−1.51692	+	0.875797i	−0.517122	+	0.855912i	$0.672997\pi$
$661$	−39.0000	+	22.5167i	−1.51692	+	0.875797i	−0.999802	+	0.0198848i	$0.993670\pi$
$662$	7.74597	−	4.47214i	0.301056	−	0.173814i
$663$		0			0
$664$	15.0000	+	8.66025i	0.582113	+	0.336083i
$665$	−34.8569	−	40.2492i	−1.35169	−	1.56080i
$666$		0			0
$667$	10.0000			0.387202
$668$	−23.2379	+	40.2492i	−0.899101	+	1.55729i
$669$		0			0
$670$	−75.0000	+	43.3013i	−2.89750	+	1.67287i
$671$	7.74597	+	13.4164i	0.299030	+	0.517935i
$672$		0			0
$673$	−1.00000	+	1.73205i	−0.0385472	+	0.0667657i	−0.884655	−	0.466246i	$-0.845606\pi$
$673$	−1.00000	+	1.73205i	−0.0385472	+	0.0667657i	0.846108	+	0.533011i	$0.178940\pi$
$674$		−	78.2624i		−	3.01455i
$675$		0			0
$676$	−3.00000			−0.115385
$677$	−13.5554	+	23.4787i	−0.520978	+	0.902360i	0.478724	+	0.877965i	$0.341099\pi$
$677$	−13.5554	+	23.4787i	−0.520978	+	0.902360i	−0.999702	+	0.0243951i	$0.992234\pi$
$678$		0			0
$679$	−12.0000	+	34.6410i	−0.460518	+	1.32940i
$680$		0			0
$681$		0			0
$682$	7.50000	+	4.33013i	0.287190	+	0.165809i
$683$		−	29.0689i		−	1.11229i	−0.831085	−	0.556145i	$-0.812280\pi$
$683$		−	29.0689i		−	1.11229i	0.831085	−	0.556145i	$-0.187720\pi$
$684$		0			0
$685$			86.6025i			3.30891i
$686$	1.93649	+	41.3673i	0.0739356	+	1.57941i
$687$		0			0
$688$	1.00000	+	1.73205i	0.0381246	+	0.0660338i
$689$	15.4919	+	26.8328i	0.590196	+	1.02225i
$690$		0			0
$691$	15.0000	+	8.66025i	0.570627	+	0.329452i	0.757400	−	0.652952i	$-0.226469\pi$
$691$	15.0000	+	8.66025i	0.570627	+	0.329452i	−0.186773	+	0.982403i	$0.559803\pi$
$692$	−11.6190			−0.441686
$693$		0			0
$694$	25.0000			0.948987
$695$	−11.6190	−	6.70820i	−0.440732	−	0.254457i
$696$		0			0
$697$		0			0
$698$	−15.4919	−	26.8328i	−0.586378	−	1.01564i
$699$		0			0
$700$	15.0000	+	77.9423i	0.566947	+	2.94594i
$701$			31.3050i			1.18237i	0.806535	+	0.591186i	$0.201340\pi$
$701$			31.3050i			1.18237i	−0.806535	+	0.591186i	$0.798660\pi$
$702$		0			0
$703$			5.19615i			0.195977i
$704$	25.1744	+	14.5344i	0.948796	+	0.547787i
$705$		0			0
$706$	37.5000	−	21.6506i	1.41133	−	0.814832i
$707$	38.7298	+	13.4164i	1.45659	+	0.504576i
$708$		0			0
$709$	21.5000	−	37.2391i	0.807449	−	1.39854i	−0.107176	−	0.994240i	$-0.534181\pi$
$709$	21.5000	−	37.2391i	0.807449	−	1.39854i	0.914625	−	0.404303i	$-0.132486\pi$
$710$	−96.8246			−3.63376
$711$		0			0
$712$			25.9808i			0.973670i
$713$	−1.93649	+	3.35410i	−0.0725222	+	0.125612i
$714$		0			0
$715$	−15.0000	−	25.9808i	−0.560968	−	0.971625i
$716$	−46.4758	+	26.8328i	−1.73688	+	1.00279i
$717$		0			0
$718$	10.0000	−	17.3205i	0.373197	−	0.646396i
$719$	−23.2379			−0.866627			−0.433314	−	0.901243i	$-0.642656\pi$
$719$	−23.2379			−0.866627			−0.433314	+	0.901243i	$0.642656\pi$
$720$		0			0
$721$	−3.00000	−	3.46410i	−0.111726	−	0.129010i
$722$	−15.4919	−	8.94427i	−0.576550	−	0.332871i
$723$		0			0
$724$		0			0
$725$	38.7298	−	22.3607i	1.43839	−	0.830455i
$726$		0			0
$727$	−3.00000	−	1.73205i	−0.111264	−	0.0642382i	0.443335	−	0.896356i	$-0.353795\pi$
$727$	−3.00000	−	1.73205i	−0.111264	−	0.0642382i	−0.554599	+	0.832118i	$0.687128\pi$
$728$	−15.4919	+	13.4164i	−0.574169	+	0.497245i
$729$		0			0
$730$	90.0000			3.33105
$731$		0			0
$732$		0			0
$733$	33.0000	−	19.0526i	1.21888	−	0.703722i	0.254204	−	0.967151i	$-0.418187\pi$
$733$	33.0000	−	19.0526i	1.21888	−	0.703722i	0.964679	+	0.263428i	$0.0848533\pi$
$734$	1.93649	+	3.35410i	0.0714772	+	0.123802i
$735$		0			0
$736$	−7.50000	+	12.9904i	−0.276454	+	0.478832i
$737$			22.3607i			0.823666i
$738$		0			0
$739$	44.0000			1.61857			0.809283	−	0.587419i	$-0.199856\pi$
$739$	44.0000			1.61857			0.809283	+	0.587419i	$0.199856\pi$
$740$	5.80948	−	10.0623i	0.213561	−	0.369898i
$741$		0			0
$742$	−50.0000	−	17.3205i	−1.83556	−	0.635856i
$743$	9.68246	−	5.59017i	0.355215	−	0.205083i	−0.311765	−	0.950159i	$-0.600920\pi$
$743$	9.68246	−	5.59017i	0.355215	−	0.205083i	0.666980	+	0.745076i	$0.267587\pi$
$744$		0			0
$745$	−30.0000	−	17.3205i	−1.09911	−	0.634574i
$746$		−	38.0132i		−	1.39176i
$747$		0			0
$748$		0			0
$749$	−23.2379	+	4.47214i	−0.849094	+	0.163408i
$750$		0			0
$751$	23.0000	+	39.8372i	0.839282	+	1.45368i	0.890496	+	0.454991i	$0.150358\pi$
$751$	23.0000	+	39.8372i	0.839282	+	1.45368i	−0.0512140	+	0.998688i	$0.516309\pi$
$752$	−3.87298	−	6.70820i	−0.141233	−	0.244623i
$753$		0			0
$754$	30.0000	+	17.3205i	1.09254	+	0.630776i
$755$	61.9677			2.25524
$756$		0			0
$757$	−34.0000			−1.23575			−0.617876	−	0.786276i	$-0.712006\pi$
$757$	−34.0000			−1.23575			−0.617876	+	0.786276i	$0.712006\pi$
$758$	50.3488	+	29.0689i	1.82875	+	1.05583i
$759$		0			0
$760$	22.5000	+	38.9711i	0.816161	+	1.41363i
$761$	7.74597	+	13.4164i	0.280791	+	0.486344i	0.971580	−	0.236712i	$-0.0760699\pi$
$761$	7.74597	+	13.4164i	0.280791	+	0.486344i	−0.690789	+	0.723057i	$0.742737\pi$
$762$		0			0
$763$	3.50000	+	18.1865i	0.126709	+	0.658397i
$764$			6.70820i			0.242694i
$765$		0			0
$766$		−	69.2820i		−	2.50326i
$767$	23.2379	+	13.4164i	0.839072	+	0.484438i
$768$		0			0
$769$	15.0000	−	8.66025i	0.540914	−	0.312297i	−0.204535	−	0.978859i	$-0.565568\pi$
$769$	15.0000	−	8.66025i	0.540914	−	0.312297i	0.745449	+	0.666562i	$0.232235\pi$
$770$	48.4123	+	16.7705i	1.74466	+	0.604367i
$771$		0			0
$772$	3.00000	−	5.19615i	0.107972	−	0.187014i
$773$	11.6190			0.417905			0.208952	−	0.977926i	$-0.432995\pi$
$773$	11.6190			0.417905			0.208952	+	0.977926i	$0.432995\pi$
$774$		0			0
$775$			17.3205i			0.622171i
$776$	15.4919	−	26.8328i	0.556128	−	0.963242i
$777$		0			0
$778$	40.0000	+	69.2820i	1.43407	+	2.48388i
$779$	17.4284	−	10.0623i	0.624438	−	0.360520i
$780$		0			0
$781$	−12.5000	+	21.6506i	−0.447285	+	0.774721i
$782$		0			0
$783$		0			0
$784$	−1.00000	+	6.92820i	−0.0357143	+	0.247436i
$785$	−11.6190	−	6.70820i	−0.414698	−	0.239426i
$786$		0			0
$787$	33.0000	−	19.0526i	1.17632	−	0.679150i	0.221162	−	0.975237i	$-0.429015\pi$
$787$	33.0000	−	19.0526i	1.17632	−	0.679150i	0.955161	+	0.296087i	$0.0956817\pi$
$788$	23.2379	−	13.4164i	0.827816	−	0.477940i
$789$		0			0
$790$	−15.0000	−	8.66025i	−0.533676	−	0.308118i
$791$	15.4919	+	17.8885i	0.550830	+	0.636043i
$792$		0			0
$793$	−24.0000			−0.852265
$794$	−23.2379	+	40.2492i	−0.824682	+	1.42839i
$795$		0			0
$796$	−67.5000	+	38.9711i	−2.39247	+	1.38130i
$797$	1.93649	+	3.35410i	0.0685941	+	0.118808i	0.898283	−	0.439418i	$-0.144815\pi$
$797$	1.93649	+	3.35410i	0.0685941	+	0.118808i	−0.829689	+	0.558227i	$0.811482\pi$
$798$		0			0
$799$		0			0
$800$			67.0820i			2.37171i
$801$		0			0
$802$	70.0000			2.47179
$803$	11.6190	−	20.1246i	0.410024	−	0.710182i
$804$		0			0
$805$	−7.50000	+	21.6506i	−0.264340	+	0.763085i
$806$	−11.6190	+	6.70820i	−0.409260	+	0.236286i
$807$		0			0
$808$	−30.0000	−	17.3205i	−1.05540	−	0.609333i
$809$			31.3050i			1.10062i	0.834959	+	0.550312i	$0.185491\pi$
$809$			31.3050i			1.10062i	−0.834959	+	0.550312i	$0.814509\pi$
$810$		0			0
$811$		−	36.3731i		−	1.27723i	−0.769526	−	0.638616i	$-0.779507\pi$
$811$		−	36.3731i		−	1.27723i	0.769526	−	0.638616i	$-0.220493\pi$
$812$	−34.8569	+	6.70820i	−1.22324	+	0.235412i
$813$		0			0
$814$	−2.50000	−	4.33013i	−0.0876250	−	0.151771i
$815$	−19.3649	−	33.5410i	−0.678323	−	1.17489i
$816$		0			0
$817$	9.00000	+	5.19615i	0.314870	+	0.181790i
$818$	38.7298			1.35416
$819$		0			0
$820$	−45.0000			−1.57147
$821$	19.3649	+	11.1803i	0.675840	+	0.390197i	0.798286	−	0.602279i	$-0.205740\pi$
$821$	19.3649	+	11.1803i	0.675840	+	0.390197i	−0.122446	+	0.992475i	$0.539074\pi$
$822$		0			0
$823$	−10.0000	−	17.3205i	−0.348578	−	0.603755i	0.637419	−	0.770517i	$-0.280002\pi$
$823$	−10.0000	−	17.3205i	−0.348578	−	0.603755i	−0.985997	+	0.166762i	$0.946669\pi$
$824$	1.93649	+	3.35410i	0.0674609	+	0.116846i
$825$		0			0
$826$	−45.0000	+	8.66025i	−1.56575	+	0.301329i
$827$			11.1803i			0.388779i	0.980924	+	0.194389i	$0.0622725\pi$
$827$			11.1803i			0.388779i	−0.980924	+	0.194389i	$0.937728\pi$
$828$		0			0
$829$		−	31.1769i		−	1.08282i	−0.840759	−	0.541409i	$-0.817891\pi$
$829$		−	31.1769i		−	1.08282i	0.840759	−	0.541409i	$-0.182109\pi$
$830$	58.0948	+	33.5410i	2.01650	+	1.16423i
$831$		0			0
$832$	−39.0000	+	22.5167i	−1.35208	+	0.780625i
$833$		0			0
$834$		0			0
$835$	−30.0000	+	51.9615i	−1.03819	+	1.79820i
$836$	34.8569			1.20555
$837$		0			0
$838$			34.6410i			1.19665i
$839$	−19.3649	+	33.5410i	−0.668551	+	1.15796i	0.309758	+	0.950815i	$0.399752\pi$
$839$	−19.3649	+	33.5410i	−0.668551	+	1.15796i	−0.978309	+	0.207149i	$0.933581\pi$
$840$		0			0
$841$	−4.50000	−	7.79423i	−0.155172	−	0.268767i
$842$	−21.3014	+	12.2984i	−0.734095	+	0.423830i
$843$		0			0
$844$	12.0000	−	20.7846i	0.413057	−	0.715436i
$845$	−3.87298			−0.133235
$846$		0			0
$847$	−12.0000	+	10.3923i	−0.412325	+	0.357084i
$848$	−7.74597	−	4.47214i	−0.265998	−	0.153574i
$849$		0			0
$850$		0			0
$851$	1.93649	−	1.11803i	0.0663821	−	0.0383257i
$852$		0			0
$853$	−12.0000	−	6.92820i	−0.410872	−	0.237217i	0.280292	−	0.959915i	$-0.409569\pi$
$853$	−12.0000	−	6.92820i	−0.410872	−	0.237217i	−0.691164	+	0.722698i	$0.742902\pi$
$854$	30.9839	−	26.8328i	1.06025	−	0.918200i
$855$		0			0
$856$	20.0000			0.683586
$857$	−13.5554	+	23.4787i	−0.463045	+	0.802018i	−0.999111	−	0.0421586i	$-0.986577\pi$
$857$	−13.5554	+	23.4787i	−0.463045	+	0.802018i	0.536066	+	0.844176i	$0.319910\pi$
$858$		0			0
$859$	19.5000	−	11.2583i	0.665331	−	0.384129i	−0.128974	−	0.991648i	$-0.541168\pi$
$859$	19.5000	−	11.2583i	0.665331	−	0.384129i	0.794305	+	0.607519i	$0.207835\pi$
$860$	−11.6190	−	20.1246i	−0.396203	−	0.686244i
$861$		0			0
$862$	2.50000	−	4.33013i	0.0851503	−	0.147485i
$863$		−	8.94427i		−	0.304467i	−0.988345	−	0.152233i	$-0.951353\pi$
$863$		−	8.94427i		−	0.304467i	0.988345	−	0.152233i	$-0.0486465\pi$
$864$		0			0
$865$	−15.0000			−0.510015
$866$	11.6190	−	20.1246i	0.394828	−	0.683862i
$867$		0			0
$868$	4.50000	−	12.9904i	0.152740	−	0.440922i
$869$	−3.87298	+	2.23607i	−0.131382	+	0.0758534i
$870$		0			0
$871$	−30.0000	−	17.3205i	−1.01651	−	0.586883i
$872$		−	15.6525i		−	0.530060i
$873$		0			0
$874$			25.9808i			0.878812i
$875$	9.68246	+	50.3115i	0.327327	+	1.70084i
$876$		0			0
$877$	23.0000	+	39.8372i	0.776655	+	1.34521i	0.933860	+	0.357640i	$0.116418\pi$
$877$	23.0000	+	39.8372i	0.776655	+	1.34521i	−0.157205	+	0.987566i	$0.550248\pi$
$878$	42.6028	+	73.7902i	1.43778	+	2.49030i
$879$		0			0
$880$	7.50000	+	4.33013i	0.252825	+	0.145969i
$881$	−34.8569			−1.17436			−0.587179	−	0.809457i	$-0.699761\pi$
$881$	−34.8569			−1.17436			−0.587179	+	0.809457i	$0.699761\pi$
$882$		0			0
$883$	8.00000			0.269221			0.134611	−	0.990899i	$-0.457022\pi$
$883$	8.00000			0.269221			0.134611	+	0.990899i	$0.457022\pi$
$884$		0			0
$885$		0			0
$886$	−27.5000	−	47.6314i	−0.923881	−	1.60021i
$887$	−3.87298	−	6.70820i	−0.130042	−	0.225239i	0.793651	−	0.608374i	$-0.208178\pi$
$887$	−3.87298	−	6.70820i	−0.130042	−	0.225239i	−0.923693	+	0.383135i	$0.874845\pi$
$888$		0			0
$889$	5.00000	+	25.9808i	0.167695	+	0.871367i
$890$			100.623i			3.37289i
$891$		0			0
$892$			5.19615i			0.173980i
$893$	−34.8569	−	20.1246i	−1.16644	−	0.673444i
$894$		0			0
$895$	−60.0000	+	34.6410i	−2.00558	+	1.15792i
$896$	13.5554	−	39.1312i	0.452856	−	1.30728i
$897$		0			0
$898$	10.0000	−	17.3205i	0.333704	−	0.577993i
$899$	−7.74597			−0.258342
$900$		0			0
$901$		0			0
$902$	−9.68246	+	16.7705i	−0.322391	+	0.558397i
$903$		0			0
$904$	−10.0000	−	17.3205i	−0.332595	−	0.576072i
$905$		0			0
$906$		0			0
$907$	8.00000	−	13.8564i	0.265636	−	0.460094i	−0.702094	−	0.712084i	$-0.747752\pi$
$907$	8.00000	−	13.8564i	0.265636	−	0.460094i	0.967730	+	0.251990i	$0.0810849\pi$
$908$	−46.4758			−1.54235
$909$		0			0
$910$	−60.0000	+	51.9615i	−1.98898	+	1.72251i
$911$	30.9839	+	17.8885i	1.02654	+	0.592674i	0.915992	−	0.401197i	$-0.131406\pi$
$911$	30.9839	+	17.8885i	1.02654	+	0.592674i	0.110549	+	0.993871i	$0.464739\pi$
$912$		0			0
$913$	15.0000	−	8.66025i	0.496428	−	0.286613i
$914$	48.4123	−	27.9508i	1.60134	−	0.924532i
$915$		0			0
$916$	−36.0000	−	20.7846i	−1.18947	−	0.686743i
$917$	−15.4919	+	13.4164i	−0.511589	+	0.443049i
$918$		0			0
$919$	−28.0000			−0.923635			−0.461817	−	0.886975i	$-0.652802\pi$
$919$	−28.0000			−0.923635			−0.461817	+	0.886975i	$0.652802\pi$
$920$	9.68246	−	16.7705i	0.319221	−	0.552907i
$921$		0			0
$922$	−7.50000	+	4.33013i	−0.246999	+	0.142605i
$923$	−19.3649	−	33.5410i	−0.637404	−	1.10402i
$924$		0			0
$925$	5.00000	−	8.66025i	0.164399	−	0.284747i
$926$		−	17.8885i		−	0.587854i
$927$		0			0
$928$	−30.0000			−0.984798
$929$	−7.74597	+	13.4164i	−0.254137	+	0.440178i	−0.964661	−	0.263495i	$-0.915125\pi$
$929$	−7.74597	+	13.4164i	−0.254137	+	0.440178i	0.710524	+	0.703673i	$0.248458\pi$
$930$		0			0
$931$	13.5000	+	33.7750i	0.442445	+	1.10693i
$932$	−46.4758	+	26.8328i	−1.52237	+	0.878938i
$933$		0			0
$934$	−45.0000	−	25.9808i	−1.47244	−	0.850117i
$935$		0			0
$936$		0			0
$937$		−	20.7846i		−	0.679004i	−0.940605	−	0.339502i	$-0.889742\pi$
$937$		−	20.7846i		−	0.679004i	0.940605	−	0.339502i	$-0.110258\pi$
$938$	58.0948	−	11.1803i	1.89686	−	0.365051i
$939$		0			0
$940$	45.0000	+	77.9423i	1.46774	+	2.54220i
$941$	1.93649	+	3.35410i	0.0631278	+	0.109341i	0.895862	−	0.444332i	$-0.146559\pi$
$941$	1.93649	+	3.35410i	0.0631278	+	0.109341i	−0.832734	+	0.553673i	$0.813226\pi$
$942$		0			0
$943$	−7.50000	−	4.33013i	−0.244234	−	0.141008i
$944$	−7.74597			−0.252110
$945$		0			0
$946$	−10.0000			−0.325128
$947$	13.5554	+	7.82624i	0.440493	+	0.254319i	0.703807	−	0.710392i	$-0.251482\pi$
$947$	13.5554	+	7.82624i	0.440493	+	0.254319i	−0.263314	+	0.964710i	$0.584815\pi$
$948$		0			0
$949$	18.0000	+	31.1769i	0.584305	+	1.01205i
$950$	58.0948	+	100.623i	1.88484	+	3.26464i
$951$		0			0
$952$		0			0
$953$		−	22.3607i		−	0.724333i	−0.932113	−	0.362167i	$-0.882037\pi$
$953$		−	22.3607i		−	0.724333i	0.932113	−	0.362167i	$-0.117963\pi$
$954$		0			0
$955$			8.66025i			0.280239i
$956$	−23.2379	−	13.4164i	−0.751567	−	0.433918i
$957$		0			0
$958$	60.0000	−	34.6410i	1.93851	−	1.11920i
$959$	19.3649	−	55.9017i	0.625326	−	1.80516i
$960$		0			0
$961$	−14.0000	+	24.2487i	−0.451613	+	0.782216i
$962$	7.74597			0.249740
$963$		0			0
$964$			51.9615i			1.67357i
$965$	3.87298	−	6.70820i	0.124676	−	0.215945i
$966$		0			0
$967$	−28.0000	−	48.4974i	−0.900419	−	1.55957i	−0.826951	−	0.562274i	$-0.809926\pi$
$967$	−28.0000	−	48.4974i	−0.900419	−	1.55957i	−0.0734686	−	0.997298i	$-0.523407\pi$
$968$	11.6190	−	6.70820i	0.373447	−	0.215610i
$969$		0			0
$970$	60.0000	−	103.923i	1.92648	−	3.33677i
$971$	−23.2379			−0.745740			−0.372870	−	0.927884i	$-0.621626\pi$
$971$	−23.2379			−0.745740			−0.372870	+	0.927884i	$0.621626\pi$
$972$		0			0
$973$	6.00000	+	6.92820i	0.192351	+	0.222108i
$974$	−19.3649	−	11.1803i	−0.620492	−	0.358241i
$975$		0			0
$976$	6.00000	−	3.46410i	0.192055	−	0.110883i
$977$	15.4919	−	8.94427i	0.495631	−	0.286153i	−0.231277	−	0.972888i	$-0.574290\pi$
$977$	15.4919	−	8.94427i	0.495631	−	0.286153i	0.726907	+	0.686735i	$0.240957\pi$
$978$		0			0
$979$	22.5000	+	12.9904i	0.719103	+	0.415174i
$980$	11.6190	−	80.4984i	0.371154	−	2.57143i
$981$		0			0
$982$	85.0000			2.71246
$983$	27.1109	−	46.9574i	0.864703	−	1.49771i	−0.00263900	−	0.999997i	$-0.500840\pi$
$983$	27.1109	−	46.9574i	0.864703	−	1.49771i	0.867342	−	0.497713i	$-0.165827\pi$
$984$		0			0
$985$	30.0000	−	17.3205i	0.955879	−	0.551877i
$986$		0			0
$987$		0			0
$988$	−27.0000	+	46.7654i	−0.858984	+	1.48780i
$989$		−	4.47214i		−	0.142206i
$990$		0			0
$991$	26.0000			0.825917			0.412959	−	0.910750i	$-0.364495\pi$
$991$	26.0000			0.825917			0.412959	+	0.910750i	$0.364495\pi$
$992$	5.80948	−	10.0623i	0.184451	−	0.319479i
$993$		0			0
$994$	62.5000	+	21.6506i	1.98238	+	0.686716i
$995$	−87.1421	+	50.3115i	−2.76259	+	1.59498i
$996$		0			0
$997$	24.0000	+	13.8564i	0.760088	+	0.438837i	0.829327	−	0.558763i	$-0.188724\pi$
$997$	24.0000	+	13.8564i	0.760088	+	0.438837i	−0.0692396	+	0.997600i	$0.522057\pi$
$998$		−	84.9706i		−	2.68970i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.o.c.188.2		4
3.2	odd	2	inner	567.2.o.c.188.1		4
7.6	odd	2		567.2.o.d.188.2		4
9.2	odd	6		189.2.c.b.188.4	yes	4
9.4	even	3		567.2.o.d.377.1		4
9.5	odd	6		567.2.o.d.377.2		4
9.7	even	3		189.2.c.b.188.1	✓	4
21.20	even	2		567.2.o.d.188.1		4
36.7	odd	6		3024.2.k.i.1889.1		4
36.11	even	6		3024.2.k.i.1889.3		4
63.13	odd	6	inner	567.2.o.c.377.1		4
63.20	even	6		189.2.c.b.188.3	yes	4
63.34	odd	6		189.2.c.b.188.2	yes	4
63.41	even	6	inner	567.2.o.c.377.2		4
252.83	odd	6		3024.2.k.i.1889.2		4
252.223	even	6		3024.2.k.i.1889.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.c.b.188.1	✓	4	9.7	even	3
189.2.c.b.188.2	yes	4	63.34	odd	6
189.2.c.b.188.3	yes	4	63.20	even	6
189.2.c.b.188.4	yes	4	9.2	odd	6
567.2.o.c.188.1		4	3.2	odd	2	inner
567.2.o.c.188.2		4	1.1	even	1	trivial
567.2.o.c.377.1		4	63.13	odd	6	inner
567.2.o.c.377.2		4	63.41	even	6	inner
567.2.o.d.188.1		4	21.20	even	2
567.2.o.d.188.2		4	7.6	odd	2
567.2.o.d.377.1		4	9.4	even	3
567.2.o.d.377.2		4	9.5	odd	6
3024.2.k.i.1889.1		4	36.7	odd	6
3024.2.k.i.1889.2		4	252.83	odd	6
3024.2.k.i.1889.3		4	36.11	even	6
3024.2.k.i.1889.4		4	252.223	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.93649 + 1.11803i) q^{2} +(1.50000 + 2.59808i) q^{4} +(1.93649 + 3.35410i) q^{5} +(-0.500000 - 2.59808i) q^{7} +2.23607i q^{8} +O(q^{10})\)	\(q+(1.93649 + 1.11803i) q^{2} +(1.50000 + 2.59808i) q^{4} +(1.93649 + 3.35410i) q^{5} +(-0.500000 - 2.59808i) q^{7} +2.23607i q^{8} +8.66025i q^{10} +(1.93649 + 1.11803i) q^{11} +(-3.00000 + 1.73205i) q^{13} +(1.93649 - 5.59017i) q^{14} +(0.500000 - 0.866025i) q^{16} -5.19615i q^{19} +(-5.80948 + 10.0623i) q^{20} +(2.50000 + 4.33013i) q^{22} +(-1.93649 + 1.11803i) q^{23} +(-5.00000 + 8.66025i) q^{25} -7.74597 q^{26} +(6.00000 - 5.19615i) q^{28} +(-3.87298 - 2.23607i) q^{29} +(1.50000 - 0.866025i) q^{31} +(5.80948 - 3.35410i) q^{32} +(7.74597 - 6.70820i) q^{35} -1.00000 q^{37} +(5.80948 - 10.0623i) q^{38} +(-7.50000 + 4.33013i) q^{40} +(1.93649 + 3.35410i) q^{41} +(-1.00000 + 1.73205i) q^{43} +6.70820i q^{44} -5.00000 q^{46} +(3.87298 - 6.70820i) q^{47} +(-6.50000 + 2.59808i) q^{49} +(-19.3649 + 11.1803i) q^{50} +(-9.00000 - 5.19615i) q^{52} -8.94427i q^{53} +8.66025i q^{55} +(5.80948 - 1.11803i) q^{56} +(-5.00000 - 8.66025i) q^{58} +(-3.87298 - 6.70820i) q^{59} +(6.00000 + 3.46410i) q^{61} +3.87298 q^{62} +13.0000 q^{64} +(-11.6190 - 6.70820i) q^{65} +(5.00000 + 8.66025i) q^{67} +(22.5000 - 4.33013i) q^{70} +11.1803i q^{71} -10.3923i q^{73} +(-1.93649 - 1.11803i) q^{74} +(13.5000 - 7.79423i) q^{76} +(1.93649 - 5.59017i) q^{77} +(-1.00000 + 1.73205i) q^{79} +3.87298 q^{80} +8.66025i q^{82} +(3.87298 - 6.70820i) q^{83} +(-3.87298 + 2.23607i) q^{86} +(-2.50000 + 4.33013i) q^{88} +11.6190 q^{89} +(6.00000 + 6.92820i) q^{91} +(-5.80948 - 3.35410i) q^{92} +(15.0000 - 8.66025i) q^{94} +(17.4284 - 10.0623i) q^{95} +(-12.0000 - 6.92820i) q^{97} +(-15.4919 - 2.23607i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 6 q^{4} - 2 q^{7}+O(q^{10}) \) 4 * q + 6 * q^4 - 2 * q^7	\( 4 q + 6 q^{4} - 2 q^{7} - 12 q^{13} + 2 q^{16} + 10 q^{22} - 20 q^{25} + 24 q^{28} + 6 q^{31} - 4 q^{37} - 30 q^{40} - 4 q^{43} - 20 q^{46} - 26 q^{49} - 36 q^{52} - 20 q^{58} + 24 q^{61} + 52 q^{64} + 20 q^{67} + 90 q^{70} + 54 q^{76} - 4 q^{79} - 10 q^{88} + 24 q^{91} + 60 q^{94} - 48 q^{97}+O(q^{100}) \) 4 * q + 6 * q^4 - 2 * q^7 - 12 * q^13 + 2 * q^16 + 10 * q^22 - 20 * q^25 + 24 * q^28 + 6 * q^31 - 4 * q^37 - 30 * q^40 - 4 * q^43 - 20 * q^46 - 26 * q^49 - 36 * q^52 - 20 * q^58 + 24 * q^61 + 52 * q^64 + 20 * q^67 + 90 * q^70 + 54 * q^76 - 4 * q^79 - 10 * q^88 + 24 * q^91 + 60 * q^94 - 48 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more