LMFDB - Embedded newform 576.2.bb.e.49.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [576,2,Mod(49,576)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(576, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("576.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 576 = 2^{6} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	576.bb (of order $12$, degree $4$, 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:	$4.59938315643$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 144)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			49.5
Character	$\chi$	$=$	576.49
Dual form			576.2.bb.e.529.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.08700 + 1.34849i) q^{3} +(2.90072 - 0.777246i) q^{5} +(1.04527 - 0.603486i) q^{7} +(-0.636858 - 2.93162i) q^{9} +O(q^{10})$	\(q+(-1.08700 + 1.34849i) q^{3} +(2.90072 - 0.777246i) q^{5} +(1.04527 - 0.603486i) q^{7} +(-0.636858 - 2.93162i) q^{9} +(1.36579 - 5.09718i) q^{11} +(-0.541655 - 2.02149i) q^{13} +(-2.10498 + 4.75646i) q^{15} -3.20404 q^{17} +(1.87633 - 1.87633i) q^{19} +(-0.322412 + 2.06553i) q^{21} +(-3.61927 - 2.08959i) q^{23} +(3.47994 - 2.00914i) q^{25} +(4.64553 + 2.32788i) q^{27} +(7.94194 + 2.12804i) q^{29} +(-1.39155 + 2.41023i) q^{31} +(5.38890 + 7.38239i) q^{33} +(2.56298 - 2.56298i) q^{35} +(-5.10207 - 5.10207i) q^{37} +(3.31474 + 1.46694i) q^{39} +(9.93271 + 5.73465i) q^{41} +(0.293160 - 1.09409i) q^{43} +(-4.12594 - 8.00882i) q^{45} +(1.84507 + 3.19576i) q^{47} +(-2.77161 + 4.80057i) q^{49} +(3.48279 - 4.32062i) q^{51} +(-0.613957 - 0.613957i) q^{53} -15.8471i q^{55} +(0.490642 + 4.56978i) q^{57} +(11.8105 - 3.16461i) q^{59} +(-7.40505 - 1.98418i) q^{61} +(-2.43488 - 2.68000i) q^{63} +(-3.14238 - 5.44277i) q^{65} +(2.64353 + 9.86577i) q^{67} +(6.75194 - 2.60917i) q^{69} +12.8889i q^{71} +2.87605i q^{73} +(-1.07338 + 6.87661i) q^{75} +(-1.64847 - 6.15216i) q^{77} +(0.913281 + 1.58185i) q^{79} +(-8.18882 + 3.73406i) q^{81} +(2.82747 + 0.757618i) q^{83} +(-9.29402 + 2.49032i) q^{85} +(-11.5025 + 8.39646i) q^{87} -2.11965i q^{89} +(-1.78611 - 1.78611i) q^{91} +(-1.73756 - 4.49642i) q^{93} +(3.98433 - 6.90107i) q^{95} +(-3.06298 - 5.30524i) q^{97} +(-15.8128 - 0.757786i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 2 q^{3} + 4 q^{5}+O(q^{10}) $ 72 * q - 2 * q^3 + 4 * q^5	$ 72 q - 2 q^{3} + 4 q^{5} + 2 q^{11} - 16 q^{13} + 20 q^{15} - 16 q^{17} - 28 q^{19} - 16 q^{21} - 8 q^{27} + 4 q^{29} - 28 q^{31} - 32 q^{33} + 16 q^{35} + 16 q^{37} + 10 q^{43} + 40 q^{45} + 56 q^{47} + 4 q^{49} + 54 q^{51} - 8 q^{53} + 14 q^{59} - 32 q^{61} + 108 q^{63} - 64 q^{65} + 18 q^{67} + 32 q^{69} - 86 q^{75} - 36 q^{77} - 44 q^{79} - 44 q^{81} - 20 q^{83} - 8 q^{85} + 80 q^{91} - 4 q^{93} - 48 q^{95} + 40 q^{97} - 28 q^{99}+O(q^{100}) $ 72 * q - 2 * q^3 + 4 * q^5 + 2 * q^11 - 16 * q^13 + 20 * q^15 - 16 * q^17 - 28 * q^19 - 16 * q^21 - 8 * q^27 + 4 * q^29 - 28 * q^31 - 32 * q^33 + 16 * q^35 + 16 * q^37 + 10 * q^43 + 40 * q^45 + 56 * q^47 + 4 * q^49 + 54 * q^51 - 8 * q^53 + 14 * q^59 - 32 * q^61 + 108 * q^63 - 64 * q^65 + 18 * q^67 + 32 * q^69 - 86 * q^75 - 36 * q^77 - 44 * q^79 - 44 * q^81 - 20 * q^83 - 8 * q^85 + 80 * q^91 - 4 * q^93 - 48 * q^95 + 40 * q^97 - 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/576\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$325$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	−1.08700	+	1.34849i	−0.627580	+	0.778552i
$3$	−1.08700	+	1.34849i	−0.627580	+	0.778552i
$4$		0			0
$5$	2.90072	−	0.777246i	1.29724	−	0.347595i	0.456835	−	0.889551i	$-0.348983\pi$
$5$	2.90072	−	0.777246i	1.29724	−	0.347595i	0.840406	+	0.541957i	$0.182316\pi$
$6$		0			0
$7$	1.04527	−	0.603486i	0.395074	−	0.228096i	−0.289282	−	0.957244i	$-0.593417\pi$
$7$	1.04527	−	0.603486i	0.395074	−	0.228096i	0.684357	+	0.729148i	$0.260083\pi$
$8$		0			0
$9$	−0.636858	−	2.93162i	−0.212286	−	0.977208i
$10$		0			0
$11$	1.36579	−	5.09718i	0.411800	−	1.53686i	−0.379360	−	0.925249i	$-0.623856\pi$
$11$	1.36579	−	5.09718i	0.411800	−	1.53686i	0.791160	−	0.611609i	$-0.209478\pi$
$12$		0			0
$13$	−0.541655	−	2.02149i	−0.150228	−	0.560659i	−0.999467	−	0.0326501i	$-0.989605\pi$
$13$	−0.541655	−	2.02149i	−0.150228	−	0.560659i	0.849239	−	0.528009i	$-0.177061\pi$
$14$		0			0
$15$	−2.10498	+	4.75646i	−0.543503	+	1.22811i
$16$		0			0
$17$	−3.20404			−0.777093			−0.388547	−	0.921429i	$-0.627023\pi$
$17$	−3.20404			−0.777093			−0.388547	+	0.921429i	$0.627023\pi$
$18$		0			0
$19$	1.87633	−	1.87633i	0.430459	−	0.430459i	−0.458325	−	0.888784i	$-0.651551\pi$
$19$	1.87633	−	1.87633i	0.430459	−	0.430459i	0.888784	+	0.458325i	$0.151551\pi$
$20$		0			0
$21$	−0.322412	+	2.06553i	−0.0703561	+	0.450735i
$22$		0			0
$23$	−3.61927	−	2.08959i	−0.754670	−	0.435709i	0.0727090	−	0.997353i	$-0.476836\pi$
$23$	−3.61927	−	2.08959i	−0.754670	−	0.435709i	−0.827379	+	0.561644i	$0.810169\pi$
$24$		0			0
$25$	3.47994	−	2.00914i	0.695988	−	0.401829i
$26$		0			0
$27$	4.64553	+	2.32788i	0.894033	+	0.448000i
$28$		0			0
$29$	7.94194	+	2.12804i	1.47478	+	0.395166i	0.904568	−	0.426330i	$-0.140194\pi$
$29$	7.94194	+	2.12804i	1.47478	+	0.395166i	0.570214	+	0.821496i	$0.306860\pi$
$30$		0			0
$31$	−1.39155	+	2.41023i	−0.249930	+	0.432891i	−0.963506	−	0.267687i	$-0.913741\pi$
$31$	−1.39155	+	2.41023i	−0.249930	+	0.432891i	0.713576	+	0.700577i	$0.247074\pi$
$32$		0			0
$33$	5.38890	+	7.38239i	0.938087	+	1.28511i
$34$		0			0
$35$	2.56298	−	2.56298i	0.433222	−	0.433222i
$36$		0			0
$37$	−5.10207	−	5.10207i	−0.838775	−	0.838775i	0.149922	−	0.988698i	$-0.452098\pi$
$37$	−5.10207	−	5.10207i	−0.838775	−	0.838775i	−0.988698	+	0.149922i	$0.952098\pi$
$38$		0			0
$39$	3.31474	+	1.46694i	0.530783	+	0.234898i
$40$		0			0
$41$	9.93271	+	5.73465i	1.55123	+	0.895602i	0.998042	+	0.0625444i	$0.0199215\pi$
$41$	9.93271	+	5.73465i	1.55123	+	0.895602i	0.553186	+	0.833058i	$0.313412\pi$
$42$		0			0
$43$	0.293160	−	1.09409i	0.0447065	−	0.166847i	−0.939963	−	0.341275i	$-0.889141\pi$
$43$	0.293160	−	1.09409i	0.0447065	−	0.166847i	0.984670	+	0.174428i	$0.0558078\pi$
$44$		0			0
$45$	−4.12594	−	8.00882i	−0.615059	−	1.19388i
$46$		0			0
$47$	1.84507	+	3.19576i	0.269132	+	0.466150i	0.968638	−	0.248477i	$-0.0799300\pi$
$47$	1.84507	+	3.19576i	0.269132	+	0.466150i	−0.699506	+	0.714627i	$0.746597\pi$
$48$		0			0
$49$	−2.77161	+	4.80057i	−0.395944	+	0.685795i
$50$		0			0
$51$	3.48279	−	4.32062i	0.487688	−	0.605007i
$52$		0			0
$53$	−0.613957	−	0.613957i	−0.0843335	−	0.0843335i	0.663682	−	0.748015i	$-0.268993\pi$
$53$	−0.613957	−	0.613957i	−0.0843335	−	0.0843335i	−0.748015	+	0.663682i	$0.768993\pi$
$54$		0			0
$55$		−	15.8471i		−	2.13682i
$56$		0			0
$57$	0.490642	+	4.56978i	0.0649871	+	0.605282i
$58$		0			0
$59$	11.8105	−	3.16461i	1.53759	−	0.411997i	0.612106	−	0.790776i	$-0.290323\pi$
$59$	11.8105	−	3.16461i	1.53759	−	0.411997i	0.925487	+	0.378779i	$0.123656\pi$
$60$		0			0
$61$	−7.40505	−	1.98418i	−0.948119	−	0.254048i	−0.248555	−	0.968618i	$-0.579956\pi$
$61$	−7.40505	−	1.98418i	−0.948119	−	0.254048i	−0.699564	+	0.714570i	$0.746622\pi$
$62$		0			0
$63$	−2.43488	−	2.68000i	−0.306766	−	0.337648i
$64$		0			0
$65$	−3.14238	−	5.44277i	−0.389765	−	0.675092i
$66$		0			0
$67$	2.64353	+	9.86577i	0.322958	+	1.20530i	0.916349	+	0.400381i	$0.131122\pi$
$67$	2.64353	+	9.86577i	0.322958	+	1.20530i	−0.593391	+	0.804915i	$0.702211\pi$
$68$		0			0
$69$	6.75194	−	2.60917i	0.812838	−	0.314107i
$70$		0			0
$71$			12.8889i			1.52963i	0.644251	+	0.764814i	$0.277169\pi$
$71$			12.8889i			1.52963i	−0.644251	+	0.764814i	$0.722831\pi$
$72$		0			0
$73$			2.87605i			0.336616i	0.985734	+	0.168308i	$0.0538304\pi$
$73$			2.87605i			0.336616i	−0.985734	+	0.168308i	$0.946170\pi$
$74$		0			0
$75$	−1.07338	+	6.87661i	−0.123944	+	0.794043i
$76$		0			0
$77$	−1.64847	−	6.15216i	−0.187860	−	0.701104i
$78$		0			0
$79$	0.913281	+	1.58185i	0.102752	+	0.177972i	0.912818	−	0.408367i	$-0.133902\pi$
$79$	0.913281	+	1.58185i	0.102752	+	0.177972i	−0.810065	+	0.586339i	$0.800568\pi$
$80$		0			0
$81$	−8.18882	+	3.73406i	−0.909869	+	0.414895i
$82$		0			0
$83$	2.82747	+	0.757618i	0.310355	+	0.0831594i	0.410635	−	0.911800i	$-0.365307\pi$
$83$	2.82747	+	0.757618i	0.310355	+	0.0831594i	−0.100280	+	0.994959i	$0.531974\pi$
$84$		0			0
$85$	−9.29402	+	2.49032i	−1.00808	+	0.270114i
$86$		0			0
$87$	−11.5025	+	8.39646i	−1.23320	+	0.900195i
$88$		0			0
$89$		−	2.11965i		−	0.224682i	−0.993670	−	0.112341i	$-0.964165\pi$
$89$		−	2.11965i		−	0.224682i	0.993670	−	0.112341i	$-0.0358349\pi$
$90$		0			0
$91$	−1.78611	−	1.78611i	−0.187236	−	0.187236i
$92$		0			0
$93$	−1.73756	−	4.49642i	−0.180177	−	0.466257i
$94$		0			0
$95$	3.98433	−	6.90107i	0.408784	−	0.708035i
$96$		0			0
$97$	−3.06298	−	5.30524i	−0.310999	−	0.538666i	0.667580	−	0.744538i	$-0.267330\pi$
$97$	−3.06298	−	5.30524i	−0.310999	−	0.538666i	−0.978579	+	0.205872i	$0.933997\pi$
$98$		0			0
$99$	−15.8128	−	0.757786i	−1.58925	−	0.0761603i
$100$		0			0
$101$	−3.38172	+	12.6207i	−0.336493	+	1.25581i	0.565748	+	0.824579i	$0.308588\pi$
$101$	−3.38172	+	12.6207i	−0.336493	+	1.25581i	−0.902241	+	0.431232i	$0.858079\pi$
$102$		0			0
$103$	−11.4364	−	6.60279i	−1.12686	−	0.650592i	−0.183715	−	0.982979i	$-0.558813\pi$
$103$	−11.4364	−	6.60279i	−1.12686	−	0.650592i	−0.943143	+	0.332387i	$0.892146\pi$
$104$		0			0
$105$	0.670194	+	6.24211i	0.0654042	+	0.609167i
$106$		0			0
$107$	−6.92566	−	6.92566i	−0.669529	−	0.669529i	0.288078	−	0.957607i	$-0.406984\pi$
$107$	−6.92566	−	6.92566i	−0.669529	−	0.669529i	−0.957607	+	0.288078i	$0.906984\pi$
$108$		0			0
$109$	−5.36289	+	5.36289i	−0.513672	+	0.513672i	−0.915650	−	0.401977i	$-0.868323\pi$
$109$	−5.36289	+	5.36289i	−0.513672	+	0.513672i	0.401977	+	0.915650i	$0.368323\pi$
$110$		0			0
$111$	12.4261	−	1.33414i	1.17943	−	0.126631i
$112$		0			0
$113$	3.03493	−	5.25666i	0.285502	−	0.494505i	−0.687228	−	0.726441i	$-0.741173\pi$
$113$	3.03493	−	5.25666i	0.285502	−	0.494505i	0.972731	+	0.231937i	$0.0745062\pi$
$114$		0			0
$115$	−12.1226	−	3.24824i	−1.13044	−	0.302900i
$116$		0			0
$117$	−5.58128	+	2.87533i	−0.515989	+	0.265824i
$118$		0			0
$119$	−3.34908	+	1.93359i	−0.307010	+	0.177252i
$120$		0			0
$121$	−14.5896	−	8.42332i	−1.32633	−	0.765757i
$122$		0			0
$123$	−18.5300	+	7.16060i	−1.67079	+	0.645650i
$124$		0			0
$125$	−2.08464	+	2.08464i	−0.186456	+	0.186456i
$126$		0			0
$127$	−11.7086			−1.03897			−0.519484	−	0.854480i	$-0.673876\pi$
$127$	−11.7086			−1.03897			−0.519484	+	0.854480i	$0.673876\pi$
$128$		0			0
$129$	1.15670	+	1.58460i	0.101842	+	0.139516i
$130$		0			0
$131$	2.31247	+	8.63027i	0.202042	+	0.754030i	0.990331	+	0.138725i	$0.0443004\pi$
$131$	2.31247	+	8.63027i	0.202042	+	0.754030i	−0.788289	+	0.615305i	$0.789033\pi$
$132$		0			0
$133$	0.828929	−	3.09360i	0.0718772	−	0.268250i
$134$		0			0
$135$	15.2847	+	3.14180i	1.31550	+	0.270403i
$136$		0			0
$137$	1.32169	−	0.763080i	0.112920	−	0.0651943i	−0.442476	−	0.896780i	$-0.645900\pi$
$137$	1.32169	−	0.763080i	0.112920	−	0.0651943i	0.555396	+	0.831586i	$0.312567\pi$
$138$		0			0
$139$	16.8571	−	4.51685i	1.42980	−	0.383114i	0.540852	−	0.841118i	$-0.318102\pi$
$139$	16.8571	−	4.51685i	1.42980	−	0.383114i	0.888950	+	0.458004i	$0.151435\pi$
$140$		0			0
$141$	−6.31505	−	0.985729i	−0.531823	−	0.0830134i
$142$		0			0
$143$	−11.0437			−0.923518
$144$		0			0
$145$	24.6914			2.05051
$146$		0			0
$147$	−3.46078	−	8.95571i	−0.285441	−	0.738655i
$148$		0			0
$149$	17.1123	−	4.58523i	1.40189	−	0.375637i	0.522870	−	0.852412i	$-0.324861\pi$
$149$	17.1123	−	4.58523i	1.40189	−	0.375637i	0.879025	+	0.476776i	$0.158195\pi$
$150$		0			0
$151$	−4.49848	+	2.59720i	−0.366081	+	0.211357i	−0.671745	−	0.740783i	$-0.734455\pi$
$151$	−4.49848	+	2.59720i	−0.366081	+	0.211357i	0.305664	+	0.952139i	$0.401122\pi$
$152$		0			0
$153$	2.04052	+	9.39303i	0.164966	+	0.759381i
$154$		0			0
$155$	−2.16315	+	8.07299i	−0.173748	+	0.648438i
$156$		0			0
$157$	2.74719	+	10.2527i	0.219250	+	0.818252i	0.984627	+	0.174670i	$0.0558858\pi$
$157$	2.74719	+	10.2527i	0.219250	+	0.818252i	−0.765377	+	0.643582i	$0.777448\pi$
$158$		0			0
$159$	1.49529	−	0.160544i	0.118584	−	0.0127320i
$160$		0			0
$161$	−5.04415			−0.397534
$162$		0			0
$163$	−2.62311	+	2.62311i	−0.205458	+	0.205458i	−0.802334	−	0.596876i	$-0.796409\pi$
$163$	−2.62311	+	2.62311i	−0.205458	+	0.205458i	0.596876	+	0.802334i	$0.296409\pi$
$164$		0			0
$165$	21.3696	+	17.2258i	1.66362	+	1.34102i
$166$		0			0
$167$	5.07413	+	2.92955i	0.392648	+	0.226695i	0.683307	−	0.730131i	$-0.260541\pi$
$167$	5.07413	+	2.92955i	0.392648	+	0.226695i	−0.290659	+	0.956827i	$0.593874\pi$
$168$		0			0
$169$	7.46532	−	4.31010i	0.574255	−	0.331546i
$170$		0			0
$171$	−6.69564	−	4.30573i	−0.512028	−	0.329267i
$172$		0			0
$173$	0.719924	+	0.192903i	0.0547348	+	0.0146662i	0.286083	−	0.958205i	$-0.407647\pi$
$173$	0.719924	+	0.192903i	0.0547348	+	0.0146662i	−0.231348	+	0.972871i	$0.574314\pi$
$174$		0			0
$175$	2.42498	−	4.20019i	0.183311	−	0.317505i
$176$		0			0
$177$	−8.57055	+	19.3663i	−0.644202	+	1.45566i
$178$		0			0
$179$	0.114862	−	0.114862i	0.00858517	−	0.00858517i	−0.702801	−	0.711386i	$-0.748068\pi$
$179$	0.114862	−	0.114862i	0.00858517	−	0.00858517i	0.711386	+	0.702801i	$0.248068\pi$
$180$		0			0
$181$	−7.86110	−	7.86110i	−0.584311	−	0.584311i	0.351774	−	0.936085i	$-0.385578\pi$
$181$	−7.86110	−	7.86110i	−0.584311	−	0.584311i	−0.936085	+	0.351774i	$0.885578\pi$
$182$		0			0
$183$	10.7249	−	7.82884i	0.792810	−	0.578724i
$184$		0			0
$185$	−18.7652	−	10.8341i	−1.37965	−	0.796540i
$186$		0			0
$187$	−4.37603	+	16.3316i	−0.320007	+	1.19428i
$188$		0			0
$189$	6.26067	−	0.370257i	0.455397	−	0.0269322i
$190$		0			0
$191$	−2.25437	−	3.90468i	−0.163120	−	0.282532i	0.772866	−	0.634569i	$-0.218822\pi$
$191$	−2.25437	−	3.90468i	−0.163120	−	0.282532i	−0.935986	+	0.352037i	$0.885489\pi$
$192$		0			0
$193$	9.64610	−	16.7075i	0.694342	−	1.20264i	−0.276060	−	0.961140i	$-0.589029\pi$
$193$	9.64610	−	16.7075i	0.694342	−	1.20264i	0.970402	−	0.241495i	$-0.0776377\pi$
$194$		0			0
$195$	10.7553	+	1.67882i	0.770203	+	0.120222i
$196$		0			0
$197$	−6.03688	−	6.03688i	−0.430110	−	0.430110i	0.458556	−	0.888666i	$-0.348367\pi$
$197$	−6.03688	−	6.03688i	−0.430110	−	0.430110i	−0.888666	+	0.458556i	$0.848367\pi$
$198$		0			0
$199$			8.81333i			0.624760i	0.949957	+	0.312380i	$0.101126\pi$
$199$			8.81333i			0.624760i	−0.949957	+	0.312380i	$0.898874\pi$
$200$		0			0
$201$	−16.1774	−	7.15933i	−1.14107	−	0.504980i
$202$		0			0
$203$	9.58570	−	2.56848i	0.672784	−	0.180272i
$204$		0			0
$205$	33.2692	+	8.91447i	2.32362	+	0.622613i
$206$		0			0
$207$	−3.82092	+	11.9411i	−0.265572	+	0.829964i
$208$		0			0
$209$	−7.00132	−	12.1266i	−0.484292	−	0.838818i
$210$		0			0
$211$	−0.261630	−	0.976416i	−0.0180113	−	0.0672192i	0.956335	−	0.292272i	$-0.0944112\pi$
$211$	−0.261630	−	0.976416i	−0.0180113	−	0.0672192i	−0.974347	+	0.225053i	$0.927745\pi$
$212$		0			0
$213$	−17.3805	−	14.0102i	−1.19089	−	0.959964i
$214$		0			0
$215$		−	3.40150i		−	0.231981i
$216$		0			0
$217$			3.35912i			0.228032i
$218$		0			0
$219$	−3.87833	−	3.12627i	−0.262073	−	0.211254i
$220$		0			0
$221$	1.73548	+	6.47692i	0.116741	+	0.435685i
$222$		0			0
$223$	4.44475	+	7.69854i	0.297643	+	0.515532i	0.975596	−	0.219573i	$-0.0704663\pi$
$223$	4.44475	+	7.69854i	0.297643	+	0.515532i	−0.677954	+	0.735105i	$0.737133\pi$
$224$		0			0
$225$	−8.10628	−	8.92233i	−0.540419	−	0.594822i
$226$		0			0
$227$	21.7441	+	5.82630i	1.44320	+	0.386705i	0.893655	−	0.448756i	$-0.148133\pi$
$227$	21.7441	+	5.82630i	1.44320	+	0.386705i	0.549550	+	0.835461i	$0.314799\pi$
$228$		0			0
$229$	13.3954	−	3.58930i	0.885196	−	0.237187i	0.212548	−	0.977151i	$-0.431824\pi$
$229$	13.3954	−	3.58930i	0.885196	−	0.237187i	0.672647	+	0.739963i	$0.265157\pi$
$230$		0			0
$231$	10.0880	+	4.46446i	0.663743	+	0.293740i
$232$		0			0
$233$			6.70075i			0.438981i	0.975615	+	0.219491i	$0.0704395\pi$
$233$			6.70075i			0.438981i	−0.975615	+	0.219491i	$0.929561\pi$
$234$		0			0
$235$	7.83593	+	7.83593i	0.511160	+	0.511160i
$236$		0			0
$237$	−3.12585	−	0.487920i	−0.203046	−	0.0316938i
$238$		0			0
$239$	−1.04479	+	1.80963i	−0.0675819	+	0.117055i	−0.897836	−	0.440329i	$-0.854862\pi$
$239$	−1.04479	+	1.80963i	−0.0675819	+	0.117055i	0.830254	+	0.557385i	$0.188195\pi$
$240$		0			0
$241$	4.31263	+	7.46970i	0.277801	+	0.481166i	0.970838	−	0.239736i	$-0.0770610\pi$
$241$	4.31263	+	7.46970i	0.277801	+	0.481166i	−0.693037	+	0.720902i	$0.743728\pi$
$242$		0			0
$243$	3.86591	−	15.1015i	0.247998	−	0.968760i
$244$		0			0
$245$	−4.30844	+	16.0793i	−0.275256	+	1.02727i
$246$		0			0
$247$	−4.80929	−	2.77665i	−0.306008	−	0.176674i
$248$		0			0
$249$	−4.09510	+	2.98929i	−0.259517	+	0.189438i
$250$		0			0
$251$	−16.7058	−	16.7058i	−1.05446	−	1.05446i	−0.998429	−	0.0560334i	$-0.982155\pi$
$251$	−16.7058	−	16.7058i	−1.05446	−	1.05446i	−0.0560334	−	0.998429i	$-0.517845\pi$
$252$		0			0
$253$	−15.5941	+	15.5941i	−0.980396	+	0.980396i
$254$		0			0
$255$	6.74442	−	15.2399i	0.422352	−	0.954359i
$256$		0			0
$257$	7.26980	−	12.5917i	0.453477	−	0.785446i	−0.545122	−	0.838357i	$-0.683517\pi$
$257$	7.26980	−	12.5917i	0.453477	−	0.785446i	0.998599	+	0.0529109i	$0.0168499\pi$
$258$		0			0
$259$	−8.41207	−	2.25401i	−0.522700	−	0.140057i
$260$		0			0
$261$	1.18071	−	24.6380i	0.0730840	−	1.52506i
$262$		0			0
$263$	−7.27433	+	4.19984i	−0.448555	+	0.258973i	−0.707220	−	0.706994i	$-0.750051\pi$
$263$	−7.27433	+	4.19984i	−0.448555	+	0.258973i	0.258665	+	0.965967i	$0.416717\pi$
$264$		0			0
$265$	−2.25811	−	1.30372i	−0.138715	−	0.0800871i
$266$		0			0
$267$	2.85832	+	2.30406i	0.174927	+	0.141006i
$268$		0			0
$269$	3.63413	−	3.63413i	0.221577	−	0.221577i	−0.587585	−	0.809162i	$-0.699921\pi$
$269$	3.63413	−	3.63413i	0.221577	−	0.221577i	0.809162	+	0.587585i	$0.199921\pi$
$270$		0			0
$271$	−2.61554			−0.158882			−0.0794412	−	0.996840i	$-0.525314\pi$
$271$	−2.61554			−0.158882			−0.0794412	+	0.996840i	$0.525314\pi$
$272$		0			0
$273$	4.35007	−	0.467052i	0.263278	−	0.0282673i
$274$		0			0
$275$	−5.48812	−	20.4820i	−0.330946	−	1.23511i
$276$		0			0
$277$	−2.76263	+	10.3103i	−0.165990	+	0.619484i	0.831922	+	0.554893i	$0.187241\pi$
$277$	−2.76263	+	10.3103i	−0.165990	+	0.619484i	−0.997912	+	0.0645907i	$0.979426\pi$
$278$		0			0
$279$	7.95212	+	2.54452i	0.476081	+	0.152336i
$280$		0			0
$281$	−6.21844	+	3.59022i	−0.370961	+	0.214174i	−0.673878	−	0.738842i	$-0.735373\pi$
$281$	−6.21844	+	3.59022i	−0.370961	+	0.214174i	0.302917	+	0.953017i	$0.402039\pi$
$282$		0			0
$283$	−13.9481	+	3.73738i	−0.829127	+	0.222164i	−0.648333	−	0.761357i	$-0.724533\pi$
$283$	−13.9481	+	3.73738i	−0.829127	+	0.222164i	−0.180794	+	0.983521i	$0.557867\pi$
$284$		0			0
$285$	4.97506	+	12.8743i	0.294697	+	0.762608i
$286$		0			0
$287$	13.8431			0.817134
$288$		0			0
$289$	−6.73414			−0.396126
$290$		0			0
$291$	10.4835	+	1.63640i	0.614556	+	0.0959273i
$292$		0			0
$293$	−24.3455	+	6.52336i	−1.42228	+	0.381099i	−0.886292	−	0.463127i	$-0.846727\pi$
$293$	−24.3455	+	6.52336i	−1.42228	+	0.381099i	−0.535988	+	0.844226i	$0.680061\pi$
$294$		0			0
$295$	31.7992	−	18.3593i	1.85142	−	1.06892i
$296$		0			0
$297$	18.2104	−	20.4998i	1.05668	−	1.18952i
$298$		0			0
$299$	−2.26367	+	8.44814i	−0.130911	+	0.488568i
$300$		0			0
$301$	−0.353836	−	1.32053i	−0.0203948	−	0.0761144i
$302$		0			0
$303$	−13.3430	−	18.2790i	−0.766537	−	1.05010i
$304$		0			0
$305$	−23.0222			−1.31824
$306$		0			0
$307$	−3.57698	+	3.57698i	−0.204149	+	0.204149i	−0.801775	−	0.597626i	$-0.796111\pi$
$307$	−3.57698	+	3.57698i	−0.204149	+	0.204149i	0.597626	+	0.801775i	$0.296111\pi$
$308$		0			0
$309$	21.3351	−	8.24460i	1.21371	−	0.469019i
$310$		0			0
$311$	3.71609	+	2.14548i	0.210720	+	0.121659i	0.601646	−	0.798763i	$-0.294512\pi$
$311$	3.71609	+	2.14548i	0.210720	+	0.121659i	−0.390926	+	0.920422i	$0.627845\pi$
$312$		0			0
$313$	8.68061	−	5.01175i	0.490657	−	0.283281i	−0.234190	−	0.972191i	$-0.575244\pi$
$313$	8.68061	−	5.01175i	0.490657	−	0.283281i	0.724847	+	0.688910i	$0.241910\pi$
$314$		0			0
$315$	−9.14593	−	5.88142i	−0.515315	−	0.331381i
$316$		0			0
$317$	26.6623	+	7.14413i	1.49750	+	0.401254i	0.912262	−	0.409606i	$-0.134334\pi$
$317$	26.6623	+	7.14413i	1.49750	+	0.401254i	0.585239	+	0.810861i	$0.301001\pi$
$318$		0			0
$319$	21.6940	−	37.5751i	1.21463	−	2.10380i
$320$		0			0
$321$	16.8674	−	1.81099i	0.941446	−	0.101080i
$322$		0			0
$323$	−6.01183	+	6.01183i	−0.334507	+	0.334507i
$324$		0			0
$325$	−5.94639	−	5.94639i	−0.329846	−	0.329846i
$326$		0			0
$327$	−1.40235	−	13.0613i	−0.0775499	−	0.722291i
$328$		0			0
$329$	3.85720	+	2.22695i	0.212654	+	0.122776i
$330$		0			0
$331$	1.23731	−	4.61769i	0.0680085	−	0.253811i	−0.923549	−	0.383481i	$-0.874725\pi$
$331$	1.23731	−	4.61769i	0.0680085	−	0.253811i	0.991557	+	0.129670i	$0.0413918\pi$
$332$		0			0
$333$	−11.7081	+	18.2066i	−0.641597	+	0.997718i
$334$		0			0
$335$	15.3363	+	26.5632i	0.837909	+	1.45130i
$336$		0			0
$337$	−7.47777	+	12.9519i	−0.407340	+	0.705534i	−0.994591	−	0.103871i	$-0.966877\pi$
$337$	−7.47777	+	12.9519i	−0.407340	+	0.705534i	0.587251	+	0.809405i	$0.300210\pi$
$338$		0			0
$339$	3.78958	+	9.80657i	0.205822	+	0.532620i
$340$		0			0
$341$	10.3848	+	10.3848i	0.562371	+	0.562371i
$342$		0			0
$343$			15.1393i			0.817446i
$344$		0			0
$345$	17.5575	−	12.8164i	0.945265	−	0.690011i
$346$		0			0
$347$	−29.4830	+	7.89996i	−1.58273	+	0.424092i	−0.939771	−	0.341806i	$-0.888961\pi$
$347$	−29.4830	+	7.89996i	−1.58273	+	0.424092i	−0.642962	+	0.765898i	$0.722295\pi$
$348$		0			0
$349$	−32.4685	−	8.69992i	−1.73800	−	0.465696i	−0.756000	−	0.654572i	$-0.772849\pi$
$349$	−32.4685	−	8.69992i	−1.73800	−	0.465696i	−0.982001	+	0.188876i	$0.939515\pi$
$350$		0			0
$351$	2.18949	−	10.6518i	0.116867	−	0.568550i
$352$		0			0
$353$	16.5277	+	28.6268i	0.879680	+	1.52365i	0.851692	+	0.524043i	$0.175577\pi$
$353$	16.5277	+	28.6268i	0.879680	+	1.52365i	0.0279885	+	0.999608i	$0.491090\pi$
$354$		0			0
$355$	10.0178	+	37.3870i	0.531691	+	1.98430i
$356$		0			0
$357$	1.03302	−	6.61802i	0.0546732	−	0.350263i
$358$		0			0
$359$		−	13.5739i		−	0.716404i	−0.933644	−	0.358202i	$-0.883390\pi$
$359$		−	13.5739i		−	0.716404i	0.933644	−	0.358202i	$-0.116610\pi$
$360$		0			0
$361$			11.9588i			0.629410i
$362$		0			0
$363$	27.2177	−	10.5178i	1.42856	−	0.552042i
$364$		0			0
$365$	2.23540	+	8.34262i	0.117006	+	0.436673i
$366$		0			0
$367$	1.88219	+	3.26006i	0.0982497	+	0.170174i	0.910960	−	0.412494i	$-0.135342\pi$
$367$	1.88219	+	3.26006i	0.0982497	+	0.170174i	−0.812711	+	0.582668i	$0.802009\pi$
$368$		0			0
$369$	10.4861	−	32.7711i	0.545885	−	1.70600i
$370$		0			0
$371$	−1.01227	−	0.271236i	−0.0525542	−	0.0140819i
$372$		0			0
$373$	20.6979	−	5.54598i	1.07170	−	0.287160i	0.320506	−	0.947247i	$-0.396147\pi$
$373$	20.6979	−	5.54598i	1.07170	−	0.287160i	0.751189	+	0.660087i	$0.229480\pi$
$374$		0			0
$375$	−0.545113	−	5.07712i	−0.0281495	−	0.262181i
$376$		0			0
$377$		−	17.2072i		−	0.886215i
$378$		0			0
$379$	−0.0423205	−	0.0423205i	−0.00217386	−	0.00217386i	0.706019	−	0.708193i	$-0.250489\pi$
$379$	−0.0423205	−	0.0423205i	−0.00217386	−	0.00217386i	−0.708193	+	0.706019i	$0.750489\pi$
$380$		0			0
$381$	12.7272	−	15.7889i	0.652035	−	0.808890i
$382$		0			0
$383$	6.83724	−	11.8424i	0.349367	−	0.605121i	−0.636770	−	0.771053i	$-0.719730\pi$
$383$	6.83724	−	11.8424i	0.349367	−	0.605121i	0.986137	+	0.165933i	$0.0530634\pi$
$384$		0			0
$385$	−9.56348	−	16.5644i	−0.487400	−	0.844201i
$386$		0			0
$387$	−3.39416	−	0.162655i	−0.172535	−	0.00826824i
$388$		0			0
$389$	3.68890	−	13.7672i	0.187035	−	0.698023i	−0.807151	−	0.590345i	$-0.798992\pi$
$389$	3.68890	−	13.7672i	0.187035	−	0.698023i	0.994186	−	0.107678i	$-0.0343416\pi$
$390$		0			0
$391$	11.5963	+	6.69511i	0.586449	+	0.338586i
$392$		0			0
$393$	−14.1515	−	6.26276i	−0.713849	−	0.315914i
$394$		0			0
$395$	3.87866	+	3.87866i	0.195157	+	0.195157i
$396$		0			0
$397$	16.1526	−	16.1526i	0.810677	−	0.810677i	−0.174058	−	0.984735i	$-0.555688\pi$
$397$	16.1526	−	16.1526i	0.810677	−	0.810677i	0.984735	+	0.174058i	$0.0556881\pi$
$398$		0			0
$399$	3.27065	+	4.48055i	0.163737	+	0.224308i
$400$		0			0
$401$	1.96568	−	3.40466i	0.0981615	−	0.170021i	−0.812762	−	0.582596i	$-0.802037\pi$
$401$	1.96568	−	3.40466i	0.0981615	−	0.170021i	0.910924	+	0.412575i	$0.135370\pi$
$402$		0			0
$403$	5.62599	+	1.50748i	0.280251	+	0.0750929i
$404$		0			0
$405$	−20.8512	+	17.1962i	−1.03610	+	0.854485i
$406$		0			0
$407$	−32.9745	+	19.0379i	−1.63449	+	0.943671i
$408$		0			0
$409$	17.7471	+	10.2463i	0.877536	+	0.506646i	0.869845	−	0.493325i	$-0.164219\pi$
$409$	17.7471	+	10.2463i	0.877536	+	0.506646i	0.00769067	+	0.999970i	$0.497552\pi$
$410$		0			0
$411$	−0.407675	+	2.61176i	−0.0201091	+	0.128829i
$412$		0			0
$413$	10.4353	−	10.4353i	0.513489	−	0.513489i
$414$		0			0
$415$	8.79055			0.431511
$416$		0			0
$417$	−12.2328	+	27.6415i	−0.599041	+	1.35361i
$418$		0			0
$419$	1.48550	+	5.54398i	0.0725716	+	0.270841i	0.992672	−	0.120842i	$-0.0385595\pi$
$419$	1.48550	+	5.54398i	0.0725716	+	0.270841i	−0.920100	+	0.391683i	$0.871893\pi$
$420$		0			0
$421$	−10.0100	+	37.3580i	−0.487859	+	1.82072i	0.0789649	+	0.996877i	$0.474838\pi$
$421$	−10.0100	+	37.3580i	−0.487859	+	1.82072i	−0.566824	+	0.823839i	$0.691828\pi$
$422$		0			0
$423$	8.19372	−	7.44431i	0.398392	−	0.361955i
$424$		0			0
$425$	−11.1499	+	6.43738i	−0.540848	+	0.312259i
$426$		0			0
$427$	−8.93769	+	2.39485i	−0.432525	+	0.115895i
$428$		0			0
$429$	12.0045	−	14.8923i	0.579582	−	0.719007i
$430$		0			0
$431$	−29.0431			−1.39896			−0.699479	−	0.714653i	$-0.746585\pi$
$431$	−29.0431			−1.39896			−0.699479	+	0.714653i	$0.746585\pi$
$432$		0			0
$433$	28.4001			1.36482			0.682411	−	0.730969i	$-0.260932\pi$
$433$	28.4001			1.36482			0.682411	+	0.730969i	$0.260932\pi$
$434$		0			0
$435$	−26.8395	+	33.2961i	−1.28686	+	1.59642i
$436$		0			0
$437$	−10.7117	+	2.87019i	−0.512409	+	0.137300i
$438$		0			0
$439$	−2.37559	+	1.37154i	−0.113381	+	0.0654603i	−0.555618	−	0.831438i	$-0.687518\pi$
$439$	−2.37559	+	1.37154i	−0.113381	+	0.0654603i	0.442237	+	0.896898i	$0.354185\pi$
$440$		0			0
$441$	15.8386	+	5.06803i	0.754218	+	0.241335i
$442$		0			0
$443$	1.83055	−	6.83170i	0.0869720	−	0.324584i	−0.908708	−	0.417432i	$-0.862930\pi$
$443$	1.83055	−	6.83170i	0.0869720	−	0.324584i	0.995680	+	0.0928477i	$0.0295970\pi$
$444$		0			0
$445$	−1.64749	−	6.14850i	−0.0780983	−	0.291467i
$446$		0			0
$447$	−12.4180	+	28.0599i	−0.587349	+	1.32719i
$448$		0			0
$449$	2.27698			0.107457			0.0537287	−	0.998556i	$-0.482889\pi$
$449$	2.27698			0.107457			0.0537287	+	0.998556i	$0.482889\pi$
$450$		0			0
$451$	42.7965	−	42.7965i	2.01521	−	2.01521i
$452$		0			0
$453$	1.38755	−	8.88931i	0.0651928	−	0.417656i
$454$		0			0
$455$	−6.56927	−	3.79277i	−0.307972	−	0.177808i
$456$		0			0
$457$	−21.7536	+	12.5595i	−1.01759	+	0.587507i	−0.913406	−	0.407051i	$-0.866557\pi$
$457$	−21.7536	+	12.5595i	−1.01759	+	0.587507i	−0.104187	+	0.994558i	$0.533224\pi$
$458$		0			0
$459$	−14.8845	−	7.45861i	−0.694747	−	0.348138i
$460$		0			0
$461$	−21.4217	−	5.73994i	−0.997710	−	0.267336i	−0.277224	−	0.960805i	$-0.589415\pi$
$461$	−21.4217	−	5.73994i	−0.997710	−	0.267336i	−0.720486	+	0.693470i	$0.756081\pi$
$462$		0			0
$463$	−19.5447	+	33.8525i	−0.908321	+	1.57326i	−0.0919260	+	0.995766i	$0.529302\pi$
$463$	−19.5447	+	33.8525i	−0.908321	+	1.57326i	−0.816396	+	0.577493i	$0.804031\pi$
$464$		0			0
$465$	−8.53501	−	11.6923i	−0.395802	−	0.542219i
$466$		0			0
$467$	−4.46264	+	4.46264i	−0.206506	+	0.206506i	−0.802781	−	0.596274i	$-0.796647\pi$
$467$	−4.46264	+	4.46264i	−0.206506	+	0.206506i	0.596274	+	0.802781i	$0.296647\pi$
$468$		0			0
$469$	8.71705	+	8.71705i	0.402516	+	0.402516i
$470$		0			0
$471$	−16.8118	−	7.44009i	−0.774648	−	0.342821i
$472$		0			0
$473$	−5.17638	−	2.98858i	−0.238010	−	0.137415i
$474$		0			0
$475$	2.75970	−	10.2993i	0.126624	−	0.472565i
$476$		0			0
$477$	−1.40889	+	2.19090i	−0.0645085	+	0.100314i
$478$		0			0
$479$	−2.80441	−	4.85738i	−0.128137	−	0.221939i	0.794818	−	0.606848i	$-0.207566\pi$
$479$	−2.80441	−	4.85738i	−0.128137	−	0.221939i	−0.922955	+	0.384909i	$0.874233\pi$
$480$		0			0
$481$	−7.55020	+	13.0773i	−0.344260	+	0.596275i
$482$		0			0
$483$	5.48299	−	6.80199i	0.249485	−	0.309501i
$484$		0			0
$485$	−13.0083	−	13.0083i	−0.590678	−	0.590678i
$486$		0			0
$487$			34.1026i			1.54534i	0.634810	+	0.772668i	$0.281078\pi$
$487$			34.1026i			1.54534i	−0.634810	+	0.772668i	$0.718922\pi$
$488$		0			0
$489$	−0.685919	−	6.38857i	−0.0310183	−	0.288901i
$490$		0			0
$491$	14.5988	−	3.91173i	0.658833	−	0.176534i	0.0861138	−	0.996285i	$-0.472555\pi$
$491$	14.5988	−	3.91173i	0.658833	−	0.176534i	0.572719	+	0.819751i	$0.305888\pi$
$492$		0			0
$493$	−25.4463	−	6.81831i	−1.14604	−	0.307081i
$494$		0			0
$495$	−46.4576	+	10.0923i	−2.08811	+	0.453616i
$496$		0			0
$497$	7.77826	+	13.4723i	0.348902	+	0.604317i
$498$		0			0
$499$	−2.37206	−	8.85266i	−0.106188	−	0.396300i	0.892289	−	0.451464i	$-0.149098\pi$
$499$	−2.37206	−	8.85266i	−0.106188	−	0.396300i	−0.998477	+	0.0551648i	$0.982432\pi$
$500$		0			0
$501$	−9.46606	+	3.65800i	−0.422912	+	0.163427i
$502$		0			0
$503$		−	6.41865i		−	0.286194i	−0.989709	−	0.143097i	$-0.954294\pi$
$503$		−	6.41865i		−	0.286194i	0.989709	−	0.143097i	$-0.0457060\pi$
$504$		0			0
$505$			39.2377i			1.74605i
$506$		0			0
$507$	−2.30267	+	14.7520i	−0.102265	+	0.655159i
$508$		0			0
$509$	−6.23386	−	23.2651i	−0.276311	−	1.03121i	−0.954958	−	0.296742i	$-0.904100\pi$
$509$	−6.23386	−	23.2651i	−0.276311	−	1.03121i	0.678647	−	0.734465i	$-0.262567\pi$
$510$		0			0
$511$	1.73566	+	3.00625i	0.0767810	+	0.132989i
$512$		0			0
$513$	13.0844	−	4.34868i	0.577691	−	0.191999i
$514$		0			0
$515$	−38.3057	−	10.2640i	−1.68795	−	0.452285i
$516$		0			0
$517$	18.8094	−	5.03995i	0.827235	−	0.221657i
$518$		0			0
$519$	−1.04269	+	0.761126i	−0.0457689	+	0.0334097i
$520$		0			0
$521$			15.3122i			0.670839i	0.942069	+	0.335420i	$0.108878\pi$
$521$			15.3122i			0.670839i	−0.942069	+	0.335420i	$0.891122\pi$
$522$		0			0
$523$	19.6619	+	19.6619i	0.859756	+	0.859756i	0.991309	−	0.131553i	$-0.0419965\pi$
$523$	19.6619	+	19.6619i	0.859756	+	0.859756i	−0.131553	+	0.991309i	$0.541996\pi$
$524$		0			0
$525$	3.02797	+	7.83568i	0.132151	+	0.341977i
$526$		0			0
$527$	4.45858	−	7.72248i	0.194219	−	0.336397i
$528$		0			0
$529$	−2.76726	−	4.79304i	−0.120316	−	0.208393i
$530$		0			0
$531$	−16.7990	−	32.6084i	−0.729016	−	1.41509i
$532$		0			0
$533$	6.21241	−	23.1850i	0.269089	−	1.00426i
$534$		0			0
$535$	−25.4723	−	14.7065i	−1.10127	−	0.635816i
$536$		0			0
$537$	0.0300353	+	0.279745i	0.00129612	+	0.0120719i
$538$		0			0
$539$	20.6839	+	20.6839i	0.890921	+	0.890921i
$540$		0			0
$541$	12.1084	−	12.1084i	0.520580	−	0.520580i	−0.397167	−	0.917746i	$-0.630007\pi$
$541$	12.1084	−	12.1084i	0.520580	−	0.520580i	0.917746	+	0.397167i	$0.130007\pi$
$542$		0			0
$543$	19.1456	−	2.05560i	0.821618	−	0.0882144i
$544$		0			0
$545$	−11.3880	+	19.7245i	−0.487807	+	0.844906i
$546$		0			0
$547$	−36.4729	−	9.77287i	−1.55947	−	0.417858i	−0.626972	−	0.779042i	$-0.715706\pi$
$547$	−36.4729	−	9.77287i	−1.55947	−	0.417858i	−0.932495	+	0.361184i	$0.882373\pi$
$548$		0			0
$549$	−1.10089	+	22.9724i	−0.0469848	+	0.980440i
$550$		0			0
$551$	18.8946	−	10.9088i	0.804936	−	0.464730i
$552$		0			0
$553$	1.90925	+	1.10231i	0.0811895	+	0.0468748i
$554$		0			0
$555$	35.0076	−	13.5281i	1.48599	−	0.574235i
$556$		0			0
$557$	−29.5565	+	29.5565i	−1.25235	+	1.25235i	−0.297685	+	0.954664i	$0.596214\pi$
$557$	−29.5565	+	29.5565i	−1.25235	+	1.25235i	−0.954664	+	0.297685i	$0.903786\pi$
$558$		0			0
$559$	−2.37048			−0.100260
$560$		0			0
$561$	−17.2662	−	23.6535i	−0.728981	−	0.998650i
$562$		0			0
$563$	−6.91061	−	25.7907i	−0.291247	−	1.08695i	−0.944152	−	0.329510i	$-0.893116\pi$
$563$	−6.91061	−	25.7907i	−0.291247	−	1.08695i	0.652905	−	0.757440i	$-0.273550\pi$
$564$		0			0
$565$	4.71778	−	17.6070i	0.198478	−	0.740731i
$566$		0			0
$567$	−6.30607	+	8.84493i	−0.264830	+	0.371452i
$568$		0			0
$569$	9.49763	−	5.48346i	0.398161	−	0.229879i	−0.287529	−	0.957772i	$-0.592834\pi$
$569$	9.49763	−	5.48346i	0.398161	−	0.229879i	0.685690	+	0.727893i	$0.259500\pi$
$570$		0			0
$571$	36.2420	−	9.71100i	1.51668	−	0.406393i	0.598032	−	0.801472i	$-0.295950\pi$
$571$	36.2420	−	9.71100i	1.51668	−	0.406393i	0.918647	+	0.395080i	$0.129283\pi$
$572$		0			0
$573$	7.71592	+	1.20439i	0.322337	+	0.0503142i
$574$		0			0
$575$	−16.7931			−0.700322
$576$		0			0
$577$	−29.3500			−1.22186			−0.610929	−	0.791686i	$-0.709204\pi$
$577$	−29.3500			−1.22186			−0.610929	+	0.791686i	$0.709204\pi$
$578$		0			0
$579$	12.0447	+	31.1688i	0.500559	+	1.29533i
$580$		0			0
$581$	3.41268	−	0.914424i	0.141582	−	0.0379367i
$582$		0			0
$583$	−3.96799	+	2.29092i	−0.164337	+	0.0948802i
$584$		0			0
$585$	−13.9549	+	12.6785i	−0.576963	+	0.524193i
$586$		0			0
$587$	−0.643018	+	2.39978i	−0.0265402	+	0.0990494i	−0.977925	−	0.208954i	$-0.932994\pi$
$587$	−0.643018	+	2.39978i	−0.0265402	+	0.0990494i	0.951385	+	0.308003i	$0.0996608\pi$
$588$		0			0
$589$	1.91139	+	7.13339i	0.0787573	+	0.293926i
$590$		0			0
$591$	14.7028	−	1.57859i	0.604791	−	0.0649344i
$592$		0			0
$593$	−3.31760			−0.136238			−0.0681188	−	0.997677i	$-0.521700\pi$
$593$	−3.31760			−0.136238			−0.0681188	+	0.997677i	$0.521700\pi$
$594$		0			0
$595$	−8.21187	+	8.21187i	−0.336654	+	0.336654i
$596$		0			0
$597$	−11.8847	−	9.58009i	−0.486408	−	0.392087i
$598$		0			0
$599$	−16.9013	−	9.75798i	−0.690569	−	0.398700i	0.113256	−	0.993566i	$-0.463872\pi$
$599$	−16.9013	−	9.75798i	−0.690569	−	0.398700i	−0.803825	+	0.594866i	$0.797205\pi$
$600$		0			0
$601$	−5.79012	+	3.34293i	−0.236184	+	0.136361i	−0.613422	−	0.789756i	$-0.710207\pi$
$601$	−5.79012	+	3.34293i	−0.236184	+	0.136361i	0.377238	+	0.926116i	$0.376874\pi$
$602$		0			0
$603$	27.2392	−	14.0329i	1.10926	−	0.571465i
$604$		0			0
$605$	−48.8674	−	13.0940i	−1.98674	−	0.532346i
$606$		0			0
$607$	4.11486	−	7.12715i	0.167017	−	0.289282i	−0.770353	−	0.637618i	$-0.779920\pi$
$607$	4.11486	−	7.12715i	0.167017	−	0.289282i	0.937370	+	0.348336i	$0.113253\pi$
$608$		0			0
$609$	−6.95609	+	15.7182i	−0.281875	+	0.636933i
$610$		0			0
$611$	5.46079	−	5.46079i	0.220920	−	0.220920i
$612$		0			0
$613$	−5.65366	−	5.65366i	−0.228349	−	0.228349i	0.583654	−	0.812003i	$-0.301623\pi$
$613$	−5.65366	−	5.65366i	−0.228349	−	0.228349i	−0.812003	+	0.583654i	$0.801623\pi$
$614$		0			0
$615$	−48.1848	+	35.1733i	−1.94300	+	1.41832i
$616$		0			0
$617$	24.8990	+	14.3754i	1.00240	+	0.578733i	0.908956	−	0.416891i	$-0.136880\pi$
$617$	24.8990	+	14.3754i	1.00240	+	0.578733i	0.0934395	+	0.995625i	$0.470214\pi$
$618$		0			0
$619$	5.61764	−	20.9653i	0.225792	−	0.842668i	−0.756293	−	0.654232i	$-0.772992\pi$
$619$	5.61764	−	20.9653i	0.225792	−	0.842668i	0.982086	−	0.188435i	$-0.0603416\pi$
$620$		0			0
$621$	−11.9491	−	18.1325i	−0.479502	−	0.727631i
$622$		0			0
$623$	−1.27918	−	2.21560i	−0.0512491	−	0.0887661i
$624$		0			0
$625$	−14.4724	+	25.0669i	−0.578896	+	1.00268i
$626$		0			0
$627$	23.9631	+	3.74045i	0.956995	+	0.149379i
$628$		0			0
$629$	16.3472	+	16.3472i	0.651807	+	0.651807i
$630$		0			0
$631$			13.0320i			0.518796i	0.965770	+	0.259398i	$0.0835242\pi$
$631$			13.0320i			0.518796i	−0.965770	+	0.259398i	$0.916476\pi$
$632$		0			0
$633$	1.60108	+	0.708559i	0.0636372	+	0.0281627i
$634$		0			0
$635$	−33.9633	+	9.10043i	−1.34779	+	0.361140i
$636$		0			0
$637$	11.2055	+	3.00251i	0.443979	+	0.118964i
$638$		0			0
$639$	37.7853	−	8.20839i	1.49476	−	0.324719i
$640$		0			0
$641$	6.70219	+	11.6085i	0.264721	+	0.458510i	0.967490	−	0.252908i	$-0.0813869\pi$
$641$	6.70219	+	11.6085i	0.264721	+	0.458510i	−0.702770	+	0.711417i	$0.748054\pi$
$642$		0			0
$643$	−2.65048	−	9.89172i	−0.104525	−	0.390091i	0.893766	−	0.448533i	$-0.148053\pi$
$643$	−2.65048	−	9.89172i	−0.104525	−	0.390091i	−0.998291	+	0.0584419i	$0.981387\pi$
$644$		0			0
$645$	4.58690	+	3.69744i	0.180609	+	0.145586i
$646$		0			0
$647$		−	25.5231i		−	1.00342i	−0.865036	−	0.501709i	$-0.832705\pi$
$647$		−	25.5231i		−	1.00342i	0.865036	−	0.501709i	$-0.167295\pi$
$648$		0			0
$649$		−	64.5223i		−	2.53272i
$650$		0			0
$651$	−4.52975	−	3.65137i	−0.177535	−	0.143108i
$652$		0			0
$653$	4.44634	+	16.5940i	0.173999	+	0.649372i	0.996720	+	0.0809269i	$0.0257880\pi$
$653$	4.44634	+	16.5940i	0.173999	+	0.649372i	−0.822721	+	0.568445i	$0.807545\pi$
$654$		0			0
$655$	13.4157	+	23.2366i	0.524194	+	0.907930i
$656$		0			0
$657$	8.43150	−	1.83164i	0.328944	−	0.0714590i
$658$		0			0
$659$	4.84828	+	1.29909i	0.188862	+	0.0506054i	0.352010	−	0.935996i	$-0.385498\pi$
$659$	4.84828	+	1.29909i	0.188862	+	0.0506054i	−0.163148	+	0.986602i	$0.552165\pi$
$660$		0			0
$661$	24.2257	−	6.49124i	0.942269	−	0.252480i	0.245190	−	0.969475i	$-0.421150\pi$
$661$	24.2257	−	6.49124i	0.942269	−	0.252480i	0.697079	+	0.716995i	$0.254483\pi$
$662$		0			0
$663$	−10.6205	−	4.70013i	−0.412468	−	0.182538i
$664$		0			0
$665$		−	9.61796i		−	0.372969i
$666$		0			0
$667$	−24.2973	−	24.2973i	−0.940795	−	0.940795i
$668$		0			0
$669$	−15.2129	−	2.37461i	−0.588163	−	0.0918076i
$670$		0			0
$671$	−20.2274	+	35.0349i	−0.780871	+	1.35251i
$672$		0			0
$673$	−12.8215	−	22.2075i	−0.494233	−	0.856037i	0.505745	−	0.862683i	$-0.331218\pi$
$673$	−12.8215	−	22.2075i	−0.494233	−	0.856037i	−0.999978	+	0.00664596i	$0.997885\pi$
$674$		0			0
$675$	20.8432	−	1.23267i	0.802256	−	0.0474455i
$676$		0			0
$677$	−6.01329	+	22.4419i	−0.231110	+	0.862513i	0.748755	+	0.662847i	$0.230652\pi$
$677$	−6.01329	+	22.4419i	−0.231110	+	0.862513i	−0.979864	+	0.199665i	$0.936015\pi$
$678$		0			0
$679$	−6.40328	−	3.69694i	−0.245735	−	0.141875i
$680$		0			0
$681$	−31.4925	+	22.9885i	−1.20680	+	0.880921i
$682$		0			0
$683$	29.4647	+	29.4647i	1.12744	+	1.12744i	0.990593	+	0.136843i	$0.0436957\pi$
$683$	29.4647	+	29.4647i	1.12744	+	1.12744i	0.136843	+	0.990593i	$0.456304\pi$
$684$		0			0
$685$	3.24076	−	3.24076i	0.123823	−	0.123823i
$686$		0			0
$687$	−9.72072	+	21.9652i	−0.370869	+	0.838025i
$688$		0			0
$689$	−0.908553	+	1.57366i	−0.0346131	+	0.0599517i
$690$		0			0
$691$	18.9096	+	5.06682i	0.719357	+	0.192751i	0.599885	−	0.800087i	$-0.295213\pi$
$691$	18.9096	+	5.06682i	0.719357	+	0.192751i	0.119472	+	0.992838i	$0.461880\pi$
$692$		0			0
$693$	−16.9860	+	8.75073i	−0.645244	+	0.332413i
$694$		0			0
$695$	45.3871	−	26.2042i	1.72163	−	0.993984i
$696$		0			0
$697$	−31.8248	−	18.3740i	−1.20545	−	0.695966i
$698$		0			0
$699$	−9.03591	−	7.28373i	−0.341770	−	0.275496i
$700$		0			0
$701$	7.85067	−	7.85067i	0.296516	−	0.296516i	−0.543132	−	0.839647i	$-0.682762\pi$
$701$	7.85067	−	7.85067i	0.296516	−	0.296516i	0.839647	+	0.543132i	$0.182762\pi$
$702$		0			0
$703$	−19.1463			−0.722117
$704$		0			0
$705$	−19.0844	+	2.04902i	−0.718758	+	0.0771707i
$706$		0			0
$707$	4.08164	+	15.2329i	0.153506	+	0.572892i
$708$		0			0
$709$	−12.9865	+	48.4664i	−0.487720	+	1.82020i	0.0797675	+	0.996813i	$0.474582\pi$
$709$	−12.9865	+	48.4664i	−0.487720	+	1.82020i	−0.567487	+	0.823382i	$0.692084\pi$
$710$		0			0
$711$	4.05576	−	3.68481i	0.152103	−	0.138191i
$712$		0			0
$713$	10.0728	−	5.81552i	0.377229	−	0.217793i
$714$		0			0
$715$	−32.0346	+	8.58364i	−1.19803	+	0.321010i
$716$		0			0
$717$	−1.30458	−	3.37596i	−0.0487206	−	0.126078i
$718$		0			0
$719$	46.4032			1.73055			0.865273	−	0.501301i	$-0.167145\pi$
$719$	46.4032			1.73055			0.865273	+	0.501301i	$0.167145\pi$
$720$		0			0
$721$	−15.9388			−0.593591
$722$		0			0
$723$	−14.7607	−	2.30402i	−0.548955	−	0.0856875i
$724$		0			0
$725$	31.9130	−	8.55107i	1.18522	−	0.317579i
$726$		0			0
$727$	−13.4929	+	7.79014i	−0.500425	+	0.288920i	−0.728889	−	0.684632i	$-0.759963\pi$
$727$	−13.4929	+	7.79014i	−0.500425	+	0.288920i	0.228464	+	0.973552i	$0.426630\pi$
$728$		0			0
$729$	16.1620	+	21.6285i	0.598591	+	0.801055i
$730$		0			0
$731$	−0.939296	+	3.50550i	−0.0347411	+	0.129656i
$732$		0			0
$733$	−6.02884	−	22.5000i	−0.222680	−	0.831055i	−0.983321	−	0.181881i	$-0.941781\pi$
$733$	−6.02884	−	22.5000i	−0.222680	−	0.831055i	0.760640	−	0.649174i	$-0.224885\pi$
$734$		0			0
$735$	−16.9996	−	23.2881i	−0.627038	−	0.858996i
$736$		0			0
$737$	53.8981			1.98536
$738$		0			0
$739$	−17.1341	+	17.1341i	−0.630288	+	0.630288i	−0.948140	−	0.317853i	$-0.897038\pi$
$739$	−17.1341	+	17.1341i	−0.630288	+	0.630288i	0.317853	+	0.948140i	$0.397038\pi$
$740$		0			0
$741$	8.97199	−	3.46707i	0.329594	−	0.127366i
$742$		0			0
$743$	34.9775	+	20.1943i	1.28320	+	0.740855i	0.977432	−	0.211251i	$-0.0677537\pi$
$743$	34.9775	+	20.1943i	1.28320	+	0.740855i	0.305767	+	0.952106i	$0.401087\pi$
$744$		0			0
$745$	46.0742	−	26.6009i	1.68803	−	0.974583i
$746$		0			0
$747$	0.420353	−	8.77156i	0.0153799	−	0.320935i
$748$		0			0
$749$	−11.4187	−	3.05964i	−0.417231	−	0.111797i
$750$		0			0
$751$	−2.44188	+	4.22946i	−0.0891056	+	0.154335i	−0.907133	−	0.420843i	$-0.861734\pi$
$751$	−2.44188	+	4.22946i	−0.0891056	+	0.154335i	0.818028	+	0.575179i	$0.195068\pi$
$752$		0			0
$753$	40.6869	−	4.36842i	1.48271	−	0.159194i
$754$		0			0
$755$	−11.0302	+	11.0302i	−0.401429	+	0.401429i
$756$		0			0
$757$	−20.1502	−	20.1502i	−0.732371	−	0.732371i	0.238718	−	0.971089i	$-0.423273\pi$
$757$	−20.1502	−	20.1502i	−0.732371	−	0.732371i	−0.971089	+	0.238718i	$0.923273\pi$
$758$		0			0
$759$	−4.07772	−	37.9794i	−0.148012	−	1.37857i
$760$		0			0
$761$	16.9178	+	9.76748i	0.613268	+	0.354071i	0.774244	−	0.632888i	$-0.218131\pi$
$761$	16.9178	+	9.76748i	0.613268	+	0.354071i	−0.160975	+	0.986958i	$0.551464\pi$
$762$		0			0
$763$	−2.36923	+	8.84210i	−0.0857720	+	0.320105i
$764$		0			0
$765$	13.2197	+	25.6606i	0.477958	+	0.927760i
$766$		0			0
$767$	−12.7944	−	22.1606i	−0.461980	−	0.800172i
$768$		0			0
$769$	−14.3355	+	24.8299i	−0.516952	+	0.895388i	0.482854	+	0.875701i	$0.339600\pi$
$769$	−14.3355	+	24.8299i	−0.516952	+	0.895388i	−0.999806	+	0.0196866i	$0.993733\pi$
$770$		0			0
$771$	9.07747	+	23.4904i	0.326917	+	0.845986i
$772$		0			0
$773$	−33.6600	−	33.6600i	−1.21067	−	1.21067i	−0.970808	−	0.239857i	$-0.922899\pi$
$773$	−33.6600	−	33.6600i	−1.21067	−	1.21067i	−0.239857	−	0.970808i	$-0.577101\pi$
$774$		0			0
$775$			11.1833i			0.401716i
$776$		0			0
$777$	12.1834	−	8.89349i	0.437078	−	0.319052i
$778$		0			0
$779$	29.3971	−	7.87693i	1.05326	−	0.282220i
$780$		0			0
$781$	65.6969	+	17.6034i	2.35082	+	0.629901i
$782$		0			0
$783$	31.9407	+	28.3737i	1.14147	+	1.01399i
$784$		0			0
$785$	15.9377	+	27.6049i	0.568840	+	0.985260i
$786$		0			0
$787$	−7.32646	−	27.3427i	−0.261160	−	0.974662i	−0.964559	−	0.263867i	$-0.915002\pi$
$787$	−7.32646	−	27.3427i	−0.261160	−	0.974662i	0.703399	−	0.710795i	$-0.251665\pi$
$788$		0			0
$789$	2.24376	−	14.3746i	0.0798800	−	0.511749i
$790$		0			0
$791$		−	7.32616i		−	0.260488i
$792$		0			0
$793$			16.0439i			0.569737i
$794$		0			0
$795$	4.21263	−	1.62790i	0.149407	−	0.0577357i
$796$		0			0
$797$	−9.55450	−	35.6579i	−0.338438	−	1.26307i	−0.900094	−	0.435696i	$-0.856502\pi$
$797$	−9.55450	−	35.6579i	−0.338438	−	1.26307i	0.561656	−	0.827371i	$-0.310164\pi$
$798$		0			0
$799$	−5.91169	−	10.2393i	−0.209140	−	0.362242i
$800$		0			0
$801$	−6.21400	+	1.34991i	−0.219561	+	0.0476969i
$802$		0			0
$803$	14.6598	+	3.92807i	0.517332	+	0.138619i
$804$		0			0
$805$	−14.6317	+	3.92054i	−0.515698	+	0.138181i
$806$		0			0
$807$	0.950290	+	8.85089i	0.0334518	+	0.311566i
$808$		0			0
$809$		−	10.0300i		−	0.352637i	−0.984333	−	0.176318i	$-0.943581\pi$
$809$		−	10.0300i		−	0.352637i	0.984333	−	0.176318i	$-0.0564189\pi$
$810$		0			0
$811$	−29.2218	−	29.2218i	−1.02612	−	1.02612i	−0.999650	−	0.0264676i	$-0.991574\pi$
$811$	−29.2218	−	29.2218i	−1.02612	−	1.02612i	−0.0264676	−	0.999650i	$-0.508426\pi$
$812$		0			0
$813$	2.84309	−	3.52703i	0.0997115	−	0.123698i
$814$		0			0
$815$	−5.57011	+	9.64772i	−0.195112	+	0.337945i
$816$		0			0
$817$	−1.50280	−	2.60293i	−0.0525765	−	0.0910651i
$818$		0			0
$819$	−4.09871	+	6.37371i	−0.143221	+	0.222716i
$820$		0			0
$821$	5.55428	−	20.7288i	0.193846	−	0.723442i	−0.798717	−	0.601707i	$-0.794488\pi$
$821$	5.55428	−	20.7288i	0.193846	−	0.723442i	0.992563	−	0.121735i	$-0.0388457\pi$
$822$		0			0
$823$	6.52191	+	3.76543i	0.227340	+	0.131255i	0.609344	−	0.792906i	$-0.291433\pi$
$823$	6.52191	+	3.76543i	0.227340	+	0.131255i	−0.382005	+	0.924160i	$0.624766\pi$
$824$		0			0
$825$	33.5853	+	14.8632i	1.16929	+	0.517471i
$826$		0			0
$827$	7.34158	+	7.34158i	0.255292	+	0.255292i	0.823136	−	0.567844i	$-0.192222\pi$
$827$	7.34158	+	7.34158i	0.255292	+	0.255292i	−0.567844	+	0.823136i	$0.692222\pi$
$828$		0			0
$829$	19.0212	−	19.0212i	0.660632	−	0.660632i	−0.294897	−	0.955529i	$-0.595285\pi$
$829$	19.0212	−	19.0212i	0.660632	−	0.660632i	0.955529	+	0.294897i	$0.0952852\pi$
$830$		0			0
$831$	−10.9003	−	14.9326i	−0.378128	−	0.518008i
$832$		0			0
$833$	8.88034	−	15.3812i	0.307686	−	0.532927i
$834$		0			0
$835$	16.9956	+	4.55396i	0.588157	+	0.157596i
$836$		0			0
$837$	−12.0752	+	7.95746i	−0.417381	+	0.275050i
$838$		0			0
$839$	36.1808	−	20.8890i	1.24910	−	0.721168i	0.278170	−	0.960532i	$-0.410272\pi$
$839$	36.1808	−	20.8890i	1.24910	−	0.721168i	0.970930	+	0.239364i	$0.0769388\pi$
$840$		0			0
$841$	33.4311	+	19.3015i	1.15280	+	0.665568i
$842$		0			0
$843$	1.91807	−	12.2881i	0.0660619	−	0.423224i
$844$		0			0
$845$	18.3048	−	18.3048i	0.629704	−	0.629704i
$846$		0			0
$847$	−20.3334			−0.698665
$848$		0			0
$849$	10.1218	−	22.8714i	0.347378	−	0.784944i
$850$		0			0
$851$	7.80455	+	29.1270i	0.267537	+	0.998460i
$852$		0			0
$853$	8.76788	−	32.7222i	0.300207	−	1.12039i	−0.636787	−	0.771040i	$-0.719737\pi$
$853$	8.76788	−	32.7222i	0.300207	−	1.12039i	0.936994	−	0.349347i	$-0.113596\pi$
$854$		0			0
$855$	−22.7688	−	7.28556i	−0.778676	−	0.249161i
$856$		0			0
$857$	11.2530	−	6.49690i	0.384394	−	0.221930i	−0.295334	−	0.955394i	$-0.595431\pi$
$857$	11.2530	−	6.49690i	0.384394	−	0.221930i	0.679728	+	0.733464i	$0.262098\pi$
$858$		0			0
$859$	−31.4765	+	8.43410i	−1.07396	+	0.287768i	−0.752121	−	0.659025i	$-0.770969\pi$
$859$	−31.4765	+	8.43410i	−1.07396	+	0.287768i	−0.321843	+	0.946793i	$0.604302\pi$
$860$		0			0
$861$	−15.0475	+	18.6673i	−0.512817	+	0.636181i
$862$		0			0
$863$	21.7785			0.741348			0.370674	−	0.928763i	$-0.379127\pi$
$863$	21.7785			0.741348			0.370674	+	0.928763i	$0.379127\pi$
$864$		0			0
$865$	2.23823			0.0761022
$866$		0			0
$867$	7.32002	−	9.08093i	0.248601	−	0.308405i
$868$		0			0
$869$	9.31032	−	2.49469i	0.315831	−	0.0846267i
$870$		0			0
$871$	18.5116	−	10.6877i	0.627243	−	0.362139i
$872$		0			0
$873$	−13.6023	+	12.3582i	−0.460368	+	0.418262i
$874$		0			0
$875$	−0.920957	+	3.43706i	−0.0311340	+	0.116194i
$876$		0			0
$877$	−1.27840	−	4.77106i	−0.0431685	−	0.161107i	0.940977	−	0.338471i	$-0.109910\pi$
$877$	−1.27840	−	4.77106i	−0.0431685	−	0.161107i	−0.984145	+	0.177364i	$0.943243\pi$
$878$		0			0
$879$	17.6669	−	39.9206i	0.595890	−	1.34649i
$880$		0			0
$881$	−1.82954			−0.0616389			−0.0308194	−	0.999525i	$-0.509812\pi$
$881$	−1.82954			−0.0616389			−0.0308194	+	0.999525i	$0.509812\pi$
$882$		0			0
$883$	37.7173	−	37.7173i	1.26929	−	1.26929i	0.322834	−	0.946456i	$-0.395365\pi$
$883$	37.7173	−	37.7173i	1.26929	−	1.26929i	0.946456	−	0.322834i	$-0.104635\pi$
$884$		0			0
$885$	−9.80843	+	62.8375i	−0.329707	+	2.11226i
$886$		0			0
$887$	23.5347	+	13.5877i	0.790217	+	0.456232i	0.840039	−	0.542526i	$-0.182532\pi$
$887$	23.5347	+	13.5877i	0.790217	+	0.456232i	−0.0498220	+	0.998758i	$0.515865\pi$
$888$		0			0
$889$	−12.2386	+	7.06596i	−0.410469	+	0.236985i
$890$		0			0
$891$	7.84899	+	46.8398i	0.262951	+	1.56919i
$892$		0			0
$893$	9.45826	+	2.53433i	0.316509	+	0.0848082i
$894$		0			0
$895$	0.243906	−	0.422458i	0.00815288	−	0.0141212i
$896$		0			0
$897$	−8.93163	−	12.2357i	−0.298218	−	0.408537i
$898$		0			0
$899$	−16.1807	+	16.1807i	−0.539655	+	0.539655i
$900$		0			0
$901$	1.96714	+	1.96714i	0.0655350	+	0.0655350i
$902$		0			0
$903$	2.16535	+	0.958277i	0.0720583	+	0.0318895i
$904$		0			0
$905$	−28.9128	−	16.6928i	−0.961095	−	0.554889i
$906$		0			0
$907$	8.11719	−	30.2938i	0.269527	−	1.00589i	−0.689894	−	0.723911i	$-0.742343\pi$
$907$	8.11719	−	30.2938i	0.269527	−	1.00589i	0.959421	−	0.281978i	$-0.0909905\pi$
$908$		0			0
$909$	39.1529	+	1.87629i	1.29862	+	0.0622328i
$910$		0			0
$911$	−20.6608	−	35.7856i	−0.684524	−	1.18563i	−0.973586	−	0.228320i	$-0.926677\pi$
$911$	−20.6608	−	35.7856i	−0.684524	−	1.18563i	0.289062	−	0.957310i	$-0.406657\pi$
$912$		0			0
$913$	7.72343	−	13.3774i	0.255608	−	0.442727i
$914$		0			0
$915$	25.0251	−	31.0452i	0.827304	−	1.02632i
$916$		0			0
$917$	7.62540	+	7.62540i	0.251813	+	0.251813i
$918$		0			0
$919$		−	2.92729i		−	0.0965624i	−0.998834	−	0.0482812i	$-0.984626\pi$
$919$		−	2.92729i		−	0.0965624i	0.998834	−	0.0482812i	$-0.0153744\pi$
$920$		0			0
$921$	−0.935347	−	8.71171i	−0.0308207	−	0.287061i
$922$		0			0
$923$	26.0547	−	6.98133i	0.857600	−	0.229793i
$924$		0			0
$925$	−28.0057	−	7.50411i	−0.920822	−	0.246734i
$926$		0			0
$927$	−12.0735	+	37.7321i	−0.396547	+	1.23929i
$928$		0			0
$929$	−27.6953	−	47.9696i	−0.908652	−	1.57383i	−0.815938	−	0.578139i	$-0.803779\pi$
$929$	−27.6953	−	47.9696i	−0.908652	−	1.57383i	−0.0927142	−	0.995693i	$-0.529554\pi$
$930$		0			0
$931$	3.80699	+	14.2079i	0.124769	+	0.465645i
$932$		0			0
$933$	−6.93256	+	2.67897i	−0.226962	+	0.0877055i
$934$		0			0
$935$			50.7746i			1.66051i
$936$		0			0
$937$			6.46687i			0.211263i	0.994405	+	0.105632i	$0.0336864\pi$
$937$			6.46687i			0.211263i	−0.994405	+	0.105632i	$0.966314\pi$
$938$		0			0
$939$	−2.67753	+	17.1535i	−0.0873778	+	0.559784i
$940$		0			0
$941$	8.14789	+	30.4083i	0.265614	+	0.991283i	0.961874	+	0.273494i	$0.0881793\pi$
$941$	8.14789	+	30.4083i	0.265614	+	0.991283i	−0.696260	+	0.717790i	$0.745154\pi$
$942$		0			0
$943$	−23.9661	−	41.5105i	−0.780443	−	1.35177i
$944$		0			0
$945$	17.8727	−	5.94009i	0.581398	−	0.193231i
$946$		0			0
$947$	−1.87280	−	0.501815i	−0.0608578	−	0.0163068i	0.228262	−	0.973600i	$-0.426696\pi$
$947$	−1.87280	−	0.501815i	−0.0608578	−	0.0163068i	−0.289120	+	0.957293i	$0.593362\pi$
$948$		0			0
$949$	5.81390	−	1.55783i	0.188727	−	0.0505693i
$950$		0			0
$951$	−38.6157	+	28.1882i	−1.25220	+	0.914063i
$952$		0			0
$953$			10.9796i			0.355665i	0.984061	+	0.177832i	$0.0569085\pi$
$953$			10.9796i			0.355665i	−0.984061	+	0.177832i	$0.943092\pi$
$954$		0			0
$955$	−9.57418	−	9.57418i	−0.309813	−	0.309813i
$956$		0			0
$957$	27.0883	+	70.0983i	0.875640	+	2.26596i
$958$		0			0
$959$	0.921016	−	1.59525i	0.0297412	−	0.0515132i
$960$		0			0
$961$	11.6272	+	20.1389i	0.375070	+	0.649641i
$962$		0			0
$963$	−15.8928	+	24.7141i	−0.512137	+	0.796400i
$964$		0			0
$965$	14.9948	−	55.9613i	0.482699	−	1.80146i
$966$		0			0
$967$	6.19539	+	3.57691i	0.199230	+	0.115026i	0.596296	−	0.802764i	$-0.296638\pi$
$967$	6.19539	+	3.57691i	0.199230	+	0.115026i	−0.397066	+	0.917790i	$0.629972\pi$
$968$		0			0
$969$	−1.57204	−	14.6418i	−0.0505011	−	0.470361i
$970$		0			0
$971$	−40.8697	−	40.8697i	−1.31157	−	1.31157i	−0.920258	−	0.391312i	$-0.872021\pi$
$971$	−40.8697	−	40.8697i	−1.31157	−	1.31157i	−0.391312	−	0.920258i	$-0.627979\pi$
$972$		0			0
$973$	14.8944	−	14.8944i	0.477491	−	0.477491i
$974$		0			0
$975$	14.4824	−	1.55492i	0.463807	−	0.0497974i
$976$		0			0
$977$	−24.1070	+	41.7545i	−0.771250	+	1.33584i	0.165629	+	0.986188i	$0.447035\pi$
$977$	−24.1070	+	41.7545i	−0.771250	+	1.33584i	−0.936878	+	0.349655i	$0.886299\pi$
$978$		0			0
$979$	−10.8042	−	2.89498i	−0.345304	−	0.0925240i
$980$		0			0
$981$	19.1374	+	12.3066i	0.611010	+	0.392919i
$982$		0			0
$983$	−0.339797	+	0.196182i	−0.0108378	+	0.00625722i	−0.505409	−	0.862880i	$-0.668658\pi$
$983$	−0.339797	+	0.196182i	−0.0108378	+	0.00625722i	0.494571	+	0.869137i	$0.335325\pi$
$984$		0			0
$985$	−22.2034	−	12.8192i	−0.707460	−	0.408452i
$986$		0			0
$987$	−7.19580	+	2.78070i	−0.229045	+	0.0885105i
$988$		0			0
$989$	−3.34722	+	3.34722i	−0.106435	+	0.106435i
$990$		0			0
$991$	−1.35162			−0.0429357			−0.0214678	−	0.999770i	$-0.506834\pi$
$991$	−1.35162			−0.0429357			−0.0214678	+	0.999770i	$0.506834\pi$
$992$		0			0
$993$	4.88197	+	6.68793i	0.154924	+	0.212235i
$994$		0			0
$995$	6.85012	+	25.5650i	0.217163	+	0.810465i
$996$		0			0
$997$	−3.67972	+	13.7329i	−0.116538	+	0.434926i	−0.999397	−	0.0347118i	$-0.988949\pi$
$997$	−3.67972	+	13.7329i	−0.116538	+	0.434926i	0.882859	+	0.469637i	$0.155615\pi$
$998$		0			0
$999$	−11.8248	−	35.5788i	−0.374122	−	1.12566i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	576.2.bb.e.49.5		72
3.2	odd	2		1728.2.bc.e.1009.4		72
4.3	odd	2		144.2.x.e.85.10	yes	72
9.2	odd	6		1728.2.bc.e.1585.15		72
9.7	even	3	inner	576.2.bb.e.241.5		72
12.11	even	2		432.2.y.e.37.9		72
16.3	odd	4		144.2.x.e.13.3	✓	72
16.13	even	4	inner	576.2.bb.e.337.5		72
36.7	odd	6		144.2.x.e.133.3	yes	72
36.11	even	6		432.2.y.e.181.16		72
48.29	odd	4		1728.2.bc.e.145.15		72
48.35	even	4		432.2.y.e.253.16		72
144.29	odd	12		1728.2.bc.e.721.4		72
144.61	even	12	inner	576.2.bb.e.529.5		72
144.83	even	12		432.2.y.e.397.9		72
144.115	odd	12		144.2.x.e.61.10	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.x.e.13.3	✓	72	16.3	odd	4
144.2.x.e.61.10	yes	72	144.115	odd	12
144.2.x.e.85.10	yes	72	4.3	odd	2
144.2.x.e.133.3	yes	72	36.7	odd	6
432.2.y.e.37.9		72	12.11	even	2
432.2.y.e.181.16		72	36.11	even	6
432.2.y.e.253.16		72	48.35	even	4
432.2.y.e.397.9		72	144.83	even	12
576.2.bb.e.49.5		72	1.1	even	1	trivial
576.2.bb.e.241.5		72	9.7	even	3	inner
576.2.bb.e.337.5		72	16.13	even	4	inner
576.2.bb.e.529.5		72	144.61	even	12	inner
1728.2.bc.e.145.15		72	48.29	odd	4
1728.2.bc.e.721.4		72	144.29	odd	12
1728.2.bc.e.1009.4		72	3.2	odd	2
1728.2.bc.e.1585.15		72	9.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	576.bb (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.08700 + 1.34849i) q^{3} +(2.90072 - 0.777246i) q^{5} +(1.04527 - 0.603486i) q^{7} +(-0.636858 - 2.93162i) q^{9} +O(q^{10})\)	\(q+(-1.08700 + 1.34849i) q^{3} +(2.90072 - 0.777246i) q^{5} +(1.04527 - 0.603486i) q^{7} +(-0.636858 - 2.93162i) q^{9} +(1.36579 - 5.09718i) q^{11} +(-0.541655 - 2.02149i) q^{13} +(-2.10498 + 4.75646i) q^{15} -3.20404 q^{17} +(1.87633 - 1.87633i) q^{19} +(-0.322412 + 2.06553i) q^{21} +(-3.61927 - 2.08959i) q^{23} +(3.47994 - 2.00914i) q^{25} +(4.64553 + 2.32788i) q^{27} +(7.94194 + 2.12804i) q^{29} +(-1.39155 + 2.41023i) q^{31} +(5.38890 + 7.38239i) q^{33} +(2.56298 - 2.56298i) q^{35} +(-5.10207 - 5.10207i) q^{37} +(3.31474 + 1.46694i) q^{39} +(9.93271 + 5.73465i) q^{41} +(0.293160 - 1.09409i) q^{43} +(-4.12594 - 8.00882i) q^{45} +(1.84507 + 3.19576i) q^{47} +(-2.77161 + 4.80057i) q^{49} +(3.48279 - 4.32062i) q^{51} +(-0.613957 - 0.613957i) q^{53} -15.8471i q^{55} +(0.490642 + 4.56978i) q^{57} +(11.8105 - 3.16461i) q^{59} +(-7.40505 - 1.98418i) q^{61} +(-2.43488 - 2.68000i) q^{63} +(-3.14238 - 5.44277i) q^{65} +(2.64353 + 9.86577i) q^{67} +(6.75194 - 2.60917i) q^{69} +12.8889i q^{71} +2.87605i q^{73} +(-1.07338 + 6.87661i) q^{75} +(-1.64847 - 6.15216i) q^{77} +(0.913281 + 1.58185i) q^{79} +(-8.18882 + 3.73406i) q^{81} +(2.82747 + 0.757618i) q^{83} +(-9.29402 + 2.49032i) q^{85} +(-11.5025 + 8.39646i) q^{87} -2.11965i q^{89} +(-1.78611 - 1.78611i) q^{91} +(-1.73756 - 4.49642i) q^{93} +(3.98433 - 6.90107i) q^{95} +(-3.06298 - 5.30524i) q^{97} +(-15.8128 - 0.757786i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 2 q^{3} + 4 q^{5}+O(q^{10}) \) 72 * q - 2 * q^3 + 4 * q^5	\( 72 q - 2 q^{3} + 4 q^{5} + 2 q^{11} - 16 q^{13} + 20 q^{15} - 16 q^{17} - 28 q^{19} - 16 q^{21} - 8 q^{27} + 4 q^{29} - 28 q^{31} - 32 q^{33} + 16 q^{35} + 16 q^{37} + 10 q^{43} + 40 q^{45} + 56 q^{47} + 4 q^{49} + 54 q^{51} - 8 q^{53} + 14 q^{59} - 32 q^{61} + 108 q^{63} - 64 q^{65} + 18 q^{67} + 32 q^{69} - 86 q^{75} - 36 q^{77} - 44 q^{79} - 44 q^{81} - 20 q^{83} - 8 q^{85} + 80 q^{91} - 4 q^{93} - 48 q^{95} + 40 q^{97} - 28 q^{99}+O(q^{100}) \) 72 * q - 2 * q^3 + 4 * q^5 + 2 * q^11 - 16 * q^13 + 20 * q^15 - 16 * q^17 - 28 * q^19 - 16 * q^21 - 8 * q^27 + 4 * q^29 - 28 * q^31 - 32 * q^33 + 16 * q^35 + 16 * q^37 + 10 * q^43 + 40 * q^45 + 56 * q^47 + 4 * q^49 + 54 * q^51 - 8 * q^53 + 14 * q^59 - 32 * q^61 + 108 * q^63 - 64 * q^65 + 18 * q^67 + 32 * q^69 - 86 * q^75 - 36 * q^77 - 44 * q^79 - 44 * q^81 - 20 * q^83 - 8 * q^85 + 80 * q^91 - 4 * q^93 - 48 * q^95 + 40 * q^97 - 28 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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