LMFDB - Embedded newform 572.2.bh.a.57.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(57,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 2, 15]))

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

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

chi := DirichletCharacter("572.57");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.bh (of order $20$, degree $8$, 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:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$14$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			57.6
Character	$\chi$	$=$	572.57
Dual form			572.2.bh.a.281.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.673845 + 0.489577i) q^{3} +(-1.19803 - 0.610425i) q^{5} +(-1.96669 + 0.311493i) q^{7} +(-0.712670 + 2.19337i) q^{9} +O(q^{10})$	\(q+(-0.673845 + 0.489577i) q^{3} +(-1.19803 - 0.610425i) q^{5} +(-1.96669 + 0.311493i) q^{7} +(-0.712670 + 2.19337i) q^{9} +(2.00696 - 2.64048i) q^{11} +(3.54077 - 0.680419i) q^{13} +(1.10613 - 0.175194i) q^{15} +(-1.65795 - 5.10265i) q^{17} +(-4.60335 - 0.729099i) q^{19} +(1.17274 - 1.17274i) q^{21} -7.98537i q^{23} +(-1.87628 - 2.58247i) q^{25} +(-1.36575 - 4.20335i) q^{27} +(-1.13586 + 1.56338i) q^{29} +(-0.985993 - 1.93512i) q^{31} +(-0.0596627 + 2.76183i) q^{33} +(2.54629 + 0.827339i) q^{35} +(-0.374726 - 2.36593i) q^{37} +(-2.05281 + 2.19197i) q^{39} +(8.37942 + 1.32717i) q^{41} -5.37023 q^{43} +(2.19269 - 2.19269i) q^{45} +(0.512814 + 0.0812217i) q^{47} +(-2.88656 + 0.937901i) q^{49} +(3.61534 + 2.62670i) q^{51} +(-2.72195 + 8.37731i) q^{53} +(-4.01620 + 1.93826i) q^{55} +(3.45889 - 1.76239i) q^{57} +(-1.11282 - 7.02608i) q^{59} +(5.24481 - 1.70414i) q^{61} +(0.718379 - 4.53567i) q^{63} +(-4.65728 - 1.34621i) q^{65} +(6.30211 - 6.30211i) q^{67} +(3.90945 + 5.38090i) q^{69} +(-0.418067 - 0.213016i) q^{71} +(10.3766 - 1.64350i) q^{73} +(2.52864 + 0.821604i) q^{75} +(-3.12457 + 5.81814i) q^{77} +(-14.5112 - 4.71499i) q^{79} +(-2.61921 - 1.90297i) q^{81} +(-2.70092 + 5.30086i) q^{83} +(-1.12852 + 7.12517i) q^{85} -1.60957i q^{87} +(5.84930 + 5.84930i) q^{89} +(-6.75164 + 2.44110i) q^{91} +(1.61180 + 0.821251i) q^{93} +(5.06988 + 3.68348i) q^{95} +(3.38164 + 6.63685i) q^{97} +(4.36125 + 6.28380i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 28 q^{9}+O(q^{10}) $ 112 * q - 28 * q^9	$ 112 q - 28 q^{9} + 8 q^{11} - 10 q^{13} + 4 q^{15} - 24 q^{27} - 20 q^{29} - 16 q^{31} - 54 q^{33} + 100 q^{35} - 12 q^{37} + 40 q^{39} - 20 q^{41} - 4 q^{45} - 10 q^{47} - 76 q^{53} - 20 q^{55} + 18 q^{59} + 40 q^{61} + 80 q^{63} + 92 q^{67} + 8 q^{71} - 30 q^{73} - 80 q^{79} + 12 q^{81} + 40 q^{85} + 32 q^{89} - 12 q^{91} - 114 q^{93} + 54 q^{97} - 90 q^{99}+O(q^{100}) $ 112 * q - 28 * q^9 + 8 * q^11 - 10 * q^13 + 4 * q^15 - 24 * q^27 - 20 * q^29 - 16 * q^31 - 54 * q^33 + 100 * q^35 - 12 * q^37 + 40 * q^39 - 20 * q^41 - 4 * q^45 - 10 * q^47 - 76 * q^53 - 20 * q^55 + 18 * q^59 + 40 * q^61 + 80 * q^63 + 92 * q^67 + 8 * q^71 - 30 * q^73 - 80 * q^79 + 12 * q^81 + 40 * q^85 + 32 * q^89 - 12 * q^91 - 114 * q^93 + 54 * q^97 - 90 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{10}\right)$

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
$3$	−0.673845	+	0.489577i	−0.389044	+	0.282657i	−0.765064	−	0.643955i	$-0.777293\pi$
$3$	−0.673845	+	0.489577i	−0.389044	+	0.282657i	0.376019	+	0.926612i	$0.377293\pi$
$4$		0			0
$5$	−1.19803	−	0.610425i	−0.535774	−	0.272990i	0.165098	−	0.986277i	$-0.447206\pi$
$5$	−1.19803	−	0.610425i	−0.535774	−	0.272990i	−0.700872	+	0.713287i	$0.747206\pi$
$6$		0			0
$7$	−1.96669	+	0.311493i	−0.743338	+	0.117733i	−0.516605	−	0.856224i	$-0.672804\pi$
$7$	−1.96669	+	0.311493i	−0.743338	+	0.117733i	−0.226733	+	0.973957i	$0.572804\pi$
$8$		0			0
$9$	−0.712670	+	2.19337i	−0.237557	+	0.731124i
$10$		0			0
$11$	2.00696	−	2.64048i	0.605121	−	0.796134i
$11$	2.00696	−	2.64048i	0.605121	−	0.796134i
$12$		0			0
$13$	3.54077	−	0.680419i	0.982032	−	0.188714i
$13$	3.54077	−	0.680419i	0.982032	−	0.188714i
$14$		0			0
$15$	1.10613	−	0.175194i	0.285603	−	0.0452350i
$16$		0			0
$17$	−1.65795	−	5.10265i	−0.402112	−	1.23757i	−0.923283	−	0.384122i	$-0.874504\pi$
$17$	−1.65795	−	5.10265i	−0.402112	−	1.23757i	0.521170	−	0.853453i	$-0.325496\pi$
$18$		0			0
$19$	−4.60335	−	0.729099i	−1.05608	−	0.167267i	−0.395839	−	0.918320i	$-0.629546\pi$
$19$	−4.60335	−	0.729099i	−1.05608	−	0.167267i	−0.660242	+	0.751053i	$0.729546\pi$
$20$		0			0
$21$	1.17274	−	1.17274i	0.255913	−	0.255913i
$22$		0			0
$23$		−	7.98537i		−	1.66506i	−0.553977	−	0.832532i	$-0.686890\pi$
$23$		−	7.98537i		−	1.66506i	0.553977	−	0.832532i	$-0.313110\pi$
$24$		0			0
$25$	−1.87628	−	2.58247i	−0.375255	−	0.516495i
$26$		0			0
$27$	−1.36575	−	4.20335i	−0.262839	−	0.808936i
$28$		0			0
$29$	−1.13586	+	1.56338i	−0.210924	+	0.290312i	−0.901350	−	0.433091i	$-0.857423\pi$
$29$	−1.13586	+	1.56338i	−0.210924	+	0.290312i	0.690426	+	0.723403i	$0.257423\pi$
$30$		0			0
$31$	−0.985993	−	1.93512i	−0.177090	−	0.347558i	0.785351	−	0.619051i	$-0.212483\pi$
$31$	−0.985993	−	1.93512i	−0.177090	−	0.347558i	−0.962440	+	0.271493i	$0.912483\pi$
$32$		0			0
$33$	−0.0596627	+	2.76183i	−0.0103859	+	0.480773i
$34$		0			0
$35$	2.54629	+	0.827339i	0.430401	+	0.139846i
$36$		0			0
$37$	−0.374726	−	2.36593i	−0.0616047	−	0.388956i	−0.999155	−	0.0411063i	$-0.986912\pi$
$37$	−0.374726	−	2.36593i	−0.0616047	−	0.388956i	0.937550	−	0.347850i	$-0.113088\pi$
$38$		0			0
$39$	−2.05281	+	2.19197i	−0.328713	+	0.350997i
$40$		0			0
$41$	8.37942	+	1.32717i	1.30865	+	0.207269i	0.771505	−	0.636223i	$-0.219504\pi$
$41$	8.37942	+	1.32717i	1.30865	+	0.207269i	0.537141	+	0.843492i	$0.319504\pi$
$42$		0			0
$43$	−5.37023			−0.818953			−0.409476	−	0.912321i	$-0.634289\pi$
$43$	−5.37023			−0.818953			−0.409476	+	0.912321i	$0.634289\pi$
$44$		0			0
$45$	2.19269	−	2.19269i	0.326867	−	0.326867i
$46$		0			0
$47$	0.512814	+	0.0812217i	0.0748015	+	0.0118474i	0.193723	−	0.981056i	$-0.437944\pi$
$47$	0.512814	+	0.0812217i	0.0748015	+	0.0118474i	−0.118921	+	0.992904i	$0.537944\pi$
$48$		0			0
$49$	−2.88656	+	0.937901i	−0.412366	+	0.133986i
$50$		0			0
$51$	3.61534	+	2.62670i	0.506249	+	0.367811i
$52$		0			0
$53$	−2.72195	+	8.37731i	−0.373889	+	1.15071i	0.570336	+	0.821411i	$0.306813\pi$
$53$	−2.72195	+	8.37731i	−0.373889	+	1.15071i	−0.944225	+	0.329300i	$0.893187\pi$
$54$		0			0
$55$	−4.01620	+	1.93826i	−0.541545	+	0.261355i
$56$		0			0
$57$	3.45889	−	1.76239i	0.458141	−	0.233435i
$58$		0			0
$59$	−1.11282	−	7.02608i	−0.144877	−	0.914718i	−0.947853	−	0.318707i	$-0.896751\pi$
$59$	−1.11282	−	7.02608i	−0.144877	−	0.914718i	0.802976	−	0.596011i	$-0.203249\pi$
$60$		0			0
$61$	5.24481	−	1.70414i	0.671529	−	0.218193i	0.0466460	−	0.998911i	$-0.485147\pi$
$61$	5.24481	−	1.70414i	0.671529	−	0.218193i	0.624883	+	0.780719i	$0.285147\pi$
$62$		0			0
$63$	0.718379	−	4.53567i	0.0905073	−	0.571441i
$64$		0			0
$65$	−4.65728	−	1.34621i	−0.577664	−	0.166977i
$66$		0			0
$67$	6.30211	−	6.30211i	0.769925	−	0.769925i	−0.208168	−	0.978093i	$-0.566750\pi$
$67$	6.30211	−	6.30211i	0.769925	−	0.769925i	0.978093	+	0.208168i	$0.0667501\pi$
$68$		0			0
$69$	3.90945	+	5.38090i	0.470642	+	0.647784i
$70$		0			0
$71$	−0.418067	−	0.213016i	−0.0496154	−	0.0252803i	0.429007	−	0.903301i	$-0.358864\pi$
$71$	−0.418067	−	0.213016i	−0.0496154	−	0.0252803i	−0.478622	+	0.878021i	$0.658864\pi$
$72$		0			0
$73$	10.3766	−	1.64350i	1.21449	−	0.192357i	0.483871	−	0.875139i	$-0.339230\pi$
$73$	10.3766	−	1.64350i	1.21449	−	0.192357i	0.730622	+	0.682783i	$0.239230\pi$
$74$		0			0
$75$	2.52864	+	0.821604i	0.291982	+	0.0948707i
$76$		0			0
$77$	−3.12457	+	5.81814i	−0.356078	+	0.663039i
$78$		0			0
$79$	−14.5112	−	4.71499i	−1.63264	−	0.530477i	−0.657765	−	0.753223i	$-0.728498\pi$
$79$	−14.5112	−	4.71499i	−1.63264	−	0.530477i	−0.974876	+	0.222746i	$0.928498\pi$
$80$		0			0
$81$	−2.61921	−	1.90297i	−0.291024	−	0.211441i
$82$		0			0
$83$	−2.70092	+	5.30086i	−0.296465	+	0.581845i	−0.990406	−	0.138187i	$-0.955873\pi$
$83$	−2.70092	+	5.30086i	−0.296465	+	0.581845i	0.693942	+	0.720031i	$0.255873\pi$
$84$		0			0
$85$	−1.12852	+	7.12517i	−0.122405	+	0.772833i
$86$		0			0
$87$		−	1.60957i		−	0.172564i
$88$		0			0
$89$	5.84930	+	5.84930i	0.620025	+	0.620025i	0.945538	−	0.325513i	$-0.105537\pi$
$89$	5.84930	+	5.84930i	0.620025	+	0.620025i	−0.325513	+	0.945538i	$0.605537\pi$
$90$		0			0
$91$	−6.75164	+	2.44110i	−0.707764	+	0.255896i
$92$		0			0
$93$	1.61180	+	0.821251i	0.167135	+	0.0851598i
$94$		0			0
$95$	5.06988	+	3.68348i	0.520158	+	0.377917i
$96$		0			0
$97$	3.38164	+	6.63685i	0.343354	+	0.673870i	0.996521	−	0.0833438i	$-0.0265600\pi$
$97$	3.38164	+	6.63685i	0.343354	+	0.673870i	−0.653167	+	0.757214i	$0.726560\pi$
$98$		0			0
$99$	4.36125	+	6.28380i	0.438322	+	0.631545i
$100$		0			0
$101$	−3.44697	+	10.6087i	−0.342986	+	1.05560i	0.619667	+	0.784865i	$0.287268\pi$
$101$	−3.44697	+	10.6087i	−0.342986	+	1.05560i	−0.962653	+	0.270738i	$0.912732\pi$
$102$		0			0
$103$	−9.22643	+	12.6991i	−0.909108	+	1.25128i	0.0583629	+	0.998295i	$0.481412\pi$
$103$	−9.22643	+	12.6991i	−0.909108	+	1.25128i	−0.967470	+	0.252984i	$0.918588\pi$
$104$		0			0
$105$	−2.12085	+	0.689105i	−0.206974	+	0.0672498i
$106$		0			0
$107$	−0.00485148	−	0.00667750i	−0.000469011	−	0.000645538i	0.808782	−	0.588108i	$-0.200127\pi$
$107$	−0.00485148	−	0.00667750i	−0.000469011	−	0.000645538i	−0.809251	+	0.587462i	$0.800127\pi$
$108$		0			0
$109$	−11.9962	−	11.9962i	−1.14903	−	1.14903i	−0.986743	−	0.162288i	$-0.948113\pi$
$109$	−11.9962	−	11.9962i	−1.14903	−	1.14903i	−0.162288	−	0.986743i	$-0.551887\pi$
$110$		0			0
$111$	1.41081	+	1.41081i	0.133908	+	0.133908i
$112$		0			0
$113$	16.1339	−	11.7220i	1.51775	−	1.10271i	0.555164	−	0.831741i	$-0.312655\pi$
$113$	16.1339	−	11.7220i	1.51775	−	1.10271i	0.962588	−	0.270971i	$-0.0873447\pi$
$114$		0			0
$115$	−4.87447	+	9.56668i	−0.454547	+	0.892098i
$116$		0			0
$117$	−1.03098	+	8.25113i	−0.0953146	+	0.762818i
$118$		0			0
$119$	4.85011	+	9.51888i	0.444609	+	0.872594i
$120$		0			0
$121$	−2.94423	−	10.5987i	−0.267657	−	0.963514i
$122$		0			0
$123$	−6.29618	+	3.20806i	−0.567708	+	0.289261i
$124$		0			0
$125$	1.72311	+	10.8793i	0.154120	+	0.973076i
$126$		0			0
$127$	0.631334	+	1.94305i	0.0560218	+	0.172417i	0.975152	−	0.221536i	$-0.0711071\pi$
$127$	0.631334	+	1.94305i	0.0560218	+	0.172417i	−0.919130	+	0.393954i	$0.871107\pi$
$128$		0			0
$129$	3.61870	−	2.62914i	0.318609	−	0.231483i
$130$		0			0
$131$		−	11.9356i		−	1.04281i	−0.853308	−	0.521407i	$-0.825407\pi$
$131$		−	11.9356i		−	1.04281i	0.853308	−	0.521407i	$-0.174593\pi$
$132$		0			0
$133$	9.28046			0.804718
$134$		0			0
$135$	−0.929625	+	5.86942i	−0.0800094	+	0.505159i
$136$		0			0
$137$	6.05144	−	11.8766i	0.517010	−	1.01469i	−0.473953	−	0.880550i	$-0.657173\pi$
$137$	6.05144	−	11.8766i	0.517010	−	1.01469i	0.990963	−	0.134138i	$-0.0428267\pi$
$138$		0			0
$139$	−12.2874	+	16.9122i	−1.04221	+	1.43448i	−0.146833	+	0.989161i	$0.546908\pi$
$139$	−12.2874	+	16.9122i	−1.04221	+	1.43448i	−0.895374	+	0.445315i	$0.853092\pi$
$140$		0			0
$141$	−0.385321	+	0.196331i	−0.0324499	+	0.0165340i
$142$		0			0
$143$	5.30954	−	10.7149i	0.444006	−	0.896024i
$144$		0			0
$145$	2.31512	−	1.17961i	0.192260	−	0.0979614i
$146$		0			0
$147$	1.48592	−	2.04519i	0.122557	−	0.168685i
$148$		0			0
$149$	−8.26543	+	16.2218i	−0.677131	+	1.32894i	0.255042	+	0.966930i	$0.417911\pi$
$149$	−8.26543	+	16.2218i	−0.677131	+	1.32894i	−0.932173	+	0.362014i	$0.882089\pi$
$150$		0			0
$151$	−1.23616	+	7.80478i	−0.100597	+	0.635144i	0.884943	+	0.465700i	$0.154197\pi$
$151$	−1.23616	+	7.80478i	−0.100597	+	0.635144i	−0.985540	+	0.169444i	$0.945803\pi$
$152$		0			0
$153$	12.3736			1.00034
$154$		0			0
$155$			2.92020i			0.234556i
$156$		0			0
$157$	−3.86792	+	2.81021i	−0.308694	+	0.224279i	−0.731336	−	0.682018i	$-0.761103\pi$
$157$	−3.86792	+	2.81021i	−0.308694	+	0.224279i	0.422642	+	0.906297i	$0.361103\pi$
$158$		0			0
$159$	−2.26716	−	6.97761i	−0.179798	−	0.553360i
$160$		0			0
$161$	2.48738	+	15.7047i	0.196033	+	1.23771i
$162$		0			0
$163$	10.1493	−	5.17133i	0.794956	−	0.405050i	−0.00883612	−	0.999961i	$-0.502813\pi$
$163$	10.1493	−	5.17133i	0.794956	−	0.405050i	0.803792	+	0.594911i	$0.202813\pi$
$164$		0			0
$165$	1.75737	−	3.27233i	0.136811	−	0.254750i
$166$		0			0
$167$	3.76579	+	7.39078i	0.291406	+	0.571916i	0.989575	−	0.144017i	$-0.0460019\pi$
$167$	3.76579	+	7.39078i	0.291406	+	0.571916i	−0.698170	+	0.715932i	$0.746002\pi$
$168$		0			0
$169$	12.0741	−	4.81841i	0.928774	−	0.370647i
$170$		0			0
$171$	4.87985	−	9.57725i	0.373172	−	0.732391i
$172$		0			0
$173$	13.5674	−	9.85732i	1.03151	−	0.749439i	0.0629026	−	0.998020i	$-0.479964\pi$
$173$	13.5674	−	9.85732i	1.03151	−	0.749439i	0.968611	+	0.248581i	$0.0799643\pi$
$174$		0			0
$175$	4.49447	+	4.49447i	0.339750	+	0.339750i
$176$		0			0
$177$	4.18967	+	4.18967i	0.314915	+	0.314915i
$178$		0			0
$179$	−10.3010	−	14.1781i	−0.769932	−	1.05972i	−0.996322	−	0.0856842i	$-0.972692\pi$
$179$	−10.3010	−	14.1781i	−0.769932	−	1.05972i	0.226390	−	0.974037i	$-0.427308\pi$
$180$		0			0
$181$	−19.5171	+	6.34148i	−1.45069	+	0.471359i	−0.925213	−	0.379448i	$-0.876114\pi$
$181$	−19.5171	+	6.34148i	−1.45069	+	0.471359i	−0.525479	+	0.850806i	$0.676114\pi$
$182$		0			0
$183$	−2.69988	+	3.71606i	−0.199581	+	0.274699i
$184$		0			0
$185$	−0.995291	+	3.06319i	−0.0731752	+	0.225210i
$186$		0			0
$187$	−16.8009	−	5.86303i	−1.22860	−	0.428747i
$188$		0			0
$189$	3.99532	+	7.84126i	0.290617	+	0.570368i
$190$		0			0
$191$	2.62056	+	1.90395i	0.189617	+	0.137765i	0.678544	−	0.734560i	$-0.262611\pi$
$191$	2.62056	+	1.90395i	0.189617	+	0.137765i	−0.488926	+	0.872325i	$0.662611\pi$
$192$		0			0
$193$	−2.14882	−	1.09488i	−0.154675	−	0.0788110i	0.374939	−	0.927049i	$-0.377664\pi$
$193$	−2.14882	−	1.09488i	−0.154675	−	0.0788110i	−0.529615	+	0.848238i	$0.677664\pi$
$194$		0			0
$195$	3.79736	−	1.37296i	0.271934	−	0.0983195i
$196$		0			0
$197$	−10.1537	−	10.1537i	−0.723424	−	0.723424i	0.245877	−	0.969301i	$-0.420924\pi$
$197$	−10.1537	−	10.1537i	−0.723424	−	0.723424i	−0.969301	+	0.245877i	$0.920924\pi$
$198$		0			0
$199$		−	14.6268i		−	1.03687i	−0.855118	−	0.518434i	$-0.826515\pi$
$199$		−	14.6268i		−	1.03687i	0.855118	−	0.518434i	$-0.173485\pi$
$200$		0			0
$201$	−1.16128	+	7.33201i	−0.0819101	+	0.517160i
$202$		0			0
$203$	1.74690	−	3.42849i	0.122609	−	0.240633i
$204$		0			0
$205$	−9.22864	−	6.70500i	−0.644556	−	0.468297i
$206$		0			0
$207$	17.5149	+	5.69093i	1.21737	+	0.395547i
$208$		0			0
$209$	−11.1639	+	10.6918i	−0.772223	+	0.739565i
$210$		0			0
$211$	−16.2341	−	5.27479i	−1.11760	−	0.363131i	−0.308751	−	0.951143i	$-0.599911\pi$
$211$	−16.2341	−	5.27479i	−1.11760	−	0.363131i	−0.808853	+	0.588011i	$0.799911\pi$
$212$		0			0
$213$	0.386000	−	0.0611364i	0.0264483	−	0.00418899i
$214$		0			0
$215$	6.43368	+	3.27813i	0.438774	+	0.223566i
$216$		0			0
$217$	2.54192	+	3.49865i	0.172556	+	0.237504i
$218$		0			0
$219$	−6.18762	+	6.18762i	−0.418120	+	0.418120i
$220$		0			0
$221$	−9.34236	−	16.9392i	−0.628435	−	1.13945i
$222$		0			0
$223$	3.97149	−	25.0750i	0.265950	−	1.67914i	−0.387262	−	0.921970i	$-0.626579\pi$
$223$	3.97149	−	25.0750i	0.265950	−	1.67914i	0.653212	−	0.757175i	$-0.273421\pi$
$224$		0			0
$225$	7.00149	−	2.27492i	0.466766	−	0.151661i
$226$		0			0
$227$	1.48013	+	9.34514i	0.0982394	+	0.620259i	0.986855	+	0.161607i	$0.0516676\pi$
$227$	1.48013	+	9.34514i	0.0982394	+	0.620259i	−0.888616	+	0.458652i	$0.848332\pi$
$228$		0			0
$229$	−4.90282	+	2.49811i	−0.323987	+	0.165080i	−0.608418	−	0.793617i	$-0.708196\pi$
$229$	−4.90282	+	2.49811i	−0.323987	+	0.165080i	0.284430	+	0.958697i	$0.408196\pi$
$230$		0			0
$231$	−0.742952	−	5.45024i	−0.0488827	−	0.358600i
$232$		0			0
$233$	−3.94322	+	12.1360i	−0.258329	+	0.795054i	0.734827	+	0.678255i	$0.237263\pi$
$233$	−3.94322	+	12.1360i	−0.258329	+	0.795054i	−0.993156	+	0.116799i	$0.962737\pi$
$234$		0			0
$235$	−0.564785	−	0.410340i	−0.0368425	−	0.0267676i
$236$		0			0
$237$	12.0867	−	3.92719i	0.785113	−	0.255099i
$238$		0			0
$239$	22.0811	+	3.49730i	1.42831	+	0.226221i	0.822216	−	0.569175i	$-0.192738\pi$
$239$	22.0811	+	3.49730i	1.42831	+	0.226221i	0.606089	+	0.795397i	$0.292738\pi$
$240$		0			0
$241$	−7.47250	+	7.47250i	−0.481346	+	0.481346i	−0.905561	−	0.424215i	$-0.860550\pi$
$241$	−7.47250	+	7.47250i	−0.481346	+	0.481346i	0.424215	+	0.905561i	$0.360550\pi$
$242$		0			0
$243$	15.9556			1.02355
$244$		0			0
$245$	4.03070	+	0.638400i	0.257512	+	0.0407859i
$246$		0			0
$247$	−16.7955	+	0.550638i	−1.06867	+	0.0350363i
$248$		0			0
$249$	−0.775175	−	4.89426i	−0.0491247	−	0.310161i
$250$		0			0
$251$	−0.237872	−	0.0772893i	−0.0150143	−	0.00487846i	0.301500	−	0.953466i	$-0.402513\pi$
$251$	−0.237872	−	0.0772893i	−0.0150143	−	0.00487846i	−0.316515	+	0.948588i	$0.602513\pi$
$252$		0			0
$253$	−21.0852	−	16.0263i	−1.32561	−	1.00756i
$254$		0			0
$255$	−2.72787	−	5.35375i	−0.170826	−	0.335265i
$256$		0			0
$257$	18.3603	−	25.2708i	1.14528	−	1.57635i	0.390187	−	0.920735i	$-0.372410\pi$
$257$	18.3603	−	25.2708i	1.14528	−	1.57635i	0.755097	−	0.655613i	$-0.227590\pi$
$258$		0			0
$259$	1.47394	+	4.53632i	0.0915862	+	0.281873i
$260$		0			0
$261$	−2.61958	−	3.60554i	−0.162148	−	0.223177i
$262$		0			0
$263$		−	6.49276i		−	0.400361i	−0.979759	−	0.200180i	$-0.935847\pi$
$263$		−	6.49276i		−	0.400361i	0.979759	−	0.200180i	$-0.0641528\pi$
$264$		0			0
$265$	8.37469	−	8.37469i	0.514453	−	0.514453i
$266$		0			0
$267$	−6.80520	−	1.07784i	−0.416471	−	0.0659626i
$268$		0			0
$269$	2.59960	+	8.00075i	0.158500	+	0.487814i	0.998499	−	0.0547748i	$-0.0174441\pi$
$269$	2.59960	+	8.00075i	0.158500	+	0.487814i	−0.839998	+	0.542589i	$0.817444\pi$
$270$		0			0
$271$	19.1101	−	3.02675i	1.16086	−	0.183862i	0.453857	−	0.891075i	$-0.350048\pi$
$271$	19.1101	−	3.02675i	1.16086	−	0.183862i	0.707001	+	0.707213i	$0.250048\pi$
$272$		0			0
$273$	3.35445	−	4.95036i	0.203021	−	0.299610i
$274$		0			0
$275$	−10.5846	−	0.228654i	−0.638273	−	0.0137884i
$276$		0			0
$277$	−1.38866	+	4.27385i	−0.0834363	+	0.256791i	−0.984068	−	0.177793i	$-0.943104\pi$
$277$	−1.38866	+	4.27385i	−0.0834363	+	0.256791i	0.900632	+	0.434583i	$0.143104\pi$
$278$		0			0
$279$	4.94713	−	0.783548i	0.296177	−	0.0469098i
$280$		0			0
$281$	4.10823	+	2.09325i	0.245077	+	0.124873i	0.572215	−	0.820104i	$-0.306084\pi$
$281$	4.10823	+	2.09325i	0.245077	+	0.124873i	−0.327138	+	0.944976i	$0.606084\pi$
$282$		0			0
$283$	−2.89919	+	2.10639i	−0.172339	+	0.125212i	−0.670611	−	0.741809i	$-0.733968\pi$
$283$	−2.89919	+	2.10639i	−0.172339	+	0.125212i	0.498272	+	0.867021i	$0.333968\pi$
$284$		0			0
$285$	−5.21965			−0.309186
$286$		0			0
$287$	−16.8931			−0.997169
$288$		0			0
$289$	−9.53494	+	6.92754i	−0.560879	+	0.407502i
$290$		0			0
$291$	−5.52795	−	2.81663i	−0.324054	−	0.165114i
$292$		0			0
$293$	−14.7643	+	2.33844i	−0.862540	+	0.136613i	−0.572004	−	0.820251i	$-0.693834\pi$
$293$	−14.7643	+	2.33844i	−0.862540	+	0.136613i	−0.290536	+	0.956864i	$0.593834\pi$
$294$		0			0
$295$	−2.95571	+	9.09673i	−0.172088	+	0.529632i
$296$		0			0
$297$	−13.8399	−	4.82972i	−0.803070	−	0.280249i
$298$		0			0
$299$	−5.43340	−	28.2743i	−0.314221	−	1.63515i
$300$		0			0
$301$	10.5616	−	1.67279i	0.608759	−	0.0964179i
$302$		0			0
$303$	−2.87104	−	8.83616i	−0.164937	−	0.507624i
$304$		0			0
$305$	−7.32367	−	1.15996i	−0.419352	−	0.0664189i
$306$		0			0
$307$	−9.64590	+	9.64590i	−0.550521	+	0.550521i	−0.926591	−	0.376070i	$-0.877275\pi$
$307$	−9.64590	+	9.64590i	−0.550521	+	0.550521i	0.376070	+	0.926591i	$0.377275\pi$
$308$		0			0
$309$		−	13.0743i		−	0.743769i
$310$		0			0
$311$	8.80640	+	12.1210i	0.499365	+	0.687317i	0.982081	−	0.188460i	$-0.0603495\pi$
$311$	8.80640	+	12.1210i	0.499365	+	0.687317i	−0.482716	+	0.875777i	$0.660350\pi$
$312$		0			0
$313$	−5.83216	−	17.9495i	−0.329653	−	1.01457i	−0.969296	−	0.245896i	$-0.920918\pi$
$313$	−5.83216	−	17.9495i	−0.329653	−	1.01457i	0.639643	−	0.768672i	$-0.279082\pi$
$314$		0			0
$315$	−3.62933	+	4.99534i	−0.204489	+	0.281455i
$316$		0			0
$317$	−1.41295	−	2.77308i	−0.0793594	−	0.155752i	0.847917	−	0.530129i	$-0.177856\pi$
$317$	−1.41295	−	2.77308i	−0.0793594	−	0.155752i	−0.927276	+	0.374377i	$0.877856\pi$
$318$		0			0
$319$	1.84844	+	6.13685i	0.103493	+	0.343598i
$320$		0			0
$321$	0.00653829	+	0.00212442i	0.000364932	+	0.000118574i
$322$		0			0
$323$	3.91179	+	24.6981i	0.217658	+	1.37424i
$324$		0			0
$325$	−8.40062	−	7.86728i	−0.465983	−	0.436398i
$326$		0			0
$327$	13.9567	+	2.21052i	0.771806	+	0.122242i
$328$		0			0
$329$	−1.03384			−0.0569977
$330$		0			0
$331$	17.9455	−	17.9455i	0.986376	−	0.986376i	−0.0135324	−	0.999908i	$-0.504308\pi$
$331$	17.9455	−	17.9455i	0.986376	−	0.986376i	0.999908	+	0.0135324i	$0.00430763\pi$
$332$		0			0
$333$	5.45642	+	0.864212i	0.299010	+	0.0473585i
$334$		0			0
$335$	−11.3971	+	3.70313i	−0.622688	+	0.202324i
$336$		0			0
$337$	5.87696	+	4.26986i	0.320138	+	0.232594i	0.736235	−	0.676726i	$-0.236602\pi$
$337$	5.87696	+	4.26986i	0.320138	+	0.232594i	−0.416096	+	0.909321i	$0.636602\pi$
$338$		0			0
$339$	−5.13295	+	15.7976i	−0.278783	+	0.858007i
$340$		0			0
$341$	−7.08849	−	1.28022i	−0.383863	−	0.0693276i
$342$		0			0
$343$	17.8040	−	9.07161i	0.961328	−	0.489821i
$344$		0			0
$345$	−1.39899	−	8.83288i	−0.0753192	−	0.475547i
$346$		0			0
$347$	3.51705	−	1.14276i	0.188805	−	0.0613465i	−0.213088	−	0.977033i	$-0.568352\pi$
$347$	3.51705	−	1.14276i	0.188805	−	0.0613465i	0.401893	+	0.915686i	$0.368352\pi$
$348$		0			0
$349$	−0.832429	+	5.25575i	−0.0445589	+	0.281334i	−0.999900	−	0.0141729i	$-0.995488\pi$
$349$	−0.832429	+	5.25575i	−0.0445589	+	0.281334i	0.955341	+	0.295507i	$0.0954885\pi$
$350$		0			0
$351$	−7.69585	−	13.9538i	−0.410774	−	0.744799i
$352$		0			0
$353$	21.9233	−	21.9233i	1.16686	−	1.16686i	0.183918	−	0.982942i	$-0.441122\pi$
$353$	21.9233	−	21.9233i	1.16686	−	1.16686i	0.982942	−	0.183918i	$-0.0588779\pi$
$354$		0			0
$355$	0.370825	+	0.510397i	0.0196814	+	0.0270891i
$356$		0			0
$357$	−7.92844	−	4.03974i	−0.419618	−	0.213806i
$358$		0			0
$359$	14.9674	−	2.37061i	0.789951	−	0.125116i	0.251594	−	0.967833i	$-0.419045\pi$
$359$	14.9674	−	2.37061i	0.789951	−	0.125116i	0.538357	+	0.842717i	$0.319045\pi$
$360$		0			0
$361$	2.58916	+	0.841269i	0.136272	+	0.0442773i
$362$		0			0
$363$	7.17281	+	5.70042i	0.376475	+	0.299194i
$364$		0			0
$365$	−13.4347	−	4.36520i	−0.703205	−	0.228485i
$366$		0			0
$367$	11.9604	+	8.68971i	0.624326	+	0.453599i	0.854430	−	0.519567i	$-0.173907\pi$
$367$	11.9604	+	8.68971i	0.624326	+	0.453599i	−0.230104	+	0.973166i	$0.573907\pi$
$368$		0			0
$369$	−8.88274	+	17.4334i	−0.462417	+	0.907545i
$370$		0			0
$371$	2.74376	−	17.3234i	0.142449	−	0.899387i
$372$		0			0
$373$		−	11.0856i		−	0.573989i	−0.957932	−	0.286994i	$-0.907344\pi$
$373$		−	11.0856i		−	0.573989i	0.957932	−	0.286994i	$-0.0926561\pi$
$374$		0			0
$375$	−6.48737	−	6.48737i	−0.335006	−	0.335006i
$376$		0			0
$377$	−2.95807	+	6.30842i	−0.152348	+	0.324900i
$378$		0			0
$379$	23.7450	+	12.0987i	1.21970	+	0.621467i	0.940835	−	0.338864i	$-0.110043\pi$
$379$	23.7450	+	12.0987i	1.21970	+	0.621467i	0.278863	+	0.960331i	$0.410043\pi$
$380$		0			0
$381$	−1.37669	−	1.00022i	−0.0705300	−	0.0512431i
$382$		0			0
$383$	−13.0768	−	25.6647i	−0.668195	−	1.31141i	−0.937377	−	0.348317i	$-0.886753\pi$
$383$	−13.0768	−	25.6647i	−0.668195	−	1.31141i	0.269182	−	0.963089i	$-0.413247\pi$
$384$		0			0
$385$	7.29486	−	5.06298i	0.371781	−	0.258033i
$386$		0			0
$387$	3.82720	−	11.7789i	0.194548	−	0.598756i
$388$		0			0
$389$	0.837049	−	1.15210i	0.0424401	−	0.0584137i	−0.787270	−	0.616609i	$-0.788506\pi$
$389$	0.837049	−	1.15210i	0.0424401	−	0.0584137i	0.829710	+	0.558195i	$0.188506\pi$
$390$		0			0
$391$	−40.7465	+	13.2393i	−2.06064	+	0.669543i
$392$		0			0
$393$	5.84337	+	8.04271i	0.294759	+	0.405701i
$394$		0			0
$395$	14.5067	+	14.5067i	0.729911	+	0.729911i
$396$		0			0
$397$	17.7646	+	17.7646i	0.891578	+	0.891578i	0.994672	−	0.103094i	$-0.0328742\pi$
$397$	17.7646	+	17.7646i	0.891578	+	0.891578i	−0.103094	+	0.994672i	$0.532874\pi$
$398$		0			0
$399$	−6.25359	+	4.54350i	−0.313071	+	0.227459i
$400$		0			0
$401$	11.1765	−	21.9350i	0.558126	−	1.09538i	−0.423736	−	0.905786i	$-0.639282\pi$
$401$	11.1765	−	21.9350i	0.558126	−	1.09538i	0.981862	−	0.189597i	$-0.0607183\pi$
$402$		0			0
$403$	−4.80786	−	6.18092i	−0.239497	−	0.307894i
$404$		0			0
$405$	1.97627	+	3.87864i	0.0982015	+	0.192731i
$406$		0			0
$407$	−6.99924	−	3.75887i	−0.346940	−	0.186320i
$408$		0			0
$409$	−26.4440	+	13.4739i	−1.30757	+	0.666241i	−0.962230	−	0.272236i	$-0.912237\pi$
$409$	−26.4440	+	13.4739i	−1.30757	+	0.666241i	−0.345341	+	0.938477i	$0.612237\pi$
$410$		0			0
$411$	1.73679	+	10.9656i	0.0856694	+	0.540895i
$412$		0			0
$413$	4.37715	+	13.4715i	0.215385	+	0.662888i
$414$		0			0
$415$	6.47155	−	4.70186i	0.317676	−	0.230805i
$416$		0			0
$417$		−	17.4119i		−	0.852662i
$418$		0			0
$419$	27.9511			1.36550			0.682751	−	0.730651i	$-0.260783\pi$
$419$	27.9511			1.36550			0.682751	+	0.730651i	$0.260783\pi$
$420$		0			0
$421$	−0.152842	+	0.965004i	−0.00744905	+	0.0470314i	−0.991133	−	0.132874i	$-0.957579\pi$
$421$	−0.152842	+	0.965004i	−0.00744905	+	0.0470314i	0.983684	+	0.179906i	$0.0575793\pi$
$422$		0			0
$423$	−0.543616	+	1.06691i	−0.0264315	+	0.0518748i
$424$		0			0
$425$	−10.0667	+	13.8556i	−0.488306	+	0.672095i
$426$		0			0
$427$	−9.78407	+	4.98523i	−0.473484	+	0.241252i
$428$		0			0
$429$	1.66795	+	9.81960i	0.0805295	+	0.474095i
$430$		0			0
$431$	−13.1374	+	6.69385i	−0.632808	+	0.322432i	−0.740806	−	0.671719i	$-0.765556\pi$
$431$	−13.1374	+	6.69385i	−0.632808	+	0.322432i	0.107998	+	0.994151i	$0.465556\pi$
$432$		0			0
$433$	9.02603	−	12.4233i	0.433763	−	0.597024i	−0.535049	−	0.844821i	$-0.679707\pi$
$433$	9.02603	−	12.4233i	0.433763	−	0.597024i	0.968812	+	0.247797i	$0.0797068\pi$
$434$		0			0
$435$	−0.982519	+	1.92830i	−0.0471082	+	0.0924550i
$436$		0			0
$437$	−5.82212	+	36.7594i	−0.278510	+	1.75844i
$438$		0			0
$439$	−2.73576			−0.130571			−0.0652853	−	0.997867i	$-0.520796\pi$
$439$	−2.73576			−0.130571			−0.0652853	+	0.997867i	$0.520796\pi$
$440$		0			0
$441$		−	6.99972i		−	0.333320i
$442$		0			0
$443$	16.4870	−	11.9785i	0.783322	−	0.569117i	−0.122652	−	0.992450i	$-0.539140\pi$
$443$	16.4870	−	11.9785i	0.783322	−	0.569117i	0.905974	+	0.423333i	$0.139140\pi$
$444$		0			0
$445$	−3.43706	−	10.5782i	−0.162932	−	0.501454i
$446$		0			0
$447$	−2.37221	−	14.9776i	−0.112202	−	0.708414i
$448$		0			0
$449$	−2.52763	+	1.28789i	−0.119286	+	0.0607795i	−0.512615	−	0.858618i	$-0.671323\pi$
$449$	−2.52763	+	1.28789i	−0.119286	+	0.0607795i	0.393329	+	0.919398i	$0.371323\pi$
$450$		0			0
$451$	20.3215	−	19.4621i	0.956903	−	0.916434i
$452$		0			0
$453$	−2.98806	−	5.86440i	−0.140391	−	0.275534i
$454$		0			0
$455$	9.57875	+	1.19687i	0.449059	+	0.0561102i
$456$		0			0
$457$	3.04081	−	5.96792i	0.142243	−	0.279168i	−0.808884	−	0.587969i	$-0.799928\pi$
$457$	3.04081	−	5.96792i	0.142243	−	0.279168i	0.951127	+	0.308801i	$0.0999278\pi$
$458$		0			0
$459$	−19.1839	+	13.9379i	−0.895427	+	0.650566i
$460$		0			0
$461$	−3.49796	−	3.49796i	−0.162916	−	0.162916i	0.620941	−	0.783857i	$-0.286751\pi$
$461$	−3.49796	−	3.49796i	−0.162916	−	0.162916i	−0.783857	+	0.620941i	$0.786751\pi$
$462$		0			0
$463$	7.17366	+	7.17366i	0.333388	+	0.333388i	0.853872	−	0.520484i	$-0.174248\pi$
$463$	7.17366	+	7.17366i	0.333388	+	0.333388i	−0.520484	+	0.853872i	$0.674248\pi$
$464$		0			0
$465$	−1.42966	−	1.96776i	−0.0662990	−	0.0912528i
$466$		0			0
$467$	−10.2260	+	3.32264i	−0.473205	+	0.153754i	−0.535904	−	0.844279i	$-0.680029\pi$
$467$	−10.2260	+	3.32264i	−0.473205	+	0.153754i	0.0626991	+	0.998032i	$0.480029\pi$
$468$		0			0
$469$	−10.4312	+	14.3573i	−0.481669	+	0.662960i
$470$		0			0
$471$	1.23056	−	3.78729i	0.0567014	−	0.174509i
$472$		0			0
$473$	−10.7778	+	14.1800i	−0.495565	+	0.651996i
$474$		0			0
$475$	6.75428	+	13.2560i	0.309907	+	0.608228i
$476$		0			0
$477$	−16.4347	−	11.9405i	−0.752493	−	0.546718i
$478$		0			0
$479$	4.81886	+	2.45533i	0.220179	+	0.112187i	0.560602	−	0.828086i	$-0.310570\pi$
$479$	4.81886	+	2.45533i	0.220179	+	0.112187i	−0.340422	+	0.940273i	$0.610570\pi$
$480$		0			0
$481$	−2.93664	−	8.12223i	−0.133899	−	0.370342i
$482$		0			0
$483$	−9.36477	−	9.36477i	−0.426112	−	0.426112i
$484$		0			0
$485$		−	10.0154i		−	0.454775i
$486$		0			0
$487$	−4.48827	+	28.3378i	−0.203383	+	1.28411i	0.648838	+	0.760926i	$0.275255\pi$
$487$	−4.48827	+	28.3378i	−0.203383	+	1.28411i	−0.852221	+	0.523182i	$0.824745\pi$
$488$		0			0
$489$	−4.30729	+	8.45354i	−0.194783	+	0.382282i
$490$		0			0
$491$	27.2643	+	19.8087i	1.23042	+	0.893954i	0.996922	−	0.0784030i	$-0.0249821\pi$
$491$	27.2643	+	19.8087i	1.23042	+	0.893954i	0.233500	+	0.972357i	$0.424982\pi$
$492$		0			0
$493$	9.86057	+	3.20389i	0.444098	+	0.144296i
$494$		0			0
$495$	−1.38911	−	10.1904i	−0.0624357	−	0.458023i
$496$		0			0
$497$	0.888560	+	0.288711i	0.0398574	+	0.0129504i
$498$		0			0
$499$	2.21183	−	0.350319i	0.0990151	−	0.0156825i	−0.106730	−	0.994288i	$-0.534038\pi$
$499$	2.21183	−	0.350319i	0.0990151	−	0.0156825i	0.205745	+	0.978606i	$0.434038\pi$
$500$		0			0
$501$	−6.15591	−	3.13659i	−0.275026	−	0.140133i
$502$		0			0
$503$	6.37746	+	8.77782i	0.284357	+	0.391384i	0.927171	−	0.374639i	$-0.122233\pi$
$503$	6.37746	+	8.77782i	0.284357	+	0.391384i	−0.642814	+	0.766022i	$0.722233\pi$
$504$		0			0
$505$	10.6054	−	10.6054i	0.471933	−	0.471933i
$506$		0			0
$507$	−5.77706	+	9.15804i	−0.256568	+	0.406723i
$508$		0			0
$509$	−0.612747	+	3.86873i	−0.0271595	+	0.171479i	−0.997540	−	0.0701046i	$-0.977667\pi$
$509$	−0.612747	+	3.86873i	−0.0271595	+	0.171479i	0.970380	+	0.241583i	$0.0776667\pi$
$510$		0			0
$511$	−19.8957	+	6.46449i	−0.880132	+	0.285972i
$512$		0			0
$513$	3.22237	+	20.3453i	0.142271	+	0.898266i
$514$		0			0
$515$	18.8054	−	9.58181i	0.828664	−	0.422225i
$516$		0			0
$517$	1.24366	−	1.19106i	0.0546961	−	0.0523829i
$518$		0			0
$519$	−4.31643	+	13.2846i	−0.189470	+	0.583130i
$520$		0			0
$521$	7.17939	+	5.21613i	0.314535	+	0.228523i	0.733840	−	0.679323i	$-0.237726\pi$
$521$	7.17939	+	5.21613i	0.314535	+	0.228523i	−0.419305	+	0.907845i	$0.637726\pi$
$522$		0			0
$523$	−12.2021	+	3.96471i	−0.533562	+	0.173365i	−0.563391	−	0.826190i	$-0.690504\pi$
$523$	−12.2021	+	3.96471i	−0.533562	+	0.173365i	0.0298294	+	0.999555i	$0.490504\pi$
$524$		0			0
$525$	−5.22896	−	0.828186i	−0.228211	−	0.0361450i
$526$		0			0
$527$	−8.23951	+	8.23951i	−0.358919	+	0.358919i
$528$		0			0
$529$	−40.7661			−1.77244
$530$		0			0
$531$	16.2039	+	2.56644i	0.703189	+	0.111374i
$532$		0			0
$533$	30.5726	−	1.00232i	1.32425	−	0.0434153i
$534$		0			0
$535$	0.00173610	+	0.0109613i	7.50580e−5	+	0.000473898i
$536$		0			0
$537$	13.8825	+	4.51071i	0.599076	+	0.194651i
$538$		0			0
$539$	−3.31671	+	9.50423i	−0.142861	+	0.409376i
$540$		0			0
$541$	19.5500	+	38.3690i	0.840520	+	1.64961i	0.757286	+	0.653083i	$0.226525\pi$
$541$	19.5500	+	38.3690i	0.840520	+	1.64961i	0.0832335	+	0.996530i	$0.473475\pi$
$542$		0			0
$543$	10.0468	−	13.8283i	0.431151	−	0.593428i
$544$		0			0
$545$	7.04901	+	21.6946i	0.301947	+	0.929296i
$546$		0			0
$547$	−20.0043	−	27.5336i	−0.855323	−	1.17725i	−0.982665	−	0.185392i	$-0.940645\pi$
$547$	−20.0043	−	27.5336i	−0.855323	−	1.17725i	0.127342	−	0.991859i	$-0.459355\pi$
$548$		0			0
$549$			12.7183i			0.542804i
$550$		0			0
$551$	6.36862	−	6.36862i	0.271312	−	0.271312i
$552$		0			0
$553$	30.0077	+	4.75276i	1.27606	+	0.202108i
$554$		0			0
$555$	−0.828995	−	2.55139i	−0.0351889	−	0.108300i
$556$		0			0
$557$	2.50628	−	0.396956i	0.106195	−	0.0168196i	−0.103111	−	0.994670i	$-0.532880\pi$
$557$	2.50628	−	0.396956i	0.106195	−	0.0168196i	0.209306	+	0.977850i	$0.432880\pi$
$558$		0			0
$559$	−19.0147	+	3.65401i	−0.804238	+	0.154548i
$560$		0			0
$561$	14.1916	−	4.27454i	0.599169	−	0.180471i
$562$		0			0
$563$	−11.8349	+	36.4240i	−0.498781	+	1.53509i	0.312199	+	0.950017i	$0.398934\pi$
$563$	−11.8349	+	36.4240i	−0.498781	+	1.53509i	−0.810980	+	0.585074i	$0.801066\pi$
$564$		0			0
$565$	−26.4843	+	4.19470i	−1.11420	+	0.176472i
$566$		0			0
$567$	5.74393	+	2.92668i	0.241223	+	0.122909i
$568$		0			0
$569$	10.5944	−	7.69726i	0.444139	−	0.322686i	−0.343139	−	0.939285i	$-0.611490\pi$
$569$	10.5944	−	7.69726i	0.444139	−	0.322686i	0.787277	+	0.616599i	$0.211490\pi$
$570$		0			0
$571$	3.69763			0.154741			0.0773704	−	0.997002i	$-0.475348\pi$
$571$	3.69763			0.154741			0.0773704	+	0.997002i	$0.475348\pi$
$572$		0			0
$573$	−2.69798			−0.112710
$574$		0			0
$575$	−20.6220	+	14.9828i	−0.859996	+	0.624824i
$576$		0			0
$577$	2.08964	+	1.06472i	0.0869928	+	0.0443250i	0.496946	−	0.867782i	$-0.334455\pi$
$577$	2.08964	+	1.06472i	0.0869928	+	0.0443250i	−0.409953	+	0.912107i	$0.634455\pi$
$578$		0			0
$579$	1.98400	−	0.314234i	0.0824521	−	0.0130591i
$580$		0			0
$581$	3.66069	−	11.2664i	0.151871	−	0.467411i
$582$		0			0
$583$	16.6572	+	24.0002i	0.689872	+	0.993985i
$584$		0			0
$585$	6.27185	−	9.25574i	0.259309	−	0.382678i
$586$		0			0
$587$	32.8284	−	5.19950i	1.35497	−	0.214606i	0.563654	−	0.826011i	$-0.309395\pi$
$587$	32.8284	−	5.19950i	1.35497	−	0.214606i	0.791318	+	0.611405i	$0.209395\pi$
$588$		0			0
$589$	3.12798	+	9.62692i	0.128886	+	0.396670i
$590$		0			0
$591$	11.8131	+	1.87101i	0.485925	+	0.0769629i
$592$		0			0
$593$	−2.05472	+	2.05472i	−0.0843773	+	0.0843773i	−0.748036	−	0.663658i	$-0.769003\pi$
$593$	−2.05472	+	2.05472i	−0.0843773	+	0.0843773i	0.663658	+	0.748036i	$0.269003\pi$
$594$		0			0
$595$		−	14.3645i		−	0.588887i
$596$		0			0
$597$	7.16095	+	9.85620i	0.293078	+	0.403387i
$598$		0			0
$599$	5.63639	+	17.3470i	0.230297	+	0.708780i	0.997711	+	0.0676282i	$0.0215432\pi$
$599$	5.63639	+	17.3470i	0.230297	+	0.708780i	−0.767414	+	0.641152i	$0.778457\pi$
$600$		0			0
$601$	10.3712	−	14.2747i	0.423048	−	0.582276i	−0.543292	−	0.839544i	$-0.682822\pi$
$601$	10.3712	−	14.2747i	0.423048	−	0.582276i	0.966340	+	0.257268i	$0.0828223\pi$
$602$		0			0
$603$	9.33155	+	18.3142i	0.380010	+	0.745812i
$604$		0			0
$605$	−2.94242	+	14.4947i	−0.119626	+	0.589294i
$606$		0			0
$607$	22.4089	+	7.28110i	0.909550	+	0.295531i	0.726173	−	0.687512i	$-0.241297\pi$
$607$	22.4089	+	7.28110i	0.909550	+	0.295531i	0.183377	+	0.983043i	$0.441297\pi$
$608$		0			0
$609$	0.501368	+	3.16551i	0.0203164	+	0.128273i
$610$		0			0
$611$	1.87102	−	0.0613412i	0.0756933	−	0.00248160i
$612$		0			0
$613$	−46.1718	−	7.31289i	−1.86486	−	0.295365i	−0.880839	−	0.473416i	$-0.843021\pi$
$613$	−46.1718	−	7.31289i	−1.86486	−	0.295365i	−0.984021	+	0.178052i	$0.943021\pi$
$614$		0			0
$615$	9.50128			0.383129
$616$		0			0
$617$	−13.8419	+	13.8419i	−0.557252	+	0.557252i	−0.928524	−	0.371272i	$-0.878922\pi$
$617$	−13.8419	+	13.8419i	−0.557252	+	0.557252i	0.371272	+	0.928524i	$0.378922\pi$
$618$		0			0
$619$	−18.8715	−	2.98895i	−0.758510	−	0.120136i	−0.234813	−	0.972041i	$-0.575448\pi$
$619$	−18.8715	−	2.98895i	−0.758510	−	0.120136i	−0.523697	+	0.851905i	$0.675448\pi$
$620$		0			0
$621$	−33.5653	+	10.9060i	−1.34693	+	0.437644i
$622$		0			0
$623$	−13.3258	−	9.68173i	−0.533885	−	0.387890i
$624$		0			0
$625$	−0.355413	+	1.09385i	−0.0142165	+	0.0437539i
$626$		0			0
$627$	2.28830	−	12.6702i	0.0913857	−	0.505998i
$628$		0			0
$629$	−11.4512	+	5.83469i	−0.456591	+	0.232644i
$630$		0			0
$631$	4.77617	+	30.1556i	0.190136	+	1.20047i	0.879443	+	0.476004i	$0.157915\pi$
$631$	4.77617	+	30.1556i	0.190136	+	1.20047i	−0.689307	+	0.724470i	$0.742085\pi$
$632$		0			0
$633$	13.5217	−	4.39347i	0.537439	−	0.174625i
$634$		0			0
$635$	0.429729	−	2.71320i	0.0170533	−	0.107670i
$636$		0			0
$637$	−9.58248	+	5.28496i	−0.379672	+	0.209398i
$638$		0			0
$639$	0.765167	−	0.765167i	0.0302695	−	0.0302695i
$640$		0			0
$641$	−28.8555	−	39.7162i	−1.13972	−	1.56869i	−0.768125	−	0.640301i	$-0.778810\pi$
$641$	−28.8555	−	39.7162i	−1.13972	−	1.56869i	−0.371598	−	0.928394i	$-0.621190\pi$
$642$		0			0
$643$	38.2949	+	19.5122i	1.51020	+	0.769486i	0.996099	−	0.0882419i	$-0.0281249\pi$
$643$	38.2949	+	19.5122i	1.51020	+	0.769486i	0.514103	+	0.857728i	$0.328125\pi$
$644$		0			0
$645$	−5.94020	+	0.940835i	−0.233895	+	0.0370453i
$646$		0			0
$647$	−4.30150	−	1.39764i	−0.169109	−	0.0549469i	0.223239	−	0.974764i	$-0.428337\pi$
$647$	−4.30150	−	1.39764i	−0.169109	−	0.0549469i	−0.392348	+	0.919817i	$0.628337\pi$
$648$		0			0
$649$	−20.7856	−	11.1627i	−0.815906	−	0.438173i
$650$		0			0
$651$	−3.42571	−	1.11308i	−0.134264	−	0.0436251i
$652$		0			0
$653$	−41.0371	−	29.8152i	−1.60591	−	1.16676i	−0.874788	−	0.484507i	$-0.838999\pi$
$653$	−41.0371	−	29.8152i	−1.60591	−	1.16676i	−0.731117	−	0.682252i	$-0.761001\pi$
$654$		0			0
$655$	−7.28577	+	14.2991i	−0.284678	+	0.558713i
$656$		0			0
$657$	−3.79031	+	23.9311i	−0.147874	+	0.933641i
$658$		0			0
$659$		−	23.1331i		−	0.901136i	−0.892742	−	0.450568i	$-0.851221\pi$
$659$		−	23.1331i		−	0.901136i	0.892742	−	0.450568i	$-0.148779\pi$
$660$		0			0
$661$	15.8327	+	15.8327i	0.615820	+	0.615820i	0.944457	−	0.328636i	$-0.106589\pi$
$661$	15.8327	+	15.8327i	0.615820	+	0.615820i	−0.328636	+	0.944457i	$0.606589\pi$
$662$		0			0
$663$	14.5883	+	6.84058i	0.566564	+	0.265666i
$664$		0			0
$665$	−11.1182	−	5.66503i	−0.431147	−	0.219680i
$666$		0			0
$667$	12.4841	+	9.07027i	0.483388	+	0.351202i
$668$		0			0
$669$	9.59996	+	18.8410i	0.371156	+	0.728434i
$670$		0			0
$671$	6.02637	−	17.2689i	0.232645	−	0.666660i
$672$		0			0
$673$	6.80968	−	20.9580i	0.262494	−	0.807873i	−0.729766	−	0.683697i	$-0.760371\pi$
$673$	6.80968	−	20.9580i	0.262494	−	0.807873i	0.992260	−	0.124176i	$-0.0396288\pi$
$674$		0			0
$675$	−8.29252	+	11.4137i	−0.319179	+	0.439312i
$676$		0			0
$677$	9.65328	−	3.13654i	0.371006	−	0.120547i	−0.117579	−	0.993064i	$-0.537513\pi$
$677$	9.65328	−	3.13654i	0.371006	−	0.120547i	0.488585	+	0.872516i	$0.337513\pi$
$678$		0			0
$679$	−8.71797	−	11.9993i	−0.334565	−	0.460489i
$680$		0			0
$681$	−5.57254	−	5.57254i	−0.213540	−	0.213540i
$682$		0			0
$683$	10.4940	+	10.4940i	0.401541	+	0.401541i	0.878776	−	0.477235i	$-0.158361\pi$
$683$	10.4940	+	10.4940i	0.401541	+	0.401541i	−0.477235	+	0.878776i	$0.658361\pi$
$684$		0			0
$685$	−14.4996	+	10.5346i	−0.554001	+	0.402505i
$686$		0			0
$687$	2.08072	−	4.08364i	0.0793844	−	0.155801i
$688$		0			0
$689$	−3.93772	+	31.5142i	−0.150015	+	1.20059i
$690$		0			0
$691$	15.6648	+	30.7438i	0.595916	+	1.16955i	0.970216	+	0.242243i	$0.0778830\pi$
$691$	15.6648	+	30.7438i	0.595916	+	1.16955i	−0.374300	+	0.927308i	$0.622117\pi$
$692$		0			0
$693$	−10.5346	−	10.9998i	−0.400175	−	0.417847i
$694$		0			0
$695$	25.0443	−	12.7607i	0.949986	−	0.484042i
$696$		0			0
$697$	−7.12059	−	44.9576i	−0.269712	−	1.70289i
$698$		0			0
$699$	−3.28438	−	10.1083i	−0.124227	−	0.382330i
$700$		0			0
$701$	7.80247	−	5.66882i	0.294695	−	0.214109i	−0.430606	−	0.902540i	$-0.641700\pi$
$701$	7.80247	−	5.66882i	0.294695	−	0.214109i	0.725302	+	0.688431i	$0.241700\pi$
$702$		0			0
$703$			11.1644i			0.421074i
$704$		0			0
$705$	0.581470			0.0218994
$706$		0			0
$707$	3.47459	−	21.9377i	0.130675	−	0.825051i
$708$		0			0
$709$	20.1435	−	39.5339i	0.756507	−	1.48473i	−0.114482	−	0.993425i	$-0.536521\pi$
$709$	20.1435	−	39.5339i	0.756507	−	1.48473i	0.870989	−	0.491303i	$-0.163479\pi$
$710$		0			0
$711$	20.6834	−	28.4683i	0.775689	−	1.06764i
$712$		0			0
$713$	−15.4526	+	7.87351i	−0.578706	+	0.294865i
$714$		0			0
$715$	−12.9016	+	9.59564i	−0.482493	+	0.358857i
$716$		0			0
$717$	−16.5914	+	8.45374i	−0.619617	+	0.315711i
$718$		0			0
$719$	−12.8691	+	17.7128i	−0.479938	+	0.660578i	−0.978493	−	0.206280i	$-0.933864\pi$
$719$	−12.8691	+	17.7128i	−0.479938	+	0.660578i	0.498555	+	0.866858i	$0.333864\pi$
$720$		0			0
$721$	14.1898	−	27.8491i	0.528457	−	1.03716i
$722$		0			0
$723$	1.37694	−	8.69367i	0.0512090	−	0.323321i
$724$		0			0
$725$	6.16857			0.229095
$726$		0			0
$727$		−	4.70847i		−	0.174628i	−0.996181	−	0.0873138i	$-0.972172\pi$
$727$		−	4.70847i		−	0.174628i	0.996181	−	0.0873138i	$-0.0278283\pi$
$728$		0			0
$729$	−2.89395	+	2.10258i	−0.107183	+	0.0778733i
$730$		0			0
$731$	8.90358	+	27.4024i	0.329311	+	1.01351i
$732$		0			0
$733$	−8.06757	−	50.9366i	−0.297983	−	1.88139i	−0.450028	−	0.893014i	$-0.648586\pi$
$733$	−8.06757	−	50.9366i	−0.297983	−	1.88139i	0.152046	−	0.988373i	$-0.451414\pi$
$734$		0			0
$735$	−3.02861	+	1.54315i	−0.111712	+	0.0569201i
$736$		0			0
$737$	−3.99249	−	29.2886i	−0.147065	−	1.07886i
$738$		0			0
$739$	−20.8235	−	40.8684i	−0.766004	−	1.50337i	−0.861400	−	0.507927i	$-0.830412\pi$
$739$	−20.8235	−	40.8684i	−0.766004	−	1.50337i	0.0953962	−	0.995439i	$-0.469588\pi$
$740$		0			0
$741$	11.0480	−	8.59372i	0.405857	−	0.315698i
$742$		0			0
$743$	14.0414	−	27.5578i	0.515129	−	1.01100i	−0.476168	−	0.879354i	$-0.657975\pi$
$743$	14.0414	−	27.5578i	0.515129	−	1.01100i	0.991297	−	0.131644i	$-0.0420255\pi$
$744$		0			0
$745$	19.8044	−	14.3888i	0.725578	−	0.527163i
$746$		0			0
$747$	−9.70189	−	9.70189i	−0.354973	−	0.354973i
$748$		0			0
$749$	0.0116213	+	0.0116213i	0.000424635	+	0.000424635i
$750$		0			0
$751$	−2.90460	−	3.99784i	−0.105990	−	0.145883i	0.752727	−	0.658333i	$-0.228738\pi$
$751$	−2.90460	−	3.99784i	−0.105990	−	0.145883i	−0.858717	+	0.512450i	$0.828738\pi$
$752$		0			0
$753$	0.198128	−	0.0643756i	0.00722018	−	0.00234598i
$754$		0			0
$755$	6.24518	−	8.59576i	0.227285	−	0.312832i
$756$		0			0
$757$	−2.75278	+	8.47218i	−0.100051	+	0.307927i	−0.988537	−	0.150978i	$-0.951758\pi$
$757$	−2.75278	+	8.47218i	−0.100051	+	0.307927i	0.888486	+	0.458904i	$0.151758\pi$
$758$		0			0
$759$	22.0542	+	0.476428i	0.800518	+	0.0172932i
$760$		0			0
$761$	−13.9523	−	27.3829i	−0.505770	−	0.992629i	−0.992861	−	0.119278i	$-0.961942\pi$
$761$	−13.9523	−	27.3829i	−0.505770	−	0.992629i	0.487091	−	0.873351i	$-0.338058\pi$
$762$		0			0
$763$	27.3296	+	19.8561i	0.989398	+	0.718840i
$764$		0			0
$765$	−14.8239	−	7.55315i	−0.535959	−	0.273085i
$766$		0			0
$767$	−8.72092	−	24.1205i	−0.314894	−	0.870942i
$768$		0			0
$769$	21.1539	+	21.1539i	0.762830	+	0.762830i	0.976833	−	0.214003i	$-0.0686503\pi$
$769$	21.1539	+	21.1539i	0.762830	+	0.762830i	−0.214003	+	0.976833i	$0.568650\pi$
$770$		0			0
$771$			26.0174i			0.936992i
$772$		0			0
$773$	−0.691690	+	4.36716i	−0.0248784	+	0.157076i	−0.997000	−	0.0774012i	$-0.975338\pi$
$773$	−0.691690	+	4.36716i	−0.0248784	+	0.157076i	0.972122	+	0.234477i	$0.0753378\pi$
$774$		0			0
$775$	−3.14740	+	6.17712i	−0.113058	+	0.221889i
$776$		0			0
$777$	−3.21408	−	2.33517i	−0.115305	−	0.0837737i
$778$		0			0
$779$	−37.6058	−	12.2189i	−1.34737	−	0.437786i
$780$		0			0
$781$	−1.40151	+	0.676382i	−0.0501498	+	0.0242029i
$782$		0			0
$783$	8.12274	+	2.63924i	0.290283	+	0.0943187i
$784$		0			0
$785$	6.34930	−	1.00563i	0.226616	−	0.0358925i
$786$		0			0
$787$	−13.2320	−	6.74206i	−0.471671	−	0.240328i	0.201963	−	0.979393i	$-0.435268\pi$
$787$	−13.2320	−	6.74206i	−0.471671	−	0.240328i	−0.673634	+	0.739065i	$0.735268\pi$
$788$		0			0
$789$	3.17871	+	4.37511i	0.113165	+	0.155758i
$790$		0			0
$791$	−28.0791	+	28.0791i	−0.998377	+	0.998377i
$792$		0			0
$793$	17.4111	−	9.60264i	0.618287	−	0.341000i
$794$		0			0
$795$	−1.54319	+	9.74329i	−0.0547312	+	0.345559i
$796$		0			0
$797$	16.5440	−	5.37548i	0.586019	−	0.190409i	−0.000976177	−	1.00000i	$-0.500311\pi$
$797$	16.5440	−	5.37548i	0.586019	−	0.190409i	0.586995	+	0.809590i	$0.300311\pi$
$798$		0			0
$799$	−0.435774	−	2.75137i	−0.0154166	−	0.0973364i
$800$		0			0
$801$	−16.9983	+	8.66107i	−0.600606	+	0.306024i
$802$		0			0
$803$	16.4859	−	30.6977i	0.581773	−	1.08330i
$804$		0			0
$805$	6.60661	−	20.3330i	0.232852	−	0.716645i
$806$		0			0
$807$	−5.66871	−	4.11856i	−0.199548	−	0.144980i
$808$		0			0
$809$	8.85564	−	2.87737i	0.311348	−	0.101163i	−0.149175	−	0.988811i	$-0.547662\pi$
$809$	8.85564	−	2.87737i	0.311348	−	0.101163i	0.460523	+	0.887648i	$0.347662\pi$
$810$		0			0
$811$	25.6281	+	4.05910i	0.899926	+	0.142534i	0.589221	−	0.807972i	$-0.299435\pi$
$811$	25.6281	+	4.05910i	0.899926	+	0.142534i	0.310705	+	0.950506i	$0.399435\pi$
$812$		0			0
$813$	−11.3954	+	11.3954i	−0.399655	+	0.399655i
$814$		0			0
$815$	−15.3159			−0.536491
$816$		0			0
$817$	24.7210	+	3.91543i	0.864880	+	0.136984i
$818$		0			0
$819$	−0.542543	−	16.5485i	−0.0189580	−	0.578253i
$820$		0			0
$821$	−4.30187	−	27.1609i	−0.150136	−	0.947923i	−0.941606	−	0.336715i	$-0.890684\pi$
$821$	−4.30187	−	27.1609i	−0.150136	−	0.947923i	0.791470	−	0.611208i	$-0.209316\pi$
$822$		0			0
$823$	14.6233	+	4.75141i	0.509738	+	0.165624i	0.552583	−	0.833458i	$-0.313642\pi$
$823$	14.6233	+	4.75141i	0.509738	+	0.165624i	−0.0428452	+	0.999082i	$0.513642\pi$
$824$		0			0
$825$	7.24430	−	5.02788i	0.252214	−	0.175048i
$826$		0			0
$827$	5.37885	+	10.5566i	0.187041	+	0.367089i	0.965417	−	0.260709i	$-0.0839564\pi$
$827$	5.37885	+	10.5566i	0.187041	+	0.367089i	−0.778376	+	0.627798i	$0.783956\pi$
$828$		0			0
$829$	−12.6780	+	17.4498i	−0.440325	+	0.606055i	−0.970284	−	0.241968i	$-0.922207\pi$
$829$	−12.6780	+	17.4498i	−0.440325	+	0.606055i	0.529959	+	0.848023i	$0.322207\pi$
$830$		0			0
$831$	−1.15664	−	3.55976i	−0.0401233	−	0.123487i
$832$		0			0
$833$	9.57156	+	13.1741i	0.331635	+	0.456456i
$834$		0			0
$835$		−	11.1531i		−	0.385969i
$836$		0			0
$837$	−6.78737	+	6.78737i	−0.234606	+	0.234606i
$838$		0			0
$839$	−36.9639	−	5.85450i	−1.27614	−	0.202120i	−0.518658	−	0.854982i	$-0.673568\pi$
$839$	−36.9639	−	5.85450i	−1.27614	−	0.202120i	−0.757477	+	0.652862i	$0.773568\pi$
$840$		0			0
$841$	7.80752	+	24.0291i	0.269225	+	0.828589i
$842$		0			0
$843$	−3.79312	+	0.600771i	−0.130642	+	0.0206916i
$844$		0			0
$845$	−17.4063	−	1.59772i	−0.598796	−	0.0549633i
$846$		0			0
$847$	9.09179	+	19.9271i	0.312397	+	0.684705i
$848$		0			0
$849$	0.922367	−	2.83875i	0.0316555	−	0.0974258i
$850$		0			0
$851$	−18.8928	+	2.99233i	−0.647637	+	0.102576i
$852$		0			0
$853$	1.92122	+	0.978913i	0.0657815	+	0.0335173i	0.486572	−	0.873641i	$-0.338247\pi$
$853$	1.92122	+	0.978913i	0.0657815	+	0.0335173i	−0.420790	+	0.907158i	$0.638247\pi$
$854$		0			0
$855$	−11.6924	+	8.49502i	−0.399871	+	0.290524i
$856$		0			0
$857$	49.5689			1.69324			0.846621	−	0.532197i	$-0.178633\pi$
$857$	49.5689			1.69324			0.846621	+	0.532197i	$0.178633\pi$
$858$		0			0
$859$	−17.1182			−0.584067			−0.292033	−	0.956408i	$-0.594332\pi$
$859$	−17.1182			−0.584067			−0.292033	+	0.956408i	$0.594332\pi$
$860$		0			0
$861$	11.3833	−	8.27047i	0.387943	−	0.281857i
$862$		0			0
$863$	−42.7205	−	21.7672i	−1.45422	−	0.740964i	−0.464718	−	0.885459i	$-0.653844\pi$
$863$	−42.7205	−	21.7672i	−1.45422	−	0.740964i	−0.989505	+	0.144495i	$0.953844\pi$
$864$		0			0
$865$	−22.2713	+	3.52743i	−0.757248	+	0.119936i
$866$		0			0
$867$	3.03350	−	9.33617i	0.103023	−	0.317073i
$868$		0			0
$869$	−41.5733	+	28.8538i	−1.41028	+	0.978798i
$870$		0			0
$871$	18.0262	−	26.6024i	0.610795	−	0.901387i
$872$		0			0
$873$	−16.9671	+	2.68732i	−0.574249	+	0.0909521i
$874$		0			0
$875$	−6.77765	−	20.8595i	−0.229127	−	0.705179i
$876$		0			0
$877$	17.7230	+	2.80704i	0.598462	+	0.0947871i	0.448314	−	0.893876i	$-0.352025\pi$
$877$	17.7230	+	2.80704i	0.598462	+	0.0947871i	0.150149	+	0.988663i	$0.452025\pi$
$878$		0			0
$879$	8.80400	−	8.80400i	0.296952	−	0.296952i
$880$		0			0
$881$			44.6473i			1.50421i	0.659045	+	0.752103i	$0.270961\pi$
$881$			44.6473i			1.50421i	−0.659045	+	0.752103i	$0.729039\pi$
$882$		0			0
$883$	−22.9763	−	31.6241i	−0.773213	−	1.06424i	−0.995999	−	0.0893684i	$-0.971515\pi$
$883$	−22.9763	−	31.6241i	−0.773213	−	1.06424i	0.222786	−	0.974867i	$-0.428485\pi$
$884$		0			0
$885$	−2.46186	−	7.57683i	−0.0827545	−	0.254692i
$886$		0			0
$887$	−12.5732	+	17.3055i	−0.422167	+	0.581063i	−0.966133	−	0.258044i	$-0.916922\pi$
$887$	−12.5732	+	17.3055i	−0.422167	+	0.581063i	0.543966	+	0.839107i	$0.316922\pi$
$888$		0			0
$889$	−1.84688	−	3.62471i	−0.0619424	−	0.121569i
$890$		0			0
$891$	−10.2814	+	3.09679i	−0.344440	+	0.103746i
$892$		0			0
$893$	−2.30144	−	0.747783i	−0.0770148	−	0.0250236i
$894$		0			0
$895$	3.68620	+	23.2737i	0.123216	+	0.777955i
$896$		0			0
$897$	17.5037	+	16.3924i	0.584432	+	0.547327i
$898$		0			0
$899$	4.14528	+	0.656547i	0.138253	+	0.0218971i
$900$		0			0
$901$	47.2593			1.57444
$902$		0			0
$903$	−6.29790	+	6.29790i	−0.209581	+	0.209581i
$904$		0			0
$905$	27.2530	+	4.31645i	0.905920	+	0.143484i
$906$		0			0
$907$	−4.58141	+	1.48859i	−0.152123	+	0.0494278i	−0.384089	−	0.923296i	$-0.625484\pi$
$907$	−4.58141	+	1.48859i	−0.152123	+	0.0494278i	0.231966	+	0.972724i	$0.425484\pi$
$908$		0			0
$909$	−20.8122	−	15.1210i	−0.690299	−	0.501531i
$910$		0			0
$911$	11.1801	−	34.4089i	0.370415	−	1.14002i	−0.576106	−	0.817375i	$-0.695428\pi$
$911$	11.1801	−	34.4089i	0.370415	−	1.14002i	0.946520	−	0.322644i	$-0.104572\pi$
$912$		0			0
$913$	8.57615	+	17.7703i	0.283829	+	0.588112i
$914$		0			0
$915$	5.50290	−	2.80387i	0.181920	−	0.0926931i
$916$		0			0
$917$	3.71784	+	23.4735i	0.122774	+	0.775164i
$918$		0			0
$919$	−36.5309	+	11.8696i	−1.20504	+	0.391542i	−0.841614	−	0.540079i	$-0.818394\pi$
$919$	−36.5309	+	11.8696i	−1.20504	+	0.391542i	−0.363429	+	0.931622i	$0.618394\pi$
$920$		0			0
$921$	1.77743	−	11.2222i	0.0585683	−	0.369786i
$922$		0			0
$923$	−1.62522	−	0.469778i	−0.0534947	−	0.0154629i
$924$		0			0
$925$	−5.40686	+	5.40686i	−0.177776	+	0.177776i
$926$		0			0
$927$	−21.2784	−	29.2873i	−0.698876	−	0.961920i
$928$		0			0
$929$	−26.2708	−	13.3856i	−0.861916	−	0.439168i	−0.0336042	−	0.999435i	$-0.510699\pi$
$929$	−26.2708	−	13.3856i	−0.861916	−	0.439168i	−0.828312	+	0.560267i	$0.810699\pi$
$930$		0			0
$931$	13.9717	−	2.21290i	0.457903	−	0.0725248i
$932$		0			0
$933$	−11.8683	−	3.85624i	−0.388550	−	0.126248i
$934$		0			0
$935$	16.5490	+	17.2797i	0.541209	+	0.565108i
$936$		0			0
$937$	44.6158	+	14.4966i	1.45754	+	0.473582i	0.927316	−	0.374278i	$-0.122109\pi$
$937$	44.6158	+	14.4966i	1.45754	+	0.473582i	0.530220	+	0.847860i	$0.322109\pi$
$938$		0			0
$939$	12.7177	+	9.23992i	0.415025	+	0.301533i
$940$		0			0
$941$	7.03070	−	13.7985i	0.229194	−	0.449819i	−0.747556	−	0.664199i	$-0.768773\pi$
$941$	7.03070	−	13.7985i	0.229194	−	0.449819i	0.976750	+	0.214379i	$0.0687729\pi$
$942$		0			0
$943$	10.5979	−	66.9128i	0.345116	−	2.17898i
$944$		0			0
$945$		−	11.8329i		−	0.384924i
$946$		0			0
$947$	−16.6041	−	16.6041i	−0.539560	−	0.539560i	0.383840	−	0.923400i	$-0.374601\pi$
$947$	−16.6041	−	16.6041i	−0.539560	−	0.539560i	−0.923400	+	0.383840i	$0.874601\pi$
$948$		0			0
$949$	35.6230	−	12.8797i	1.15637	−	0.418093i
$950$		0			0
$951$	2.30974	+	1.17687i	0.0748986	+	0.0381627i
$952$		0			0
$953$	−17.5017	−	12.7157i	−0.566936	−	0.411903i	0.267055	−	0.963681i	$-0.413949\pi$
$953$	−17.5017	−	12.7157i	−0.566936	−	0.411903i	−0.833991	+	0.551778i	$0.813949\pi$
$954$		0			0
$955$	−1.97729	−	3.88064i	−0.0639835	−	0.125575i
$956$		0			0
$957$	−4.25002	−	3.23033i	−0.137384	−	0.104422i
$958$		0			0
$959$	−8.20181	+	25.2426i	−0.264850	+	0.815126i
$960$		0			0
$961$	15.4488	−	21.2635i	0.498350	−	0.685919i
$962$		0			0
$963$	0.0181037	−	0.00588226i	0.000583385	−	0.000189553i
$964$		0			0
$965$	1.90600	+	2.62339i	0.0613564	+	0.0844498i
$966$		0			0
$967$	−7.75419	−	7.75419i	−0.249358	−	0.249358i	0.571349	−	0.820707i	$-0.306420\pi$
$967$	−7.75419	−	7.75419i	−0.249358	−	0.249358i	−0.820707	+	0.571349i	$0.806420\pi$
$968$		0			0
$969$	−14.7275	−	14.7275i	−0.473117	−	0.473117i
$970$		0			0
$971$	−3.40519	+	2.47401i	−0.109278	+	0.0793949i	−0.641082	−	0.767472i	$-0.721514\pi$
$971$	−3.40519	+	2.47401i	−0.109278	+	0.0793949i	0.531804	+	0.846867i	$0.321514\pi$
$972$		0			0
$973$	18.8975	−	37.0885i	0.605827	−	1.18900i
$974$		0			0
$975$	9.51235	+	1.18857i	0.304639	+	0.0380649i
$976$		0			0
$977$	−19.1634	−	37.6103i	−0.613091	−	1.20326i	−0.963763	−	0.266761i	$-0.914047\pi$
$977$	−19.1634	−	37.6103i	−0.613091	−	1.20326i	0.350672	−	0.936498i	$-0.385953\pi$
$978$		0			0
$979$	27.1842	−	3.70563i	0.868812	−	0.118433i
$980$		0			0
$981$	34.8616	−	17.7629i	1.11304	−	0.567125i
$982$		0			0
$983$	−7.39010	−	46.6593i	−0.235708	−	1.48820i	−0.767349	−	0.641230i	$-0.778424\pi$
$983$	−7.39010	−	46.6593i	−0.235708	−	1.48820i	0.531641	−	0.846970i	$-0.321576\pi$
$984$		0			0
$985$	5.96635	+	18.3626i	0.190104	+	0.585080i
$986$		0			0
$987$	0.696650	−	0.506146i	0.0221746	−	0.0161108i
$988$		0			0
$989$			42.8833i			1.36361i
$990$		0			0
$991$	−11.4603			−0.364049			−0.182025	−	0.983294i	$-0.558265\pi$
$991$	−11.4603			−0.364049			−0.182025	+	0.983294i	$0.558265\pi$
$992$		0			0
$993$	−3.30679	+	20.8782i	−0.104938	+	0.662550i
$994$		0			0
$995$	−8.92858	+	17.5233i	−0.283055	+	0.555527i
$996$		0			0
$997$	−24.5283	+	33.7604i	−0.776820	+	1.06920i	0.218805	+	0.975769i	$0.429784\pi$
$997$	−24.5283	+	33.7604i	−0.776820	+	1.06920i	−0.995626	+	0.0934330i	$0.970216\pi$
$998$		0			0
$999$	−9.43306	+	4.80638i	−0.298449	+	0.152067i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.bh.a.57.6	✓	112
11.6	odd	10	inner	572.2.bh.a.369.6	yes	112
13.8	odd	4	inner	572.2.bh.a.541.6	yes	112
143.138	even	20	inner	572.2.bh.a.281.6	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.bh.a.57.6	✓	112	1.1	even	1	trivial
572.2.bh.a.281.6	yes	112	143.138	even	20	inner
572.2.bh.a.369.6	yes	112	11.6	odd	10	inner
572.2.bh.a.541.6	yes	112	13.8	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.bh (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.673845 + 0.489577i) q^{3} +(-1.19803 - 0.610425i) q^{5} +(-1.96669 + 0.311493i) q^{7} +(-0.712670 + 2.19337i) q^{9} +O(q^{10})\)	\(q+(-0.673845 + 0.489577i) q^{3} +(-1.19803 - 0.610425i) q^{5} +(-1.96669 + 0.311493i) q^{7} +(-0.712670 + 2.19337i) q^{9} +(2.00696 - 2.64048i) q^{11} +(3.54077 - 0.680419i) q^{13} +(1.10613 - 0.175194i) q^{15} +(-1.65795 - 5.10265i) q^{17} +(-4.60335 - 0.729099i) q^{19} +(1.17274 - 1.17274i) q^{21} -7.98537i q^{23} +(-1.87628 - 2.58247i) q^{25} +(-1.36575 - 4.20335i) q^{27} +(-1.13586 + 1.56338i) q^{29} +(-0.985993 - 1.93512i) q^{31} +(-0.0596627 + 2.76183i) q^{33} +(2.54629 + 0.827339i) q^{35} +(-0.374726 - 2.36593i) q^{37} +(-2.05281 + 2.19197i) q^{39} +(8.37942 + 1.32717i) q^{41} -5.37023 q^{43} +(2.19269 - 2.19269i) q^{45} +(0.512814 + 0.0812217i) q^{47} +(-2.88656 + 0.937901i) q^{49} +(3.61534 + 2.62670i) q^{51} +(-2.72195 + 8.37731i) q^{53} +(-4.01620 + 1.93826i) q^{55} +(3.45889 - 1.76239i) q^{57} +(-1.11282 - 7.02608i) q^{59} +(5.24481 - 1.70414i) q^{61} +(0.718379 - 4.53567i) q^{63} +(-4.65728 - 1.34621i) q^{65} +(6.30211 - 6.30211i) q^{67} +(3.90945 + 5.38090i) q^{69} +(-0.418067 - 0.213016i) q^{71} +(10.3766 - 1.64350i) q^{73} +(2.52864 + 0.821604i) q^{75} +(-3.12457 + 5.81814i) q^{77} +(-14.5112 - 4.71499i) q^{79} +(-2.61921 - 1.90297i) q^{81} +(-2.70092 + 5.30086i) q^{83} +(-1.12852 + 7.12517i) q^{85} -1.60957i q^{87} +(5.84930 + 5.84930i) q^{89} +(-6.75164 + 2.44110i) q^{91} +(1.61180 + 0.821251i) q^{93} +(5.06988 + 3.68348i) q^{95} +(3.38164 + 6.63685i) q^{97} +(4.36125 + 6.28380i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 28 q^{9}+O(q^{10}) \) 112 * q - 28 * q^9	\( 112 q - 28 q^{9} + 8 q^{11} - 10 q^{13} + 4 q^{15} - 24 q^{27} - 20 q^{29} - 16 q^{31} - 54 q^{33} + 100 q^{35} - 12 q^{37} + 40 q^{39} - 20 q^{41} - 4 q^{45} - 10 q^{47} - 76 q^{53} - 20 q^{55} + 18 q^{59} + 40 q^{61} + 80 q^{63} + 92 q^{67} + 8 q^{71} - 30 q^{73} - 80 q^{79} + 12 q^{81} + 40 q^{85} + 32 q^{89} - 12 q^{91} - 114 q^{93} + 54 q^{97} - 90 q^{99}+O(q^{100}) \) 112 * q - 28 * q^9 + 8 * q^11 - 10 * q^13 + 4 * q^15 - 24 * q^27 - 20 * q^29 - 16 * q^31 - 54 * q^33 + 100 * q^35 - 12 * q^37 + 40 * q^39 - 20 * q^41 - 4 * q^45 - 10 * q^47 - 76 * q^53 - 20 * q^55 + 18 * q^59 + 40 * q^61 + 80 * q^63 + 92 * q^67 + 8 * q^71 - 30 * q^73 - 80 * q^79 + 12 * q^81 + 40 * q^85 + 32 * q^89 - 12 * q^91 - 114 * q^93 + 54 * q^97 - 90 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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