LMFDB - Embedded newform 572.2.bv.a.41.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(41,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([0, 18, 5]))

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

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

chi := DirichletCharacter("572.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.bv (of order $60$, degree $16$, 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:	$224$
Relative dimension:	$14$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			41.13
Character	$\chi$	$=$	572.41
Dual form			572.2.bv.a.293.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.52983 - 1.69905i) q^{3} +(3.46848 - 0.549353i) q^{5} +(-0.174489 - 0.00914460i) q^{7} +(-0.232798 - 2.21493i) q^{9} +O(q^{10})$	\(q+(1.52983 - 1.69905i) q^{3} +(3.46848 - 0.549353i) q^{5} +(-0.174489 - 0.00914460i) q^{7} +(-0.232798 - 2.21493i) q^{9} +(2.93100 - 1.55217i) q^{11} +(-3.56614 - 0.531621i) q^{13} +(4.37280 - 6.73352i) q^{15} +(-3.71761 + 1.65519i) q^{17} +(3.33018 + 5.12803i) q^{19} +(-0.282476 + 0.282476i) q^{21} +(-6.28941 + 3.63119i) q^{23} +(6.97326 - 2.26575i) q^{25} +(1.42954 + 1.03862i) q^{27} +(-1.06519 - 5.01133i) q^{29} +(-0.619362 + 3.91050i) q^{31} +(1.84673 - 7.35446i) q^{33} +(-0.610236 + 0.0641384i) q^{35} +(0.200534 + 0.130229i) q^{37} +(-6.35883 + 5.24575i) q^{39} +(-11.8307 + 0.620022i) q^{41} +(-0.852928 + 1.47731i) q^{43} +(-2.02423 - 7.55454i) q^{45} +(4.51259 - 8.85645i) q^{47} +(-6.93129 - 0.728508i) q^{49} +(-2.87506 + 8.84853i) q^{51} +(8.80480 - 6.39706i) q^{53} +(9.31343 - 6.99381i) q^{55} +(13.8073 + 2.18687i) q^{57} +(-0.279392 + 5.33111i) q^{59} +(-0.530365 - 1.19122i) q^{61} +(0.0203662 + 0.388610i) q^{63} +(-12.6611 + 0.115157i) q^{65} +(1.33148 + 0.356768i) q^{67} +(-3.45215 + 16.2411i) q^{69} +(2.70546 - 7.04797i) q^{71} +(-0.817028 - 1.60351i) q^{73} +(6.81827 - 15.3141i) q^{75} +(-0.525623 + 0.244034i) q^{77} +(3.92156 + 5.39756i) q^{79} +(10.4870 - 2.22908i) q^{81} +(-0.584293 - 3.68908i) q^{83} +(-11.9852 + 7.78325i) q^{85} +(-10.1440 - 5.85666i) q^{87} +(-3.89646 + 14.5418i) q^{89} +(0.617393 + 0.125373i) q^{91} +(5.69660 + 7.03472i) q^{93} +(14.3677 + 15.9570i) q^{95} +(-10.6347 - 8.61178i) q^{97} +(-4.12027 - 6.13062i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q + 28 q^{9}+O(q^{10}) $ 224 * q + 28 * q^9	$ 224 q + 28 q^{9} + 16 q^{11} + 10 q^{13} - 28 q^{15} - 48 q^{23} + 24 q^{27} + 20 q^{29} + 4 q^{31} + 60 q^{33} + 50 q^{35} + 12 q^{37} - 40 q^{39} + 20 q^{41} + 64 q^{45} - 62 q^{47} + 100 q^{53} - 22 q^{55} + 12 q^{59} - 40 q^{61} - 80 q^{63} - 44 q^{67} - 152 q^{71} + 30 q^{73} - 120 q^{75} + 80 q^{79} + 72 q^{81} + 90 q^{83} - 40 q^{85} - 8 q^{89} - 36 q^{91} - 90 q^{93} - 42 q^{97} + 144 q^{99}+O(q^{100}) $ 224 * q + 28 * q^9 + 16 * q^11 + 10 * q^13 - 28 * q^15 - 48 * q^23 + 24 * q^27 + 20 * q^29 + 4 * q^31 + 60 * q^33 + 50 * q^35 + 12 * q^37 - 40 * q^39 + 20 * q^41 + 64 * q^45 - 62 * q^47 + 100 * q^53 - 22 * q^55 + 12 * q^59 - 40 * q^61 - 80 * q^63 - 44 * q^67 - 152 * q^71 + 30 * q^73 - 120 * q^75 + 80 * q^79 + 72 * q^81 + 90 * q^83 - 40 * q^85 - 8 * q^89 - 36 * q^91 - 90 * q^93 - 42 * q^97 + 144 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{3}{10}\right)$

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
$3$	1.52983	−	1.69905i	0.883246	−	0.980945i	−0.116679	−	0.993170i	$-0.537225\pi$
$3$	1.52983	−	1.69905i	0.883246	−	0.980945i	0.999925	+	0.0122251i	$0.00389148\pi$
$4$		0			0
$5$	3.46848	−	0.549353i	1.55115	−	0.245678i	0.678712	−	0.734404i	$-0.262538\pi$
$5$	3.46848	−	0.549353i	1.55115	−	0.245678i	0.872437	+	0.488726i	$0.162538\pi$
$6$		0			0
$7$	−0.174489	−	0.00914460i	−0.0659508	−	0.00345633i	0.0193320	−	0.999813i	$-0.493846\pi$
$7$	−0.174489	−	0.00914460i	−0.0659508	−	0.00345633i	−0.0852828	+	0.996357i	$0.527179\pi$
$8$		0			0
$9$	−0.232798	−	2.21493i	−0.0775995	−	0.738310i
$10$		0			0
$11$	2.93100	−	1.55217i	0.883731	−	0.467996i
$11$	2.93100	−	1.55217i	0.883731	−	0.467996i
$12$		0			0
$13$	−3.56614	−	0.531621i	−0.989070	−	0.147445i
$13$	−3.56614	−	0.531621i	−0.989070	−	0.147445i
$14$		0			0
$15$	4.37280	−	6.73352i	1.12905	−	1.73859i
$16$		0			0
$17$	−3.71761	+	1.65519i	−0.901652	+	0.401441i	−0.804586	−	0.593836i	$-0.797613\pi$
$17$	−3.71761	+	1.65519i	−0.901652	+	0.401441i	−0.0970664	+	0.995278i	$0.530946\pi$
$18$		0			0
$19$	3.33018	+	5.12803i	0.763995	+	1.17645i	0.979794	+	0.200012i	$0.0640980\pi$
$19$	3.33018	+	5.12803i	0.763995	+	1.17645i	−0.215798	+	0.976438i	$0.569235\pi$
$20$		0			0
$21$	−0.282476	+	0.282476i	−0.0616413	+	0.0616413i
$22$		0			0
$23$	−6.28941	+	3.63119i	−1.31143	+	0.757156i	−0.982333	−	0.187140i	$-0.940078\pi$
$23$	−6.28941	+	3.63119i	−1.31143	+	0.757156i	−0.329099	+	0.944295i	$0.606745\pi$
$24$		0			0
$25$	6.97326	−	2.26575i	1.39465	−	0.453150i
$26$		0			0
$27$	1.42954	+	1.03862i	0.275115	+	0.199883i
$28$		0			0
$29$	−1.06519	−	5.01133i	−0.197801	−	0.930581i	−0.959294	−	0.282408i	$-0.908867\pi$
$29$	−1.06519	−	5.01133i	−0.197801	−	0.930581i	0.761493	−	0.648173i	$-0.224466\pi$
$30$		0			0
$31$	−0.619362	+	3.91050i	−0.111241	+	0.702347i	0.867529	+	0.497386i	$0.165707\pi$
$31$	−0.619362	+	3.91050i	−0.111241	+	0.702347i	−0.978770	+	0.204961i	$0.934293\pi$
$32$		0			0
$33$	1.84673	−	7.35446i	0.321474	−	1.28025i
$34$		0			0
$35$	−0.610236	+	0.0641384i	−0.103149	+	0.0108414i
$36$		0			0
$37$	0.200534	+	0.130229i	0.0329676	+	0.0214094i	0.561018	−	0.827804i	$-0.310410\pi$
$37$	0.200534	+	0.130229i	0.0329676	+	0.0214094i	−0.528050	+	0.849213i	$0.677077\pi$
$38$		0			0
$39$	−6.35883	+	5.24575i	−1.01823	+	0.839993i
$40$		0			0
$41$	−11.8307	+	0.620022i	−1.84765	+	0.0968312i	−0.943698	−	0.330807i	$-0.892679\pi$
$41$	−11.8307	+	0.620022i	−1.84765	+	0.0968312i	−0.903950	+	0.427638i	$0.859346\pi$
$42$		0			0
$43$	−0.852928	+	1.47731i	−0.130070	+	0.225288i	−0.923703	−	0.383108i	$-0.874854\pi$
$43$	−0.852928	+	1.47731i	−0.130070	+	0.225288i	0.793633	+	0.608397i	$0.208187\pi$
$44$		0			0
$45$	−2.02423	−	7.55454i	−0.301755	−	1.12616i
$46$		0			0
$47$	4.51259	−	8.85645i	0.658228	−	1.29185i	−0.284625	−	0.958639i	$-0.591869\pi$
$47$	4.51259	−	8.85645i	0.658228	−	1.29185i	0.942854	−	0.333207i	$-0.108131\pi$
$48$		0			0
$49$	−6.93129	−	0.728508i	−0.990184	−	0.104073i
$50$		0			0
$51$	−2.87506	+	8.84853i	−0.402589	+	1.23904i
$52$		0			0
$53$	8.80480	−	6.39706i	1.20943	−	0.878704i	0.214254	−	0.976778i	$-0.431268\pi$
$53$	8.80480	−	6.39706i	1.20943	−	0.878704i	0.995179	+	0.0980738i	$0.0312681\pi$
$54$		0			0
$55$	9.31343	−	6.99381i	1.25582	−	0.943045i
$56$		0			0
$57$	13.8073	+	2.18687i	1.82883	+	0.289658i
$58$		0			0
$59$	−0.279392	+	5.33111i	−0.0363737	+	0.694051i	0.918207	+	0.396100i	$0.129637\pi$
$59$	−0.279392	+	5.33111i	−0.0363737	+	0.694051i	−0.954581	+	0.297951i	$0.903697\pi$
$60$		0			0
$61$	−0.530365	−	1.19122i	−0.0679063	−	0.152520i	0.876404	−	0.481577i	$-0.159936\pi$
$61$	−0.530365	−	1.19122i	−0.0679063	−	0.152520i	−0.944310	+	0.329057i	$0.893269\pi$
$62$		0			0
$63$	0.0203662	+	0.388610i	0.00256590	+	0.0489603i
$64$		0			0
$65$	−12.6611	+	0.115157i	−1.57042	+	0.0142834i
$66$		0			0
$67$	1.33148	+	0.356768i	0.162666	+	0.0435862i	0.339233	−	0.940702i	$-0.389833\pi$
$67$	1.33148	+	0.356768i	0.162666	+	0.0435862i	−0.176567	+	0.984289i	$0.556499\pi$
$68$		0			0
$69$	−3.45215	+	16.2411i	−0.415590	+	1.95520i
$70$		0			0
$71$	2.70546	−	7.04797i	0.321079	−	0.836441i	−0.674124	−	0.738618i	$-0.735479\pi$
$71$	2.70546	−	7.04797i	0.321079	−	0.836441i	0.995204	−	0.0978227i	$-0.0311878\pi$
$72$		0			0
$73$	−0.817028	−	1.60351i	−0.0956260	−	0.187676i	0.838238	−	0.545304i	$-0.183586\pi$
$73$	−0.817028	−	1.60351i	−0.0956260	−	0.187676i	−0.933864	+	0.357627i	$0.883586\pi$
$74$		0			0
$75$	6.81827	−	15.3141i	0.787306	−	1.76832i
$76$		0			0
$77$	−0.525623	+	0.244034i	−0.0599003	+	0.0278102i
$78$		0			0
$79$	3.92156	+	5.39756i	0.441210	+	0.607273i	0.970480	−	0.241180i	$-0.0775344\pi$
$79$	3.92156	+	5.39756i	0.441210	+	0.607273i	−0.529271	+	0.848453i	$0.677534\pi$
$80$		0			0
$81$	10.4870	−	2.22908i	1.16522	−	0.247676i
$82$		0			0
$83$	−0.584293	−	3.68908i	−0.0641345	−	0.404929i	−0.998781	−	0.0493520i	$-0.984284\pi$
$83$	−0.584293	−	3.68908i	−0.0641345	−	0.404929i	0.934647	−	0.355577i	$-0.115716\pi$
$84$		0			0
$85$	−11.9852	+	7.78325i	−1.29997	+	0.844212i
$86$		0			0
$87$	−10.1440	−	5.85666i	−1.08755	−	0.627900i
$88$		0			0
$89$	−3.89646	+	14.5418i	−0.413024	+	1.54143i	0.375736	+	0.926727i	$0.377390\pi$
$89$	−3.89646	+	14.5418i	−0.413024	+	1.54143i	−0.788760	+	0.614701i	$0.789277\pi$
$90$		0			0
$91$	0.617393	+	0.125373i	0.0647204	+	0.0131427i
$92$		0			0
$93$	5.69660	+	7.03472i	0.590710	+	0.729466i
$94$		0			0
$95$	14.3677	+	15.9570i	1.47410	+	1.63715i
$96$		0			0
$97$	−10.6347	−	8.61178i	−1.07979	−	0.874394i	−0.0872315	−	0.996188i	$-0.527802\pi$
$97$	−10.6347	−	8.61178i	−1.07979	−	0.874394i	−0.992555	+	0.121794i	$0.961135\pi$
$98$		0			0
$99$	−4.12027	−	6.13062i	−0.414103	−	0.616151i
$100$		0			0
$101$	14.5929	+	6.49718i	1.45205	+	0.646494i	0.972897	−	0.231238i	$-0.0742776\pi$
$101$	14.5929	+	6.49718i	1.45205	+	0.646494i	0.479152	+	0.877732i	$0.340944\pi$
$102$		0			0
$103$	−9.85748	−	3.20289i	−0.971287	−	0.315590i	−0.219951	−	0.975511i	$-0.570590\pi$
$103$	−9.85748	−	3.20289i	−0.971287	−	0.315590i	−0.751335	+	0.659921i	$0.770590\pi$
$104$		0			0
$105$	−0.824582	+	1.13494i	−0.0804709	+	0.110759i
$106$		0			0
$107$	13.6697	+	12.3082i	1.32150	+	1.18988i	0.966986	+	0.254830i	$0.0820195\pi$
$107$	13.6697	+	12.3082i	1.32150	+	1.18988i	0.354512	+	0.935052i	$0.384647\pi$
$108$		0			0
$109$	−3.11059	−	3.11059i	−0.297940	−	0.297940i	0.542266	−	0.840207i	$-0.317566\pi$
$109$	−3.11059	−	3.11059i	−0.297940	−	0.297940i	−0.840207	+	0.542266i	$0.817566\pi$
$110$		0			0
$111$	0.528047	−	0.141490i	0.0501200	−	0.0134296i
$112$		0			0
$113$	0.758467	+	0.161217i	0.0713506	+	0.0151660i	0.243449	−	0.969914i	$-0.421721\pi$
$113$	0.758467	+	0.161217i	0.0713506	+	0.0151660i	−0.172098	+	0.985080i	$0.555055\pi$
$114$		0			0
$115$	−19.8199	+	16.0498i	−1.84821	+	1.49665i
$116$		0			0
$117$	−0.347310	+	8.02252i	−0.0321088	+	0.741682i
$118$		0			0
$119$	0.663819	−	0.254816i	0.0608522	−	0.0233590i
$120$		0			0
$121$	6.18156	−	9.09881i	0.561960	−	0.827164i
$122$		0			0
$123$	−17.0455	+	21.0495i	−1.53694	+	1.89797i
$124$		0			0
$125$	7.29709	−	3.71805i	0.652672	−	0.332553i
$126$		0			0
$127$	−0.110582	+	1.05212i	−0.00981258	+	0.0933604i	−0.998332	−	0.0577330i	$-0.981613\pi$
$127$	−0.110582	+	1.05212i	−0.00981258	+	0.0933604i	0.988519	+	0.151093i	$0.0482794\pi$
$128$		0			0
$129$	1.20519	+	3.70920i	0.106111	+	0.326577i
$130$		0			0
$131$			10.5806i			0.924429i	0.886768	+	0.462215i	$0.152945\pi$
$131$			10.5806i			0.924429i	−0.886768	+	0.462215i	$0.847055\pi$
$132$		0			0
$133$	−0.534187	−	0.925239i	−0.0463199	−	0.0802284i
$134$		0			0
$135$	5.52889	+	2.81711i	0.475851	+	0.242458i
$136$		0			0
$137$	−1.54752	−	0.594036i	−0.132213	−	0.0507519i	0.291362	−	0.956613i	$-0.405892\pi$
$137$	−1.54752	−	0.594036i	−0.132213	−	0.0507519i	−0.423575	+	0.905861i	$0.639225\pi$
$138$		0			0
$139$	1.59264	−	1.43402i	0.135086	−	0.121632i	−0.598818	−	0.800885i	$-0.704363\pi$
$139$	1.59264	−	1.43402i	0.135086	−	0.121632i	0.733904	+	0.679253i	$0.237696\pi$
$140$		0			0
$141$	−8.14403	−	21.2159i	−0.685851	−	1.78670i
$142$		0			0
$143$	−11.2775	+	3.97706i	−0.943075	+	0.332579i
$144$		0			0
$145$	−6.44758	−	16.7965i	−0.535442	−	1.39487i
$146$		0			0
$147$	−11.8414	+	10.6621i	−0.976666	+	0.879394i
$148$		0			0
$149$	−5.38809	−	2.06829i	−0.441409	−	0.169441i	0.127505	−	0.991838i	$-0.459303\pi$
$149$	−5.38809	−	2.06829i	−0.441409	−	0.169441i	−0.568914	+	0.822397i	$0.692636\pi$
$150$		0			0
$151$	−11.7453	−	5.98451i	−0.955816	−	0.487013i	−0.0947475	−	0.995501i	$-0.530204\pi$
$151$	−11.7453	−	5.98451i	−0.955816	−	0.487013i	−0.861069	+	0.508489i	$0.830204\pi$
$152$		0			0
$153$	4.53157	+	7.84891i	0.366356	+	0.634547i
$154$		0			0
$155$			13.9037i			1.11677i
$156$		0			0
$157$	2.35801	+	7.25721i	0.188190	+	0.579188i	0.999989	−	0.00474864i	$-0.00151154\pi$
$157$	2.35801	+	7.25721i	0.188190	+	0.579188i	−0.811799	+	0.583937i	$0.801512\pi$
$158$		0			0
$159$	2.60093	−	24.7462i	0.206267	−	1.96250i
$160$		0			0
$161$	1.13064	−	0.576090i	0.0891070	−	0.0454023i
$162$		0			0
$163$	−8.51838	+	10.5193i	−0.667211	+	0.823937i	−0.992573	−	0.121653i	$-0.961181\pi$
$163$	−8.51838	+	10.5193i	−0.667211	+	0.823937i	0.325362	+	0.945590i	$0.394514\pi$
$164$		0			0
$165$	2.36514	−	26.5233i	0.184126	−	2.06483i
$166$		0			0
$167$	5.59218	−	2.14664i	0.432736	−	0.166112i	−0.132243	−	0.991217i	$-0.542218\pi$
$167$	5.59218	−	2.14664i	0.432736	−	0.166112i	0.564978	+	0.825106i	$0.308884\pi$
$168$		0			0
$169$	12.4348	+	3.79167i	0.956520	+	0.291667i
$170$		0			0
$171$	10.5830	−	8.56991i	0.809299	−	0.655357i
$172$		0			0
$173$	−9.17180	−	1.94953i	−0.697319	−	0.148220i	−0.154405	−	0.988008i	$-0.549346\pi$
$173$	−9.17180	−	1.94953i	−0.697319	−	0.148220i	−0.542915	+	0.839788i	$0.682679\pi$
$174$		0			0
$175$	−1.23748	+	0.331581i	−0.0935446	+	0.0250652i
$176$		0			0
$177$	8.63038	+	8.63038i	0.648699	+	0.648699i
$178$		0			0
$179$	19.7004	+	17.7383i	1.47248	+	1.32582i	0.827250	+	0.561834i	$0.189904\pi$
$179$	19.7004	+	17.7383i	1.47248	+	1.32582i	0.645228	+	0.763990i	$0.276763\pi$
$180$		0			0
$181$	5.55386	−	7.64423i	0.412815	−	0.568191i	−0.551087	−	0.834448i	$-0.685787\pi$
$181$	5.55386	−	7.64423i	0.412815	−	0.568191i	0.963902	+	0.266256i	$0.0857868\pi$
$182$		0			0
$183$	−2.83530	−	0.921246i	−0.209592	−	0.0681005i
$184$		0			0
$185$	0.767090	+	0.341531i	0.0563976	+	0.0251098i
$186$		0			0
$187$	−8.32720	+	10.6217i	−0.608945	+	0.776735i
$188$		0			0
$189$	−0.239942	−	0.194301i	−0.0174532	−	0.0141333i
$190$		0			0
$191$	−7.96802	−	8.84939i	−0.576546	−	0.640319i	0.382370	−	0.924009i	$-0.375108\pi$
$191$	−7.96802	−	8.84939i	−0.576546	−	0.640319i	−0.958916	+	0.283690i	$0.908441\pi$
$192$		0			0
$193$	−1.99745	−	2.46665i	−0.143780	−	0.177553i	0.700169	−	0.713977i	$-0.253108\pi$
$193$	−1.99745	−	2.46665i	−0.143780	−	0.177553i	−0.843949	+	0.536424i	$0.819775\pi$
$194$		0			0
$195$	−19.1737	+	21.6880i	−1.37306	+	1.55311i
$196$		0			0
$197$	3.23183	−	12.0613i	0.230258	−	0.859335i	−0.749971	−	0.661471i	$-0.769933\pi$
$197$	3.23183	−	12.0613i	0.230258	−	0.859335i	0.980229	−	0.197865i	$-0.0634007\pi$
$198$		0			0
$199$	1.54735	+	0.893363i	0.109689	+	0.0633288i	0.553841	−	0.832623i	$-0.313162\pi$
$199$	1.54735	+	0.893363i	0.109689	+	0.0633288i	−0.444152	+	0.895951i	$0.646495\pi$
$200$		0			0
$201$	2.64310	−	1.71645i	0.186430	−	0.121069i
$202$		0			0
$203$	0.140038	+	0.884165i	0.00982874	+	0.0620562i
$204$		0			0
$205$	−40.6940	+	8.64977i	−2.84219	+	0.604126i
$206$		0			0
$207$	9.50700	+	13.0853i	0.660782	+	0.909488i
$208$		0			0
$209$	17.7203	+	9.86127i	1.22574	+	0.682118i
$210$		0			0
$211$	4.44909	−	9.99283i	0.306288	−	0.687935i	−0.693172	−	0.720772i	$-0.743788\pi$
$211$	4.44909	−	9.99283i	0.306288	−	0.687935i	0.999461	+	0.0328371i	$0.0104543\pi$
$212$		0			0
$213$	−7.83594	−	15.3789i	−0.536910	−	1.05374i
$214$		0			0
$215$	−2.14679	+	5.59259i	−0.146410	+	0.381411i
$216$		0			0
$217$	0.143832	−	0.676677i	0.00976396	−	0.0459358i
$218$		0			0
$219$	−3.97435	−	1.06492i	−0.268562	−	0.0719608i
$220$		0			0
$221$	14.1375	−	3.92627i	0.950988	−	0.264110i
$222$		0			0
$223$	0.701092	+	13.3776i	0.0469486	+	0.895832i	0.916017	+	0.401140i	$0.131386\pi$
$223$	0.701092	+	13.3776i	0.0469486	+	0.895832i	−0.869068	+	0.494692i	$0.835281\pi$
$224$		0			0
$225$	−6.64184	−	14.9178i	−0.442789	−	0.994520i
$226$		0			0
$227$	1.40839	−	26.8737i	0.0934780	−	1.78367i	−0.402587	−	0.915382i	$-0.631889\pi$
$227$	1.40839	−	26.8737i	0.0934780	−	1.78367i	0.496065	−	0.868285i	$-0.334778\pi$
$228$		0			0
$229$	1.63995	+	0.259743i	0.108371	+	0.0171643i	0.210384	−	0.977619i	$-0.432528\pi$
$229$	1.63995	+	0.259743i	0.108371	+	0.0171643i	−0.102013	+	0.994783i	$0.532528\pi$
$230$		0			0
$231$	−0.389488	+	1.26639i	−0.0256264	+	0.0833221i
$232$		0			0
$233$	−8.60095	+	6.24895i	−0.563467	+	0.409383i	−0.832726	−	0.553685i	$-0.813221\pi$
$233$	−8.60095	+	6.24895i	−0.563467	+	0.409383i	0.269259	+	0.963068i	$0.413221\pi$
$234$		0			0
$235$	10.7865	−	33.1974i	0.703633	−	2.16556i
$236$		0			0
$237$	15.1700	+	1.59443i	0.985398	+	0.103569i
$238$		0			0
$239$	−9.71349	+	19.0638i	−0.628313	+	1.23313i	0.329068	+	0.944306i	$0.393266\pi$
$239$	−9.71349	+	19.0638i	−0.628313	+	1.23313i	−0.957381	+	0.288828i	$0.906734\pi$
$240$		0			0
$241$	6.29253	+	23.4840i	0.405337	+	1.51274i	0.803433	+	0.595396i	$0.203005\pi$
$241$	6.29253	+	23.4840i	0.405337	+	1.51274i	−0.398095	+	0.917344i	$0.630329\pi$
$242$		0			0
$243$	9.60548	−	16.6372i	0.616192	−	1.06728i
$244$		0			0
$245$	−24.4412	+	1.28091i	−1.56149	+	0.0818344i
$246$		0			0
$247$	−9.14973	−	20.0577i	−0.582183	−	1.27624i
$248$		0			0
$249$	−7.16178	−	4.65092i	−0.453859	−	0.294740i
$250$		0			0
$251$	12.9579	−	1.36193i	0.817898	−	0.0859645i	0.313666	−	0.949533i	$-0.398443\pi$
$251$	12.9579	−	1.36193i	0.817898	−	0.0859645i	0.504231	+	0.863569i	$0.331776\pi$
$252$		0			0
$253$	−12.7981	+	20.4052i	−0.804607	+	1.28287i
$254$		0			0
$255$	−5.11112	+	32.2704i	−0.320071	+	2.02085i
$256$		0			0
$257$	−1.48410	−	6.98214i	−0.0925756	−	0.435534i	−0.999886	−	0.0150733i	$-0.995202\pi$
$257$	−1.48410	−	6.98214i	−0.0925756	−	0.435534i	0.907311	−	0.420461i	$-0.138131\pi$
$258$		0			0
$259$	−0.0338002	−	0.0245573i	−0.00210024	−	0.00152592i
$260$		0			0
$261$	−10.8518	+	3.52595i	−0.671707	+	0.218251i
$262$		0			0
$263$	−3.66480	+	2.11587i	−0.225981	+	0.130470i	−0.608717	−	0.793388i	$-0.708315\pi$
$263$	−3.66480	+	2.11587i	−0.225981	+	0.130470i	0.382735	+	0.923858i	$0.374982\pi$
$264$		0			0
$265$	27.0250	−	27.0250i	1.66013	−	1.66013i
$266$		0			0
$267$	18.7463	+	28.8667i	1.14725	+	1.76661i
$268$		0			0
$269$	−10.3382	+	4.60286i	−0.630331	+	0.280641i	−0.696931	−	0.717138i	$-0.745452\pi$
$269$	−10.3382	+	4.60286i	−0.630331	+	0.280641i	0.0666000	+	0.997780i	$0.478785\pi$
$270$		0			0
$271$	12.7102	−	19.5721i	0.772092	−	1.18892i	−0.205551	−	0.978646i	$-0.565899\pi$
$271$	12.7102	−	19.5721i	0.772092	−	1.18892i	0.977643	−	0.210271i	$-0.0674347\pi$
$272$		0			0
$273$	1.15752	−	0.857179i	0.0700563	−	0.0518789i
$274$		0			0
$275$	16.9218	−	17.4646i	1.02042	−	1.05315i
$276$		0			0
$277$	−2.87990	−	27.4004i	−0.173036	−	1.64633i	−0.644616	−	0.764506i	$-0.722983\pi$
$277$	−2.87990	−	27.4004i	−0.173036	−	1.64633i	0.471580	−	0.881823i	$-0.343684\pi$
$278$		0			0
$279$	8.80567	+	0.461486i	0.527182	+	0.0276284i
$280$		0			0
$281$	26.0895	−	4.13216i	1.55637	−	0.246504i	0.681847	−	0.731495i	$-0.261177\pi$
$281$	26.0895	−	4.13216i	1.55637	−	0.246504i	0.874519	+	0.484991i	$0.161177\pi$
$282$		0			0
$283$	15.0009	−	16.6602i	0.891714	−	0.990348i	−0.108279	−	0.994121i	$-0.534534\pi$
$283$	15.0009	−	16.6602i	0.891714	−	0.990348i	0.999993	+	0.00377206i	$0.00120069\pi$
$284$		0			0
$285$	49.0918			2.90795
$286$		0			0
$287$	2.07001			0.122189
$288$		0			0
$289$	−0.294255	+	0.326804i	−0.0173091	+	0.0192238i
$290$		0			0
$291$	−30.9010	+	4.89424i	−1.81145	+	0.286906i
$292$		0			0
$293$	13.9161	+	0.729310i	0.812985	+	0.0426067i	0.454296	−	0.890851i	$-0.349891\pi$
$293$	13.9161	+	0.729310i	0.812985	+	0.0426067i	0.358688	+	0.933457i	$0.383224\pi$
$294$		0			0
$295$	1.95960	+	18.6443i	0.114092	+	1.08551i
$296$		0			0
$297$	5.80210	+	0.825319i	0.336672	+	0.0478899i
$298$		0			0
$299$	24.3593	−	9.60577i	1.40874	−	0.555516i
$300$		0			0
$301$	0.162336	−	0.249976i	0.00935691	−	0.0144084i
$302$		0			0
$303$	33.3637	−	14.8545i	1.91669	−	0.853366i
$304$		0			0
$305$	−2.49396	−	3.84036i	−0.142804	−	0.219898i
$306$		0			0
$307$	−6.56306	+	6.56306i	−0.374574	+	0.374574i	−0.869140	−	0.494566i	$-0.835327\pi$
$307$	−6.56306	+	6.56306i	−0.374574	+	0.374574i	0.494566	+	0.869140i	$0.335327\pi$
$308$		0			0
$309$	−20.5221	+	11.8484i	−1.16746	+	0.674034i
$310$		0			0
$311$	5.07149	−	1.64783i	0.287578	−	0.0934397i	−0.161676	−	0.986844i	$-0.551690\pi$
$311$	5.07149	−	1.64783i	0.287578	−	0.0934397i	0.449254	+	0.893404i	$0.351690\pi$
$312$		0			0
$313$	−18.5371	−	13.4680i	−1.04778	−	0.761254i	−0.0759881	−	0.997109i	$-0.524211\pi$
$313$	−18.5371	−	13.4680i	−1.04778	−	0.761254i	−0.971788	+	0.235855i	$0.924211\pi$
$314$		0			0
$315$	0.284124	+	1.33670i	0.0160086	+	0.0753144i
$316$		0			0
$317$	5.49747	−	34.7096i	0.308768	−	1.94949i	−0.00499888	−	0.999988i	$-0.501591\pi$
$317$	5.49747	−	34.7096i	0.308768	−	1.94949i	0.313767	−	0.949500i	$-0.398409\pi$
$318$		0			0
$319$	−10.9005	−	13.0349i	−0.610311	−	0.729813i
$320$		0			0
$321$	41.8245	−	4.39593i	2.33442	−	0.245357i
$322$		0			0
$323$	−20.8681	−	13.5519i	−1.16113	−	0.754049i
$324$		0			0
$325$	−26.0722	+	4.37286i	−1.44622	+	0.242562i
$326$		0			0
$327$	−10.0437	+	0.526368i	−0.555418	+	0.0291082i
$328$		0			0
$329$	−0.868387	+	1.50409i	−0.0478757	+	0.0829232i
$330$		0			0
$331$	−1.04181	−	3.88810i	−0.0572633	−	0.213709i	0.931366	−	0.364085i	$-0.118618\pi$
$331$	−1.04181	−	3.88810i	−0.0572633	−	0.213709i	−0.988629	+	0.150376i	$0.951952\pi$
$332$		0			0
$333$	0.241763	−	0.474486i	0.0132485	−	0.0260017i
$334$		0			0
$335$	4.81419	+	0.505992i	0.263027	+	0.0276453i
$336$		0			0
$337$	2.76141	−	8.49875i	0.150424	−	0.462956i	−0.847245	−	0.531202i	$-0.821740\pi$
$337$	2.76141	−	8.49875i	0.150424	−	0.462956i	0.997669	+	0.0682462i	$0.0217403\pi$
$338$		0			0
$339$	1.43424	−	1.04204i	0.0778972	−	0.0565956i
$340$		0			0
$341$	4.25439	+	12.4230i	0.230388	+	0.672746i
$342$		0			0
$343$	2.41082	+	0.381836i	0.130172	+	0.0206172i
$344$		0			0
$345$	−3.05162	+	58.2283i	−0.164293	+	3.13491i
$346$		0			0
$347$	1.74670	+	3.92316i	0.0937679	+	0.210606i	0.954340	−	0.298722i	$-0.0965605\pi$
$347$	1.74670	+	3.92316i	0.0937679	+	0.210606i	−0.860572	+	0.509329i	$0.829894\pi$
$348$		0			0
$349$	−0.128018	−	2.44273i	−0.00685266	−	0.130757i	−0.999913	−	0.0131546i	$-0.995813\pi$
$349$	−0.128018	−	2.44273i	−0.00685266	−	0.130757i	0.993061	−	0.117602i	$-0.0375207\pi$
$350$		0			0
$351$	−4.54579	−	4.46384i	−0.242636	−	0.238262i
$352$		0			0
$353$	19.0956	+	5.11666i	1.01636	+	0.272332i	0.728284	−	0.685276i	$-0.240318\pi$
$353$	19.0956	+	5.11666i	1.01636	+	0.272332i	0.288074	+	0.957608i	$0.406985\pi$
$354$		0			0
$355$	5.51201	−	25.9320i	0.292547	−	1.37633i
$356$		0			0
$357$	0.582584	−	1.51768i	0.0308336	−	0.0803244i
$358$		0			0
$359$	−10.3836	−	20.3790i	−0.548027	−	1.07556i	−0.984424	−	0.175809i	$-0.943746\pi$
$359$	−10.3836	−	20.3790i	−0.548027	−	1.07556i	0.436397	−	0.899754i	$-0.356254\pi$
$360$		0			0
$361$	−7.47856	+	16.7971i	−0.393608	+	0.884059i
$362$		0			0
$363$	−6.00257	−	24.4224i	−0.315053	−	1.28184i
$364$		0			0
$365$	−3.71474	−	5.11290i	−0.194438	−	0.267621i
$366$		0			0
$367$	−0.892510	+	0.189709i	−0.0465886	+	0.00990272i	−0.231147	−	0.972919i	$-0.574248\pi$
$367$	−0.892510	+	0.189709i	−0.0465886	+	0.00990272i	0.184558	+	0.982822i	$0.440915\pi$
$368$		0			0
$369$	4.12748	+	26.0599i	0.214868	+	1.35662i
$370$		0			0
$371$	−1.59484	+	1.03570i	−0.0828001	+	0.0537710i
$372$		0			0
$373$	−21.2026	−	12.2413i	−1.09783	−	0.633832i	−0.162179	−	0.986761i	$-0.551852\pi$
$373$	−21.2026	−	12.2413i	−1.09783	−	0.633832i	−0.935650	+	0.352930i	$0.885185\pi$
$374$		0			0
$375$	4.84615	−	18.0861i	0.250254	−	0.933961i
$376$		0			0
$377$	1.13450	+	18.4374i	0.0584296	+	0.949574i
$378$		0			0
$379$	−19.3639	−	23.9124i	−0.994657	−	1.22830i	−0.973539	−	0.228523i	$-0.926611\pi$
$379$	−19.3639	−	23.9124i	−0.994657	−	1.22830i	−0.0211188	−	0.999777i	$-0.506723\pi$
$380$		0			0
$381$	1.61843	+	1.79744i	0.0829145	+	0.0920859i
$382$		0			0
$383$	−3.60008	−	2.91529i	−0.183956	−	0.148964i	0.532919	−	0.846166i	$-0.321095\pi$
$383$	−3.60008	−	2.91529i	−0.183956	−	0.148964i	−0.716875	+	0.697202i	$0.754428\pi$
$384$		0			0
$385$	−1.68905	+	1.13518i	−0.0860820	+	0.0578540i
$386$		0			0
$387$	3.47071	+	1.54526i	0.176426	+	0.0785499i
$388$		0			0
$389$	5.92244	+	1.92432i	0.300279	+	0.0975667i	0.455282	−	0.890347i	$-0.349539\pi$
$389$	5.92244	+	1.92432i	0.300279	+	0.0975667i	−0.155002	+	0.987914i	$0.549539\pi$
$390$		0			0
$391$	17.3713	−	23.9095i	0.878502	−	1.20915i
$392$		0			0
$393$	17.9769	+	16.1865i	0.906814	+	0.816499i
$394$		0			0
$395$	16.5670	+	16.5670i	0.833576	+	0.833576i
$396$		0			0
$397$	−8.75253	+	2.34523i	−0.439277	+	0.117704i	−0.471678	−	0.881771i	$-0.656351\pi$
$397$	−8.75253	+	2.34523i	−0.439277	+	0.117704i	0.0324007	+	0.999475i	$0.489685\pi$
$398$		0			0
$399$	−2.38924	−	0.507848i	−0.119612	−	0.0254242i
$400$		0			0
$401$	−5.76870	+	4.67140i	−0.288075	+	0.233279i	−0.762454	−	0.647042i	$-0.776006\pi$
$401$	−5.76870	+	4.67140i	−0.288075	+	0.233279i	0.474379	+	0.880321i	$0.342673\pi$
$402$		0			0
$403$	4.28764	−	13.6161i	0.213583	−	0.678268i
$404$		0			0
$405$	35.1493	−	13.4926i	1.74659	−	0.670451i
$406$		0			0
$407$	0.789903	+	0.0704376i	0.0391541	+	0.00349146i
$408$		0			0
$409$	−0.235923	+	0.291341i	−0.0116657	+	0.0144059i	−0.782945	−	0.622090i	$-0.786284\pi$
$409$	−0.235923	+	0.291341i	−0.0116657	+	0.0144059i	0.771280	+	0.636496i	$0.219617\pi$
$410$		0			0
$411$	−3.37673	+	1.72053i	−0.166562	+	0.0848675i
$412$		0			0
$413$	0.0975017	−	0.927667i	0.00479775	−	0.0456475i
$414$		0			0
$415$	−4.05321	−	12.4745i	−0.198964	−	0.612349i
$416$		0			0
$417$		−	4.89976i		−	0.239942i
$418$		0			0
$419$	7.66947	+	13.2839i	0.374678	+	0.648962i	0.990279	−	0.139097i	$-0.0444199\pi$
$419$	7.66947	+	13.2839i	0.374678	+	0.648962i	−0.615601	+	0.788058i	$0.711087\pi$
$420$		0			0
$421$	−36.4446	−	18.5695i	−1.77620	−	0.905020i	−0.924735	−	0.380612i	$-0.875713\pi$
$421$	−36.4446	−	18.5695i	−1.77620	−	0.905020i	−0.851467	−	0.524408i	$-0.824287\pi$
$422$		0			0
$423$	−20.6669	−	7.93329i	−1.00486	−	0.385730i
$424$		0			0
$425$	−22.1736	+	19.9652i	−1.07558	+	0.968454i
$426$		0			0
$427$	0.0816499	+	0.212705i	0.00395131	+	0.0102935i
$428$		0			0
$429$	−10.4955	+	25.2453i	−0.506727	+	1.21885i
$430$		0			0
$431$	0.147884	+	0.385250i	0.00712331	+	0.0185569i	0.937096	−	0.349072i	$-0.113503\pi$
$431$	0.147884	+	0.385250i	0.00712331	+	0.0185569i	−0.929973	+	0.367629i	$0.880170\pi$
$432$		0			0
$433$	−13.9173	+	12.5312i	−0.668823	+	0.602211i	−0.931966	−	0.362546i	$-0.881908\pi$
$433$	−13.9173	+	12.5312i	−0.668823	+	0.602211i	0.263143	+	0.964757i	$0.415241\pi$
$434$		0			0
$435$	−38.4017	−	14.7410i	−1.84122	−	0.706779i
$436$		0			0
$437$	−39.5657	−	20.1597i	−1.89268	−	0.964371i
$438$		0			0
$439$	16.6762	+	28.8841i	0.795913	+	1.37856i	0.922258	+	0.386575i	$0.126342\pi$
$439$	16.6762	+	28.8841i	0.795913	+	1.37856i	−0.126345	+	0.991986i	$0.540325\pi$
$440$		0			0
$441$			15.5219i			0.739139i
$442$		0			0
$443$	−2.62935	−	8.09229i	−0.124924	−	0.384476i	0.868963	−	0.494877i	$-0.164787\pi$
$443$	−2.62935	−	8.09229i	−0.124924	−	0.384476i	−0.993887	+	0.110400i	$0.964787\pi$
$444$		0			0
$445$	−5.52621	+	52.5784i	−0.261968	+	2.49246i
$446$		0			0
$447$	−11.7570	+	5.99047i	−0.556085	+	0.283340i
$448$		0			0
$449$	−22.0819	+	27.2688i	−1.04211	+	1.28690i	−0.0852429	+	0.996360i	$0.527167\pi$
$449$	−22.0819	+	27.2688i	−1.04211	+	1.28690i	−0.956864	+	0.290535i	$0.906167\pi$
$450$		0			0
$451$	−33.7135	+	20.1805i	−1.58751	+	0.950264i
$452$		0			0
$453$	−28.1362	+	10.8005i	−1.32195	+	0.507451i
$454$		0			0
$455$	2.21029	+	0.0956874i	0.103620	+	0.00448589i
$456$		0			0
$457$	−18.7696	+	15.1994i	−0.878007	+	0.710996i	−0.958297	−	0.285776i	$-0.907749\pi$
$457$	−18.7696	+	15.1994i	−0.878007	+	0.710996i	0.0802896	+	0.996772i	$0.474416\pi$
$458$		0			0
$459$	−7.03357	−	1.49503i	−0.328299	−	0.0697821i
$460$		0			0
$461$	4.62137	−	1.23829i	0.215239	−	0.0576730i	−0.149588	−	0.988748i	$-0.547795\pi$
$461$	4.62137	−	1.23829i	0.215239	−	0.0576730i	0.364827	+	0.931075i	$0.381128\pi$
$462$		0			0
$463$	9.22687	+	9.22687i	0.428809	+	0.428809i	0.888223	−	0.459413i	$-0.151940\pi$
$463$	9.22687	+	9.22687i	0.428809	+	0.428809i	−0.459413	+	0.888223i	$0.651940\pi$
$464$		0			0
$465$	23.6231	+	21.2703i	1.09549	+	0.986387i
$466$		0			0
$467$	−5.81371	+	8.00188i	−0.269026	+	0.370283i	−0.922061	−	0.387045i	$-0.873496\pi$
$467$	−5.81371	+	8.00188i	−0.269026	+	0.370283i	0.653034	+	0.757328i	$0.273496\pi$
$468$		0			0
$469$	−0.229066	−	0.0744281i	−0.0105773	−	0.00343677i
$470$		0			0
$471$	15.9377	+	7.09591i	0.734369	+	0.326962i
$472$		0			0
$473$	−0.206897	+	5.65390i	−0.00951314	+	0.259967i
$474$		0			0
$475$	34.8410	+	28.2137i	1.59862	+	1.29453i
$476$		0			0
$477$	−16.2188	−	18.0128i	−0.742607	−	0.824749i
$478$		0			0
$479$	1.89028	+	2.33430i	0.0863691	+	0.106657i	0.818499	−	0.574508i	$-0.194807\pi$
$479$	1.89028	+	2.33430i	0.0863691	+	0.106657i	−0.732130	+	0.681165i	$0.761473\pi$
$480$		0			0
$481$	−0.645902	−	0.571022i	−0.0294506	−	0.0260364i
$482$		0			0
$483$	0.750882	−	2.80233i	0.0341663	−	0.127510i
$484$		0			0
$485$	−41.6170	−	24.0276i	−1.88973	−	1.09104i
$486$		0			0
$487$	−8.39006	+	5.44857i	−0.380190	+	0.246898i	−0.720559	−	0.693394i	$-0.756115\pi$
$487$	−8.39006	+	5.44857i	−0.380190	+	0.246898i	0.340369	+	0.940292i	$0.389448\pi$
$488$		0			0
$489$	4.84116	+	30.5659i	0.218925	+	1.38224i
$490$		0			0
$491$	29.1456	−	6.19509i	1.31532	−	0.279580i	0.503759	−	0.863844i	$-0.331950\pi$
$491$	29.1456	−	6.19509i	1.31532	−	0.279580i	0.811564	+	0.584264i	$0.198617\pi$
$492$		0			0
$493$	12.2546	+	16.8671i	0.551921	+	0.759655i
$494$		0			0
$495$	−17.6589	−	19.0004i	−0.793710	−	0.854006i
$496$		0			0
$497$	−0.536526	+	1.20506i	−0.0240665	+	0.0540542i
$498$		0			0
$499$	−8.92752	−	17.5213i	−0.399651	−	0.784359i	0.600230	−	0.799828i	$-0.295076\pi$
$499$	−8.92752	−	17.5213i	−0.399651	−	0.784359i	−0.999880	+	0.0154689i	$0.995076\pi$
$500$		0			0
$501$	4.90784	−	12.7854i	0.219266	−	0.571207i
$502$		0			0
$503$	2.56252	−	12.0557i	0.114257	−	0.537538i	−0.883369	−	0.468678i	$-0.844731\pi$
$503$	2.56252	−	12.0557i	0.114257	−	0.537538i	0.997626	−	0.0688599i	$-0.0219361\pi$
$504$		0			0
$505$	54.1844	+	14.5187i	2.41117	+	0.646072i
$506$		0			0
$507$	25.4653	−	15.3266i	1.13095	−	0.680679i
$508$		0			0
$509$	0.0539871	+	1.03013i	0.00239293	+	0.0456599i	0.999565	−	0.0294923i	$-0.00938906\pi$
$509$	0.0539871	+	1.03013i	0.00239293	+	0.0456599i	−0.997172	+	0.0751522i	$0.976056\pi$
$510$		0			0
$511$	0.127899	+	0.287267i	0.00565793	+	0.0127079i
$512$		0			0
$513$	−0.565454	+	10.7895i	−0.0249654	+	0.476368i
$514$		0			0
$515$	−35.9500	−	5.69391i	−1.58414	−	0.250904i
$516$		0			0
$517$	−0.520275	−	32.9626i	−0.0228817	−	1.44969i
$518$		0			0
$519$	−17.3436	+	12.6009i	−0.761300	+	0.553117i
$520$		0			0
$521$	6.09476	−	18.7578i	0.267016	−	0.821792i	−0.724206	−	0.689584i	$-0.757793\pi$
$521$	6.09476	−	18.7578i	0.267016	−	0.821792i	0.991222	−	0.132208i	$-0.0422067\pi$
$522$		0			0
$523$	7.44855	+	0.782874i	0.325702	+	0.0342327i	0.265969	−	0.963982i	$-0.414308\pi$
$523$	7.44855	+	0.782874i	0.325702	+	0.0342327i	0.0597335	+	0.998214i	$0.480975\pi$
$524$		0			0
$525$	−1.32976	+	2.60980i	−0.0580354	+	0.113901i
$526$		0			0
$527$	−4.17006	−	15.5629i	−0.181651	−	0.677929i
$528$		0			0
$529$	14.8711	−	25.7575i	0.646570	−	1.11989i
$530$		0			0
$531$	11.8731	−	0.622241i	0.515247	−	0.0270030i
$532$		0			0
$533$	42.5197	+	4.07837i	1.84173	+	0.176654i
$534$		0			0
$535$	54.1745	+	35.1813i	2.34217	+	1.52102i
$536$		0			0
$537$	60.2765	−	6.33531i	2.60112	−	0.273389i
$538$		0			0
$539$	−21.4464	+	8.62325i	−0.923762	+	0.371430i
$540$		0			0
$541$	−4.60043	+	29.0460i	−0.197788	+	1.24878i	0.666392	+	0.745601i	$0.267838\pi$
$541$	−4.60043	+	29.0460i	−0.197788	+	1.24878i	−0.864180	+	0.503182i	$0.832162\pi$
$542$		0			0
$543$	−4.49145	−	21.1306i	−0.192747	−	0.906802i
$544$		0			0
$545$	−12.4978	−	9.08020i	−0.535348	−	0.388953i
$546$		0			0
$547$	−10.2305	+	3.32409i	−0.437424	+	0.142128i	−0.519447	−	0.854503i	$-0.673862\pi$
$547$	−10.2305	+	3.32409i	−0.437424	+	0.142128i	0.0820226	+	0.996630i	$0.473862\pi$
$548$		0			0
$549$	−2.51500	+	1.45203i	−0.107338	+	0.0619713i
$550$		0			0
$551$	22.1510	−	22.1510i	0.943662	−	0.943662i
$552$		0			0
$553$	−0.634912	−	0.977678i	−0.0269992	−	0.0415751i
$554$		0			0
$555$	1.75379	−	0.780838i	0.0744443	−	0.0331447i
$556$		0			0
$557$	0.524865	−	0.808221i	0.0222393	−	0.0342454i	−0.827376	−	0.561648i	$-0.810167\pi$
$557$	0.524865	−	0.808221i	0.0222393	−	0.0342454i	0.849615	+	0.527403i	$0.176834\pi$
$558$		0			0
$559$	3.82704	−	4.81488i	0.161866	−	0.203648i
$560$		0			0
$561$	5.30758	+	30.3977i	0.224086	+	1.28339i
$562$		0			0
$563$	−4.58846	−	43.6563i	−0.193381	−	1.83989i	−0.474541	−	0.880234i	$-0.657386\pi$
$563$	−4.58846	−	43.6563i	−0.193381	−	1.83989i	0.281160	−	0.959661i	$-0.409281\pi$
$564$		0			0
$565$	2.71929	+	0.142512i	0.114401	+	0.00599552i
$566$		0			0
$567$	−1.85025	+	0.293051i	−0.0777034	+	0.0123070i
$568$		0			0
$569$	−15.7635	+	17.5071i	−0.660840	+	0.733937i	−0.976638	−	0.214889i	$-0.931061\pi$
$569$	−15.7635	+	17.5071i	−0.660840	+	0.733937i	0.315798	+	0.948826i	$0.397728\pi$
$570$		0			0
$571$	34.6847			1.45151			0.725755	−	0.687953i	$-0.241491\pi$
$571$	34.6847			1.45151			0.725755	+	0.687953i	$0.241491\pi$
$572$		0			0
$573$	−27.2252			−1.13735
$574$		0			0
$575$	−35.6303	+	39.5714i	−1.48589	+	1.65024i
$576$		0			0
$577$	−16.1938	+	2.56484i	−0.674155	+	0.106776i	−0.484120	−	0.875002i	$-0.660860\pi$
$577$	−16.1938	+	2.56484i	−0.674155	+	0.106776i	−0.190035	+	0.981777i	$0.560860\pi$
$578$		0			0
$579$	−7.24671	−	0.379784i	−0.301163	−	0.0157833i
$580$		0			0
$581$	0.0682177	+	0.649048i	0.00283015	+	0.0269271i
$582$		0			0
$583$	15.8776	−	32.4163i	0.657583	−	1.34255i
$584$		0			0
$585$	3.20256	+	28.0167i	0.132409	+	1.15835i
$586$		0			0
$587$	−8.52951	+	13.1343i	−0.352050	+	0.542110i	−0.969686	−	0.244354i	$-0.921424\pi$
$587$	−8.52951	+	13.1343i	−0.352050	+	0.542110i	0.617636	+	0.786464i	$0.288091\pi$
$588$		0			0
$589$	−22.1157	+	9.84656i	−0.911263	+	0.405720i
$590$		0			0
$591$	−15.5486	−	23.9428i	−0.639586	−	0.984875i
$592$		0			0
$593$	24.9487	−	24.9487i	1.02452	−	1.02452i	0.0248277	−	0.999692i	$-0.492096\pi$
$593$	24.9487	−	24.9487i	1.02452	−	1.02452i	0.999692	−	0.0248277i	$-0.00790370\pi$
$594$		0			0
$595$	2.16246	−	1.24849i	0.0886521	−	0.0511833i
$596$		0			0
$597$	3.88505	−	1.26233i	0.159004	−	0.0516636i
$598$		0			0
$599$	19.2778	+	14.0061i	0.787669	+	0.572275i	0.907271	−	0.420547i	$-0.138162\pi$
$599$	19.2778	+	14.0061i	0.787669	+	0.572275i	−0.119602	+	0.992822i	$0.538162\pi$
$600$		0			0
$601$	−3.42728	−	16.1241i	−0.139801	−	0.657714i	−0.991110	−	0.133048i	$-0.957524\pi$
$601$	−3.42728	−	16.1241i	−0.139801	−	0.657714i	0.851308	−	0.524666i	$-0.175810\pi$
$602$		0			0
$603$	0.480250	−	3.03218i	0.0195573	−	0.123480i
$604$		0			0
$605$	16.4421	−	34.9549i	0.668468	−	1.42112i
$606$		0			0
$607$	−33.3818	+	3.50857i	−1.35492	+	0.142408i	−0.753988	−	0.656888i	$-0.771872\pi$
$607$	−33.3818	+	3.50857i	−1.35492	+	0.142408i	−0.600937	+	0.799297i	$0.705206\pi$
$608$		0			0
$609$	1.71647	+	1.11469i	0.0695549	+	0.0451695i
$610$		0			0
$611$	−20.8008	+	29.1844i	−0.841510	+	1.18067i
$612$		0			0
$613$	21.8763	−	1.14649i	0.883575	−	0.0463062i	0.394851	−	0.918745i	$-0.370796\pi$
$613$	21.8763	−	1.14649i	0.883575	−	0.0463062i	0.488723	+	0.872439i	$0.337463\pi$
$614$		0			0
$615$	−47.5584	+	82.3736i	−1.91774	+	3.32162i
$616$		0			0
$617$	6.10373	+	22.7794i	0.245727	+	0.917065i	0.973017	+	0.230735i	$0.0741129\pi$
$617$	6.10373	+	22.7794i	0.245727	+	0.917065i	−0.727290	+	0.686330i	$0.759220\pi$
$618$		0			0
$619$	−1.71760	+	3.37098i	−0.0690361	+	0.135491i	−0.922945	−	0.384931i	$-0.874225\pi$
$619$	−1.71760	+	3.37098i	−0.0690361	+	0.135491i	0.853909	+	0.520422i	$0.174225\pi$
$620$		0			0
$621$	−12.7624	−	1.34138i	−0.512137	−	0.0538278i
$622$		0			0
$623$	0.812871	−	2.50176i	0.0325670	−	0.100231i
$624$		0			0
$625$	−6.39176	+	4.64389i	−0.255671	+	0.185756i
$626$		0			0
$627$	43.8638	−	15.0216i	1.75175	−	0.599904i
$628$		0			0
$629$	−0.961060	−	0.152217i	−0.0383200	−	0.00606929i
$630$		0			0
$631$	2.30342	−	43.9519i	0.0916978	−	1.74970i	−0.435711	−	0.900087i	$-0.643503\pi$
$631$	2.30342	−	43.9519i	0.0916978	−	1.74970i	0.527408	−	0.849612i	$-0.323164\pi$
$632$		0			0
$633$	−10.1719	−	22.8465i	−0.404298	−	0.908068i
$634$		0			0
$635$	0.194433	+	3.71000i	0.00771583	+	0.147227i
$636$		0			0
$637$	24.3307	+	6.28278i	0.964017	+	0.248933i
$638$		0			0
$639$	−16.2406	−	4.35165i	−0.642468	−	0.172149i
$640$		0			0
$641$	−5.47836	+	25.7737i	−0.216382	+	1.01800i	0.727089	+	0.686543i	$0.240873\pi$
$641$	−5.47836	+	25.7737i	−0.216382	+	1.01800i	−0.943471	+	0.331455i	$0.892461\pi$
$642$		0			0
$643$	−4.31756	+	11.2476i	−0.170268	+	0.443564i	−0.991989	−	0.126327i	$-0.959681\pi$
$643$	−4.31756	+	11.2476i	−0.170268	+	0.443564i	0.821721	+	0.569891i	$0.193014\pi$
$644$		0			0
$645$	6.21784	+	12.2032i	0.244827	+	0.480501i
$646$		0			0
$647$	−10.2275	+	22.9712i	−0.402083	+	0.903093i	0.593107	+	0.805124i	$0.297901\pi$
$647$	−10.2275	+	22.9712i	−0.402083	+	0.903093i	−0.995189	+	0.0979688i	$0.968765\pi$
$648$		0			0
$649$	7.45587	+	16.0592i	0.292668	+	0.630377i
$650$		0			0
$651$	−0.929667	−	1.27958i	−0.0364365	−	0.0501506i
$652$		0			0
$653$	30.3974	−	6.46117i	1.18954	−	0.252845i	0.429712	−	0.902966i	$-0.358615\pi$
$653$	30.3974	−	6.46117i	1.18954	−	0.252845i	0.759831	+	0.650121i	$0.225282\pi$
$654$		0			0
$655$	5.81247	+	36.6985i	0.227112	+	1.43393i
$656$		0			0
$657$	−3.36145	+	2.18295i	−0.131143	+	0.0851652i
$658$		0			0
$659$	−20.3661	−	11.7584i	−0.793350	−	0.458041i	0.0477907	−	0.998857i	$-0.484782\pi$
$659$	−20.3661	−	11.7584i	−0.793350	−	0.458041i	−0.841140	+	0.540817i	$0.818115\pi$
$660$		0			0
$661$	6.13994	−	22.9146i	0.238816	−	0.891273i	−0.737575	−	0.675265i	$-0.764029\pi$
$661$	6.13994	−	22.9146i	0.238816	−	0.891273i	0.976391	−	0.216009i	$-0.0693040\pi$
$662$		0			0
$663$	14.9570	−	30.0267i	0.580880	−	1.16614i
$664$		0			0
$665$	−2.36110	−	2.91571i	−0.0915595	−	0.113067i
$666$		0			0
$667$	24.8965	+	27.6504i	0.963997	+	1.07063i
$668$		0			0
$669$	23.8017	+	19.2743i	0.920229	+	0.745187i
$670$		0			0
$671$	−3.40347	−	2.66825i	−0.131390	−	0.103007i
$672$		0			0
$673$	−37.4375	−	16.6682i	−1.44311	−	0.642513i	−0.472097	−	0.881547i	$-0.656503\pi$
$673$	−37.4375	−	16.6682i	−1.44311	−	0.642513i	−0.971011	+	0.239033i	$0.923170\pi$
$674$		0			0
$675$	12.3218	+	4.00359i	0.474266	+	0.154098i
$676$		0			0
$677$	−1.73424	+	2.38698i	−0.0666522	+	0.0917389i	−0.841042	−	0.540970i	$-0.818057\pi$
$677$	−1.73424	+	2.38698i	−0.0666522	+	0.0917389i	0.774389	+	0.632709i	$0.218057\pi$
$678$		0			0
$679$	1.77689	+	1.59991i	0.0681906	+	0.0613991i
$680$		0			0
$681$	−43.5050	−	43.5050i	−1.66711	−	1.66711i
$682$		0			0
$683$	−31.7151	+	8.49805i	−1.21355	+	0.325169i	−0.808152	−	0.588973i	$-0.799532\pi$
$683$	−31.7151	+	8.49805i	−1.21355	+	0.325169i	−0.405394	+	0.914142i	$0.632866\pi$
$684$		0			0
$685$	−5.69386	−	1.21027i	−0.217551	−	0.0462420i
$686$		0			0
$687$	2.95016	−	2.38899i	0.112556	−	0.0911458i
$688$		0			0
$689$	−34.8000	+	18.1320i	−1.32577	+	0.690775i
$690$		0			0
$691$	−12.3259	+	4.73147i	−0.468900	+	0.179994i	−0.581333	−	0.813666i	$-0.697469\pi$
$691$	−12.3259	+	4.73147i	−0.468900	+	0.179994i	0.112434	+	0.993659i	$0.464135\pi$
$692$		0			0
$693$	0.662881	+	1.10741i	0.0251808	+	0.0420669i
$694$		0			0
$695$	4.73624	−	5.84877i	0.179656	−	0.221857i
$696$		0			0
$697$	42.9557	−	21.8870i	1.62706	−	0.829031i
$698$		0			0
$699$	−2.54071	+	24.1732i	−0.0960984	+	0.914315i
$700$		0			0
$701$	6.79035	+	20.8986i	0.256468	+	0.789328i	0.993537	+	0.113510i	$0.0362093\pi$
$701$	6.79035	+	20.8986i	0.256468	+	0.789328i	−0.737069	+	0.675818i	$0.763791\pi$
$702$		0			0
$703$			1.46203i			0.0551415i
$704$		0			0
$705$	−39.9024	−	69.1130i	−1.50281	−	2.60295i
$706$		0			0
$707$	−2.48689	−	1.26714i	−0.0935293	−	0.0476556i
$708$		0			0
$709$	14.7910	+	5.67773i	0.555487	+	0.213232i	0.619885	−	0.784693i	$-0.287179\pi$
$709$	14.7910	+	5.67773i	0.555487	+	0.213232i	−0.0643976	+	0.997924i	$0.520513\pi$
$710$		0			0
$711$	11.0423	−	9.94251i	0.414118	−	0.372873i
$712$		0			0
$713$	−10.3044	−	26.8438i	−0.385901	−	1.00531i
$714$		0			0
$715$	−36.9311	+	19.9897i	−1.38114	+	0.747573i
$716$		0			0
$717$	17.5303	+	45.6680i	0.654681	+	1.70550i
$718$		0			0
$719$	22.9007	−	20.6199i	0.854052	−	0.768992i	−0.120604	−	0.992701i	$-0.538483\pi$
$719$	22.9007	−	20.6199i	0.854052	−	0.768992i	0.974656	+	0.223709i	$0.0718165\pi$
$720$		0			0
$721$	1.69074	+	0.649013i	0.0629663	+	0.0241705i
$722$		0			0
$723$	49.5269	+	25.2352i	1.84193	+	0.938509i
$724$		0			0
$725$	−18.7823	−	32.5318i	−0.697556	−	1.20820i
$726$		0			0
$727$			23.4551i			0.869901i	0.900454	+	0.434950i	$0.143234\pi$
$727$			23.4551i			0.869901i	−0.900454	+	0.434950i	$0.856766\pi$
$728$		0			0
$729$	−3.63342	−	11.1825i	−0.134571	−	0.414168i
$730$		0			0
$731$	0.725622	−	6.90383i	0.0268381	−	0.255347i
$732$		0			0
$733$	21.2825	−	10.8440i	0.786085	−	0.400530i	−0.0143898	−	0.999896i	$-0.504581\pi$
$733$	21.2825	−	10.8440i	0.786085	−	0.400530i	0.800475	+	0.599366i	$0.204581\pi$
$734$		0			0
$735$	−35.2145	+	43.4863i	−1.29891	+	1.60402i
$736$		0			0
$737$	4.45633	−	1.02098i	0.164151	−	0.0376085i
$738$		0			0
$739$	36.6480	−	14.0678i	1.34812	−	0.517494i	0.426112	−	0.904670i	$-0.359883\pi$
$739$	36.6480	−	14.0678i	1.34812	−	0.517494i	0.922006	+	0.387177i	$0.126550\pi$
$740$		0			0
$741$	−48.0764	−	15.1390i	−1.76613	−	0.556144i
$742$		0			0
$743$	−25.2722	+	20.4650i	−0.927145	+	0.750788i	−0.968670	−	0.248350i	$-0.920112\pi$
$743$	−25.2722	+	20.4650i	−0.927145	+	0.750788i	0.0415249	+	0.999137i	$0.486778\pi$
$744$		0			0
$745$	−19.8247	−	4.21386i	−0.726320	−	0.154384i
$746$		0			0
$747$	−8.03503	+	2.15298i	−0.293986	+	0.0787734i
$748$		0			0
$749$	−2.27266	−	2.27266i	−0.0830412	−	0.0830412i
$750$		0			0
$751$	−12.0396	−	10.8405i	−0.439333	−	0.395577i	0.419564	−	0.907726i	$-0.362183\pi$
$751$	−12.0396	−	10.8405i	−0.439333	−	0.395577i	−0.858897	+	0.512149i	$0.828850\pi$
$752$		0			0
$753$	17.5094	−	24.0996i	0.638079	−	0.878240i
$754$		0			0
$755$	−44.0258	−	14.3048i	−1.60226	−	0.520607i
$756$		0			0
$757$	−30.0600	−	13.3836i	−1.09255	−	0.486434i	−0.220267	−	0.975440i	$-0.570693\pi$
$757$	−30.0600	−	13.3836i	−1.09255	−	0.486434i	−0.872280	+	0.489006i	$0.837360\pi$
$758$		0			0
$759$	15.0906	+	52.9610i	0.547754	+	1.92236i
$760$		0			0
$761$	3.68963	+	2.98780i	0.133749	+	0.108308i	0.693861	−	0.720109i	$-0.255908\pi$
$761$	3.68963	+	2.98780i	0.133749	+	0.108308i	−0.560112	+	0.828417i	$0.689242\pi$
$762$		0			0
$763$	0.514320	+	0.571210i	0.0186196	+	0.0206792i
$764$		0			0
$765$	20.0295	+	24.7343i	0.724167	+	0.894272i
$766$		0			0
$767$	3.83048	−	18.8630i	0.138311	−	0.681102i
$768$		0			0
$769$	−7.85523	+	29.3161i	−0.283267	+	1.05717i	0.666829	+	0.745210i	$0.267651\pi$
$769$	−7.85523	+	29.3161i	−0.283267	+	1.05717i	−0.950096	+	0.311956i	$0.899016\pi$
$770$		0			0
$771$	−14.1334	−	8.15992i	−0.509002	−	0.293872i
$772$		0			0
$773$	24.0379	−	15.6104i	0.864582	−	0.561466i	−0.0344217	−	0.999407i	$-0.510959\pi$
$773$	24.0379	−	15.6104i	0.864582	−	0.561466i	0.899004	+	0.437941i	$0.144292\pi$
$774$		0			0
$775$	4.54124	+	28.6722i	0.163126	+	1.02994i
$776$		0			0
$777$	−0.0934325	+	0.0198597i	−0.00335187	+	0.000712463i
$778$		0			0
$779$	−42.5779	−	58.6035i	−1.52551	−	2.09969i
$780$		0			0
$781$	−3.00990	−	24.8570i	−0.107703	−	0.889452i
$782$		0			0
$783$	3.68214	−	8.27022i	0.131589	−	0.295554i
$784$		0			0
$785$	12.1655	+	23.8761i	0.434204	+	0.852174i
$786$		0			0
$787$	4.33955	−	11.3049i	0.154688	−	0.402977i	−0.834234	−	0.551411i	$-0.814090\pi$
$787$	4.33955	−	11.3049i	0.154688	−	0.402977i	0.988922	+	0.148434i	$0.0474231\pi$
$788$		0			0
$789$	−2.01155	+	9.46359i	−0.0716130	+	0.336913i
$790$		0			0
$791$	−0.130870	−	0.0350666i	−0.00465321	−	0.00124682i
$792$		0			0
$793$	1.25808	+	4.53001i	0.0446758	+	0.160865i
$794$		0			0
$795$	−4.57312	−	87.2603i	−0.162192	−	3.09480i
$796$		0			0
$797$	−9.16067	−	20.5752i	−0.324488	−	0.728811i	0.675476	−	0.737382i	$-0.263938\pi$
$797$	−9.16067	−	20.5752i	−0.324488	−	0.728811i	−0.999963	+	0.00857132i	$0.997272\pi$
$798$		0			0
$799$	−2.11696	+	40.3940i	−0.0748926	+	1.42904i
$800$		0			0
$801$	33.1161	+	5.24508i	1.17010	+	0.185326i
$802$		0			0
$803$	−4.88363	−	3.43173i	−0.172339	−	0.121103i
$804$		0			0
$805$	3.60512	−	2.61928i	0.127064	−	0.0923174i
$806$		0			0
$807$	−7.99518	+	24.6066i	−0.281444	+	0.866195i
$808$		0			0
$809$	53.8065	+	5.65529i	1.89174	+	0.198829i	0.978162	−	0.207845i	$-0.0666449\pi$
$809$	53.8065	+	5.65529i	1.89174	+	0.198829i	0.913573	+	0.406674i	$0.133312\pi$
$810$		0			0
$811$	−8.33176	+	16.3520i	−0.292568	+	0.574196i	−0.989769	−	0.142679i	$-0.954428\pi$
$811$	−8.33176	+	16.3520i	−0.292568	+	0.574196i	0.697201	+	0.716875i	$0.254428\pi$
$812$		0			0
$813$	−13.8093	−	51.5371i	−0.484315	−	1.80749i
$814$		0			0
$815$	−23.7670	+	41.1656i	−0.832521	+	1.44197i
$816$		0			0
$817$	−10.4161	+	0.545885i	−0.364414	+	0.0190981i
$818$		0			0
$819$	0.133965	−	1.39667i	0.00468110	−	0.0488035i
$820$		0			0
$821$	−1.41521	−	0.919046i	−0.0493911	−	0.0320749i	0.519707	−	0.854344i	$-0.326041\pi$
$821$	−1.41521	−	0.919046i	−0.0493911	−	0.0320749i	−0.569098	+	0.822269i	$0.692708\pi$
$822$		0			0
$823$	28.1857	−	2.96243i	0.982490	−	0.103264i	0.400359	−	0.916358i	$-0.368886\pi$
$823$	28.1857	−	2.96243i	0.982490	−	0.103264i	0.582132	+	0.813095i	$0.302219\pi$
$824$		0			0
$825$	−3.78563	−	55.4687i	−0.131799	−	1.93117i
$826$		0			0
$827$	3.38244	−	21.3559i	0.117619	−	0.742618i	−0.856427	−	0.516268i	$-0.827321\pi$
$827$	3.38244	−	21.3559i	0.117619	−	0.742618i	0.974046	−	0.226350i	$-0.0726792\pi$
$828$		0			0
$829$	9.75621	+	45.8994i	0.338847	+	1.59415i	0.736383	+	0.676564i	$0.236532\pi$
$829$	9.75621	+	45.8994i	0.338847	+	1.59415i	−0.397536	+	0.917586i	$0.630135\pi$
$830$		0			0
$831$	−50.9602	−	37.0248i	−1.76779	−	1.28438i
$832$		0			0
$833$	26.9736	−	8.76426i	0.934581	−	0.303664i
$834$		0			0
$835$	18.2171	−	10.5176i	0.630428	−	0.363978i
$836$		0			0
$837$	−4.94693	+	4.94693i	−0.170991	+	0.170991i
$838$		0			0
$839$	9.65488	+	14.8672i	0.333323	+	0.513273i	0.965101	−	0.261876i	$-0.0843413\pi$
$839$	9.65488	+	14.8672i	0.333323	+	0.513273i	−0.631778	+	0.775149i	$0.717675\pi$
$840$		0			0
$841$	2.51402	−	1.11932i	0.0866905	−	0.0385971i
$842$		0			0
$843$	32.8916	−	50.6487i	1.13285	−	1.74443i
$844$		0			0
$845$	45.2126	+	6.32026i	1.55536	+	0.217423i
$846$		0			0
$847$	−1.16182	+	1.53112i	−0.0399207	+	0.0526098i
$848$		0			0
$849$	−5.35765	−	50.9746i	−0.183874	−	1.74944i
$850$		0			0
$851$	−1.73413	−	0.0908818i	−0.0594451	−	0.00311539i
$852$		0			0
$853$	−25.5198	+	4.04193i	−0.873780	+	0.138393i	−0.577188	−	0.816611i	$-0.695850\pi$
$853$	−25.5198	+	4.04193i	−0.873780	+	0.138393i	−0.296592	+	0.955004i	$0.595850\pi$
$854$		0			0
$855$	31.9988	−	35.5383i	1.09434	−	1.21538i
$856$		0			0
$857$	20.4701			0.699247			0.349623	−	0.936890i	$-0.386310\pi$
$857$	20.4701			0.699247			0.349623	+	0.936890i	$0.386310\pi$
$858$		0			0
$859$	24.2013			0.825738			0.412869	−	0.910790i	$-0.364527\pi$
$859$	24.2013			0.825738			0.412869	+	0.910790i	$0.364527\pi$
$860$		0			0
$861$	3.16675	−	3.51703i	0.107923	−	0.119860i
$862$		0			0
$863$	37.8287	−	5.99148i	1.28770	−	0.203952i	0.525224	−	0.850964i	$-0.323982\pi$
$863$	37.8287	−	5.99148i	1.28770	−	0.203952i	0.762480	+	0.647012i	$0.223982\pi$
$864$		0			0
$865$	−32.8831	−	1.72333i	−1.11806	−	0.0585951i
$866$		0			0
$867$	0.105094	+	0.999907i	0.00356920	+	0.0339586i
$868$		0			0
$869$	19.8720	+	9.73336i	0.674112	+	0.330182i
$870$		0			0
$871$	−4.55857	−	1.98013i	−0.154461	−	0.0670941i
$872$		0			0
$873$	−16.5988	+	25.5598i	−0.561783	+	0.865070i
$874$		0			0
$875$	−1.30727	+	0.582032i	−0.0441936	+	0.0196763i
$876$		0			0
$877$	−9.78930	−	15.0742i	−0.330561	−	0.509019i	0.633840	−	0.773464i	$-0.281478\pi$
$877$	−9.78930	−	15.0742i	−0.330561	−	0.509019i	−0.964401	+	0.264445i	$0.914811\pi$
$878$		0			0
$879$	22.5283	−	22.5283i	0.759861	−	0.759861i
$880$		0			0
$881$	14.7907	−	8.53939i	0.498310	−	0.287699i	−0.229705	−	0.973260i	$-0.573776\pi$
$881$	14.7907	−	8.53939i	0.498310	−	0.287699i	0.728015	+	0.685561i	$0.240443\pi$
$882$		0			0
$883$	45.3079	−	14.7214i	1.52473	−	0.495415i	0.577616	−	0.816309i	$-0.303983\pi$
$883$	45.3079	−	14.7214i	1.52473	−	0.495415i	0.947115	+	0.320894i	$0.103983\pi$
$884$		0			0
$885$	34.6754	+	25.1931i	1.16560	+	0.846858i
$886$		0			0
$887$	4.62467	+	21.7574i	0.155281	+	0.730541i	0.985027	+	0.172399i	$0.0551520\pi$
$887$	4.62467	+	21.7574i	0.155281	+	0.730541i	−0.829746	+	0.558141i	$0.811515\pi$
$888$		0			0
$889$	0.0289166	−	0.182572i	0.000969832	−	0.00612328i
$890$		0			0
$891$	27.2775	−	22.8110i	0.913831	−	0.764197i
$892$		0			0
$893$	60.4438	−	6.35290i	2.02268	−	0.212592i
$894$		0			0
$895$	78.0750	+	50.7025i	2.60976	+	1.69480i
$896$		0			0
$897$	20.9450	−	56.0828i	0.699332	−	1.87255i
$898$		0			0
$899$	20.2565	−	1.06160i	0.675594	−	0.0354064i
$900$		0			0
$901$	−22.1445	+	38.3554i	−0.737739	+	1.27780i
$902$		0			0
$903$	−0.176374	−	0.658237i	−0.00586936	−	0.0219048i
$904$		0			0
$905$	15.0641	−	29.5649i	0.500746	−	0.982769i
$906$		0			0
$907$	6.07103	+	0.638091i	0.201585	+	0.0211875i	0.204783	−	0.978807i	$-0.434351\pi$
$907$	6.07103	+	0.638091i	0.201585	+	0.0211875i	−0.00319766	+	0.999995i	$0.501018\pi$
$908$		0			0
$909$	10.9936	−	33.8348i	0.364634	−	1.12223i
$910$		0			0
$911$	−17.4600	+	12.6854i	−0.578476	+	0.420288i	−0.838174	−	0.545402i	$-0.816377\pi$
$911$	−17.4600	+	12.6854i	−0.578476	+	0.420288i	0.259698	+	0.965690i	$0.416377\pi$
$912$		0			0
$913$	−7.43863	−	9.90578i	−0.246183	−	0.327834i
$914$		0			0
$915$	−10.3403	−	1.63774i	−0.341839	−	0.0541420i
$916$		0			0
$917$	0.0967551	−	1.84620i	0.00319514	−	0.0609668i
$918$		0			0
$919$	−17.6132	−	39.5598i	−0.581005	−	1.30496i	−0.929906	−	0.367798i	$-0.880112\pi$
$919$	−17.6132	−	39.5598i	−0.581005	−	1.30496i	0.348901	−	0.937160i	$-0.386555\pi$
$920$		0			0
$921$	1.11059	+	21.1913i	0.0365951	+	0.698277i
$922$		0			0
$923$	−13.3949	+	23.6958i	−0.440899	+	0.779957i
$924$		0			0
$925$	1.69344	+	0.453757i	0.0556801	+	0.0149194i
$926$		0			0
$927$	−4.79937	+	22.5793i	−0.157632	+	0.741600i
$928$		0			0
$929$	−3.03990	+	7.91922i	−0.0997360	+	0.259821i	−0.974366	−	0.224971i	$-0.927771\pi$
$929$	−3.03990	+	7.91922i	−0.0997360	+	0.259821i	0.874629	+	0.484792i	$0.161105\pi$
$930$		0			0
$931$	−19.3466	−	37.9699i	−0.634060	−	1.24441i
$932$		0			0
$933$	4.95877	−	11.1376i	0.162343	−	0.364628i
$934$		0			0
$935$	−23.0476	+	41.4157i	−0.753738	+	1.35444i
$936$		0			0
$937$	10.9480	+	15.0687i	0.357656	+	0.492272i	0.949494	−	0.313785i	$-0.101597\pi$
$937$	10.9480	+	15.0687i	0.357656	+	0.492272i	−0.591837	+	0.806057i	$0.701597\pi$
$938$		0			0
$939$	−51.2412	+	10.8917i	−1.67219	+	0.355436i
$940$		0			0
$941$	8.10506	+	51.1733i	0.264217	+	1.66820i	0.661073	+	0.750322i	$0.270102\pi$
$941$	8.10506	+	51.1733i	0.264217	+	1.66820i	−0.396855	+	0.917881i	$0.629898\pi$
$942$		0			0
$943$	72.1568	−	46.8592i	2.34975	−	1.52595i
$944$		0			0
$945$	−0.938972	−	0.542116i	−0.0305447	−	0.0176350i
$946$		0			0
$947$	−10.2810	+	38.3690i	−0.334086	+	1.24683i	0.570770	+	0.821110i	$0.306645\pi$
$947$	−10.2810	+	38.3690i	−0.334086	+	1.24683i	−0.904856	+	0.425717i	$0.860022\pi$
$948$		0			0
$949$	2.06118	+	6.15269i	0.0669088	+	0.199725i
$950$		0			0
$951$	−50.5631	−	62.4402i	−1.63962	−	2.02476i
$952$		0			0
$953$	13.1093	+	14.5593i	0.424651	+	0.471623i	0.917065	−	0.398739i	$-0.130552\pi$
$953$	13.1093	+	14.5593i	0.424651	+	0.471623i	−0.492414	+	0.870361i	$0.663885\pi$
$954$		0			0
$955$	−32.4983	−	26.3166i	−1.05162	−	0.851586i
$956$		0			0
$957$	−38.8227	−	1.42067i	−1.25496	−	0.0459236i
$958$		0			0
$959$	0.264593	+	0.117804i	0.00854416	+	0.00380410i
$960$		0			0
$961$	14.5743	+	4.73549i	0.470140	+	0.152758i
$962$		0			0
$963$	24.0796	−	33.1427i	0.775954	−	1.06801i
$964$		0			0
$965$	−8.28318	−	7.45820i	−0.266645	−	0.240088i
$966$		0			0
$967$	−28.9895	−	28.9895i	−0.932239	−	0.932239i	0.0656066	−	0.997846i	$-0.479102\pi$
$967$	−28.9895	−	28.9895i	−0.932239	−	0.932239i	−0.997846	+	0.0656066i	$0.979102\pi$
$968$		0			0
$969$	−54.9500	+	14.7238i	−1.76525	+	0.472997i
$970$		0			0
$971$	−23.1400	−	4.91857i	−0.742599	−	0.157844i	−0.178949	−	0.983858i	$-0.557270\pi$
$971$	−23.1400	−	4.91857i	−0.742599	−	0.157844i	−0.563650	+	0.826014i	$0.690603\pi$
$972$		0			0
$973$	−0.291012	+	0.235657i	−0.00932941	+	0.00755481i
$974$		0			0
$975$	−32.4562	+	50.9875i	−1.03943	+	1.63291i
$976$		0			0
$977$	29.6976	−	11.3999i	0.950111	−	0.364714i	0.166553	−	0.986032i	$-0.446736\pi$
$977$	29.6976	−	11.3999i	0.950111	−	0.364714i	0.783558	+	0.621319i	$0.213403\pi$
$978$		0			0
$979$	11.1507	+	48.6700i	0.356379	+	1.55550i
$980$		0			0
$981$	−6.16560	+	7.61388i	−0.196852	+	0.243092i
$982$		0			0
$983$	−6.29407	+	3.20699i	−0.200750	+	0.102287i	−0.551475	−	0.834191i	$-0.685935\pi$
$983$	−6.29407	+	3.20699i	−0.200750	+	0.102287i	0.350726	+	0.936478i	$0.385935\pi$
$984$		0			0
$985$	4.58359	−	43.6099i	0.146045	−	1.38953i
$986$		0			0
$987$	1.22704	+	3.77643i	0.0390570	+	0.120205i
$988$		0			0
$989$		−	12.3886i		−	0.393934i
$990$		0			0
$991$	19.4333	+	33.6595i	0.617319	+	1.06923i	0.989973	+	0.141258i	$0.0451146\pi$
$991$	19.4333	+	33.6595i	0.617319	+	1.06923i	−0.372654	+	0.927971i	$0.621552\pi$
$992$		0			0
$993$	−8.19986	−	4.17804i	−0.260215	−	0.132586i
$994$		0			0
$995$	5.85772	+	2.24857i	0.185702	+	0.0712844i
$996$		0			0
$997$	−10.7804	+	9.70675i	−0.341420	+	0.307416i	−0.821947	−	0.569564i	$-0.807112\pi$
$997$	−10.7804	+	9.70675i	−0.341420	+	0.307416i	0.480527	+	0.876980i	$0.340445\pi$
$998$		0			0
$999$	0.151414	+	0.394446i	0.00479052	+	0.0124797i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.bv.a.41.13	✓	224
11.7	odd	10	inner	572.2.bv.a.249.2	yes	224
13.7	odd	12	inner	572.2.bv.a.85.2	yes	224
143.7	even	60	inner	572.2.bv.a.293.13	yes	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.bv.a.41.13	✓	224	1.1	even	1	trivial
572.2.bv.a.85.2	yes	224	13.7	odd	12	inner
572.2.bv.a.249.2	yes	224	11.7	odd	10	inner
572.2.bv.a.293.13	yes	224	143.7	even	60	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.bv (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(1.52983 - 1.69905i) q^{3} +(3.46848 - 0.549353i) q^{5} +(-0.174489 - 0.00914460i) q^{7} +(-0.232798 - 2.21493i) q^{9} +O(q^{10})\)	\(q+(1.52983 - 1.69905i) q^{3} +(3.46848 - 0.549353i) q^{5} +(-0.174489 - 0.00914460i) q^{7} +(-0.232798 - 2.21493i) q^{9} +(2.93100 - 1.55217i) q^{11} +(-3.56614 - 0.531621i) q^{13} +(4.37280 - 6.73352i) q^{15} +(-3.71761 + 1.65519i) q^{17} +(3.33018 + 5.12803i) q^{19} +(-0.282476 + 0.282476i) q^{21} +(-6.28941 + 3.63119i) q^{23} +(6.97326 - 2.26575i) q^{25} +(1.42954 + 1.03862i) q^{27} +(-1.06519 - 5.01133i) q^{29} +(-0.619362 + 3.91050i) q^{31} +(1.84673 - 7.35446i) q^{33} +(-0.610236 + 0.0641384i) q^{35} +(0.200534 + 0.130229i) q^{37} +(-6.35883 + 5.24575i) q^{39} +(-11.8307 + 0.620022i) q^{41} +(-0.852928 + 1.47731i) q^{43} +(-2.02423 - 7.55454i) q^{45} +(4.51259 - 8.85645i) q^{47} +(-6.93129 - 0.728508i) q^{49} +(-2.87506 + 8.84853i) q^{51} +(8.80480 - 6.39706i) q^{53} +(9.31343 - 6.99381i) q^{55} +(13.8073 + 2.18687i) q^{57} +(-0.279392 + 5.33111i) q^{59} +(-0.530365 - 1.19122i) q^{61} +(0.0203662 + 0.388610i) q^{63} +(-12.6611 + 0.115157i) q^{65} +(1.33148 + 0.356768i) q^{67} +(-3.45215 + 16.2411i) q^{69} +(2.70546 - 7.04797i) q^{71} +(-0.817028 - 1.60351i) q^{73} +(6.81827 - 15.3141i) q^{75} +(-0.525623 + 0.244034i) q^{77} +(3.92156 + 5.39756i) q^{79} +(10.4870 - 2.22908i) q^{81} +(-0.584293 - 3.68908i) q^{83} +(-11.9852 + 7.78325i) q^{85} +(-10.1440 - 5.85666i) q^{87} +(-3.89646 + 14.5418i) q^{89} +(0.617393 + 0.125373i) q^{91} +(5.69660 + 7.03472i) q^{93} +(14.3677 + 15.9570i) q^{95} +(-10.6347 - 8.61178i) q^{97} +(-4.12027 - 6.13062i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q + 28 q^{9}+O(q^{10}) \) 224 * q + 28 * q^9	\( 224 q + 28 q^{9} + 16 q^{11} + 10 q^{13} - 28 q^{15} - 48 q^{23} + 24 q^{27} + 20 q^{29} + 4 q^{31} + 60 q^{33} + 50 q^{35} + 12 q^{37} - 40 q^{39} + 20 q^{41} + 64 q^{45} - 62 q^{47} + 100 q^{53} - 22 q^{55} + 12 q^{59} - 40 q^{61} - 80 q^{63} - 44 q^{67} - 152 q^{71} + 30 q^{73} - 120 q^{75} + 80 q^{79} + 72 q^{81} + 90 q^{83} - 40 q^{85} - 8 q^{89} - 36 q^{91} - 90 q^{93} - 42 q^{97} + 144 q^{99}+O(q^{100}) \) 224 * q + 28 * q^9 + 16 * q^11 + 10 * q^13 - 28 * q^15 - 48 * q^23 + 24 * q^27 + 20 * q^29 + 4 * q^31 + 60 * q^33 + 50 * q^35 + 12 * q^37 - 40 * q^39 + 20 * q^41 + 64 * q^45 - 62 * q^47 + 100 * q^53 - 22 * q^55 + 12 * q^59 - 40 * q^61 - 80 * q^63 - 44 * q^67 - 152 * q^71 + 30 * q^73 - 120 * q^75 + 80 * q^79 + 72 * q^81 + 90 * q^83 - 40 * q^85 - 8 * q^89 - 36 * q^91 - 90 * q^93 - 42 * q^97 + 144 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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