LMFDB - Embedded newform 572.2.bg.a.9.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(9,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 18, 20]))

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

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

chi := DirichletCharacter("572.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.bg (of order $15$, 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 $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			9.2
Character	$\chi$	$=$	572.9
Dual form			572.2.bg.a.445.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.263130 - 2.50351i) q^{3} +(1.21356 + 3.73495i) q^{5} +(0.197160 - 1.87585i) q^{7} +(-3.26389 + 0.693762i) q^{9} +O(q^{10})$	\(q+(-0.263130 - 2.50351i) q^{3} +(1.21356 + 3.73495i) q^{5} +(0.197160 - 1.87585i) q^{7} +(-3.26389 + 0.693762i) q^{9} +(-2.77810 - 1.81167i) q^{11} +(1.36372 - 3.33770i) q^{13} +(9.03117 - 4.02094i) q^{15} +(2.98366 - 3.31369i) q^{17} +(5.17517 + 2.30413i) q^{19} -4.74809 q^{21} +(4.21964 - 7.30862i) q^{23} +(-8.43205 + 6.12624i) q^{25} +(0.262002 + 0.806360i) q^{27} +(5.17932 - 2.30598i) q^{29} +(-0.0487528 + 0.150046i) q^{31} +(-3.80454 + 7.43172i) q^{33} +(7.24547 - 1.54007i) q^{35} +(-9.28006 + 4.13175i) q^{37} +(-8.71482 - 2.53584i) q^{39} +(0.403536 + 3.83939i) q^{41} +(-1.71835 - 2.97627i) q^{43} +(-6.55210 - 11.3486i) q^{45} +(0.916824 - 0.666111i) q^{47} +(3.36709 + 0.715698i) q^{49} +(-9.08095 - 6.59770i) q^{51} +(3.61632 - 11.1299i) q^{53} +(3.39511 - 12.5746i) q^{55} +(4.40668 - 13.5624i) q^{57} +(-0.555488 + 5.28512i) q^{59} +(-9.59465 + 10.6559i) q^{61} +(0.657885 + 6.25936i) q^{63} +(14.1211 + 1.04293i) q^{65} +(-2.84792 + 4.93273i) q^{67} +(-19.4075 - 8.64079i) q^{69} +(-1.78658 + 1.98420i) q^{71} +(-0.671988 - 0.488228i) q^{73} +(17.5558 + 19.4977i) q^{75} +(-3.94615 + 4.85411i) q^{77} +(-2.15248 + 6.62465i) q^{79} +(-7.19520 + 3.20351i) q^{81} +(3.36285 + 10.3498i) q^{83} +(15.9973 + 7.12246i) q^{85} +(-7.13589 - 12.3597i) q^{87} +(0.622905 - 1.07890i) q^{89} +(-5.99216 - 3.21620i) q^{91} +(0.388469 + 0.0825717i) q^{93} +(-2.32545 + 22.1252i) q^{95} +(12.3361 - 2.62212i) q^{97} +(10.3243 + 3.98576i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q + 8 q^{9}+O(q^{10}) $ 112 * q + 8 * q^9	$ 112 q + 8 q^{9} - 10 q^{11} + 11 q^{13} - 2 q^{15} + 4 q^{17} - 12 q^{19} - 40 q^{21} + 10 q^{23} - 16 q^{25} - 12 q^{27} + q^{29} + 4 q^{31} + 35 q^{33} - 5 q^{35} - 12 q^{37} + 21 q^{39} - 10 q^{41} - 32 q^{43} + 34 q^{45} + 70 q^{47} + 16 q^{49} - 48 q^{51} - 26 q^{53} + 10 q^{55} - 12 q^{57} - 5 q^{59} + 28 q^{61} + 34 q^{63} + 22 q^{65} - 68 q^{67} - 58 q^{69} + 44 q^{71} + 42 q^{73} - 24 q^{75} + 46 q^{77} - 24 q^{79} + 64 q^{81} - 114 q^{83} + 4 q^{85} - 30 q^{87} - 6 q^{89} + 77 q^{91} - 5 q^{93} - 36 q^{95} - 15 q^{97} - 40 q^{99}+O(q^{100}) $ 112 * q + 8 * q^9 - 10 * q^11 + 11 * q^13 - 2 * q^15 + 4 * q^17 - 12 * q^19 - 40 * q^21 + 10 * q^23 - 16 * q^25 - 12 * q^27 + q^29 + 4 * q^31 + 35 * q^33 - 5 * q^35 - 12 * q^37 + 21 * q^39 - 10 * q^41 - 32 * q^43 + 34 * q^45 + 70 * q^47 + 16 * q^49 - 48 * q^51 - 26 * q^53 + 10 * q^55 - 12 * q^57 - 5 * q^59 + 28 * q^61 + 34 * q^63 + 22 * q^65 - 68 * q^67 - 58 * q^69 + 44 * q^71 + 42 * q^73 - 24 * q^75 + 46 * q^77 - 24 * q^79 + 64 * q^81 - 114 * q^83 + 4 * q^85 - 30 * q^87 - 6 * q^89 + 77 * q^91 - 5 * q^93 - 36 * q^95 - 15 * q^97 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{5}\right)$

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
$3$	−0.263130	−	2.50351i	−0.151918	−	1.44540i	−0.759169	−	0.650894i	$-0.774394\pi$
$3$	−0.263130	−	2.50351i	−0.151918	−	1.44540i	0.607251	−	0.794510i	$-0.292272\pi$
$4$		0			0
$5$	1.21356	+	3.73495i	0.542720	+	1.67032i	0.726350	+	0.687325i	$0.241215\pi$
$5$	1.21356	+	3.73495i	0.542720	+	1.67032i	−0.183629	+	0.982996i	$0.558785\pi$
$6$		0			0
$7$	0.197160	−	1.87585i	0.0745194	−	0.709005i	−0.891935	−	0.452165i	$-0.850652\pi$
$7$	0.197160	−	1.87585i	0.0745194	−	0.709005i	0.966454	−	0.256840i	$-0.0826814\pi$
$8$		0			0
$9$	−3.26389	+	0.693762i	−1.08796	+	0.231254i
$10$		0			0
$11$	−2.77810	−	1.81167i	−0.837629	−	0.546239i
$11$	−2.77810	−	1.81167i	−0.837629	−	0.546239i
$12$		0			0
$13$	1.36372	−	3.33770i	0.378228	−	0.925712i
$13$	1.36372	−	3.33770i	0.378228	−	0.925712i
$14$		0			0
$15$	9.03117	−	4.02094i	2.33184	−	1.03820i
$16$		0			0
$17$	2.98366	−	3.31369i	0.723643	−	0.803687i	−0.263307	−	0.964712i	$-0.584813\pi$
$17$	2.98366	−	3.31369i	0.723643	−	0.803687i	0.986950	+	0.161025i	$0.0514799\pi$
$18$		0			0
$19$	5.17517	+	2.30413i	1.18726	+	0.528604i	0.902791	−	0.430080i	$-0.141515\pi$
$19$	5.17517	+	2.30413i	1.18726	+	0.528604i	0.284473	+	0.958684i	$0.408181\pi$
$20$		0			0
$21$	−4.74809			−1.03612
$22$		0			0
$23$	4.21964	−	7.30862i	0.879855	−	1.52395i	0.0283553	−	0.999598i	$-0.490973\pi$
$23$	4.21964	−	7.30862i	0.879855	−	1.52395i	0.851500	−	0.524355i	$-0.175694\pi$
$24$		0			0
$25$	−8.43205	+	6.12624i	−1.68641	+	1.22525i
$26$		0			0
$27$	0.262002	+	0.806360i	0.0504224	+	0.155184i
$28$		0			0
$29$	5.17932	−	2.30598i	0.961775	−	0.428210i	0.135064	−	0.990837i	$-0.456876\pi$
$29$	5.17932	−	2.30598i	0.961775	−	0.428210i	0.826711	+	0.562627i	$0.190209\pi$
$30$		0			0
$31$	−0.0487528	+	0.150046i	−0.00875626	+	0.0269490i	−0.955339	−	0.295511i	$-0.904510\pi$
$31$	−0.0487528	+	0.150046i	−0.00875626	+	0.0269490i	0.946583	+	0.322460i	$0.104510\pi$
$32$		0			0
$33$	−3.80454	+	7.43172i	−0.662285	+	1.29370i
$34$		0			0
$35$	7.24547	−	1.54007i	1.22471	−	0.260320i
$36$		0			0
$37$	−9.28006	+	4.13175i	−1.52563	+	0.679256i	−0.986619	−	0.163041i	$-0.947870\pi$
$37$	−9.28006	+	4.13175i	−1.52563	+	0.679256i	−0.539014	+	0.842297i	$0.681203\pi$
$38$		0			0
$39$	−8.71482	−	2.53584i	−1.39549	−	0.406060i
$40$		0			0
$41$	0.403536	+	3.83939i	0.0630218	+	0.599612i	0.979767	+	0.200140i	$0.0641398\pi$
$41$	0.403536	+	3.83939i	0.0630218	+	0.599612i	−0.916745	+	0.399472i	$0.869194\pi$
$42$		0			0
$43$	−1.71835	−	2.97627i	−0.262046	−	0.453877i	0.704740	−	0.709466i	$-0.251064\pi$
$43$	−1.71835	−	2.97627i	−0.262046	−	0.453877i	−0.966785	+	0.255589i	$0.917731\pi$
$44$		0			0
$45$	−6.55210	−	11.3486i	−0.976729	−	1.69174i
$46$		0			0
$47$	0.916824	−	0.666111i	0.133732	−	0.0971623i	−0.518908	−	0.854830i	$-0.673661\pi$
$47$	0.916824	−	0.666111i	0.133732	−	0.0971623i	0.652640	+	0.757668i	$0.273661\pi$
$48$		0			0
$49$	3.36709	+	0.715698i	0.481013	+	0.102243i
$50$		0			0
$51$	−9.08095	−	6.59770i	−1.27159	−	0.923862i
$52$		0			0
$53$	3.61632	−	11.1299i	0.496740	−	1.52881i	−0.317487	−	0.948263i	$-0.602839\pi$
$53$	3.61632	−	11.1299i	0.496740	−	1.52881i	0.814227	−	0.580547i	$-0.197161\pi$
$54$		0			0
$55$	3.39511	−	12.5746i	0.457796	−	1.69556i
$56$		0			0
$57$	4.40668	−	13.5624i	0.583679	−	1.79638i
$58$		0			0
$59$	−0.555488	+	5.28512i	−0.0723184	+	0.688064i	0.896962	+	0.442107i	$0.145769\pi$
$59$	−0.555488	+	5.28512i	−0.0723184	+	0.688064i	−0.969281	+	0.245957i	$0.920898\pi$
$60$		0			0
$61$	−9.59465	+	10.6559i	−1.22847	+	1.36435i	−0.319447	+	0.947604i	$0.603497\pi$
$61$	−9.59465	+	10.6559i	−1.22847	+	1.36435i	−0.909022	+	0.416749i	$0.863169\pi$
$62$		0			0
$63$	0.657885	+	6.25936i	0.0828857	+	0.788605i
$64$		0			0
$65$	14.1211	+	1.04293i	1.75151	+	0.129360i
$66$		0			0
$67$	−2.84792	+	4.93273i	−0.347928	+	0.602629i	−0.985881	−	0.167446i	$-0.946448\pi$
$67$	−2.84792	+	4.93273i	−0.347928	+	0.602629i	0.637953	+	0.770075i	$0.279781\pi$
$68$		0			0
$69$	−19.4075	−	8.64079i	−2.33639	−	1.04023i
$70$		0			0
$71$	−1.78658	+	1.98420i	−0.212029	+	0.235482i	−0.839773	−	0.542938i	$-0.817312\pi$
$71$	−1.78658	+	1.98420i	−0.212029	+	0.235482i	0.627744	+	0.778420i	$0.283978\pi$
$72$		0			0
$73$	−0.671988	−	0.488228i	−0.0786503	−	0.0571428i	0.547765	−	0.836632i	$-0.315479\pi$
$73$	−0.671988	−	0.488228i	−0.0786503	−	0.0571428i	−0.626416	+	0.779489i	$0.715479\pi$
$74$		0			0
$75$	17.5558	+	19.4977i	2.02717	+	2.25141i
$76$		0			0
$77$	−3.94615	+	4.85411i	−0.449706	+	0.553178i
$78$		0			0
$79$	−2.15248	+	6.62465i	−0.242173	+	0.745332i	0.753916	+	0.656971i	$0.228163\pi$
$79$	−2.15248	+	6.62465i	−0.242173	+	0.745332i	−0.996089	+	0.0883603i	$0.971837\pi$
$80$		0			0
$81$	−7.19520	+	3.20351i	−0.799466	+	0.355945i
$82$		0			0
$83$	3.36285	+	10.3498i	0.369120	+	1.13604i	0.947360	+	0.320169i	$0.103740\pi$
$83$	3.36285	+	10.3498i	0.369120	+	1.13604i	−0.578240	+	0.815867i	$0.696260\pi$
$84$		0			0
$85$	15.9973	+	7.12246i	1.73515	+	0.772539i
$86$		0			0
$87$	−7.13589	−	12.3597i	−0.765047	−	1.32510i
$88$		0			0
$89$	0.622905	−	1.07890i	0.0660278	−	0.114364i	−0.831122	−	0.556091i	$-0.812301\pi$
$89$	0.622905	−	1.07890i	0.0660278	−	0.114364i	0.897149	+	0.441727i	$0.145634\pi$
$90$		0			0
$91$	−5.99216	−	3.21620i	−0.628149	−	0.337149i
$92$		0			0
$93$	0.388469	+	0.0825717i	0.0402824	+	0.00856229i
$94$		0			0
$95$	−2.32545	+	22.1252i	−0.238586	+	2.27000i
$96$		0			0
$97$	12.3361	−	2.62212i	1.25254	−	0.266236i	0.466562	−	0.884488i	$-0.345492\pi$
$97$	12.3361	−	2.62212i	1.25254	−	0.266236i	0.785980	+	0.618252i	$0.212159\pi$
$98$		0			0
$99$	10.3243	+	3.98576i	1.03763	+	0.400584i
$100$		0			0
$101$	6.71559	+	7.45842i	0.668227	+	0.742141i	0.977985	−	0.208674i	$-0.0669149\pi$
$101$	6.71559	+	7.45842i	0.668227	+	0.742141i	−0.309759	+	0.950815i	$0.600248\pi$
$102$		0			0
$103$	−1.66407	−	1.20902i	−0.163966	−	0.119128i	0.502777	−	0.864416i	$-0.332312\pi$
$103$	−1.66407	−	1.20902i	−0.163966	−	0.119128i	−0.666742	+	0.745288i	$0.732312\pi$
$104$		0			0
$105$	−5.76209	−	17.7339i	−0.562322	−	1.73065i
$106$		0			0
$107$	−0.331484	−	3.15386i	−0.0320458	−	0.304895i	−0.998791	−	0.0491545i	$-0.984347\pi$
$107$	−0.331484	−	3.15386i	−0.0320458	−	0.304895i	0.966745	−	0.255741i	$-0.0823194\pi$
$108$		0			0
$109$	5.06982			0.485600			0.242800	−	0.970076i	$-0.421934\pi$
$109$	5.06982			0.485600			0.242800	+	0.970076i	$0.421934\pi$
$110$		0			0
$111$	12.7858	+	22.1456i	1.21357	+	2.10196i
$112$		0			0
$113$	1.38999	+	0.618863i	0.130759	+	0.0582177i	0.471073	−	0.882094i	$-0.343867\pi$
$113$	1.38999	+	0.618863i	0.130759	+	0.0582177i	−0.340314	+	0.940312i	$0.610533\pi$
$114$		0			0
$115$	32.4181	+	6.89069i	3.02301	+	0.642560i
$116$		0			0
$117$	−2.13547	+	11.8400i	−0.197424	+	1.09461i
$118$		0			0
$119$	−5.62772	−	6.25022i	−0.515893	−	0.572957i
$120$		0			0
$121$	4.43570	+	10.0660i	0.403246	+	0.915092i
$122$		0			0
$123$	9.50578	−	2.02052i	0.857108	−	0.182184i
$124$		0			0
$125$	−17.2283	−	12.5171i	−1.54095	−	1.11956i
$126$		0			0
$127$	−6.95835	−	1.47904i	−0.617454	−	0.131244i	−0.111443	−	0.993771i	$-0.535547\pi$
$127$	−6.95835	−	1.47904i	−0.617454	−	0.131244i	−0.506011	+	0.862527i	$0.668881\pi$
$128$		0			0
$129$	−6.99898	+	5.08506i	−0.616226	+	0.447714i
$130$		0			0
$131$	4.22276			0.368944			0.184472	−	0.982838i	$-0.440942\pi$
$131$	4.22276			0.368944			0.184472	+	0.982838i	$0.440942\pi$
$132$		0			0
$133$	5.34254	−	9.25355i	0.463257	−	0.802385i
$134$		0			0
$135$	−2.69376	+	1.95713i	−0.231842	+	0.168443i
$136$		0			0
$137$	0.964356	−	1.07103i	0.0823905	−	0.0915039i	−0.700540	−	0.713613i	$-0.747057\pi$
$137$	0.964356	−	1.07103i	0.0823905	−	0.0915039i	0.782930	+	0.622109i	$0.213724\pi$
$138$		0			0
$139$	−0.837900	+	7.97209i	−0.0710698	+	0.676184i	0.899755	+	0.436395i	$0.143745\pi$
$139$	−0.837900	+	7.97209i	−0.0710698	+	0.676184i	−0.970825	+	0.239789i	$0.922922\pi$
$140$		0			0
$141$	−1.90886	−	2.12001i	−0.160755	−	0.178537i
$142$		0			0
$143$	−9.83537	+	6.80187i	−0.822475	+	0.568801i
$144$		0			0
$145$	14.8981	+	16.5461i	1.23722	+	1.37408i
$146$		0			0
$147$	0.905776	−	8.61788i	0.0747071	−	0.710791i
$148$		0			0
$149$	9.98997	−	11.0950i	0.818411	−	0.908937i	−0.178777	−	0.983890i	$-0.557214\pi$
$149$	9.98997	−	11.0950i	0.818411	−	0.908937i	0.997187	+	0.0749527i	$0.0238806\pi$
$150$		0			0
$151$	−12.7055	+	9.23105i	−1.03396	+	0.751213i	−0.969096	−	0.246682i	$-0.920660\pi$
$151$	−12.7055	+	9.23105i	−1.03396	+	0.751213i	−0.0648588	+	0.997894i	$0.520660\pi$
$152$		0			0
$153$	−7.43943	+	12.8855i	−0.601443	+	1.04173i
$154$		0			0
$155$	−0.619578			−0.0497657
$156$		0			0
$157$	−8.88264	+	6.45362i	−0.708912	+	0.515055i	−0.882822	−	0.469707i	$-0.844360\pi$
$157$	−8.88264	+	6.45362i	−0.708912	+	0.515055i	0.173911	+	0.984761i	$0.444360\pi$
$158$		0			0
$159$	−28.8154	−	6.12490i	−2.28521	−	0.485736i
$160$		0			0
$161$	−12.8779	−	9.35637i	−1.01492	−	0.737385i
$162$		0			0
$163$	−7.92426	+	1.68435i	−0.620676	+	0.131929i	−0.507508	−	0.861647i	$-0.669433\pi$
$163$	−7.92426	+	1.68435i	−0.620676	+	0.131929i	−0.113168	+	0.993576i	$0.536100\pi$
$164$		0			0
$165$	−32.3741	−	5.19093i	−2.52032	−	0.404113i
$166$		0			0
$167$	−8.70154	−	9.66404i	−0.673346	−	0.747826i	0.305552	−	0.952175i	$-0.401159\pi$
$167$	−8.70154	−	9.66404i	−0.673346	−	0.747826i	−0.978898	+	0.204349i	$0.934492\pi$
$168$		0			0
$169$	−9.28053	−	9.10339i	−0.713887	−	0.700261i
$170$		0			0
$171$	−18.4897	−	3.93011i	−1.41394	−	0.300543i
$172$		0			0
$173$	21.1869	+	9.43302i	1.61081	+	0.717179i	0.997364	−	0.0725566i	$-0.0231158\pi$
$173$	21.1869	+	9.43302i	1.61081	+	0.717179i	0.613447	+	0.789736i	$0.289782\pi$
$174$		0			0
$175$	9.82945	+	17.0251i	0.743037	+	1.28698i
$176$		0			0
$177$	13.3775			1.00552
$178$		0			0
$179$	−0.911853	−	8.67571i	−0.0681551	−	0.648453i	−0.974264	−	0.225409i	$-0.927628\pi$
$179$	−0.911853	−	8.67571i	−0.0681551	−	0.648453i	0.906109	−	0.423044i	$-0.139038\pi$
$180$		0			0
$181$	1.34007	+	4.12432i	0.0996068	+	0.306558i	0.988427	−	0.151698i	$-0.0484742\pi$
$181$	1.34007	+	4.12432i	0.0996068	+	0.306558i	−0.888820	+	0.458256i	$0.848474\pi$
$182$		0			0
$183$	29.2019	+	21.2164i	2.15867	+	1.56836i
$184$		0			0
$185$	−26.6938	−	29.6465i	−1.96257	−	2.17965i
$186$		0			0
$187$	−14.2922	+	3.80036i	−1.04515	+	0.277910i
$188$		0			0
$189$	1.56427	−	0.332495i	0.113784	−	0.0241855i
$190$		0			0
$191$	1.34243	−	12.7724i	0.0971351	−	0.924179i	−0.832084	−	0.554650i	$-0.812852\pi$
$191$	1.34243	−	12.7724i	0.0971351	−	0.924179i	0.929219	−	0.369529i	$-0.120481\pi$
$192$		0			0
$193$	8.60720	+	1.82952i	0.619560	+	0.131691i	0.506989	−	0.861952i	$-0.330758\pi$
$193$	8.60720	+	1.82952i	0.619560	+	0.131691i	0.112570	+	0.993644i	$0.464092\pi$
$194$		0			0
$195$	−1.10470	−	35.6268i	−0.0791090	−	2.55129i
$196$		0			0
$197$	−12.9617	+	22.4504i	−0.923485	+	1.59952i	−0.129504	+	0.991579i	$0.541339\pi$
$197$	−12.9617	+	22.4504i	−0.923485	+	1.59952i	−0.793980	+	0.607943i	$0.791995\pi$
$198$		0			0
$199$	−11.7316	−	20.3196i	−0.831628	−	1.44042i	−0.896747	−	0.442544i	$-0.854076\pi$
$199$	−11.7316	−	20.3196i	−0.831628	−	1.44042i	0.0651192	−	0.997877i	$-0.479257\pi$
$200$		0			0
$201$	13.0985	+	5.83184i	0.923899	+	0.411346i
$202$		0			0
$203$	−3.30452	−	10.1703i	−0.231932	−	0.713813i
$204$		0			0
$205$	−13.8502	+	6.16652i	−0.967342	+	0.430688i
$206$		0			0
$207$	−8.70200	+	26.7820i	−0.604831	+	1.86148i
$208$		0			0
$209$	−10.2028	−	15.7768i	−0.705743	−	1.09130i
$210$		0			0
$211$	18.3057	+	20.3306i	1.26022	+	1.39961i	0.880177	+	0.474645i	$0.157424\pi$
$211$	18.3057	+	20.3306i	1.26022	+	1.39961i	0.380041	+	0.924970i	$0.375910\pi$
$212$		0			0
$213$	5.43758	+	3.95063i	0.372577	+	0.270693i
$214$		0			0
$215$	9.03090	−	10.0298i	0.615902	−	0.684029i
$216$		0			0
$217$	0.271851	+	0.121036i	0.0184544	+	0.00821645i
$218$		0			0
$219$	−1.04546	+	1.81080i	−0.0706460	+	0.122362i
$220$		0			0
$221$	−6.99123	−	14.4775i	−0.470281	−	0.973863i
$222$		0			0
$223$	−0.736958	−	7.01169i	−0.0493504	−	0.469538i	−0.991090	−	0.133195i	$-0.957476\pi$
$223$	−0.736958	−	7.01169i	−0.0493504	−	0.469538i	0.941740	−	0.336343i	$-0.109190\pi$
$224$		0			0
$225$	23.2712	−	25.8452i	1.55141	−	1.72302i
$226$		0			0
$227$	−1.84825	+	17.5849i	−0.122673	+	1.16715i	0.743967	+	0.668216i	$0.232942\pi$
$227$	−1.84825	+	17.5849i	−0.122673	+	1.16715i	−0.866639	+	0.498935i	$0.833725\pi$
$228$		0			0
$229$	0.218295	−	0.671842i	0.0144253	−	0.0443966i	−0.943585	−	0.331131i	$-0.892570\pi$
$229$	0.218295	−	0.671842i	0.0144253	−	0.0443966i	0.958010	+	0.286735i	$0.0925698\pi$
$230$		0			0
$231$	13.1907	+	8.60198i	0.867883	+	0.565968i
$232$		0			0
$233$	−2.08403	+	6.41399i	−0.136529	+	0.420195i	−0.995825	−	0.0912852i	$-0.970903\pi$
$233$	−2.08403	+	6.41399i	−0.136529	+	0.420195i	0.859295	+	0.511480i	$0.170903\pi$
$234$		0			0
$235$	3.60051	+	2.61593i	0.234872	+	0.170644i
$236$		0			0
$237$	17.1513	+	3.64562i	1.11410	+	0.236808i
$238$		0			0
$239$	−3.75012	+	2.72462i	−0.242575	+	0.176241i	−0.702430	−	0.711753i	$-0.747901\pi$
$239$	−3.75012	+	2.72462i	−0.242575	+	0.176241i	0.459855	+	0.887994i	$0.347901\pi$
$240$		0			0
$241$	−7.25147	−	12.5599i	−0.467108	−	0.809055i	0.532186	−	0.846628i	$-0.321371\pi$
$241$	−7.25147	−	12.5599i	−0.467108	−	0.809055i	−0.999294	+	0.0375728i	$0.988037\pi$
$242$		0			0
$243$	11.1851	+	19.3731i	0.717523	+	1.24279i
$244$		0			0
$245$	1.41307	+	13.4445i	0.0902778	+	0.858936i
$246$		0			0
$247$	14.7480	−	14.1310i	0.938392	−	0.899132i
$248$		0			0
$249$	25.0259	−	11.1423i	1.58595	−	0.706112i
$250$		0			0
$251$	7.04698	−	1.49788i	0.444802	−	0.0945455i	0.0199347	−	0.999801i	$-0.493654\pi$
$251$	7.04698	−	1.49788i	0.444802	−	0.0945455i	0.424867	+	0.905256i	$0.360321\pi$
$252$		0			0
$253$	−24.9634	+	12.6595i	−1.56944	+	0.795897i
$254$		0			0
$255$	13.6218	−	41.9236i	0.853030	−	2.62536i
$256$		0			0
$257$	−1.32482	+	0.589850i	−0.0826403	+	0.0367938i	−0.447641	−	0.894214i	$-0.647736\pi$
$257$	−1.32482	+	0.589850i	−0.0826403	+	0.0367938i	0.365000	+	0.931007i	$0.381069\pi$
$258$		0			0
$259$	5.92089	+	18.2226i	0.367906	+	1.13230i
$260$		0			0
$261$	−15.3050	+	11.1197i	−0.947353	+	0.688292i
$262$		0			0
$263$	7.01641	−	12.1528i	0.432650	−	0.749373i	−0.564450	−	0.825467i	$-0.690912\pi$
$263$	7.01641	−	12.1528i	0.432650	−	0.749373i	0.997101	+	0.0760946i	$0.0242451\pi$
$264$		0			0
$265$	45.9583			2.82319
$266$		0			0
$267$	−2.86495	−	1.27556i	−0.175332	−	0.0780629i
$268$		0			0
$269$	−1.06272	+	1.18027i	−0.0647954	+	0.0719626i	−0.774671	−	0.632365i	$-0.782085\pi$
$269$	−1.06272	+	1.18027i	−0.0647954	+	0.0719626i	0.709876	+	0.704327i	$0.248751\pi$
$270$		0			0
$271$	20.4911	−	9.12323i	1.24475	−	0.554197i	0.324630	−	0.945841i	$-0.394760\pi$
$271$	20.4911	−	9.12323i	1.24475	−	0.554197i	0.920117	+	0.391644i	$0.128094\pi$
$272$		0			0
$273$	−6.47507	+	15.8477i	−0.391889	+	0.959148i
$274$		0			0
$275$	34.5238	−	1.74324i	2.08187	−	0.105121i
$276$		0			0
$277$	−14.0753	+	2.99180i	−0.845705	+	0.179760i	−0.610333	−	0.792145i	$-0.708964\pi$
$277$	−14.0753	+	2.99180i	−0.845705	+	0.179760i	−0.235372	+	0.971905i	$0.575631\pi$
$278$		0			0
$279$	0.0550280	−	0.523556i	0.00329444	−	0.0313445i
$280$		0			0
$281$	−4.18075	−	12.8670i	−0.249403	−	0.767582i	−0.994881	−	0.101052i	$-0.967779\pi$
$281$	−4.18075	−	12.8670i	−0.249403	−	0.767582i	0.745479	−	0.666530i	$-0.232221\pi$
$282$		0			0
$283$	0.207263	+	1.97198i	0.0123205	+	0.117222i	0.998954	−	0.0457358i	$-0.0145632\pi$
$283$	0.207263	+	1.97198i	0.0123205	+	0.117222i	−0.986633	+	0.162958i	$0.947897\pi$
$284$		0			0
$285$	56.0026			3.31731
$286$		0			0
$287$	7.28168			0.429824
$288$		0			0
$289$	−0.301329	−	2.86695i	−0.0177252	−	0.168644i
$290$		0			0
$291$	−9.81051	−	30.1936i	−0.575102	−	1.76998i
$292$		0			0
$293$	0.0331485	−	0.315386i	0.00193655	−	0.0184251i	−0.993511	−	0.113737i	$-0.963718\pi$
$293$	0.0331485	−	0.315386i	0.00193655	−	0.0184251i	0.995448	+	0.0953114i	$0.0303847\pi$
$294$		0			0
$295$	−20.4138	+	4.33908i	−1.18854	+	0.252631i
$296$		0			0
$297$	0.732990	−	2.71481i	0.0425324	−	0.157529i
$298$		0			0
$299$	−18.6396	−	24.0508i	−1.07796	−	1.39089i
$300$		0			0
$301$	−5.92183	+	2.63657i	−0.341328	+	0.151969i
$302$		0			0
$303$	16.9052	−	18.7751i	0.971177	−	1.07860i
$304$		0			0
$305$	−51.4431	−	22.9039i	−2.94562	−	1.31148i
$306$		0			0
$307$	−12.1243			−0.691969			−0.345985	−	0.938240i	$-0.612455\pi$
$307$	−12.1243			−0.691969			−0.345985	+	0.938240i	$0.612455\pi$
$308$		0			0
$309$	−2.58893	+	4.48415i	−0.147279	+	0.255094i
$310$		0			0
$311$	−26.6333	+	19.3502i	−1.51023	+	1.09725i	−0.544161	+	0.838981i	$0.683152\pi$
$311$	−26.6333	+	19.3502i	−1.51023	+	1.09725i	−0.966073	+	0.258268i	$0.916848\pi$
$312$		0			0
$313$	3.18859	+	9.81347i	0.180230	+	0.554690i	0.999834	−	0.0182406i	$-0.00580647\pi$
$313$	3.18859	+	9.81347i	0.180230	+	0.554690i	−0.819604	+	0.572931i	$0.805806\pi$
$314$		0			0
$315$	−22.5800	+	10.0533i	−1.27224	+	0.566438i
$316$		0			0
$317$	−4.66011	+	14.3424i	−0.261738	+	0.805547i	0.730689	+	0.682711i	$0.239199\pi$
$317$	−4.66011	+	14.3424i	−0.261738	+	0.805547i	−0.992427	+	0.122836i	$0.960801\pi$
$318$		0			0
$319$	−18.5664	−	2.97697i	−1.03952	−	0.166678i
$320$		0			0
$321$	−7.80851	+	1.65975i	−0.435828	+	0.0926382i
$322$		0			0
$323$	23.0761	−	10.2741i	1.28399	−	0.571669i
$324$		0			0
$325$	8.94862	+	36.4982i	0.496380	+	2.02455i
$326$		0			0
$327$	−1.33402	−	12.6923i	−0.0737714	−	0.701888i
$328$		0			0
$329$	−1.06876	−	1.85115i	−0.0589229	−	0.102057i
$330$		0			0
$331$	7.89576	+	13.6759i	0.433990	+	0.751693i	0.997213	−	0.0746125i	$-0.0237720\pi$
$331$	7.89576	+	13.6759i	0.433990	+	0.751693i	−0.563223	+	0.826305i	$0.690439\pi$
$332$		0			0
$333$	27.4227	−	19.9238i	1.50275	−	1.09182i
$334$		0			0
$335$	−21.8796	−	4.65066i	−1.19541	−	0.254093i
$336$		0			0
$337$	4.63733	+	3.36922i	0.252611	+	0.183533i	0.706883	−	0.707330i	$-0.250101\pi$
$337$	4.63733	+	3.36922i	0.252611	+	0.183533i	−0.454272	+	0.890863i	$0.650101\pi$
$338$		0			0
$339$	1.18358	−	3.64269i	0.0642834	−	0.197844i
$340$		0			0
$341$	0.407273	−	0.328518i	0.0220551	−	0.0177903i
$342$		0			0
$343$	6.08643	−	18.7321i	0.328637	−	1.01144i
$344$		0			0
$345$	8.72074	−	82.9723i	0.469509	−	4.46708i
$346$		0			0
$347$	−0.785266	+	0.872126i	−0.0421553	+	0.0468182i	−0.763854	−	0.645389i	$-0.776695\pi$
$347$	−0.785266	+	0.872126i	−0.0421553	+	0.0468182i	0.721698	+	0.692208i	$0.243362\pi$
$348$		0			0
$349$	−0.213411	−	2.03047i	−0.0114236	−	0.108689i	0.987324	−	0.158717i	$-0.0507356\pi$
$349$	−0.213411	−	2.03047i	−0.0114236	−	0.108689i	−0.998748	+	0.0500280i	$0.984069\pi$
$350$		0			0
$351$	3.04869	+	0.225164i	0.162727	+	0.0120184i
$352$		0			0
$353$	−13.5578	+	23.4828i	−0.721608	+	1.24986i	0.238747	+	0.971082i	$0.423263\pi$
$353$	−13.5578	+	23.4828i	−0.721608	+	1.24986i	−0.960355	+	0.278780i	$0.910070\pi$
$354$		0			0
$355$	−9.57903	−	4.26486i	−0.508402	−	0.226355i
$356$		0			0
$357$	−14.1667	+	15.7337i	−0.749780	+	0.832716i
$358$		0			0
$359$	22.0817	+	16.0433i	1.16543	+	0.846734i	0.990455	−	0.137839i	$-0.0440157\pi$
$359$	22.0817	+	16.0433i	1.16543	+	0.846734i	0.174974	+	0.984573i	$0.444016\pi$
$360$		0			0
$361$	8.75983	+	9.72878i	0.461044	+	0.512041i
$362$		0			0
$363$	24.0332	−	13.7535i	1.26142	−	0.721872i
$364$		0			0
$365$	1.00801	−	3.10234i	0.0527617	−	0.162384i
$366$		0			0
$367$	−4.56891	+	2.03421i	−0.238495	+	0.106185i	−0.522504	−	0.852637i	$-0.675002\pi$
$367$	−4.56891	+	2.03421i	−0.238495	+	0.106185i	0.284009	+	0.958822i	$0.408335\pi$
$368$		0			0
$369$	−3.98072	−	12.2514i	−0.207228	−	0.637783i
$370$		0			0
$371$	−20.1650	−	8.97805i	−1.04692	−	0.466117i
$372$		0			0
$373$	−1.80465	−	3.12575i	−0.0934414	−	0.161845i	0.815516	−	0.578735i	$-0.196453\pi$
$373$	−1.80465	−	3.12575i	−0.0934414	−	0.161845i	−0.908957	+	0.416890i	$0.863120\pi$
$374$		0			0
$375$	−26.8034	+	46.4249i	−1.38412	+	2.39737i
$376$		0			0
$377$	−0.633536	−	20.4317i	−0.0326288	−	1.05229i
$378$		0			0
$379$	−18.7587	−	3.98730i	−0.963572	−	0.204814i	−0.300844	−	0.953673i	$-0.597268\pi$
$379$	−18.7587	−	3.98730i	−0.963572	−	0.204814i	−0.662728	+	0.748860i	$0.730602\pi$
$380$		0			0
$381$	−1.87185	+	17.8095i	−0.0958980	+	0.912409i
$382$		0			0
$383$	22.5241	−	4.78764i	1.15093	−	0.244637i	0.407340	−	0.913277i	$-0.366456\pi$
$383$	22.5241	−	4.78764i	1.15093	−	0.244637i	0.743587	+	0.668640i	$0.233123\pi$
$384$		0			0
$385$	−22.9188	−	8.84793i	−1.16805	−	0.450932i
$386$		0			0
$387$	7.67334	+	8.52210i	0.390058	+	0.433203i
$388$		0			0
$389$	19.9870	+	14.5214i	1.01338	+	0.736266i	0.964916	−	0.262559i	$-0.0845663\pi$
$389$	19.9870	+	14.5214i	1.01338	+	0.736266i	0.0484674	+	0.998825i	$0.484566\pi$
$390$		0			0
$391$	−11.6285	−	35.7890i	−0.588081	−	1.80993i
$392$		0			0
$393$	−1.11113	−	10.5717i	−0.0560493	−	0.533273i
$394$		0			0
$395$	−27.3549			−1.37637
$396$		0			0
$397$	−2.58748	−	4.48165i	−0.129862	−	0.224927i	0.793761	−	0.608230i	$-0.208120\pi$
$397$	−2.58748	−	4.48165i	−0.129862	−	0.224927i	−0.923623	+	0.383302i	$0.874787\pi$
$398$		0			0
$399$	−24.5722	−	10.9402i	−1.23015	−	0.547697i
$400$		0			0
$401$	6.80508	+	1.44646i	0.339829	+	0.0722329i	0.374665	−	0.927160i	$-0.377758\pi$
$401$	6.80508	+	1.44646i	0.339829	+	0.0722329i	−0.0348361	+	0.999393i	$0.511091\pi$
$402$		0			0
$403$	0.434323	+	0.367343i	0.0216352	+	0.0182986i
$404$		0			0
$405$	−20.6967	−	22.9861i	−1.02843	−	1.14219i
$406$		0			0
$407$	33.2663	+	5.33399i	1.64895	+	0.264396i
$408$		0			0
$409$	32.5605	−	6.92095i	1.61001	−	0.342219i	0.686902	−	0.726750i	$-0.258970\pi$
$409$	32.5605	−	6.92095i	1.61001	−	0.342219i	0.923112	+	0.384531i	$0.125637\pi$
$410$		0			0
$411$	−2.93508	−	2.13246i	−0.144777	−	0.105186i
$412$		0			0
$413$	9.80457	+	2.08403i	0.482451	+	0.102548i
$414$		0			0
$415$	−34.5749	+	25.1201i	−1.69722	+	1.23310i
$416$		0			0
$417$	20.1787			0.988155
$418$		0			0
$419$	−17.6926	+	30.6446i	−0.864342	+	1.49708i	0.00335673	+	0.999994i	$0.498932\pi$
$419$	−17.6926	+	30.6446i	−0.864342	+	1.49708i	−0.867699	+	0.497090i	$0.834402\pi$
$420$		0			0
$421$	−18.4863	+	13.4311i	−0.900967	+	0.654591i	−0.938714	−	0.344696i	$-0.887982\pi$
$421$	−18.4863	+	13.4311i	−0.900967	+	0.654591i	0.0377472	+	0.999287i	$0.487982\pi$
$422$		0			0
$423$	−2.53029	+	2.81017i	−0.123027	+	0.136635i
$424$		0			0
$425$	−4.85790	+	46.2198i	−0.235643	+	2.24199i
$426$		0			0
$427$	18.0973	+	20.0990i	0.875788	+	0.972661i
$428$		0			0
$429$	19.6165	+	22.8332i	0.947096	+	1.10240i
$430$		0			0
$431$	−14.1383	−	15.7021i	−0.681017	−	0.756346i	0.299218	−	0.954185i	$-0.403274\pi$
$431$	−14.1383	−	15.7021i	−0.681017	−	0.756346i	−0.980235	+	0.197839i	$0.936608\pi$
$432$		0			0
$433$	−0.202693	+	1.92850i	−0.00974081	+	0.0926776i	−0.998312	−	0.0580761i	$-0.981503\pi$
$433$	−0.202693	+	1.92850i	−0.00974081	+	0.0926776i	0.988571	+	0.150754i	$0.0481701\pi$
$434$		0			0
$435$	37.5031	−	41.6514i	1.79814	−	1.99703i
$436$		0			0
$437$	38.6773	−	28.1007i	1.85019	−	1.34424i
$438$		0			0
$439$	1.38500	−	2.39889i	0.0661025	−	0.114493i	−0.831080	−	0.556153i	$-0.812277\pi$
$439$	1.38500	−	2.39889i	0.0661025	−	0.114493i	0.897183	+	0.441660i	$0.145610\pi$
$440$		0			0
$441$	−11.4864			−0.546969
$442$		0			0
$443$	−10.8565	+	7.88770i	−0.515807	+	0.374756i	−0.815022	−	0.579430i	$-0.803275\pi$
$443$	−10.8565	+	7.88770i	−0.515807	+	0.374756i	0.299215	+	0.954186i	$0.403275\pi$
$444$		0			0
$445$	4.78558	+	1.01721i	0.226858	+	0.0482202i
$446$		0			0
$447$	−30.4051	−	22.0906i	−1.43811	−	1.04485i
$448$		0			0
$449$	−1.02827	+	0.218565i	−0.0485269	+	0.0103147i	−0.232111	−	0.972689i	$-0.574563\pi$
$449$	−1.02827	+	0.218565i	−0.0485269	+	0.0103147i	0.183584	+	0.983004i	$0.441230\pi$
$450$		0			0
$451$	5.83465	−	11.3973i	0.274743	−	0.536678i
$452$		0			0
$453$	26.4532	+	29.3793i	1.24288	+	1.38036i
$454$		0			0
$455$	4.74050	−	26.2835i	0.222238	−	1.23219i
$456$		0			0
$457$	−8.10407	−	1.72257i	−0.379092	−	0.0805786i	0.0144246	−	0.999896i	$-0.495408\pi$
$457$	−8.10407	−	1.72257i	−0.379092	−	0.0805786i	−0.393517	+	0.919317i	$0.628742\pi$
$458$		0			0
$459$	3.45375	+	1.53771i	0.161207	+	0.0717741i
$460$		0			0
$461$	−8.16527	−	14.1427i	−0.380295	−	0.658690i	0.610810	−	0.791778i	$-0.290844\pi$
$461$	−8.16527	−	14.1427i	−0.380295	−	0.658690i	−0.991104	+	0.133088i	$0.957511\pi$
$462$		0			0
$463$	9.38687			0.436245			0.218122	−	0.975921i	$-0.430007\pi$
$463$	9.38687			0.436245			0.218122	+	0.975921i	$0.430007\pi$
$464$		0			0
$465$	0.163029	+	1.55112i	0.00756030	+	0.0719315i
$466$		0			0
$467$	−3.48880	−	10.7374i	−0.161443	−	0.496869i	0.837314	−	0.546722i	$-0.184125\pi$
$467$	−3.48880	−	10.7374i	−0.161443	−	0.496869i	−0.998757	+	0.0498531i	$0.984125\pi$
$468$		0			0
$469$	8.69157	+	6.31480i	0.401340	+	0.291590i
$470$		0			0
$471$	18.4940	+	20.5397i	0.852158	+	0.946418i
$472$		0			0
$473$	−0.618266	+	11.3815i	−0.0284279	+	0.523320i
$474$		0			0
$475$	−57.7529	+	12.2758i	−2.64989	+	0.563251i
$476$		0			0
$477$	−4.08180	+	38.8357i	−0.186893	+	1.77816i
$478$		0			0
$479$	4.02793	+	0.856163i	0.184041	+	0.0391191i	0.299010	−	0.954250i	$-0.403344\pi$
$479$	4.02793	+	0.856163i	0.184041	+	0.0391191i	−0.114969	+	0.993369i	$0.536677\pi$
$480$		0			0
$481$	1.13514	+	36.6087i	0.0517580	+	1.66921i
$482$		0			0
$483$	−20.0352	+	34.7020i	−0.911634	+	1.57900i
$484$		0			0
$485$	24.7641	+	42.8927i	1.12448	+	1.94766i
$486$		0			0
$487$	−8.31741	−	3.70315i	−0.376898	−	0.167806i	0.209540	−	0.977800i	$-0.432803\pi$
$487$	−8.31741	−	3.70315i	−0.376898	−	0.167806i	−0.586438	+	0.809994i	$0.699470\pi$
$488$		0			0
$489$	6.30191	+	19.3953i	0.284982	+	0.877085i
$490$		0			0
$491$	6.14906	−	2.73774i	0.277503	−	0.123552i	−0.263266	−	0.964723i	$-0.584800\pi$
$491$	6.14906	−	2.73774i	0.277503	−	0.123552i	0.540770	+	0.841171i	$0.318133\pi$
$492$		0			0
$493$	7.81202	−	24.0429i	0.351835	−	1.08284i
$494$		0			0
$495$	−2.35746	+	43.3977i	−0.105960	+	1.95058i
$496$		0			0
$497$	3.36983	+	3.74257i	0.151157	+	0.167877i
$498$		0			0
$499$	−9.17620	−	6.66690i	−0.410783	−	0.298451i	0.363136	−	0.931736i	$-0.381706\pi$
$499$	−9.17620	−	6.66690i	−0.410783	−	0.298451i	−0.773919	+	0.633285i	$0.781706\pi$
$500$		0			0
$501$	−21.9044	+	24.3273i	−0.978617	+	1.08686i
$502$		0			0
$503$	−11.8075	−	5.25705i	−0.526471	−	0.234400i	0.126250	−	0.991998i	$-0.459706\pi$
$503$	−11.8075	−	5.25705i	−0.526471	−	0.234400i	−0.652721	+	0.757598i	$0.726373\pi$
$504$		0			0
$505$	−19.7071	+	34.1337i	−0.876953	+	1.51893i
$506$		0			0
$507$	−20.3485	+	25.6293i	−0.903707	+	1.13824i
$508$		0			0
$509$	−2.43681	−	23.1847i	−0.108010	−	1.02764i	−0.905510	−	0.424325i	$-0.860511\pi$
$509$	−2.43681	−	23.1847i	−0.108010	−	1.02764i	0.797500	−	0.603319i	$-0.206155\pi$
$510$		0			0
$511$	−1.04833	+	1.16429i	−0.0463754	+	0.0515052i
$512$		0			0
$513$	−0.502055	+	4.77674i	−0.0221663	+	0.210898i
$514$		0			0
$515$	2.49618	−	7.68244i	0.109995	−	0.338529i
$516$		0			0
$517$	−3.75380	+	0.189543i	−0.165092	+	0.00833611i
$518$		0			0
$519$	18.0408	−	55.5238i	0.791902	−	2.43722i
$520$		0			0
$521$	0.867055	+	0.629953i	0.0379864	+	0.0275987i	0.606616	−	0.794995i	$-0.292526\pi$
$521$	0.867055	+	0.629953i	0.0379864	+	0.0275987i	−0.568630	+	0.822593i	$0.692526\pi$
$522$		0			0
$523$	−4.27976	−	0.909690i	−0.187141	−	0.0397780i	0.113388	−	0.993551i	$-0.463830\pi$
$523$	−4.27976	−	0.909690i	−0.187141	−	0.0397780i	−0.300529	+	0.953773i	$0.597163\pi$
$524$		0			0
$525$	40.0361	−	29.0880i	1.74732	−	1.26950i
$526$		0			0
$527$	0.351743	+	0.609236i	0.0153222	+	0.0265388i
$528$		0			0
$529$	−24.1106	−	41.7609i	−1.04829	−	1.81569i
$530$		0			0
$531$	−1.85356	−	17.6354i	−0.0804376	−	0.765313i
$532$		0			0
$533$	13.3651	+	3.88897i	0.578905	+	0.168450i
$534$		0			0
$535$	11.3772	−	5.06548i	0.491881	−	0.219000i
$536$		0			0
$537$	−21.4798	+	4.56567i	−0.926922	+	0.197023i
$538$		0			0
$539$	−8.05752	−	8.08834i	−0.347062	−	0.348390i
$540$		0			0
$541$	10.4527	−	32.1701i	0.449396	−	1.38310i	−0.428193	−	0.903687i	$-0.640850\pi$
$541$	10.4527	−	32.1701i	0.449396	−	1.38310i	0.877590	−	0.479413i	$-0.159150\pi$
$542$		0			0
$543$	9.97267	−	4.44012i	0.427968	−	0.190544i
$544$		0			0
$545$	6.15252	+	18.9355i	0.263545	+	0.811108i
$546$		0			0
$547$	4.49692	−	3.26720i	0.192274	−	0.139695i	−0.487483	−	0.873132i	$-0.662085\pi$
$547$	4.49692	−	3.26720i	0.192274	−	0.139695i	0.679758	+	0.733437i	$0.262085\pi$
$548$		0			0
$549$	23.9232	−	41.4363i	1.02102	−	1.76846i
$550$		0			0
$551$	32.1171			1.36824
$552$		0			0
$553$	12.0025	+	5.34384i	0.510397	+	0.227243i
$554$		0			0
$555$	−67.1964	+	74.6291i	−2.85233	+	3.16783i
$556$		0			0
$557$	32.8522	−	14.6267i	1.39199	−	0.619754i	0.432536	−	0.901617i	$-0.357619\pi$
$557$	32.8522	−	14.6267i	1.39199	−	0.619754i	0.959455	+	0.281862i	$0.0909522\pi$
$558$		0			0
$559$	−12.2773	+	1.67654i	−0.519273	+	0.0709102i
$560$		0			0
$561$	13.2750	+	34.7808i	0.560469	+	1.46844i
$562$		0			0
$563$	19.2641	−	4.09471i	0.811885	−	0.172572i	0.216781	−	0.976220i	$-0.430444\pi$
$563$	19.2641	−	4.09471i	0.811885	−	0.172572i	0.595104	+	0.803649i	$0.297111\pi$
$564$		0			0
$565$	−0.624589	+	5.94256i	−0.0262766	+	0.250006i
$566$		0			0
$567$	4.59070	+	14.1287i	0.192791	+	0.593350i
$568$		0			0
$569$	−4.08780	−	38.8928i	−0.171369	−	1.63047i	−0.655303	−	0.755366i	$-0.727459\pi$
$569$	−4.08780	−	38.8928i	−0.171369	−	1.63047i	0.483934	−	0.875105i	$-0.339208\pi$
$570$		0			0
$571$	26.1222			1.09318			0.546589	−	0.837401i	$-0.315926\pi$
$571$	26.1222			1.09318			0.546589	+	0.837401i	$0.315926\pi$
$572$		0			0
$573$	−32.3291			−1.35057
$574$		0			0
$575$	9.19422	+	87.4772i	0.383426	+	3.64805i
$576$		0			0
$577$	−10.1690	−	31.2971i	−0.423343	−	1.30292i	−0.904572	−	0.426320i	$-0.859810\pi$
$577$	−10.1690	−	31.2971i	−0.423343	−	1.30292i	0.481229	−	0.876595i	$-0.340190\pi$
$578$		0			0
$579$	2.31541	−	22.0296i	0.0962250	−	0.915520i
$580$		0			0
$581$	20.0776	−	4.26764i	0.832961	−	0.177051i
$582$		0			0
$583$	−30.2102	+	24.3684i	−1.25118	+	1.00924i
$584$		0			0
$585$	−46.8134	+	6.39268i	−1.93550	+	0.264305i
$586$		0			0
$587$	28.3552	−	12.6246i	1.17035	−	0.521071i	0.272833	−	0.962061i	$-0.412039\pi$
$587$	28.3552	−	12.6246i	1.17035	−	0.521071i	0.897512	+	0.440990i	$0.145373\pi$
$588$		0			0
$589$	−0.598029	+	0.664178i	−0.0246413	+	0.0273670i
$590$		0			0
$591$	59.6154	+	26.5425i	2.45225	+	1.09181i
$592$		0			0
$593$	−9.23368			−0.379182			−0.189591	−	0.981863i	$-0.560716\pi$
$593$	−9.23368			−0.379182			−0.189591	+	0.981863i	$0.560716\pi$
$594$		0			0
$595$	16.5147	−	28.6043i	0.677036	−	1.17266i
$596$		0			0
$597$	−47.7836	+	34.7168i	−1.95565	+	1.42086i
$598$		0			0
$599$	2.86730	+	8.82465i	0.117155	+	0.360565i	0.992390	−	0.123132i	$-0.0392937\pi$
$599$	2.86730	+	8.82465i	0.117155	+	0.360565i	−0.875236	+	0.483697i	$0.839294\pi$
$600$		0			0
$601$	0.758445	−	0.337682i	0.0309376	−	0.0137743i	−0.391210	−	0.920302i	$-0.627943\pi$
$601$	0.758445	−	0.337682i	0.0309376	−	0.0137743i	0.422147	+	0.906527i	$0.361277\pi$
$602$		0			0
$603$	5.87315	−	18.0757i	0.239173	−	0.736099i
$604$		0			0
$605$	−32.2131	+	28.7828i	−1.30965	+	1.17019i
$606$		0			0
$607$	28.5593	−	6.07046i	1.15918	−	0.246392i	0.412111	−	0.911134i	$-0.364792\pi$
$607$	28.5593	−	6.07046i	1.15918	−	0.246392i	0.747074	+	0.664741i	$0.231458\pi$
$608$		0			0
$609$	−24.5919	+	10.9490i	−0.996514	+	0.443676i
$610$		0			0
$611$	−0.972990	−	3.96848i	−0.0393630	−	0.160547i
$612$		0			0
$613$	3.87967	+	36.9126i	0.156699	+	1.49089i	0.736671	+	0.676251i	$0.236397\pi$
$613$	3.87967	+	36.9126i	0.156699	+	1.49089i	−0.579973	+	0.814636i	$0.696937\pi$
$614$		0			0
$615$	19.0824	+	33.0516i	0.769475	+	1.33277i
$616$		0			0
$617$	−5.94230	−	10.2924i	−0.239228	−	0.414355i	0.721265	−	0.692659i	$-0.243561\pi$
$617$	−5.94230	−	10.2924i	−0.239228	−	0.414355i	−0.960493	+	0.278304i	$0.910228\pi$
$618$		0			0
$619$	20.5170	−	14.9065i	0.824648	−	0.599142i	−0.0933920	−	0.995629i	$-0.529771\pi$
$619$	20.5170	−	14.9065i	0.824648	−	0.599142i	0.918040	+	0.396488i	$0.129771\pi$
$620$		0			0
$621$	6.99894	+	1.48767i	0.280858	+	0.0596982i
$622$		0			0
$623$	−1.90105	−	1.38119i	−0.0761639	−	0.0553363i
$624$		0			0
$625$	9.73940	−	29.9748i	0.389576	−	1.19899i
$626$		0			0
$627$	−36.8128	+	29.6942i	−1.47016	+	1.18587i
$628$		0			0
$629$	−13.9972	+	43.0790i	−0.558105	+	1.71767i
$630$		0			0
$631$	−3.33434	+	31.7241i	−0.132738	+	1.26292i	0.701963	+	0.712213i	$0.252307\pi$
$631$	−3.33434	+	31.7241i	−0.132738	+	1.26292i	−0.834701	+	0.550703i	$0.814360\pi$
$632$		0			0
$633$	46.0811	−	51.1782i	1.83156	−	2.03415i
$634$		0			0
$635$	−2.92022	−	27.7840i	−0.115885	−	1.10258i
$636$		0			0
$637$	6.98056	−	10.2623i	0.276580	−	0.406609i
$638$		0			0
$639$	4.45466	−	7.71570i	0.176224	−	0.305228i
$640$		0			0
$641$	6.56730	+	2.92395i	0.259393	+	0.115489i	0.532313	−	0.846547i	$-0.321323\pi$
$641$	6.56730	+	2.92395i	0.259393	+	0.115489i	−0.272920	+	0.962037i	$0.587990\pi$
$642$		0			0
$643$	−23.4103	+	25.9997i	−0.923211	+	1.02533i	0.0763900	+	0.997078i	$0.475661\pi$
$643$	−23.4103	+	25.9997i	−0.923211	+	1.02533i	−0.999601	+	0.0282515i	$0.991006\pi$
$644$		0			0
$645$	−27.4861	−	19.9698i	−1.08226	−	0.786311i
$646$		0			0
$647$	−29.5866	−	32.8592i	−1.16317	−	1.29183i	−0.949087	−	0.315014i	$-0.897991\pi$
$647$	−29.5866	−	32.8592i	−1.16317	−	1.29183i	−0.214082	−	0.976816i	$-0.568676\pi$
$648$		0			0
$649$	11.1181	−	13.6762i	0.436423	−	0.536839i
$650$		0			0
$651$	0.231483	−	0.712430i	0.00907252	−	0.0279224i
$652$		0			0
$653$	−7.84735	+	3.49386i	−0.307090	+	0.136725i	−0.554496	−	0.832187i	$-0.687089\pi$
$653$	−7.84735	+	3.49386i	−0.307090	+	0.136725i	0.247405	+	0.968912i	$0.420422\pi$
$654$		0			0
$655$	5.12457	+	15.7718i	0.200233	+	0.616255i
$656$		0			0
$657$	2.53201	+	1.12732i	0.0987832	+	0.0439811i
$658$		0			0
$659$	−5.78383	−	10.0179i	−0.225306	−	0.390242i	0.731105	−	0.682265i	$-0.239005\pi$
$659$	−5.78383	−	10.0179i	−0.225306	−	0.390242i	−0.956411	+	0.292023i	$0.905672\pi$
$660$		0			0
$661$	13.4468	−	23.2905i	0.523019	−	0.905896i	−0.476622	−	0.879108i	$-0.658139\pi$
$661$	13.4468	−	23.2905i	0.523019	−	0.905896i	0.999641	−	0.0267873i	$-0.00852769\pi$
$662$		0			0
$663$	−34.4050	+	21.3121i	−1.33618	+	0.827693i
$664$		0			0
$665$	41.0450	+	8.72439i	1.59166	+	0.338318i
$666$		0			0
$667$	5.00129	−	47.5841i	0.193651	−	1.84246i
$668$		0			0
$669$	−17.3599	+	3.68997i	−0.671174	+	0.142662i
$670$		0			0
$671$	45.9600	−	12.2209i	1.77426	−	0.471784i
$672$		0			0
$673$	33.8017	+	37.5406i	1.30296	+	1.44708i	0.821041	+	0.570870i	$0.193394\pi$
$673$	33.8017	+	37.5406i	1.30296	+	1.44708i	0.481920	+	0.876215i	$0.339940\pi$
$674$		0			0
$675$	−7.14918	−	5.19418i	−0.275172	−	0.199924i
$676$		0			0
$677$	9.49139	+	29.2115i	0.364784	+	1.12269i	0.950116	+	0.311896i	$0.100964\pi$
$677$	9.49139	+	29.2115i	0.364784	+	1.12269i	−0.585333	+	0.810793i	$0.699036\pi$
$678$		0			0
$679$	−2.48652	−	23.6577i	−0.0954239	−	0.907898i
$680$		0			0
$681$	44.5104			1.70564
$682$		0			0
$683$	20.6291	+	35.7306i	0.789350	+	1.36719i	0.926366	+	0.376625i	$0.122915\pi$
$683$	20.6291	+	35.7306i	0.789350	+	1.36719i	−0.137016	+	0.990569i	$0.543751\pi$
$684$		0			0
$685$	5.17053	+	2.30207i	0.197556	+	0.0879576i
$686$		0			0
$687$	−1.73940	−	0.369722i	−0.0663624	−	0.0141058i
$688$		0			0
$689$	−32.2167	−	27.2483i	−1.22736	−	1.03808i
$690$		0			0
$691$	−14.8814	−	16.5275i	−0.566116	−	0.628736i	0.390319	−	0.920680i	$-0.372365\pi$
$691$	−14.8814	−	16.5275i	−0.566116	−	0.628736i	−0.956435	+	0.291944i	$0.905698\pi$
$692$		0			0
$693$	9.51222	−	18.5810i	0.361339	−	0.705834i
$694$		0			0
$695$	−30.7922	+	6.54508i	−1.16801	+	0.248269i
$696$		0			0
$697$	13.9266	+	10.1182i	0.527506	+	0.383256i
$698$		0			0
$699$	16.6059	+	3.52969i	0.628092	+	0.133505i
$700$		0			0
$701$	−25.4392	+	18.4827i	−0.960825	+	0.698080i	−0.953342	−	0.301892i	$-0.902382\pi$
$701$	−25.4392	+	18.4827i	−0.960825	+	0.698080i	−0.00748301	+	0.999972i	$0.502382\pi$
$702$		0			0
$703$	−57.5460			−2.17039
$704$		0			0
$705$	5.60160	−	9.70226i	0.210968	−	0.365408i
$706$		0			0
$707$	15.3149	−	11.1269i	0.575977	−	0.418472i
$708$		0			0
$709$	−13.5541	+	15.0533i	−0.509034	+	0.565340i	−0.941803	−	0.336165i	$-0.890870\pi$
$709$	−13.5541	+	15.0533i	−0.509034	+	0.565340i	0.432769	+	0.901505i	$0.357537\pi$
$710$		0			0
$711$	2.42953	−	23.1155i	0.0911146	−	0.866898i
$712$		0			0
$713$	0.890908	+	0.989454i	0.0333648	+	0.0370553i
$714$		0			0
$715$	−37.3405	−	28.4802i	−1.39645	−	1.06510i
$716$		0			0
$717$	7.80788	+	8.67153i	0.291591	+	0.323844i
$718$		0			0
$719$	2.56771	−	24.4301i	0.0957594	−	0.911090i	−0.836175	−	0.548463i	$-0.815213\pi$
$719$	2.56771	−	24.4301i	0.0957594	−	0.911090i	0.931934	−	0.362627i	$-0.118120\pi$
$720$		0			0
$721$	−2.59602	+	2.88318i	−0.0966810	+	0.107375i
$722$		0			0
$723$	−29.5358	+	21.4590i	−1.09845	+	0.798070i
$724$		0			0
$725$	−29.5453	+	51.1739i	−1.09728	+	1.90055i
$726$		0			0
$727$	−26.4962			−0.982689			−0.491344	−	0.870965i	$-0.663494\pi$
$727$	−26.4962			−0.982689			−0.491344	+	0.870965i	$0.663494\pi$
$728$		0			0
$729$	26.4420	−	19.2112i	0.979332	−	0.711527i
$730$		0			0
$731$	−14.9894	−	3.18610i	−0.554403	−	0.117842i
$732$		0			0
$733$	15.0493	+	10.9340i	0.555860	+	0.403856i	0.829941	−	0.557851i	$-0.188374\pi$
$733$	15.0493	+	10.9340i	0.555860	+	0.403856i	−0.274082	+	0.961706i	$0.588374\pi$
$734$		0			0
$735$	33.2866	−	7.07528i	1.22779	−	0.260976i
$736$		0			0
$737$	16.8483	−	8.54416i	0.620615	−	0.314728i
$738$		0			0
$739$	4.22389	+	4.69111i	0.155378	+	0.172565i	0.815808	−	0.578323i	$-0.196293\pi$
$739$	4.22389	+	4.69111i	0.155378	+	0.172565i	−0.660430	+	0.750888i	$0.729626\pi$
$740$		0			0
$741$	−39.2577	−	33.2035i	−1.44217	−	1.21976i
$742$		0			0
$743$	27.1923	+	5.77990i	0.997588	+	0.212044i	0.677642	−	0.735392i	$-0.263002\pi$
$743$	27.1923	+	5.77990i	0.997588	+	0.212044i	0.319946	+	0.947436i	$0.396335\pi$
$744$		0			0
$745$	53.5627	+	23.8476i	1.96238	+	0.873710i
$746$		0			0
$747$	−18.1563	−	31.4476i	−0.664303	−	1.15061i
$748$		0			0
$749$	−5.98153			−0.218560
$750$		0			0
$751$	2.82363	+	26.8650i	0.103036	+	0.980318i	0.916860	+	0.399208i	$0.130715\pi$
$751$	2.82363	+	26.8650i	0.103036	+	0.980318i	−0.813825	+	0.581110i	$0.802619\pi$
$752$		0			0
$753$	−5.60424	−	17.2481i	−0.204230	−	0.628555i
$754$		0			0
$755$	−49.8964	−	36.2518i	−1.81591	−	1.31934i
$756$		0			0
$757$	30.8177	+	34.2265i	1.12009	+	1.24398i	0.966726	+	0.255814i	$0.0823436\pi$
$757$	30.8177	+	34.2265i	1.12009	+	1.24398i	0.153363	+	0.988170i	$0.450990\pi$
$758$		0			0
$759$	38.2619	+	59.1651i	1.38882	+	2.14756i
$760$		0			0
$761$	−17.3769	+	3.69357i	−0.629911	+	0.133892i	−0.511794	−	0.859108i	$-0.671019\pi$
$761$	−17.3769	+	3.69357i	−0.629911	+	0.133892i	−0.118117	+	0.993000i	$0.537686\pi$
$762$		0			0
$763$	0.999564	−	9.51021i	0.0361866	−	0.344293i
$764$		0			0
$765$	−57.1548	−	12.1486i	−2.06644	−	0.439235i
$766$		0			0
$767$	16.8826	+	9.06148i	0.609596	+	0.327191i
$768$		0			0
$769$	−0.371834	+	0.644035i	−0.0134087	+	0.0232245i	−0.872652	−	0.488343i	$-0.837602\pi$
$769$	−0.371834	+	0.644035i	−0.0134087	+	0.0232245i	0.859243	+	0.511567i	$0.170935\pi$
$770$		0			0
$771$	1.82530	+	3.16151i	0.0657365	+	0.113859i
$772$		0			0
$773$	−40.9526	−	18.2333i	−1.47296	−	0.655805i	−0.495827	−	0.868421i	$-0.665135\pi$
$773$	−40.9526	−	18.2333i	−1.47296	−	0.655805i	−0.977136	+	0.212616i	$0.931802\pi$
$774$		0			0
$775$	−0.508130	−	1.56386i	−0.0182526	−	0.0561756i
$776$		0			0
$777$	44.0626	−	19.6179i	1.58074	−	0.703789i
$778$		0			0
$779$	−6.75810	+	20.7993i	−0.242134	+	0.745212i
$780$		0			0
$781$	8.55804	−	2.27562i	0.306231	−	0.0814280i
$782$		0			0
$783$	3.21645	+	3.57223i	0.114946	+	0.127661i
$784$		0			0
$785$	−34.8836	−	25.3444i	−1.24505	−	0.904580i
$786$		0			0
$787$	−6.37419	+	7.07926i	−0.227215	+	0.252348i	−0.845963	−	0.533242i	$-0.820974\pi$
$787$	−6.37419	+	7.07926i	−0.227215	+	0.252348i	0.618748	+	0.785590i	$0.287640\pi$
$788$		0			0
$789$	−32.2709	−	14.3679i	−1.14887	−	0.511511i
$790$		0			0
$791$	1.43494	−	2.48539i	0.0510207	−	0.0883704i
$792$		0			0
$793$	22.4819	+	46.5558i	0.798357	+	1.65325i
$794$		0			0
$795$	−12.0930	−	115.057i	−0.428894	−	4.08065i
$796$		0			0
$797$	−4.43626	+	4.92697i	−0.157140	+	0.174522i	−0.816574	−	0.577241i	$-0.804129\pi$
$797$	−4.43626	+	4.92697i	−0.157140	+	0.174522i	0.659434	+	0.751763i	$0.270796\pi$
$798$		0			0
$799$	0.528203	−	5.02552i	0.0186865	−	0.177790i
$800$		0			0
$801$	−1.28459	+	3.95357i	−0.0453889	+	0.139693i
$802$		0			0
$803$	0.982344	+	2.57377i	0.0346662	+	0.0908263i
$804$		0			0
$805$	19.3174	−	59.4530i	0.680850	−	2.09544i
$806$		0			0
$807$	3.23447	+	2.34998i	0.113859	+	0.0827231i
$808$		0			0
$809$	9.67858	+	2.05725i	0.340281	+	0.0723289i	0.374883	−	0.927072i	$-0.377683\pi$
$809$	9.67858	+	2.05725i	0.340281	+	0.0723289i	−0.0346019	+	0.999401i	$0.511016\pi$
$810$		0			0
$811$	8.83875	−	6.42173i	0.310370	−	0.225497i	−0.421685	−	0.906742i	$-0.638561\pi$
$811$	8.83875	−	6.42173i	0.310370	−	0.225497i	0.732055	+	0.681245i	$0.238561\pi$
$812$		0			0
$813$	−28.2319	−	48.8992i	−0.990137	−	1.71497i
$814$		0			0
$815$	−15.9075	−	27.5527i	−0.557217	−	0.965127i
$816$		0			0
$817$	−2.03503	−	19.3620i	−0.0711966	−	0.677390i
$818$		0			0
$819$	21.7891	+	6.34019i	0.761371	+	0.221544i
$820$		0			0
$821$	−11.8257	+	5.26516i	−0.412721	+	0.183755i	−0.602584	−	0.798055i	$-0.705862\pi$
$821$	−11.8257	+	5.26516i	−0.412721	+	0.183755i	0.189863	+	0.981811i	$0.439196\pi$
$822$		0			0
$823$	−40.7605	+	8.66390i	−1.42082	+	0.302005i	−0.853328	−	0.521374i	$-0.825420\pi$
$823$	−40.7605	+	8.66390i	−1.42082	+	0.302005i	−0.567492	+	0.823379i	$0.692086\pi$
$824$		0			0
$825$	−13.4485	−	85.9721i	−0.468215	−	2.99317i
$826$		0			0
$827$	3.81608	−	11.7447i	0.132698	−	0.408402i	−0.862527	−	0.506011i	$-0.831119\pi$
$827$	3.81608	−	11.7447i	0.132698	−	0.408402i	0.995225	+	0.0976089i	$0.0311194\pi$
$828$		0			0
$829$	21.0538	−	9.37375i	0.731228	−	0.325564i	−0.00712803	−	0.999975i	$-0.502269\pi$
$829$	21.0538	−	9.37375i	0.731228	−	0.325564i	0.738356	+	0.674411i	$0.235602\pi$
$830$		0			0
$831$	11.1937	+	34.4505i	0.388304	+	1.19508i
$832$		0			0
$833$	12.4179	−	9.02210i	0.430253	−	0.312597i
$834$		0			0
$835$	25.5349	−	44.2277i	0.883671	−	1.53056i
$836$		0			0
$837$	−0.133764			−0.00462357
$838$		0			0
$839$	19.2077	+	8.55184i	0.663125	+	0.295242i	0.710565	−	0.703632i	$-0.248440\pi$
$839$	19.2077	+	8.55184i	0.663125	+	0.295242i	−0.0474398	+	0.998874i	$0.515106\pi$
$840$		0			0
$841$	2.10301	−	2.33563i	0.0725177	−	0.0805390i
$842$		0			0
$843$	−31.1127	+	13.8523i	−1.07158	+	0.477097i
$844$		0			0
$845$	22.7383	−	45.7098i	0.782220	−	1.57247i
$846$		0			0
$847$	19.7569	−	6.33610i	0.678854	−	0.217711i
$848$		0			0
$849$	4.88234	−	1.03777i	0.167561	−	0.0356163i
$850$		0			0
$851$	−8.96108	+	85.2590i	−0.307182	+	2.92264i
$852$		0			0
$853$	−12.9619	−	39.8926i	−0.443807	−	1.36590i	−0.883787	−	0.467890i	$-0.845014\pi$
$853$	−12.9619	−	39.8926i	−0.443807	−	1.36590i	0.439980	−	0.898008i	$-0.354986\pi$
$854$		0			0
$855$	−7.75959	−	73.8276i	−0.265372	−	2.52485i
$856$		0			0
$857$	52.8206			1.80432			0.902158	−	0.431405i	$-0.141982\pi$
$857$	52.8206			1.80432			0.902158	+	0.431405i	$0.141982\pi$
$858$		0			0
$859$	−18.0332			−0.615283			−0.307642	−	0.951502i	$-0.599540\pi$
$859$	−18.0332			−0.615283			−0.307642	+	0.951502i	$0.599540\pi$
$860$		0			0
$861$	−1.91603	−	18.2298i	−0.0652980	−	0.621269i
$862$		0			0
$863$	−6.31488	−	19.4352i	−0.214961	−	0.661582i	−0.999156	−	0.0410677i	$-0.986924\pi$
$863$	−6.31488	−	19.4352i	−0.214961	−	0.661582i	0.784196	−	0.620514i	$-0.213076\pi$
$864$		0			0
$865$	−9.52030	+	90.5796i	−0.323700	+	3.07980i
$866$		0			0
$867$	−7.09817	+	1.50876i	−0.241066	+	0.0512402i
$868$		0			0
$869$	17.9815	−	14.5044i	0.609980	−	0.492027i
$870$		0			0
$871$	12.5802	+	16.2324i	0.426265	+	0.550013i
$872$		0			0
$873$	−38.4446	+	17.1166i	−1.30115	+	0.579311i
$874$		0			0
$875$	−26.8769	+	29.8499i	−0.908606	+	1.00911i
$876$		0			0
$877$	5.62932	+	2.50633i	0.190088	+	0.0846328i	0.499574	−	0.866271i	$-0.333490\pi$
$877$	5.62932	+	2.50633i	0.190088	+	0.0846328i	−0.309485	+	0.950904i	$0.600157\pi$
$878$		0			0
$879$	−0.798296			−0.0269259
$880$		0			0
$881$	16.4935	−	28.5676i	0.555681	−	0.962467i	−0.442170	−	0.896931i	$-0.645791\pi$
$881$	16.4935	−	28.5676i	0.555681	−	0.962467i	0.997850	−	0.0655357i	$-0.0208756\pi$
$882$		0			0
$883$	13.8420	−	10.0568i	0.465820	−	0.338438i	−0.329990	−	0.943984i	$-0.607045\pi$
$883$	13.8420	−	10.0568i	0.465820	−	0.338438i	0.795810	+	0.605546i	$0.207045\pi$
$884$		0			0
$885$	16.2344	+	49.9644i	0.545714	+	1.67953i
$886$		0			0
$887$	−15.0661	+	6.70785i	−0.505869	+	0.225228i	−0.643771	−	0.765218i	$-0.722631\pi$
$887$	−15.0661	+	6.70785i	−0.505869	+	0.225228i	0.137901	+	0.990446i	$0.455964\pi$
$888$		0			0
$889$	−4.14637	+	12.7612i	−0.139065	+	0.427997i
$890$		0			0
$891$	25.7927	+	4.13565i	0.864087	+	0.138549i
$892$		0			0
$893$	6.27952	−	1.33475i	0.210136	−	0.0446658i
$894$		0			0
$895$	31.2968	−	13.9342i	1.04614	−	0.465769i
$896$		0			0
$897$	−55.3069	+	52.9930i	−1.84664	+	1.76938i
$898$		0			0
$899$	0.0934962	+	0.889557i	0.00311827	+	0.0296684i
$900$		0			0
$901$	−26.0911	−	45.1912i	−0.869222	−	1.50554i
$902$		0			0
$903$	8.15889	+	14.1316i	0.271511	+	0.470270i
$904$		0			0
$905$	−13.7779	+	10.0102i	−0.457992	+	0.332751i
$906$		0			0
$907$	−23.2020	−	4.93173i	−0.770409	−	0.163755i	−0.194094	−	0.980983i	$-0.562177\pi$
$907$	−23.2020	−	4.93173i	−0.770409	−	0.163755i	−0.576315	+	0.817228i	$0.695510\pi$
$908$		0			0
$909$	−27.0934	−	19.6845i	−0.898630	−	0.652893i
$910$		0			0
$911$	−9.37646	+	28.8578i	−0.310656	+	0.956100i	0.666850	+	0.745192i	$0.267642\pi$
$911$	−9.37646	+	28.8578i	−0.310656	+	0.956100i	−0.977506	+	0.210908i	$0.932358\pi$
$912$		0			0
$913$	9.40805	−	34.8451i	0.311361	−	1.15320i
$914$		0			0
$915$	−43.8041	+	134.815i	−1.44812	+	4.45685i
$916$		0			0
$917$	0.832558	−	7.92126i	0.0274935	−	0.261583i
$918$		0			0
$919$	−5.03125	+	5.58777i	−0.165966	+	0.184324i	−0.820391	−	0.571803i	$-0.806244\pi$
$919$	−5.03125	+	5.58777i	−0.165966	+	0.184324i	0.654425	+	0.756127i	$0.272911\pi$
$920$		0			0
$921$	3.19026	+	30.3533i	0.105123	+	1.00017i
$922$		0			0
$923$	4.18628	+	8.66899i	0.137793	+	0.285343i
$924$		0			0
$925$	52.9379	−	91.6911i	1.74059	−	3.01478i
$926$		0			0
$927$	6.27012	+	2.79164i	0.205938	+	0.0916895i
$928$		0			0
$929$	24.1846	−	26.8597i	0.793470	−	0.881237i	−0.201696	−	0.979448i	$-0.564645\pi$
$929$	24.1846	−	26.8597i	0.793470	−	0.881237i	0.995166	+	0.0982107i	$0.0313119\pi$
$930$		0			0
$931$	15.7762	+	11.4621i	0.517044	+	0.375654i
$932$		0			0
$933$	55.4515	+	61.5851i	1.81540	+	2.01621i
$934$		0			0
$935$	−31.5386	−	48.7688i	−1.03142	−	1.59491i
$936$		0			0
$937$	15.9619	−	49.1256i	0.521452	−	1.60486i	−0.249776	−	0.968304i	$-0.580357\pi$
$937$	15.9619	−	49.1256i	0.521452	−	1.60486i	0.771227	−	0.636560i	$-0.219643\pi$
$938$		0			0
$939$	23.7291	−	10.5649i	0.774371	−	0.344772i
$940$		0			0
$941$	−3.12005	−	9.60254i	−0.101711	−	0.313034i	0.887234	−	0.461321i	$-0.152624\pi$
$941$	−3.12005	−	9.60254i	−0.101711	−	0.313034i	−0.988944	+	0.148287i	$0.952624\pi$
$942$		0			0
$943$	29.7634	+	13.2515i	0.969231	+	0.431529i
$944$		0			0
$945$	3.14019	+	5.43896i	0.102150	+	0.176929i
$946$		0			0
$947$	5.92568	−	10.2636i	0.192559	−	0.333521i	−0.753539	−	0.657403i	$-0.771655\pi$
$947$	5.92568	−	10.2636i	0.192559	−	0.333521i	0.946097	+	0.323882i	$0.104988\pi$
$948$		0			0
$949$	−2.54596	+	1.57709i	−0.0826455	+	0.0511945i
$950$		0			0
$951$	37.1325	+	7.89275i	1.20410	+	0.255940i
$952$		0			0
$953$	−0.690027	+	6.56517i	−0.0223522	+	0.212667i	0.977645	+	0.210263i	$0.0674319\pi$
$953$	−0.690027	+	6.56517i	−0.0223522	+	0.212667i	−0.999997	+	0.00240406i	$0.999235\pi$
$954$		0			0
$955$	49.3334	−	10.4861i	1.59639	−	0.339324i
$956$		0			0
$957$	−2.56751	+	47.2644i	−0.0829958	+	1.52784i
$958$		0			0
$959$	−1.81895	−	2.02015i	−0.0587370	−	0.0652341i
$960$		0			0
$961$	25.0594	+	18.2067i	0.808367	+	0.587313i
$962$		0			0
$963$	3.26996	+	10.0639i	0.105373	+	0.324305i
$964$		0			0
$965$	3.61219	+	34.3677i	0.116280	+	1.10633i
$966$		0			0
$967$	−38.8694			−1.24995			−0.624977	−	0.780643i	$-0.714892\pi$
$967$	−38.8694			−1.24995			−0.624977	+	0.780643i	$0.714892\pi$
$968$		0			0
$969$	−31.7934	−	55.0679i	−1.02135	−	1.76903i
$970$		0			0
$971$	34.6487	+	15.4266i	1.11193	+	0.495063i	0.878708	−	0.477360i	$-0.158406\pi$
$971$	34.6487	+	15.4266i	1.11193	+	0.495063i	0.233223	+	0.972423i	$0.425073\pi$
$972$		0			0
$973$	14.7892	+	3.14355i	0.474121	+	0.100778i
$974$		0			0
$975$	89.0190	−	32.0067i	2.85089	−	1.02504i
$976$		0			0
$977$	16.0305	+	17.8037i	0.512862	+	0.569591i	0.942839	−	0.333249i	$-0.108145\pi$
$977$	16.0305	+	17.8037i	0.512862	+	0.569591i	−0.429977	+	0.902840i	$0.641478\pi$
$978$		0			0
$979$	−3.68511	+	1.86881i	−0.117777	+	0.0597273i
$980$		0			0
$981$	−16.5473	+	3.51725i	−0.528316	+	0.112297i
$982$		0			0
$983$	26.4009	+	19.1814i	0.842057	+	0.611790i	0.922945	−	0.384933i	$-0.125775\pi$
$983$	26.4009	+	19.1814i	0.842057	+	0.611790i	−0.0808873	+	0.996723i	$0.525775\pi$
$984$		0			0
$985$	−99.5808	−	21.1666i	−3.17291	−	0.674423i
$986$		0			0
$987$	−4.35316	+	3.16276i	−0.138563	+	0.100672i
$988$		0			0
$989$	−29.0032			−0.922250
$990$		0			0
$991$	28.9180	−	50.0875i	0.918611	−	1.59108i	0.117084	−	0.993122i	$-0.462645\pi$
$991$	28.9180	−	50.0875i	0.918611	−	1.59108i	0.801527	−	0.597958i	$-0.204021\pi$
$992$		0			0
$993$	32.1601	−	23.3656i	1.02057	−	0.741486i
$994$		0			0
$995$	61.6559	−	68.4759i	1.95462	−	2.17083i
$996$		0			0
$997$	1.94564	−	18.5115i	0.0616190	−	0.586266i	−0.919531	−	0.393018i	$-0.871431\pi$
$997$	1.94564	−	18.5115i	0.0616190	−	0.586266i	0.981150	−	0.193248i	$-0.0619022\pi$
$998$		0			0
$999$	−5.76308	−	6.40055i	−0.182336	−	0.202504i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.bg.a.9.2	✓	112
11.5	even	5	inner	572.2.bg.a.269.13	yes	112
13.3	even	3	inner	572.2.bg.a.185.13	yes	112
143.16	even	15	inner	572.2.bg.a.445.2	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.bg.a.9.2	✓	112	1.1	even	1	trivial
572.2.bg.a.185.13	yes	112	13.3	even	3	inner
572.2.bg.a.269.13	yes	112	11.5	even	5	inner
572.2.bg.a.445.2	yes	112	143.16	even	15	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.bg (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.263130 - 2.50351i) q^{3} +(1.21356 + 3.73495i) q^{5} +(0.197160 - 1.87585i) q^{7} +(-3.26389 + 0.693762i) q^{9} +O(q^{10})\)	\(q+(-0.263130 - 2.50351i) q^{3} +(1.21356 + 3.73495i) q^{5} +(0.197160 - 1.87585i) q^{7} +(-3.26389 + 0.693762i) q^{9} +(-2.77810 - 1.81167i) q^{11} +(1.36372 - 3.33770i) q^{13} +(9.03117 - 4.02094i) q^{15} +(2.98366 - 3.31369i) q^{17} +(5.17517 + 2.30413i) q^{19} -4.74809 q^{21} +(4.21964 - 7.30862i) q^{23} +(-8.43205 + 6.12624i) q^{25} +(0.262002 + 0.806360i) q^{27} +(5.17932 - 2.30598i) q^{29} +(-0.0487528 + 0.150046i) q^{31} +(-3.80454 + 7.43172i) q^{33} +(7.24547 - 1.54007i) q^{35} +(-9.28006 + 4.13175i) q^{37} +(-8.71482 - 2.53584i) q^{39} +(0.403536 + 3.83939i) q^{41} +(-1.71835 - 2.97627i) q^{43} +(-6.55210 - 11.3486i) q^{45} +(0.916824 - 0.666111i) q^{47} +(3.36709 + 0.715698i) q^{49} +(-9.08095 - 6.59770i) q^{51} +(3.61632 - 11.1299i) q^{53} +(3.39511 - 12.5746i) q^{55} +(4.40668 - 13.5624i) q^{57} +(-0.555488 + 5.28512i) q^{59} +(-9.59465 + 10.6559i) q^{61} +(0.657885 + 6.25936i) q^{63} +(14.1211 + 1.04293i) q^{65} +(-2.84792 + 4.93273i) q^{67} +(-19.4075 - 8.64079i) q^{69} +(-1.78658 + 1.98420i) q^{71} +(-0.671988 - 0.488228i) q^{73} +(17.5558 + 19.4977i) q^{75} +(-3.94615 + 4.85411i) q^{77} +(-2.15248 + 6.62465i) q^{79} +(-7.19520 + 3.20351i) q^{81} +(3.36285 + 10.3498i) q^{83} +(15.9973 + 7.12246i) q^{85} +(-7.13589 - 12.3597i) q^{87} +(0.622905 - 1.07890i) q^{89} +(-5.99216 - 3.21620i) q^{91} +(0.388469 + 0.0825717i) q^{93} +(-2.32545 + 22.1252i) q^{95} +(12.3361 - 2.62212i) q^{97} +(10.3243 + 3.98576i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q + 8 q^{9}+O(q^{10}) \) 112 * q + 8 * q^9	\( 112 q + 8 q^{9} - 10 q^{11} + 11 q^{13} - 2 q^{15} + 4 q^{17} - 12 q^{19} - 40 q^{21} + 10 q^{23} - 16 q^{25} - 12 q^{27} + q^{29} + 4 q^{31} + 35 q^{33} - 5 q^{35} - 12 q^{37} + 21 q^{39} - 10 q^{41} - 32 q^{43} + 34 q^{45} + 70 q^{47} + 16 q^{49} - 48 q^{51} - 26 q^{53} + 10 q^{55} - 12 q^{57} - 5 q^{59} + 28 q^{61} + 34 q^{63} + 22 q^{65} - 68 q^{67} - 58 q^{69} + 44 q^{71} + 42 q^{73} - 24 q^{75} + 46 q^{77} - 24 q^{79} + 64 q^{81} - 114 q^{83} + 4 q^{85} - 30 q^{87} - 6 q^{89} + 77 q^{91} - 5 q^{93} - 36 q^{95} - 15 q^{97} - 40 q^{99}+O(q^{100}) \) 112 * q + 8 * q^9 - 10 * q^11 + 11 * q^13 - 2 * q^15 + 4 * q^17 - 12 * q^19 - 40 * q^21 + 10 * q^23 - 16 * q^25 - 12 * q^27 + q^29 + 4 * q^31 + 35 * q^33 - 5 * q^35 - 12 * q^37 + 21 * q^39 - 10 * q^41 - 32 * q^43 + 34 * q^45 + 70 * q^47 + 16 * q^49 - 48 * q^51 - 26 * q^53 + 10 * q^55 - 12 * q^57 - 5 * q^59 + 28 * q^61 + 34 * q^63 + 22 * q^65 - 68 * q^67 - 58 * q^69 + 44 * q^71 + 42 * q^73 - 24 * q^75 + 46 * q^77 - 24 * q^79 + 64 * q^81 - 114 * q^83 + 4 * q^85 - 30 * q^87 - 6 * q^89 + 77 * q^91 - 5 * q^93 - 36 * q^95 - 15 * q^97 - 40 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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