LMFDB - Embedded newform 152.2.q.c.17.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [152,2,Mod(9,152)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(152, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

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

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

chi := DirichletCharacter("152.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 152 = 2^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	152.q (of order $9$, degree $6$, 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:	$1.21372611072$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 3 x^{17} + 21 x^{16} - 34 x^{15} + 204 x^{14} - 267 x^{13} + 1304 x^{12} - 972 x^{11} + \cdots + 1 $ x^18 - 3x^17 + 21x^16 - 34x^15 + 204x^14 - 267x^13 + 1304x^12 - 972x^11 + 4890x^10 - 2547x^9 + 12945x^8 - 2403x^7 + 14457x^6 - 6729x^5 + 8769x^4 - 686x^3 + 132x^2 + 6*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			17.1
Root			$-0.643662 + 1.11486i$ of defining polynomial
Character	$\chi$	$=$	152.17
Dual form			152.2.q.c.9.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.986147 - 0.827476i) q^{3} +(-3.98739 + 1.45129i) q^{5} +(-1.68618 - 2.92055i) q^{7} +(-0.233174 - 1.32240i) q^{9} +O(q^{10})$	\(q+(-0.986147 - 0.827476i) q^{3} +(-3.98739 + 1.45129i) q^{5} +(-1.68618 - 2.92055i) q^{7} +(-0.233174 - 1.32240i) q^{9} +(0.247839 - 0.429270i) q^{11} +(-2.70667 + 2.27116i) q^{13} +(5.13306 + 1.86828i) q^{15} +(-0.689000 + 3.90752i) q^{17} +(2.26532 - 3.72402i) q^{19} +(-0.753863 + 4.27537i) q^{21} +(-0.886425 - 0.322632i) q^{23} +(9.96280 - 8.35978i) q^{25} +(-2.79529 + 4.84159i) q^{27} +(-0.463399 - 2.62807i) q^{29} +(-3.41680 - 5.91807i) q^{31} +(-0.599617 + 0.218243i) q^{33} +(10.9620 + 9.19823i) q^{35} +6.73600 q^{37} +4.54851 q^{39} +(-1.85588 - 1.55727i) q^{41} +(-11.2724 + 4.10282i) q^{43} +(2.84894 + 4.93451i) q^{45} +(0.194129 + 1.10096i) q^{47} +(-2.18641 + 3.78698i) q^{49} +(3.91283 - 3.28326i) q^{51} +(-0.951101 - 0.346173i) q^{53} +(-0.365236 + 2.07135i) q^{55} +(-5.31547 + 1.79794i) q^{57} +(1.14470 - 6.49191i) q^{59} +(-8.89778 - 3.23853i) q^{61} +(-3.46895 + 2.91080i) q^{63} +(7.49641 - 12.9842i) q^{65} +(-1.84999 - 10.4918i) q^{67} +(0.607175 + 1.05166i) q^{69} +(-8.85275 + 3.22214i) q^{71} +(2.49328 + 2.09211i) q^{73} -16.7423 q^{75} -1.67161 q^{77} +(4.41163 + 3.70180i) q^{79} +(2.97742 - 1.08369i) q^{81} +(3.89085 + 6.73916i) q^{83} +(-2.92363 - 16.5807i) q^{85} +(-1.71768 + 2.97511i) q^{87} +(2.05797 - 1.72684i) q^{89} +(11.1970 + 4.07537i) q^{91} +(-1.52759 + 8.66341i) q^{93} +(-3.62805 + 18.1368i) q^{95} +(0.248939 - 1.41180i) q^{97} +(-0.625455 - 0.227647i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 9 q^{7} - 6 q^{9}+O(q^{10}) $ 18 * q - 9 * q^7 - 6 * q^9	$ 18 q - 9 q^{7} - 6 q^{9} - 3 q^{11} + 3 q^{13} + 33 q^{15} + 9 q^{17} - 24 q^{19} - 15 q^{21} + 6 q^{23} + 6 q^{25} - 12 q^{27} - 3 q^{29} - 6 q^{31} - 45 q^{33} - 15 q^{35} + 48 q^{37} + 12 q^{39} - 18 q^{41} - 39 q^{43} - 42 q^{45} - 27 q^{47} - 18 q^{49} + 48 q^{51} + 39 q^{53} - 27 q^{55} - 6 q^{57} + 9 q^{59} - 24 q^{61} + 3 q^{63} + 27 q^{65} + 39 q^{67} - 3 q^{69} + 12 q^{73} + 90 q^{75} + 60 q^{77} + 63 q^{79} - 6 q^{81} - 27 q^{83} - 30 q^{85} + 18 q^{87} + 66 q^{89} + 108 q^{91} + 60 q^{93} - 75 q^{95} - 81 q^{97} + 15 q^{99}+O(q^{100}) $ 18 * q - 9 * q^7 - 6 * q^9 - 3 * q^11 + 3 * q^13 + 33 * q^15 + 9 * q^17 - 24 * q^19 - 15 * q^21 + 6 * q^23 + 6 * q^25 - 12 * q^27 - 3 * q^29 - 6 * q^31 - 45 * q^33 - 15 * q^35 + 48 * q^37 + 12 * q^39 - 18 * q^41 - 39 * q^43 - 42 * q^45 - 27 * q^47 - 18 * q^49 + 48 * q^51 + 39 * q^53 - 27 * q^55 - 6 * q^57 + 9 * q^59 - 24 * q^61 + 3 * q^63 + 27 * q^65 + 39 * q^67 - 3 * q^69 + 12 * q^73 + 90 * q^75 + 60 * q^77 + 63 * q^79 - 6 * q^81 - 27 * q^83 - 30 * q^85 + 18 * q^87 + 66 * q^89 + 108 * q^91 + 60 * q^93 - 75 * q^95 - 81 * q^97 + 15 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/152\mathbb{Z}\right)^\times$.

$n$	$39$	$77$	$97$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{9}\right)$

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
$3$	−0.986147	−	0.827476i	−0.569352	−	0.477743i	0.312078	−	0.950056i	$-0.398975\pi$
$3$	−0.986147	−	0.827476i	−0.569352	−	0.477743i	−0.881431	+	0.472313i	$0.843419\pi$
$4$		0			0
$5$	−3.98739	+	1.45129i	−1.78321	+	0.649037i	−0.783600	+	0.621266i	$0.786619\pi$
$5$	−3.98739	+	1.45129i	−1.78321	+	0.649037i	−0.999614	+	0.0277715i	$0.991159\pi$
$6$		0			0
$7$	−1.68618	−	2.92055i	−0.637316	−	1.10386i	−0.986019	−	0.166631i	$-0.946711\pi$
$7$	−1.68618	−	2.92055i	−0.637316	−	1.10386i	0.348703	−	0.937233i	$-0.386622\pi$
$8$		0			0
$9$	−0.233174	−	1.32240i	−0.0777247	−	0.440799i
$10$		0			0
$11$	0.247839	−	0.429270i	0.0747264	−	0.129430i	−0.826241	−	0.563317i	$-0.809525\pi$
$11$	0.247839	−	0.429270i	0.0747264	−	0.129430i	0.900967	+	0.433887i	$0.142858\pi$
$12$		0			0
$13$	−2.70667	+	2.27116i	−0.750694	+	0.629907i	−0.935686	−	0.352833i	$-0.885218\pi$
$13$	−2.70667	+	2.27116i	−0.750694	+	0.629907i	0.184992	+	0.982740i	$0.440774\pi$
$14$		0			0
$15$	5.13306	+	1.86828i	1.32535	+	0.482388i
$16$		0			0
$17$	−0.689000	+	3.90752i	−0.167107	+	0.947712i	0.779758	+	0.626081i	$0.215342\pi$
$17$	−0.689000	+	3.90752i	−0.167107	+	0.947712i	−0.946865	+	0.321631i	$0.895769\pi$
$18$		0			0
$19$	2.26532	−	3.72402i	0.519699	−	0.854349i
$19$	2.26532	−	3.72402i	0.519699	−	0.854349i
$20$		0			0
$21$	−0.753863	+	4.27537i	−0.164506	+	0.932962i
$22$		0			0
$23$	−0.886425	−	0.322632i	−0.184832	−	0.0672735i	0.247946	−	0.968774i	$-0.420244\pi$
$23$	−0.886425	−	0.322632i	−0.184832	−	0.0672735i	−0.432778	+	0.901500i	$0.642467\pi$
$24$		0			0
$25$	9.96280	−	8.35978i	1.99256	−	1.67196i
$26$		0			0
$27$	−2.79529	+	4.84159i	−0.537954	+	0.931764i
$28$		0			0
$29$	−0.463399	−	2.62807i	−0.0860511	−	0.488020i	−0.997125	−	0.0757766i	$-0.975856\pi$
$29$	−0.463399	−	2.62807i	−0.0860511	−	0.488020i	0.911074	−	0.412243i	$-0.135255\pi$
$30$		0			0
$31$	−3.41680	−	5.91807i	−0.613675	−	1.06292i	−0.990615	−	0.136679i	$-0.956357\pi$
$31$	−3.41680	−	5.91807i	−0.613675	−	1.06292i	0.376940	−	0.926238i	$-0.376976\pi$
$32$		0			0
$33$	−0.599617	+	0.218243i	−0.104380	+	0.0379912i
$34$		0			0
$35$	10.9620	+	9.19823i	1.85292	+	1.55479i
$36$		0			0
$37$	6.73600			1.10739			0.553696	−	0.832719i	$-0.313217\pi$
$37$	6.73600			1.10739			0.553696	+	0.832719i	$0.313217\pi$
$38$		0			0
$39$	4.54851			0.728344
$40$		0			0
$41$	−1.85588	−	1.55727i	−0.289840	−	0.243205i	0.486261	−	0.873814i	$-0.338361\pi$
$41$	−1.85588	−	1.55727i	−0.289840	−	0.243205i	−0.776100	+	0.630609i	$0.782805\pi$
$42$		0			0
$43$	−11.2724	+	4.10282i	−1.71902	+	0.625674i	−0.997754	−	0.0669794i	$-0.978664\pi$
$43$	−11.2724	+	4.10282i	−1.71902	+	0.625674i	−0.721271	+	0.692653i	$0.756442\pi$
$44$		0			0
$45$	2.84894	+	4.93451i	0.424695	+	0.735593i
$46$		0			0
$47$	0.194129	+	1.10096i	0.0283166	+	0.160591i	0.995687	−	0.0927743i	$-0.0295735\pi$
$47$	0.194129	+	1.10096i	0.0283166	+	0.160591i	−0.967371	+	0.253366i	$0.918462\pi$
$48$		0			0
$49$	−2.18641	+	3.78698i	−0.312345	+	0.540997i
$50$		0			0
$51$	3.91283	−	3.28326i	0.547906	−	0.459748i
$52$		0			0
$53$	−0.951101	−	0.346173i	−0.130644	−	0.0475505i	0.275871	−	0.961195i	$-0.411034\pi$
$53$	−0.951101	−	0.346173i	−0.130644	−	0.0475505i	−0.406515	+	0.913644i	$0.633256\pi$
$54$		0			0
$55$	−0.365236	+	2.07135i	−0.0492484	+	0.279301i
$56$		0			0
$57$	−5.31547	+	1.79794i	−0.704052	+	0.238143i
$58$		0			0
$59$	1.14470	−	6.49191i	0.149027	−	0.845175i	−0.815018	−	0.579436i	$-0.803273\pi$
$59$	1.14470	−	6.49191i	0.149027	−	0.845175i	0.964045	−	0.265739i	$-0.0856160\pi$
$60$		0			0
$61$	−8.89778	−	3.23853i	−1.13924	−	0.414651i	−0.297604	−	0.954689i	$-0.596188\pi$
$61$	−8.89778	−	3.23853i	−1.13924	−	0.414651i	−0.841640	+	0.540038i	$0.818410\pi$
$62$		0			0
$63$	−3.46895	+	2.91080i	−0.437047	+	0.366726i
$64$		0			0
$65$	7.49641	−	12.9842i	0.929816	−	1.61049i
$66$		0			0
$67$	−1.84999	−	10.4918i	−0.226013	−	1.28178i	−0.860740	−	0.509045i	$-0.829999\pi$
$67$	−1.84999	−	10.4918i	−0.226013	−	1.28178i	0.634727	−	0.772736i	$-0.281112\pi$
$68$		0			0
$69$	0.607175	+	1.05166i	0.0730953	+	0.126605i
$70$		0			0
$71$	−8.85275	+	3.22214i	−1.05063	+	0.382397i	−0.808900	−	0.587947i	$-0.799936\pi$
$71$	−8.85275	+	3.22214i	−1.05063	+	0.382397i	−0.241728	+	0.970344i	$0.577714\pi$
$72$		0			0
$73$	2.49328	+	2.09211i	0.291817	+	0.244863i	0.776929	−	0.629589i	$-0.216777\pi$
$73$	2.49328	+	2.09211i	0.291817	+	0.244863i	−0.485112	+	0.874452i	$0.661221\pi$
$74$		0			0
$75$	−16.7423			−1.93324
$76$		0			0
$77$	−1.67161			−0.190497
$78$		0			0
$79$	4.41163	+	3.70180i	0.496347	+	0.416485i	0.856295	−	0.516488i	$-0.172761\pi$
$79$	4.41163	+	3.70180i	0.496347	+	0.416485i	−0.359947	+	0.932973i	$0.617205\pi$
$80$		0			0
$81$	2.97742	−	1.08369i	0.330825	−	0.120410i
$82$		0			0
$83$	3.89085	+	6.73916i	0.427077	+	0.739719i	0.996612	−	0.0822484i	$-0.0262101\pi$
$83$	3.89085	+	6.73916i	0.427077	+	0.739719i	−0.569535	+	0.821967i	$0.692877\pi$
$84$		0			0
$85$	−2.92363	−	16.5807i	−0.317112	−	1.79843i
$86$		0			0
$87$	−1.71768	+	2.97511i	−0.184155	+	0.318966i
$88$		0			0
$89$	2.05797	−	1.72684i	0.218145	−	0.183045i	−0.527166	−	0.849762i	$-0.676746\pi$
$89$	2.05797	−	1.72684i	0.218145	−	0.183045i	0.745311	+	0.666717i	$0.232301\pi$
$90$		0			0
$91$	11.1970	+	4.07537i	1.17376	+	0.427215i
$92$		0			0
$93$	−1.52759	+	8.66341i	−0.158404	+	0.898353i
$94$		0			0
$95$	−3.62805	+	18.1368i	−0.372231	+	1.86079i
$96$		0			0
$97$	0.248939	−	1.41180i	0.0252759	−	0.143347i	−0.969558	−	0.244861i	$-0.921258\pi$
$97$	0.248939	−	1.41180i	0.0252759	−	0.143347i	0.994834	+	0.101514i	$0.0323687\pi$
$98$		0			0
$99$	−0.625455	−	0.227647i	−0.0628606	−	0.0228794i
$100$		0			0
$101$	−2.85382	+	2.39464i	−0.283965	+	0.238275i	−0.773633	−	0.633634i	$-0.781563\pi$
$101$	−2.85382	+	2.39464i	−0.283965	+	0.238275i	0.489668	+	0.871909i	$0.337118\pi$
$102$		0			0
$103$	−2.28192	+	3.95240i	−0.224844	+	0.389442i	−0.956273	−	0.292477i	$-0.905521\pi$
$103$	−2.28192	+	3.95240i	−0.224844	+	0.389442i	0.731428	+	0.681918i	$0.238854\pi$
$104$		0			0
$105$	−3.19886	−	18.1416i	−0.312177	−	1.77044i
$106$		0			0
$107$	−8.64438	−	14.9725i	−0.835684	−	1.44745i	−0.893473	−	0.449118i	$-0.851738\pi$
$107$	−8.64438	−	14.9725i	−0.835684	−	1.44745i	0.0577891	−	0.998329i	$-0.481595\pi$
$108$		0			0
$109$	8.04469	−	2.92803i	0.770542	−	0.280454i	0.0733187	−	0.997309i	$-0.476641\pi$
$109$	8.04469	−	2.92803i	0.770542	−	0.280454i	0.697223	+	0.716854i	$0.254419\pi$
$110$		0			0
$111$	−6.64269	−	5.57388i	−0.630496	−	0.529049i
$112$		0			0
$113$	−12.4068			−1.16713			−0.583566	−	0.812066i	$-0.698343\pi$
$113$	−12.4068			−1.16713			−0.583566	+	0.812066i	$0.698343\pi$
$114$		0			0
$115$	4.00275			0.373259
$116$		0			0
$117$	3.63450	+	3.04971i	0.336010	+	0.281946i
$118$		0			0
$119$	12.5739	−	4.57652i	1.15265	−	0.419529i
$120$		0			0
$121$	5.37715	+	9.31350i	0.488832	+	0.846682i
$122$		0			0
$123$	0.541570	+	3.07139i	0.0488317	+	0.276938i
$124$		0			0
$125$	−16.9849	+	29.4186i	−1.51917	+	2.63128i
$126$		0			0
$127$	8.59313	−	7.21049i	0.762517	−	0.639828i	−0.176264	−	0.984343i	$-0.556401\pi$
$127$	8.59313	−	7.21049i	0.762517	−	0.639828i	0.938781	+	0.344515i	$0.111957\pi$
$128$		0			0
$129$	14.5112	+	5.28166i	1.27764	+	0.465024i
$130$		0			0
$131$	0.912664	−	5.17598i	0.0797398	−	0.452227i	−0.918628	−	0.395123i	$-0.870702\pi$
$131$	0.912664	−	5.17598i	0.0797398	−	0.452227i	0.998368	−	0.0571044i	$-0.0181868\pi$
$132$		0			0
$133$	−14.6959	−	0.336594i	−1.27430	−	0.0291864i
$134$		0			0
$135$	4.11937	−	23.3621i	0.354539	−	2.01069i
$136$		0			0
$137$	13.4952	+	4.91187i	1.15298	+	0.419649i	0.846584	−	0.532256i	$-0.178656\pi$
$137$	13.4952	+	4.91187i	1.15298	+	0.419649i	0.306393	+	0.951905i	$0.400878\pi$
$138$		0			0
$139$	−2.84328	+	2.38580i	−0.241164	+	0.202361i	−0.755356	−	0.655314i	$-0.772536\pi$
$139$	−2.84328	+	2.38580i	−0.241164	+	0.202361i	0.514192	+	0.857675i	$0.328092\pi$
$140$		0			0
$141$	0.719578	−	1.24635i	0.0605994	−	0.104961i
$142$		0			0
$143$	0.304124	+	1.72478i	0.0254322	+	0.144233i
$144$		0			0
$145$	5.66184	+	9.80660i	0.470191	+	0.814394i
$146$		0			0
$147$	5.28976	−	1.92531i	0.436292	−	0.158797i
$148$		0			0
$149$	5.99620	+	5.03141i	0.491228	+	0.412189i	0.854466	−	0.519507i	$-0.173884\pi$
$149$	5.99620	+	5.03141i	0.491228	+	0.412189i	−0.363238	+	0.931696i	$0.618329\pi$
$150$		0			0
$151$	21.1437			1.72065			0.860326	−	0.509743i	$-0.170260\pi$
$151$	21.1437			1.72065			0.860326	+	0.509743i	$0.170260\pi$
$152$		0			0
$153$	5.32794			0.430739
$154$		0			0
$155$	22.2129	+	18.6389i	1.78419	+	1.49711i
$156$		0			0
$157$	3.50177	−	1.27454i	0.279472	−	0.101719i	−0.198482	−	0.980105i	$-0.563601\pi$
$157$	3.50177	−	1.27454i	0.279472	−	0.101719i	0.477953	+	0.878385i	$0.341379\pi$
$158$		0			0
$159$	0.651477	+	1.12839i	0.0516655	+	0.0894872i
$160$		0			0
$161$	0.552409	+	3.13286i	0.0435359	+	0.246904i
$162$		0			0
$163$	2.72987	−	4.72828i	0.213820	−	0.370348i	−0.739087	−	0.673610i	$-0.764743\pi$
$163$	2.72987	−	4.72828i	0.213820	−	0.370348i	0.952907	+	0.303263i	$0.0980760\pi$
$164$		0			0
$165$	2.07417	−	1.74044i	0.161474	−	0.135493i
$166$		0			0
$167$	5.73393	+	2.08698i	0.443705	+	0.161495i	0.554204	−	0.832381i	$-0.313023\pi$
$167$	5.73393	+	2.08698i	0.443705	+	0.161495i	−0.110499	+	0.993876i	$0.535245\pi$
$168$		0			0
$169$	−0.0895628	+	0.507936i	−0.00688944	+	0.0390720i
$170$		0			0
$171$	−5.45285	−	2.12730i	−0.416990	−	0.162679i
$172$		0			0
$173$	3.82988	−	21.7203i	0.291180	−	1.65137i	−0.391153	−	0.920326i	$-0.627924\pi$
$173$	3.82988	−	21.7203i	0.291180	−	1.65137i	0.682334	−	0.731041i	$-0.260965\pi$
$174$		0			0
$175$	−41.2143	−	15.0008i	−3.11550	−	1.13395i
$176$		0			0
$177$	−6.50074	+	5.45477i	−0.488626	+	0.410006i
$178$		0			0
$179$	6.30040	−	10.9126i	0.470914	−	0.815647i	−0.528532	−	0.848913i	$-0.677258\pi$
$179$	6.30040	−	10.9126i	0.470914	−	0.815647i	0.999447	+	0.0332660i	$0.0105908\pi$
$180$		0			0
$181$	0.234375	+	1.32921i	0.0174210	+	0.0987992i	0.992278	−	0.124030i	$-0.0395819\pi$
$181$	0.234375	+	1.32921i	0.0174210	+	0.0987992i	−0.974858	+	0.222829i	$0.928471\pi$
$182$		0			0
$183$	6.09472	+	10.5564i	0.450535	+	0.780349i
$184$		0			0
$185$	−26.8591	+	9.77590i	−1.97472	+	0.718738i
$186$		0			0
$187$	1.50662	+	1.26420i	0.110175	+	0.0924477i
$188$		0			0
$189$	18.8535			1.37139
$190$		0			0
$191$	−21.6982			−1.57003			−0.785014	−	0.619477i	$-0.787345\pi$
$191$	−21.6982			−1.57003			−0.785014	+	0.619477i	$0.787345\pi$
$192$		0			0
$193$	−19.3246	−	16.2153i	−1.39101	−	1.16720i	−0.964927	−	0.262518i	$-0.915447\pi$
$193$	−19.3246	−	16.2153i	−1.39101	−	1.16720i	−0.426087	−	0.904682i	$-0.640108\pi$
$194$		0			0
$195$	−18.1367	+	6.60120i	−1.29879	+	0.472722i
$196$		0			0
$197$	−5.66192	−	9.80674i	−0.403395	−	0.698701i	0.590738	−	0.806863i	$-0.298837\pi$
$197$	−5.66192	−	9.80674i	−0.403395	−	0.698701i	−0.994133	+	0.108162i	$0.965503\pi$
$198$		0			0
$199$	0.624969	+	3.54437i	0.0443028	+	0.251254i	0.998914	−	0.0466026i	$-0.0148394\pi$
$199$	0.624969	+	3.54437i	0.0443028	+	0.251254i	−0.954611	+	0.297856i	$0.903728\pi$
$200$		0			0
$201$	−6.85737	+	11.8773i	−0.483682	+	0.837761i
$202$		0			0
$203$	−6.89403	+	5.78478i	−0.483866	+	0.406012i
$204$		0			0
$205$	9.66017	+	3.51601i	0.674695	+	0.245569i
$206$		0			0
$207$	−0.219956	+	1.24743i	−0.0152880	+	0.0867027i
$208$		0			0
$209$	−1.03718	−	1.89539i	−0.0717431	−	0.131107i
$210$		0			0
$211$	−2.88696	+	16.3728i	−0.198747	+	1.12715i	0.708235	+	0.705977i	$0.249492\pi$
$211$	−2.88696	+	16.3728i	−0.198747	+	1.12715i	−0.906981	+	0.421171i	$0.861619\pi$
$212$		0			0
$213$	11.3964	+	4.14793i	0.780865	+	0.284212i
$214$		0			0
$215$	38.9931	−	32.7191i	2.65930	−	2.23142i
$216$		0			0
$217$	−11.5227	+	19.9579i	−0.782210	+	1.35483i
$218$		0			0
$219$	−0.727572	−	4.12627i	−0.0491648	−	0.278827i
$220$		0			0
$221$	−7.00971	−	12.1412i	−0.471524	−	0.816704i
$222$		0			0
$223$	−10.1646	+	3.69962i	−0.680673	+	0.247745i	−0.659137	−	0.752023i	$-0.729078\pi$
$223$	−10.1646	+	3.69962i	−0.680673	+	0.247745i	−0.0215367	+	0.999768i	$0.506856\pi$
$224$		0			0
$225$	−13.3780	−	11.2255i	−0.891868	−	0.748366i
$226$		0			0
$227$	−9.91627			−0.658166			−0.329083	−	0.944301i	$-0.606740\pi$
$227$	−9.91627			−0.658166			−0.329083	+	0.944301i	$0.606740\pi$
$228$		0			0
$229$	22.0421			1.45658			0.728292	−	0.685267i	$-0.240315\pi$
$229$	22.0421			1.45658			0.728292	+	0.685267i	$0.240315\pi$
$230$		0			0
$231$	1.64845	+	1.38322i	0.108460	+	0.0910089i
$232$		0			0
$233$	−3.03934	+	1.10623i	−0.199114	+	0.0724715i	−0.439652	−	0.898168i	$-0.644898\pi$
$233$	−3.03934	+	1.10623i	−0.199114	+	0.0724715i	0.240538	+	0.970640i	$0.422676\pi$
$234$		0			0
$235$	−2.37188	−	4.10821i	−0.154724	−	0.267990i
$236$		0			0
$237$	−1.28737	−	7.30104i	−0.0836237	−	0.474253i
$238$		0			0
$239$	2.45440	−	4.25115i	0.158762	−	0.274984i	−0.775660	−	0.631151i	$-0.782583\pi$
$239$	2.45440	−	4.25115i	0.158762	−	0.274984i	0.934423	+	0.356166i	$0.115916\pi$
$240$		0			0
$241$	−9.74186	+	8.17439i	−0.627528	+	0.526559i	−0.900160	−	0.435560i	$-0.856550\pi$
$241$	−9.74186	+	8.17439i	−0.627528	+	0.526559i	0.272632	+	0.962119i	$0.412106\pi$
$242$		0			0
$243$	11.9274	+	4.34122i	0.765143	+	0.278489i
$244$		0			0
$245$	3.22207	−	18.2733i	0.205850	−	1.16744i
$246$		0			0
$247$	2.32641	+	15.2246i	0.148026	+	0.968718i
$248$		0			0
$249$	1.73953	−	9.86539i	0.110239	−	0.625194i
$250$		0			0
$251$	3.10677	+	1.13077i	0.196098	+	0.0713737i	0.438202	−	0.898877i	$-0.355615\pi$
$251$	3.10677	+	1.13077i	0.196098	+	0.0713737i	−0.242104	+	0.970250i	$0.577838\pi$
$252$		0			0
$253$	−0.358187	+	0.300555i	−0.0225190	+	0.0188957i
$254$		0			0
$255$	−10.8370	+	18.7703i	−0.678641	+	1.17544i
$256$		0			0
$257$	2.78411	+	15.7895i	0.173668	+	0.984921i	0.939670	+	0.342082i	$0.111132\pi$
$257$	2.78411	+	15.7895i	0.173668	+	0.984921i	−0.766002	+	0.642838i	$0.777757\pi$
$258$		0			0
$259$	−11.3581	−	19.6728i	−0.705759	−	1.22241i
$260$		0			0
$261$	−3.36730	+	1.22560i	−0.208430	+	0.0758625i
$262$		0			0
$263$	−5.72882	−	4.80705i	−0.353254	−	0.296415i	0.448841	−	0.893612i	$-0.351837\pi$
$263$	−5.72882	−	4.80705i	−0.353254	−	0.296415i	−0.802095	+	0.597196i	$0.796281\pi$
$264$		0			0
$265$	4.29481			0.263828
$266$		0			0
$267$	−3.45838			−0.211650
$268$		0			0
$269$	−21.5853	−	18.1123i	−1.31608	−	1.10432i	−0.987120	−	0.159980i	$-0.948857\pi$
$269$	−21.5853	−	18.1123i	−1.31608	−	1.10432i	−0.328961	−	0.944343i	$-0.606699\pi$
$270$		0			0
$271$	3.62220	−	1.31837i	0.220033	−	0.0800855i	−0.229651	−	0.973273i	$-0.573759\pi$
$271$	3.62220	−	1.31837i	0.220033	−	0.0800855i	0.449685	+	0.893187i	$0.351536\pi$
$272$		0			0
$273$	−7.66960	−	13.2841i	−0.464186	−	0.803993i
$274$		0			0
$275$	−1.11943	−	6.34862i	−0.0675043	−	0.382836i
$276$		0			0
$277$	−1.99251	+	3.45112i	−0.119718	+	0.207358i	−0.919656	−	0.392725i	$-0.871532\pi$
$277$	−1.99251	+	3.45112i	−0.119718	+	0.207358i	0.799938	+	0.600083i	$0.204866\pi$
$278$		0			0
$279$	−7.02932	+	5.89830i	−0.420835	+	0.353122i
$280$		0			0
$281$	−5.04675	−	1.83687i	−0.301064	−	0.109578i	0.187071	−	0.982346i	$-0.440100\pi$
$281$	−5.04675	−	1.83687i	−0.301064	−	0.109578i	−0.488135	+	0.872768i	$0.662323\pi$
$282$		0			0
$283$	−4.56670	+	25.8990i	−0.271462	+	1.53954i	0.478518	+	0.878078i	$0.341174\pi$
$283$	−4.56670	+	25.8990i	−0.271462	+	1.53954i	−0.749980	+	0.661460i	$0.769937\pi$
$284$		0			0
$285$	18.5855	−	14.8834i	1.10091	−	0.881616i
$286$		0			0
$287$	−1.41873	+	8.04603i	−0.0837451	+	0.474942i
$288$		0			0
$289$	1.18082	+	0.429783i	0.0694599	+	0.0252813i
$290$		0			0
$291$	−1.41372	+	1.18626i	−0.0828740	+	0.0695395i
$292$		0			0
$293$	13.1318	−	22.7449i	0.767168	−	1.32877i	−0.171925	−	0.985110i	$-0.554999\pi$
$293$	13.1318	−	22.7449i	0.767168	−	1.32877i	0.939093	−	0.343664i	$-0.111668\pi$
$294$		0			0
$295$	4.85729	+	27.5471i	0.282802	+	1.60385i
$296$		0			0
$297$	1.38557	+	2.39987i	0.0803988	+	0.139255i
$298$		0			0
$299$	3.13201	−	1.13996i	0.181129	−	0.0659254i
$300$		0			0
$301$	30.9898	+	26.0035i	1.78622	+	1.49882i
$302$		0			0
$303$	4.79579			0.275511
$304$		0			0
$305$	40.1790			2.30064
$306$		0			0
$307$	−4.41784	−	3.70701i	−0.252140	−	0.211570i	0.507953	−	0.861385i	$-0.330402\pi$
$307$	−4.41784	−	3.70701i	−0.252140	−	0.211570i	−0.760093	+	0.649814i	$0.774847\pi$
$308$		0			0
$309$	5.52083	−	2.00942i	0.314069	−	0.114312i
$310$		0			0
$311$	−14.8857	−	25.7828i	−0.844092	−	1.46201i	−0.886407	−	0.462907i	$-0.846807\pi$
$311$	−14.8857	−	25.7828i	−0.844092	−	1.46201i	0.0423147	−	0.999104i	$-0.486527\pi$
$312$		0			0
$313$	−0.186186	−	1.05591i	−0.0105239	−	0.0596838i	0.979094	−	0.203410i	$-0.0652025\pi$
$313$	−0.186186	−	1.05591i	−0.0105239	−	0.0596838i	−0.989617	+	0.143727i	$0.954091\pi$
$314$		0			0
$315$	9.60765	−	16.6409i	0.541330	−	0.937611i
$316$		0			0
$317$	8.99617	−	7.54869i	0.505275	−	0.423976i	−0.354188	−	0.935174i	$-0.615243\pi$
$317$	8.99617	−	7.54869i	0.505275	−	0.423976i	0.859463	+	0.511198i	$0.170798\pi$
$318$		0			0
$319$	−1.24300	−	0.452415i	−0.0695947	−	0.0253304i
$320$		0			0
$321$	−3.86475	+	21.9181i	−0.215710	+	1.22335i
$322$		0			0
$323$	12.9909	+	11.4176i	0.722832	+	0.635293i
$324$		0			0
$325$	−7.97955	+	45.2543i	−0.442626	+	2.51026i
$326$		0			0
$327$	−10.3561	−	3.76932i	−0.572695	−	0.208444i
$328$		0			0
$329$	2.88807	−	2.42338i	0.159225	−	0.133605i
$330$		0			0
$331$	−5.98328	+	10.3633i	−0.328871	+	0.569621i	−0.982288	−	0.187377i	$-0.940001\pi$
$331$	−5.98328	+	10.3633i	−0.328871	+	0.569621i	0.653417	+	0.756998i	$0.273335\pi$
$332$		0			0
$333$	−1.57066	−	8.90767i	−0.0860718	−	0.488137i
$334$		0			0
$335$	22.6033	+	39.1501i	1.23495	+	2.13900i
$336$		0			0
$337$	4.73759	−	1.72434i	0.258073	−	0.0939310i	−0.209744	−	0.977756i	$-0.567263\pi$
$337$	4.73759	−	1.72434i	0.258073	−	0.0939310i	0.467817	+	0.883825i	$0.345041\pi$
$338$		0			0
$339$	12.2349	+	10.2663i	0.664509	+	0.557590i
$340$		0			0
$341$	−3.38727			−0.183431
$342$		0			0
$343$	−8.85979			−0.478384
$344$		0			0
$345$	−3.94730	−	3.31218i	−0.212516	−	0.178322i
$346$		0			0
$347$	−18.7124	+	6.81076i	−1.00453	+	0.365621i	−0.791331	−	0.611387i	$-0.790612\pi$
$347$	−18.7124	+	6.81076i	−1.00453	+	0.365621i	−0.213203	+	0.977008i	$0.568390\pi$
$348$		0			0
$349$	0.241896	+	0.418976i	0.0129484	+	0.0224273i	0.872427	−	0.488744i	$-0.162545\pi$
$349$	0.241896	+	0.418976i	0.0129484	+	0.0224273i	−0.859479	+	0.511172i	$0.829212\pi$
$350$		0			0
$351$	−3.43011	−	19.4531i	−0.183086	−	1.03833i
$352$		0			0
$353$	6.09193	−	10.5515i	0.324241	−	0.561601i	−0.657118	−	0.753788i	$-0.728225\pi$
$353$	6.09193	−	10.5515i	0.324241	−	0.561601i	0.981358	+	0.192187i	$0.0615579\pi$
$354$		0			0
$355$	30.6231	−	25.6958i	1.62530	−	1.36379i
$356$		0			0
$357$	−16.1867	−	5.89146i	−0.856689	−	0.311809i
$358$		0			0
$359$	−0.797870	+	4.52495i	−0.0421100	+	0.238818i	−0.998597	−	0.0529582i	$-0.983135\pi$
$359$	−0.797870	+	4.52495i	−0.0421100	+	0.238818i	0.956487	+	0.291776i	$0.0942461\pi$
$360$		0			0
$361$	−8.73669	−	16.8722i	−0.459826	−	0.888009i
$362$		0			0
$363$	2.40403	−	13.6339i	0.126179	−	0.715597i
$364$		0			0
$365$	−12.9780	−	4.72359i	−0.679298	−	0.247244i
$366$		0			0
$367$	0.421581	−	0.353748i	0.0220063	−	0.0184655i	−0.631718	−	0.775198i	$-0.717650\pi$
$367$	0.421581	−	0.353748i	0.0220063	−	0.0184655i	0.653724	+	0.756733i	$0.273206\pi$
$368$		0			0
$369$	−1.62658	+	2.81733i	−0.0846766	+	0.146664i
$370$		0			0
$371$	0.592714	+	3.36145i	0.0307722	+	0.174518i
$372$		0			0
$373$	−3.33092	−	5.76932i	−0.172468	−	0.298724i	0.766814	−	0.641870i	$-0.221841\pi$
$373$	−3.33092	−	5.76932i	−0.172468	−	0.298724i	−0.939282	+	0.343145i	$0.888508\pi$
$374$		0			0
$375$	41.0928	−	14.9566i	2.12202	−	0.772353i
$376$		0			0
$377$	7.22304	+	6.06085i	0.372005	+	0.312150i
$378$		0			0
$379$	3.42807			0.176088			0.0880440	−	0.996117i	$-0.471938\pi$
$379$	3.42807			0.176088			0.0880440	+	0.996117i	$0.471938\pi$
$380$		0			0
$381$	−14.4406			−0.739815
$382$		0			0
$383$	−9.15647	−	7.68319i	−0.467874	−	0.392593i	0.378144	−	0.925747i	$-0.376562\pi$
$383$	−9.15647	−	7.68319i	−0.467874	−	0.392593i	−0.846018	+	0.533154i	$0.821007\pi$
$384$		0			0
$385$	6.66535	−	2.42599i	0.339698	−	0.123640i
$386$		0			0
$387$	8.05399	+	13.9499i	0.409407	+	0.709114i
$388$		0			0
$389$	4.44881	+	25.2304i	0.225564	+	1.27923i	0.861605	+	0.507580i	$0.169460\pi$
$389$	4.44881	+	25.2304i	0.225564	+	1.27923i	−0.636041	+	0.771655i	$0.719429\pi$
$390$		0			0
$391$	1.87144	−	3.24142i	0.0946426	−	0.163926i
$392$		0			0
$393$	−5.18302	+	4.34907i	−0.261449	+	0.219381i
$394$		0			0
$395$	−22.9633	−	8.35795i	−1.15541	−	0.420534i
$396$		0			0
$397$	5.16384	−	29.2856i	0.259166	−	1.46980i	−0.525983	−	0.850495i	$-0.676302\pi$
$397$	5.16384	−	29.2856i	0.259166	−	1.46980i	0.785149	−	0.619307i	$-0.212586\pi$
$398$		0			0
$399$	14.2138	+	12.4925i	0.711582	+	0.625405i
$400$		0			0
$401$	−1.75709	+	9.96495i	−0.0877449	+	0.497626i	0.908986	+	0.416827i	$0.136858\pi$
$401$	−1.75709	+	9.96495i	−0.0877449	+	0.497626i	−0.996730	+	0.0807983i	$0.974253\pi$
$402$		0			0
$403$	22.6890	+	8.25813i	1.13022	+	0.411367i
$404$		0			0
$405$	−10.2994	+	8.64221i	−0.511781	+	0.429435i
$406$		0			0
$407$	1.66945	−	2.89157i	0.0827514	−	0.143330i
$408$		0			0
$409$	−3.65977	−	20.7556i	−0.180964	−	1.02630i	−0.931032	−	0.364937i	$-0.881091\pi$
$409$	−3.65977	−	20.7556i	−0.180964	−	1.02630i	0.750069	−	0.661360i	$-0.230020\pi$
$410$		0			0
$411$	−9.24385	−	16.0108i	−0.455965	−	0.789755i
$412$		0			0
$413$	−20.8901	+	7.60339i	−1.02794	+	0.374138i
$414$		0			0
$415$	−25.2948	−	21.2249i	−1.24167	−	1.04189i
$416$		0			0
$417$	4.77808			0.233984
$418$		0			0
$419$	−22.9349			−1.12044			−0.560221	−	0.828343i	$-0.689284\pi$
$419$	−22.9349			−1.12044			−0.560221	+	0.828343i	$0.689284\pi$
$420$		0			0
$421$	9.77997	+	8.20637i	0.476646	+	0.399954i	0.849212	−	0.528052i	$-0.177077\pi$
$421$	9.77997	+	8.20637i	0.476646	+	0.399954i	−0.372566	+	0.928006i	$0.621522\pi$
$422$		0			0
$423$	1.41064	−	0.513431i	0.0685876	−	0.0249638i
$424$		0			0
$425$	25.8016	+	44.6897i	1.25156	+	2.16777i
$426$		0			0
$427$	5.54499	+	31.4472i	0.268341	+	1.52184i
$428$		0			0
$429$	1.12730	−	1.95254i	0.0544265	−	0.0942695i
$430$		0			0
$431$	1.90160	−	1.59563i	0.0915969	−	0.0768590i	−0.595839	−	0.803104i	$-0.703181\pi$
$431$	1.90160	−	1.59563i	0.0915969	−	0.0768590i	0.687436	+	0.726245i	$0.258736\pi$
$432$		0			0
$433$	−21.6702	−	7.88731i	−1.04140	−	0.379040i	−0.235991	−	0.971755i	$-0.575834\pi$
$433$	−21.6702	−	7.88731i	−1.04140	−	0.379040i	−0.805412	+	0.592715i	$0.798056\pi$
$434$		0			0
$435$	2.53131	−	14.3558i	0.121367	−	0.688308i
$436$		0			0
$437$	−3.20952	+	2.57020i	−0.153532	+	0.122949i
$438$		0			0
$439$	−2.86028	+	16.2214i	−0.136513	+	0.774207i	0.837280	+	0.546774i	$0.184144\pi$
$439$	−2.86028	+	16.2214i	−0.136513	+	0.774207i	−0.973794	+	0.227433i	$0.926967\pi$
$440$		0			0
$441$	5.51770	+	2.00828i	0.262748	+	0.0956323i
$442$		0			0
$443$	−18.8468	+	15.8143i	−0.895437	+	0.751360i	−0.969293	−	0.245908i	$-0.920914\pi$
$443$	−18.8468	+	15.8143i	−0.895437	+	0.751360i	0.0738565	+	0.997269i	$0.476469\pi$
$444$		0			0
$445$	−5.69978	+	9.87231i	−0.270196	+	0.467992i
$446$		0			0
$447$	−1.74977	−	9.92343i	−0.0827612	−	0.469362i
$448$		0			0
$449$	−0.283288	−	0.490669i	−0.0133692	−	0.0231561i	0.859263	−	0.511533i	$-0.170922\pi$
$449$	−0.283288	−	0.490669i	−0.0133692	−	0.0231561i	−0.872633	+	0.488377i	$0.837589\pi$
$450$		0			0
$451$	−1.12845	+	0.410722i	−0.0531366	+	0.0193401i
$452$		0			0
$453$	−20.8508	−	17.4959i	−0.979658	−	0.822031i
$454$		0			0
$455$	−50.5612			−2.37035
$456$		0			0
$457$	−27.7632			−1.29871			−0.649353	−	0.760487i	$-0.724960\pi$
$457$	−27.7632			−1.29871			−0.649353	+	0.760487i	$0.724960\pi$
$458$		0			0
$459$	−16.9926	−	14.2585i	−0.793148	−	0.665530i
$460$		0			0
$461$	27.5700	−	10.0347i	1.28406	−	0.467361i	0.392290	−	0.919842i	$-0.371683\pi$
$461$	27.5700	−	10.0347i	1.28406	−	0.467361i	0.891774	+	0.452481i	$0.149461\pi$
$462$		0			0
$463$	8.73762	+	15.1340i	0.406072	+	0.703337i	0.994446	−	0.105252i	$-0.0335650\pi$
$463$	8.73762	+	15.1340i	0.406072	+	0.703337i	−0.588374	+	0.808589i	$0.700232\pi$
$464$		0			0
$465$	−6.48202	−	36.7614i	−0.300596	−	1.70477i
$466$		0			0
$467$	14.5703	−	25.2366i	0.674235	−	1.16781i	−0.302457	−	0.953163i	$-0.597807\pi$
$467$	14.5703	−	25.2366i	0.674235	−	1.16781i	0.976692	−	0.214646i	$-0.0688598\pi$
$468$		0			0
$469$	−27.5225	+	23.0941i	−1.27087	+	1.06639i
$470$		0			0
$471$	−4.50792	−	1.64075i	−0.207714	−	0.0756016i
$472$		0			0
$473$	−1.03253	+	5.85575i	−0.0474756	+	0.269248i
$474$		0			0
$475$	−8.56313	−	56.0392i	−0.392903	−	2.57126i
$476$		0			0
$477$	−0.236005	+	1.33845i	−0.0108059	+	0.0612835i
$478$		0			0
$479$	22.3916	+	8.14988i	1.02310	+	0.372378i	0.798449	−	0.602062i	$-0.205654\pi$
$479$	22.3916	+	8.14988i	1.02310	+	0.372378i	0.224650	+	0.974440i	$0.427876\pi$
$480$		0			0
$481$	−18.2321	+	15.2986i	−0.831313	+	0.697554i
$482$		0			0
$483$	2.04761	−	3.54657i	0.0931697	−	0.161375i
$484$		0			0
$485$	1.05632	+	5.99069i	0.0479651	+	0.272023i
$486$		0			0
$487$	−13.6808	−	23.6958i	−0.619936	−	1.07376i	−0.989497	−	0.144554i	$-0.953825\pi$
$487$	−13.6808	−	23.6958i	−0.619936	−	1.07376i	0.369561	−	0.929206i	$-0.379508\pi$
$488$		0			0
$489$	−6.60460	+	2.40388i	−0.298670	+	0.108707i
$490$		0			0
$491$	6.66429	+	5.59200i	0.300755	+	0.252364i	0.780659	−	0.624958i	$-0.214884\pi$
$491$	6.66429	+	5.59200i	0.300755	+	0.252364i	−0.479903	+	0.877321i	$0.659328\pi$
$492$		0			0
$493$	10.5885			0.476882
$494$		0			0
$495$	2.82432			0.126944
$496$		0			0
$497$	24.3377	+	20.4218i	1.09170	+	0.916042i
$498$		0			0
$499$	9.00548	−	3.27773i	0.403141	−	0.146731i	−0.132488	−	0.991185i	$-0.542297\pi$
$499$	9.00548	−	3.27773i	0.403141	−	0.146731i	0.535629	+	0.844453i	$0.320074\pi$
$500$		0			0
$501$	−3.92758	−	6.80276i	−0.175471	−	0.303925i
$502$		0			0
$503$	−0.932555	−	5.28878i	−0.0415806	−	0.235815i	0.956934	−	0.290307i	$-0.0937573\pi$
$503$	−0.932555	−	5.28878i	−0.0415806	−	0.235815i	−0.998514	+	0.0544916i	$0.982646\pi$
$504$		0			0
$505$	7.90396	−	13.6901i	0.351722	−	0.609200i
$506$		0			0
$507$	0.508627	−	0.426788i	0.0225889	−	0.0189543i
$508$		0			0
$509$	−32.9898	−	12.0073i	−1.46225	−	0.532215i	−0.516264	−	0.856429i	$-0.672678\pi$
$509$	−32.9898	−	12.0073i	−1.46225	−	0.532215i	−0.945984	+	0.324215i	$0.894900\pi$
$510$		0			0
$511$	1.90600	−	10.8094i	0.0843164	−	0.478182i
$512$		0			0
$513$	11.6980	+	21.3775i	0.516478	+	0.943838i
$514$		0			0
$515$	3.36282	−	19.0715i	0.148183	−	0.840390i
$516$		0			0
$517$	0.520722	+	0.189527i	0.0229013	+	0.00833540i
$518$		0			0
$519$	−21.7499	+	18.2503i	−0.954714	+	0.801100i
$520$		0			0
$521$	17.6378	−	30.5496i	0.772728	−	1.33840i	−0.163334	−	0.986571i	$-0.552225\pi$
$521$	17.6378	−	30.5496i	0.772728	−	1.33840i	0.936063	−	0.351834i	$-0.114442\pi$
$522$		0			0
$523$	4.15379	+	23.5573i	0.181632	+	1.03009i	0.930206	+	0.367037i	$0.119628\pi$
$523$	4.15379	+	23.5573i	0.181632	+	1.03009i	−0.748574	+	0.663051i	$0.769261\pi$
$524$		0			0
$525$	28.2306	+	48.8968i	1.23208	+	2.13403i
$526$		0			0
$527$	25.4791	−	9.27364i	1.10989	−	0.403966i
$528$		0			0
$529$	−16.9374	−	14.2121i	−0.736407	−	0.617919i
$530$		0			0
$531$	−8.85180			−0.384135
$532$		0			0
$533$	8.56006			0.370778
$534$		0			0
$535$	56.1979	+	47.1557i	2.42965	+	2.03872i
$536$		0			0
$537$	−15.2431	+	5.54802i	−0.657786	+	0.239415i
$538$		0			0
$539$	1.08376	+	1.87712i	0.0466807	+	0.0808534i
$540$		0			0
$541$	4.97837	+	28.2337i	0.214037	+	1.21386i	0.882570	+	0.470181i	$0.155811\pi$
$541$	4.97837	+	28.2337i	0.214037	+	1.21386i	−0.668533	+	0.743682i	$0.733078\pi$
$542$		0			0
$543$	0.868758	−	1.50473i	0.0372820	−	0.0645743i
$544$		0			0
$545$	−27.8279	+	23.3504i	−1.19202	+	1.00022i
$546$		0			0
$547$	16.6333	+	6.05403i	0.711189	+	0.258852i	0.672180	−	0.740387i	$-0.265358\pi$
$547$	16.6333	+	6.05403i	0.711189	+	0.258852i	0.0390083	+	0.999239i	$0.487580\pi$
$548$		0			0
$549$	−2.20789	+	12.5215i	−0.0942303	+	0.534406i
$550$		0			0
$551$	−10.8367	−	4.22769i	−0.461660	−	0.180106i
$552$		0			0
$553$	3.37248	−	19.1263i	0.143413	−	0.813333i
$554$		0			0
$555$	34.5763	+	12.5848i	1.46768	+	0.534193i
$556$		0			0
$557$	8.84945	−	7.42557i	0.374963	−	0.314631i	−0.435758	−	0.900064i	$-0.643520\pi$
$557$	8.84945	−	7.42557i	0.374963	−	0.314631i	0.810721	+	0.585432i	$0.199075\pi$
$558$		0			0
$559$	21.1925	−	36.7064i	0.896346	−	1.55252i
$560$		0			0
$561$	−0.439651	−	2.49338i	−0.0185621	−	0.105271i
$562$		0			0
$563$	−3.25866	−	5.64417i	−0.137336	−	0.237873i	0.789151	−	0.614199i	$-0.210521\pi$
$563$	−3.25866	−	5.64417i	−0.137336	−	0.237873i	−0.926488	+	0.376325i	$0.877187\pi$
$564$		0			0
$565$	49.4707	−	18.0058i	2.08125	−	0.757512i
$566$		0			0
$567$	−8.18545	−	6.86841i	−0.343757	−	0.288446i
$568$		0			0
$569$	8.36986			0.350883			0.175441	−	0.984490i	$-0.443865\pi$
$569$	8.36986			0.350883			0.175441	+	0.984490i	$0.443865\pi$
$570$		0			0
$571$	1.56658			0.0655595			0.0327797	−	0.999463i	$-0.489564\pi$
$571$	1.56658			0.0655595			0.0327797	+	0.999463i	$0.489564\pi$
$572$		0			0
$573$	21.3977	+	17.9548i	0.893900	+	0.750071i
$574$		0			0
$575$	−11.5284	+	4.19600i	−0.480768	+	0.174985i
$576$		0			0
$577$	−13.8031	−	23.9076i	−0.574630	−	0.995288i	−0.996082	−	0.0884375i	$-0.971813\pi$
$577$	−13.8031	−	23.9076i	−0.574630	−	0.995288i	0.421452	−	0.906851i	$-0.361521\pi$
$578$		0			0
$579$	5.63916	+	31.9813i	0.234356	+	1.32910i
$580$		0			0
$581$	13.1214	−	22.7269i	0.544366	−	0.942870i
$582$		0			0
$583$	−0.384322	+	0.322484i	−0.0159170	+	0.0133559i
$584$		0			0
$585$	−18.9182	−	6.88566i	−0.782171	−	0.284687i
$586$		0			0
$587$	4.58760	−	26.0176i	0.189350	−	1.07386i	−0.730887	−	0.682499i	$-0.760893\pi$
$587$	4.58760	−	26.0176i	0.189350	−	1.07386i	0.920237	−	0.391361i	$-0.127996\pi$
$588$		0			0
$589$	−29.7791	−	0.682058i	−1.22703	−	0.0281037i
$590$		0			0
$591$	−2.53135	+	14.3560i	−0.104126	+	0.590527i
$592$		0			0
$593$	34.4945	+	12.5550i	1.41652	+	0.515571i	0.933036	−	0.359783i	$-0.117149\pi$
$593$	34.4945	+	12.5550i	1.41652	+	0.515571i	0.483483	+	0.875354i	$0.339372\pi$
$594$		0			0
$595$	−43.4951	+	36.4967i	−1.78312	+	1.49622i
$596$		0			0
$597$	2.31657	−	4.01242i	0.0948110	−	0.164217i
$598$		0			0
$599$	−1.74643	−	9.90447i	−0.0713570	−	0.404686i	−0.999475	−	0.0323995i	$-0.989685\pi$
$599$	−1.74643	−	9.90447i	−0.0713570	−	0.404686i	0.928118	−	0.372286i	$-0.121426\pi$
$600$		0			0
$601$	14.6079	+	25.3017i	0.595870	+	1.03208i	0.993423	+	0.114498i	$0.0365260\pi$
$601$	14.6079	+	25.3017i	0.595870	+	1.03208i	−0.397553	+	0.917579i	$0.630141\pi$
$602$		0			0
$603$	−13.4430	+	4.89285i	−0.547441	+	0.199252i
$604$		0			0
$605$	−34.9574	−	29.3327i	−1.42122	−	1.19255i
$606$		0			0
$607$	18.9985			0.771124			0.385562	−	0.922682i	$-0.374008\pi$
$607$	18.9985			0.771124			0.385562	+	0.922682i	$0.374008\pi$
$608$		0			0
$609$	11.5853			0.469460
$610$		0			0
$611$	−3.02590	−	2.53903i	−0.122415	−	0.102718i
$612$		0			0
$613$	12.5998	−	4.58595i	0.508901	−	0.185225i	−0.0747923	−	0.997199i	$-0.523829\pi$
$613$	12.5998	−	4.58595i	0.508901	−	0.185225i	0.583693	+	0.811974i	$0.301607\pi$
$614$		0			0
$615$	−6.61693	−	11.4609i	−0.266821	−	0.462147i
$616$		0			0
$617$	5.26775	+	29.8749i	0.212072	+	1.20272i	0.885916	+	0.463845i	$0.153531\pi$
$617$	5.26775	+	29.8749i	0.212072	+	1.20272i	−0.673845	+	0.738873i	$0.735358\pi$
$618$		0			0
$619$	−15.4667	+	26.7891i	−0.621659	+	1.07675i	0.367518	+	0.930017i	$0.380208\pi$
$619$	−15.4667	+	26.7891i	−0.621659	+	1.07675i	−0.989177	+	0.146729i	$0.953126\pi$
$620$		0			0
$621$	4.03987	−	3.38985i	0.162114	−	0.136030i
$622$		0			0
$623$	−8.51345	−	3.09864i	−0.341084	−	0.124144i
$624$		0			0
$625$	13.7383	−	77.9139i	0.549533	−	3.11655i
$626$		0			0
$627$	−0.545581	+	2.72738i	−0.0217884	+	0.108921i
$628$		0			0
$629$	−4.64111	+	26.3210i	−0.185053	+	1.04949i
$630$		0			0
$631$	−3.04173	−	1.10710i	−0.121089	−	0.0440729i	0.280765	−	0.959777i	$-0.409412\pi$
$631$	−3.04173	−	1.10710i	−0.121089	−	0.0440729i	−0.401854	+	0.915704i	$0.631634\pi$
$632$		0			0
$633$	16.3950	−	13.7571i	0.651644	−	0.546795i
$634$		0			0
$635$	−23.7996	+	41.2222i	−0.944460	+	1.63585i
$636$		0			0
$637$	−2.68295	−	15.2158i	−0.106302	−	0.602871i
$638$		0			0
$639$	6.32517	+	10.9555i	0.250220	+	0.433394i
$640$		0			0
$641$	37.8930	−	13.7919i	1.49669	−	0.544749i	0.541485	−	0.840710i	$-0.317862\pi$
$641$	37.8930	−	13.7919i	1.49669	−	0.544749i	0.955200	+	0.295961i	$0.0956399\pi$
$642$		0			0
$643$	1.80428	+	1.51397i	0.0711538	+	0.0597052i	0.677671	−	0.735365i	$-0.262989\pi$
$643$	1.80428	+	1.51397i	0.0711538	+	0.0597052i	−0.606517	+	0.795070i	$0.707434\pi$
$644$		0			0
$645$	−65.5271			−2.58013
$646$		0			0
$647$	−24.9858			−0.982293			−0.491147	−	0.871077i	$-0.663422\pi$
$647$	−24.9858			−0.982293			−0.491147	+	0.871077i	$0.663422\pi$
$648$		0			0
$649$	−2.50308	−	2.10034i	−0.0982546	−	0.0824454i
$650$		0			0
$651$	27.8777	−	10.1467i	1.09261	−	0.397679i
$652$		0			0
$653$	4.53457	+	7.85411i	0.177452	+	0.307355i	0.941007	−	0.338387i	$-0.109881\pi$
$653$	4.53457	+	7.85411i	0.177452	+	0.307355i	−0.763555	+	0.645742i	$0.776548\pi$
$654$		0			0
$655$	3.87270	+	21.9632i	0.151319	+	0.858172i
$656$		0			0
$657$	2.18524	−	3.78494i	0.0852542	−	0.147665i
$658$		0			0
$659$	−4.21698	+	3.53847i	−0.164270	+	0.137839i	−0.721217	−	0.692709i	$-0.756417\pi$
$659$	−4.21698	+	3.53847i	−0.164270	+	0.137839i	0.556947	+	0.830548i	$0.311973\pi$
$660$		0			0
$661$	15.0888	+	5.49187i	0.586886	+	0.213609i	0.618359	−	0.785896i	$-0.287798\pi$
$661$	15.0888	+	5.49187i	0.586886	+	0.213609i	−0.0314734	+	0.999505i	$0.510020\pi$
$662$		0			0
$663$	−3.13392	+	17.7734i	−0.121711	+	0.690260i
$664$		0			0
$665$	59.0869	−	19.9859i	2.29129	−	0.775021i
$666$		0			0
$667$	−0.437131	+	2.47909i	−0.0169258	+	0.0959908i
$668$		0			0
$669$	13.0852	+	4.76261i	0.505902	+	0.184133i
$670$		0			0
$671$	−3.59543	+	3.01692i	−0.138800	+	0.116467i
$672$		0			0
$673$	8.86987	−	15.3631i	0.341909	−	0.592203i	−0.642879	−	0.765968i	$-0.722260\pi$
$673$	8.86987	−	15.3631i	0.341909	−	0.592203i	0.984787	+	0.173765i	$0.0555934\pi$
$674$		0			0
$675$	12.6257	+	71.6038i	0.485963	+	2.75603i
$676$		0			0
$677$	−11.5028	−	19.9235i	−0.442089	−	0.765721i	0.555755	−	0.831346i	$-0.312429\pi$
$677$	−11.5028	−	19.9235i	−0.442089	−	0.765721i	−0.997844	+	0.0656249i	$0.979096\pi$
$678$		0			0
$679$	−4.54300	+	1.65352i	−0.174344	+	0.0634562i
$680$		0			0
$681$	9.77890	+	8.20547i	0.374728	+	0.314434i
$682$		0			0
$683$	33.5439			1.28352			0.641760	−	0.766905i	$-0.278204\pi$
$683$	33.5439			1.28352			0.641760	+	0.766905i	$0.278204\pi$
$684$		0			0
$685$	−60.9393			−2.32837
$686$		0			0
$687$	−21.7368	−	18.2393i	−0.829309	−	0.695873i
$688$		0			0
$689$	3.36053	−	1.22313i	0.128026	−	0.0465976i
$690$		0			0
$691$	−14.7673	−	25.5777i	−0.561774	−	0.973021i	−0.997342	−	0.0728654i	$-0.976786\pi$
$691$	−14.7673	−	25.5777i	−0.561774	−	0.973021i	0.435568	−	0.900156i	$-0.356548\pi$
$692$		0			0
$693$	0.389776	+	2.21053i	0.0148064	+	0.0839710i
$694$		0			0
$695$	7.87478	−	13.6395i	0.298708	−	0.517377i
$696$		0			0
$697$	7.36376	−	6.17892i	0.278922	−	0.234043i
$698$		0			0
$699$	3.91262	+	1.42408i	0.147989	+	0.0538635i
$700$		0			0
$701$	−7.56614	+	42.9097i	−0.285769	+	1.62068i	0.416755	+	0.909019i	$0.363167\pi$
$701$	−7.56614	+	42.9097i	−0.285769	+	1.62068i	−0.702525	+	0.711659i	$0.747944\pi$
$702$		0			0
$703$	15.2592	−	25.0850i	0.575511	−	0.946100i
$704$		0			0
$705$	−1.06043	+	6.01398i	−0.0399380	+	0.226500i
$706$		0			0
$707$	11.8057	+	4.29693i	0.444000	+	0.161603i
$708$		0			0
$709$	2.06593	−	1.73352i	0.0775875	−	0.0651036i	−0.603169	−	0.797613i	$-0.706096\pi$
$709$	2.06593	−	1.73352i	0.0775875	−	0.0651036i	0.680757	+	0.732510i	$0.261651\pi$
$710$		0			0
$711$	3.86657	−	6.69709i	0.145008	−	0.251161i
$712$		0			0
$713$	1.11937	+	6.34829i	0.0419209	+	0.237745i
$714$		0			0
$715$	−3.71581	−	6.43598i	−0.138964	−	0.240692i
$716$		0			0
$717$	−5.93813	+	2.16130i	−0.221764	+	0.0807153i
$718$		0			0
$719$	−6.88537	−	5.77751i	−0.256781	−	0.215465i	0.505305	−	0.862941i	$-0.331380\pi$
$719$	−6.88537	−	5.77751i	−0.256781	−	0.215465i	−0.762086	+	0.647476i	$0.775825\pi$
$720$		0			0
$721$	15.3909			0.573188
$722$		0			0
$723$	16.3710			0.608845
$724$		0			0
$725$	−26.5868	−	22.3090i	−0.987410	−	0.828536i
$726$		0			0
$727$	13.8891	−	5.05524i	0.515120	−	0.187488i	−0.0713622	−	0.997450i	$-0.522735\pi$
$727$	13.8891	−	5.05524i	0.515120	−	0.187488i	0.586482	+	0.809962i	$0.300512\pi$
$728$		0			0
$729$	−12.9227	−	22.3827i	−0.478618	−	0.828990i
$730$		0			0
$731$	−8.26514	−	46.8739i	−0.305697	−	1.73369i
$732$		0			0
$733$	−3.96628	+	6.86981i	−0.146498	+	0.253742i	−0.929931	−	0.367734i	$-0.880134\pi$
$733$	−3.96628	+	6.86981i	−0.146498	+	0.253742i	0.783433	+	0.621477i	$0.213467\pi$
$734$		0			0
$735$	−18.2981	+	15.3539i	−0.674936	+	0.566339i
$736$		0			0
$737$	−4.96233	−	1.80614i	−0.182790	−	0.0665301i
$738$		0			0
$739$	8.89550	−	50.4489i	0.327226	−	1.85579i	−0.166318	−	0.986072i	$-0.553188\pi$
$739$	8.89550	−	50.4489i	0.327226	−	1.85579i	0.493545	−	0.869720i	$-0.335701\pi$
$740$		0			0
$741$	10.3038	−	16.9387i	0.378520	−	0.622260i
$742$		0			0
$743$	−3.26954	+	18.5425i	−0.119948	+	0.680257i	0.864233	+	0.503091i	$0.167804\pi$
$743$	−3.26954	+	18.5425i	−0.119948	+	0.680257i	−0.984181	+	0.177166i	$0.943307\pi$
$744$		0			0
$745$	−31.2112	−	11.3600i	−1.14349	−	0.416197i
$746$		0			0
$747$	8.00459	−	6.71665i	0.292873	−	0.245749i
$748$		0			0
$749$	−29.1520	+	50.4927i	−1.06519	+	1.84496i
$750$		0			0
$751$	−5.31103	−	30.1203i	−0.193802	−	1.09911i	−0.914114	−	0.405457i	$-0.867112\pi$
$751$	−5.31103	−	30.1203i	−0.193802	−	1.09911i	0.720312	−	0.693650i	$-0.243999\pi$
$752$		0			0
$753$	−2.12805	−	3.68588i	−0.0775503	−	0.134321i
$754$		0			0
$755$	−84.3083	+	30.6857i	−3.06829	+	1.11677i
$756$		0			0
$757$	7.44350	+	6.24584i	0.270539	+	0.227009i	0.767956	−	0.640502i	$-0.221274\pi$
$757$	7.44350	+	6.24584i	0.270539	+	0.227009i	−0.497418	+	0.867511i	$0.665718\pi$
$758$		0			0
$759$	0.601927			0.0218486
$760$		0			0
$761$	−30.5544			−1.10760			−0.553798	−	0.832651i	$-0.686822\pi$
$761$	−30.5544			−1.10760			−0.553798	+	0.832651i	$0.686822\pi$
$762$		0			0
$763$	−22.1163	−	18.5577i	−0.800662	−	0.671836i
$764$		0			0
$765$	−21.2446	+	7.73239i	−0.768099	+	0.279565i
$766$		0			0
$767$	11.6459	+	20.1712i	0.420508	+	0.728341i
$768$		0			0
$769$	−3.77737	−	21.4225i	−0.136216	−	0.772517i	−0.974006	−	0.226524i	$-0.927264\pi$
$769$	−3.77737	−	21.4225i	−0.136216	−	0.772517i	0.837790	−	0.545992i	$-0.183847\pi$
$770$		0			0
$771$	10.3199	−	17.8745i	0.371661	−	0.643736i
$772$		0			0
$773$	−5.40500	+	4.53533i	−0.194404	+	0.163125i	−0.734794	−	0.678290i	$-0.762721\pi$
$773$	−5.40500	+	4.53533i	−0.194404	+	0.163125i	0.540390	+	0.841415i	$0.318277\pi$
$774$		0			0
$775$	−83.5147	−	30.3968i	−2.99993	−	1.09189i
$776$		0			0
$777$	−5.07802	+	28.7989i	−0.182173	+	1.03315i
$778$		0			0
$779$	−10.0035	+	3.38364i	−0.358411	+	0.121231i
$780$		0			0
$781$	−0.810891	+	4.59879i	−0.0290160	+	0.164558i
$782$		0			0
$783$	14.0194	+	5.10263i	0.501011	+	0.182353i
$784$		0			0
$785$	−12.1132	+	10.1642i	−0.432339	+	0.362775i
$786$		0			0
$787$	2.98205	−	5.16507i	0.106299	−	0.184115i	−0.807969	−	0.589225i	$-0.799433\pi$
$787$	2.98205	−	5.16507i	0.106299	−	0.184115i	0.914268	+	0.405110i	$0.132767\pi$
$788$		0			0
$789$	1.67174	+	9.48092i	0.0595156	+	0.337530i
$790$		0			0
$791$	20.9201	+	36.2346i	0.743832	+	1.28836i
$792$		0			0
$793$	31.4386	−	11.4427i	1.11642	−	0.406342i
$794$		0			0
$795$	−4.23531	−	3.55385i	−0.150211	−	0.126042i
$796$		0			0
$797$	46.5731			1.64970			0.824852	−	0.565349i	$-0.191258\pi$
$797$	46.5731			1.64970			0.824852	+	0.565349i	$0.191258\pi$
$798$		0			0
$799$	−4.43577			−0.156926
$800$		0			0
$801$	−2.76344	−	2.31880i	−0.0976413	−	0.0819307i
$802$		0			0
$803$	1.51602	−	0.551785i	0.0534991	−	0.0194721i
$804$		0			0
$805$	−6.74936	−	11.6902i	−0.237884	−	0.412027i
$806$		0			0
$807$	6.29888	+	35.7227i	0.221731	+	1.25750i
$808$		0			0
$809$	4.30060	−	7.44886i	0.151201	−	0.261888i	−0.780468	−	0.625196i	$-0.785019\pi$
$809$	4.30060	−	7.44886i	0.151201	−	0.261888i	0.931669	+	0.363307i	$0.118353\pi$
$810$		0			0
$811$	18.5790	−	15.5896i	0.652395	−	0.547425i	−0.255401	−	0.966835i	$-0.582208\pi$
$811$	18.5790	−	15.5896i	0.652395	−	0.547425i	0.907797	+	0.419410i	$0.137763\pi$
$812$		0			0
$813$	−4.66295	−	1.69717i	−0.163537	−	0.0595225i
$814$		0			0
$815$	−4.02296	+	22.8153i	−0.140918	+	0.799186i
$816$		0			0
$817$	−10.2566	+	51.2729i	−0.358832	+	1.79381i
$818$		0			0
$819$	2.77840	−	15.7571i	0.0970853	−	0.550598i
$820$		0			0
$821$	−25.8899	−	9.42314i	−0.903563	−	0.328870i	−0.151883	−	0.988398i	$-0.548534\pi$
$821$	−25.8899	−	9.42314i	−0.903563	−	0.328870i	−0.751679	+	0.659529i	$0.770756\pi$
$822$		0			0
$823$	42.9391	−	36.0302i	1.49676	−	1.25593i	0.611146	−	0.791518i	$-0.290709\pi$
$823$	42.9391	−	36.0302i	1.49676	−	1.25593i	0.885618	−	0.464415i	$-0.153735\pi$
$824$		0			0
$825$	−4.14940	+	7.18698i	−0.144464	+	0.250218i
$826$		0			0
$827$	7.98839	+	45.3044i	0.277784	+	1.57539i	0.729979	+	0.683470i	$0.239530\pi$
$827$	7.98839	+	45.3044i	0.277784	+	1.57539i	−0.452195	+	0.891919i	$0.649359\pi$
$828$		0			0
$829$	5.57204	+	9.65105i	0.193525	+	0.335195i	0.946416	−	0.322950i	$-0.104675\pi$
$829$	5.57204	+	9.65105i	0.193525	+	0.335195i	−0.752891	+	0.658145i	$0.771341\pi$
$830$		0			0
$831$	4.82063	−	1.75457i	0.167226	−	0.0608652i
$832$		0			0
$833$	−13.2912	−	11.1527i	−0.460514	−	0.386417i
$834$		0			0
$835$	−25.8922			−0.896037
$836$		0			0
$837$	38.2038			1.32052
$838$		0			0
$839$	−15.7318	−	13.2005i	−0.543120	−	0.455732i	0.329483	−	0.944161i	$-0.393126\pi$
$839$	−15.7318	−	13.2005i	−0.543120	−	0.455732i	−0.872603	+	0.488429i	$0.837570\pi$
$840$		0			0
$841$	20.5591	−	7.48289i	0.708934	−	0.258031i
$842$		0			0
$843$	3.45688	+	5.98749i	0.119061	+	0.206220i
$844$		0			0
$845$	−0.380041	−	2.15532i	−0.0130738	−	0.0741452i
$846$		0			0
$847$	18.1337	−	31.4085i	0.623081	−	1.07921i
$848$		0			0
$849$	25.9343	−	21.7614i	0.890062	−	0.746850i
$850$		0			0
$851$	−5.97096	−	2.17325i	−0.204682	−	0.0744981i
$852$		0			0
$853$	−0.627868	+	3.56082i	−0.0214978	+	0.121920i	−0.993668	−	0.112355i	$-0.964161\pi$
$853$	−0.627868	+	3.56082i	−0.0214978	+	0.121920i	0.972170	+	0.234275i	$0.0752717\pi$
$854$		0			0
$855$	24.8300	+	0.568703i	0.849167	+	0.0194492i
$856$		0			0
$857$	3.72296	−	21.1139i	0.127174	−	0.721238i	−0.852819	−	0.522206i	$-0.825109\pi$
$857$	3.72296	−	21.1139i	0.127174	−	0.721238i	0.979993	−	0.199032i	$-0.0637797\pi$
$858$		0			0
$859$	−31.7422	−	11.5532i	−1.08303	−	0.394191i	−0.261996	−	0.965069i	$-0.584381\pi$
$859$	−31.7422	−	11.5532i	−1.08303	−	0.394191i	−0.821035	+	0.570878i	$0.806603\pi$
$860$		0			0
$861$	8.05698	−	6.76061i	0.274581	−	0.230401i
$862$		0			0
$863$	−7.57823	+	13.1259i	−0.257966	+	0.446810i	−0.965697	−	0.259672i	$-0.916386\pi$
$863$	−7.57823	+	13.1259i	−0.257966	+	0.446810i	0.707731	+	0.706482i	$0.249719\pi$
$864$		0			0
$865$	16.2513	+	92.1657i	0.552561	+	3.13373i
$866$		0			0
$867$	−0.808826	−	1.40093i	−0.0274692	−	0.0475780i
$868$		0			0
$869$	2.68245	−	0.976331i	0.0909958	−	0.0331198i
$870$		0			0
$871$	28.8360	+	24.1963i	0.977070	+	0.819859i
$872$		0			0
$873$	−1.92501			−0.0651517
$874$		0			0
$875$	114.558			3.87277
$876$		0			0
$877$	−16.1395	−	13.5426i	−0.544991	−	0.457302i	0.328249	−	0.944591i	$-0.393541\pi$
$877$	−16.1395	−	13.5426i	−0.544991	−	0.457302i	−0.873241	+	0.487289i	$0.837986\pi$
$878$		0			0
$879$	−31.7708	+	11.5636i	−1.07160	+	0.390031i
$880$		0			0
$881$	−17.0362	−	29.5076i	−0.573966	−	0.994138i	−0.996153	−	0.0876292i	$-0.972071\pi$
$881$	−17.0362	−	29.5076i	−0.573966	−	0.994138i	0.422187	−	0.906509i	$-0.361262\pi$
$882$		0			0
$883$	−2.20860	−	12.5256i	−0.0743253	−	0.421520i	−0.999154	−	0.0411349i	$-0.986903\pi$
$883$	−2.20860	−	12.5256i	−0.0743253	−	0.421520i	0.924828	−	0.380385i	$-0.124208\pi$
$884$		0			0
$885$	18.0045	−	31.1848i	0.605216	−	1.04826i
$886$		0			0
$887$	−27.8503	+	23.3692i	−0.935122	+	0.784661i	−0.976730	−	0.214473i	$-0.931197\pi$
$887$	−27.8503	+	23.3692i	−0.935122	+	0.784661i	0.0416076	+	0.999134i	$0.486752\pi$
$888$		0			0
$889$	−35.5482	−	12.9385i	−1.19225	−	0.433943i
$890$		0			0
$891$	0.272725	−	1.54670i	0.00913663	−	0.0518164i
$892$		0			0
$893$	4.53976	+	1.77108i	0.151917	+	0.0592669i
$894$		0			0
$895$	−9.28477	+	52.6566i	−0.310356	+	1.76011i
$896$		0			0
$897$	−4.03191	−	1.46749i	−0.134621	−	0.0489982i
$898$		0			0
$899$	−13.9697	+	11.7220i	−0.465917	+	0.390951i
$900$		0			0
$901$	2.00798	−	3.47793i	0.0668956	−	0.115867i
$902$		0			0
$903$	−9.04322	−	51.2866i	−0.300939	−	1.70671i
$904$		0			0
$905$	−2.86361	−	4.95992i	−0.0951896	−	0.164873i
$906$		0			0
$907$	40.2460	−	14.6483i	1.33635	−	0.486390i	0.427686	−	0.903927i	$-0.359329\pi$
$907$	40.2460	−	14.6483i	1.33635	−	0.486390i	0.908660	+	0.417537i	$0.137107\pi$
$908$		0			0
$909$	3.83210	+	3.21551i	0.127103	+	0.106652i
$910$		0			0
$911$	59.2711			1.96374			0.981870	−	0.189555i	$-0.0607047\pi$
$911$	59.2711			1.96374			0.981870	+	0.189555i	$0.0607047\pi$
$912$		0			0
$913$	3.85723			0.127656
$914$		0			0
$915$	−39.6224	−	33.2471i	−1.30988	−	1.09912i
$916$		0			0
$917$	−16.6556	+	6.06215i	−0.550017	+	0.200190i
$918$		0			0
$919$	12.2457	+	21.2102i	0.403949	+	0.699660i	0.994199	−	0.107561i	$-0.0343040\pi$
$919$	12.2457	+	21.2102i	0.403949	+	0.699660i	−0.590249	+	0.807221i	$0.700971\pi$
$920$		0			0
$921$	1.28918	+	7.31132i	0.0424800	+	0.240916i
$922$		0			0
$923$	16.6434	−	28.8273i	0.547825	−	0.948861i
$924$		0			0
$925$	67.1095	−	56.3115i	2.20655	−	1.85151i
$926$		0			0
$927$	5.75873	+	2.09600i	0.189141	+	0.0688418i
$928$		0			0
$929$	−7.32848	+	41.5619i	−0.240440	+	1.36360i	0.590410	+	0.807104i	$0.298966\pi$
$929$	−7.32848	+	41.5619i	−0.240440	+	1.36360i	−0.830849	+	0.556497i	$0.812145\pi$
$930$		0			0
$931$	9.14987	+	16.7209i	0.299875	+	0.548007i
$932$		0			0
$933$	−6.65516	+	37.7433i	−0.217880	+	1.23566i
$934$		0			0
$935$	−7.84220	−	2.85433i	−0.256467	−	0.0933465i
$936$		0			0
$937$	−14.4074	+	12.0892i	−0.470668	+	0.394938i	−0.847038	−	0.531532i	$-0.821617\pi$
$937$	−14.4074	+	12.0892i	−0.470668	+	0.394938i	0.376370	+	0.926469i	$0.377172\pi$
$938$		0			0
$939$	−0.690137	+	1.19535i	−0.0225218	+	0.0390088i
$940$		0			0
$941$	5.38617	+	30.5465i	0.175584	+	0.995788i	0.937467	+	0.348073i	$0.113164\pi$
$941$	5.38617	+	30.5465i	0.175584	+	0.995788i	−0.761883	+	0.647714i	$0.775725\pi$
$942$		0			0
$943$	1.14267	+	1.97917i	0.0372106	+	0.0644506i
$944$		0			0
$945$	−75.1762	+	27.3619i	−2.44548	+	0.890082i
$946$		0			0
$947$	−27.3095	−	22.9154i	−0.887440	−	0.744650i	0.0802552	−	0.996774i	$-0.474426\pi$
$947$	−27.3095	−	22.9154i	−0.887440	−	0.744650i	−0.967695	+	0.252124i	$0.918871\pi$
$948$		0			0
$949$	−11.5000			−0.373307
$950$		0			0
$951$	−15.1179			−0.490232
$952$		0			0
$953$	−14.1046	−	11.8351i	−0.456892	−	0.383378i	0.385094	−	0.922877i	$-0.374169\pi$
$953$	−14.1046	−	11.8351i	−0.456892	−	0.383378i	−0.841986	+	0.539500i	$0.818613\pi$
$954$		0			0
$955$	86.5193	−	31.4904i	2.79970	−	1.01901i
$956$		0			0
$957$	0.851419	+	1.47470i	0.0275225	+	0.0476703i
$958$		0			0
$959$	−8.41006	−	47.6958i	−0.271575	−	1.54018i
$960$		0			0
$961$	−7.84902	+	13.5949i	−0.253194	+	0.438545i
$962$		0			0
$963$	−17.7839	+	14.9225i	−0.573079	+	0.480871i
$964$		0			0
$965$	100.588	+	36.6109i	3.23803	+	1.17855i
$966$		0			0
$967$	−4.30458	+	24.4125i	−0.138426	+	0.785053i	0.833986	+	0.551785i	$0.186053\pi$
$967$	−4.30458	+	24.4125i	−0.138426	+	0.785053i	−0.972412	+	0.233268i	$0.925058\pi$
$968$		0			0
$969$	−3.36312	−	22.0091i	−0.108039	−	0.707034i
$970$		0			0
$971$	0.214298	−	1.21534i	0.00687714	−	0.0390022i	−0.981176	−	0.193115i	$-0.938141\pi$
$971$	0.214298	−	1.21534i	0.00687714	−	0.0390022i	0.988053	+	0.154113i	$0.0492520\pi$
$972$		0			0
$973$	11.7621	+	4.28106i	0.377076	+	0.137245i
$974$		0			0
$975$	45.3159	−	38.0245i	1.45127	−	1.21776i
$976$		0			0
$977$	−23.6072	+	40.8888i	−0.755261	+	1.30815i	0.189984	+	0.981787i	$0.439156\pi$
$977$	−23.6072	+	40.8888i	−0.755261	+	1.30815i	−0.945245	+	0.326363i	$0.894177\pi$
$978$		0			0
$979$	−0.231236	−	1.31141i	−0.00739034	−	0.0419127i
$980$		0			0
$981$	−5.74783	−	9.95553i	−0.183514	−	0.317856i
$982$		0			0
$983$	27.7941	−	10.1162i	0.886493	−	0.322657i	0.141666	−	0.989915i	$-0.454754\pi$
$983$	27.7941	−	10.1162i	0.886493	−	0.322657i	0.744827	+	0.667258i	$0.232532\pi$
$984$		0			0
$985$	36.8087	+	30.8862i	1.17282	+	0.984115i
$986$		0			0
$987$	−4.85335			−0.154484
$988$		0			0
$989$	11.3158			0.359823
$990$		0			0
$991$	21.0034	+	17.6239i	0.667195	+	0.559843i	0.912234	−	0.409670i	$-0.134356\pi$
$991$	21.0034	+	17.6239i	0.667195	+	0.559843i	−0.245039	+	0.969513i	$0.578801\pi$
$992$		0			0
$993$	14.4758	−	5.26876i	0.459376	−	0.167199i
$994$		0			0
$995$	−7.63591	−	13.2258i	−0.242075	−	0.419285i
$996$		0			0
$997$	−0.535399	−	3.03640i	−0.0169563	−	0.0961638i	0.975155	−	0.221523i	$-0.0711028\pi$
$997$	−0.535399	−	3.03640i	−0.0169563	−	0.0961638i	−0.992111	+	0.125359i	$0.959992\pi$
$998$		0			0
$999$	−18.8291	+	32.6130i	−0.595727	+	1.03183i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	152.2.q.c.17.1	yes	18
4.3	odd	2		304.2.u.f.17.3		18
19.3	odd	18		2888.2.a.x.1.7		9
19.9	even	9	inner	152.2.q.c.9.1	✓	18
19.16	even	9		2888.2.a.y.1.3		9
76.3	even	18		5776.2.a.ce.1.3		9
76.35	odd	18		5776.2.a.cd.1.7		9
76.47	odd	18		304.2.u.f.161.3		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.2.q.c.9.1	✓	18	19.9	even	9	inner
152.2.q.c.17.1	yes	18	1.1	even	1	trivial
304.2.u.f.17.3		18	4.3	odd	2
304.2.u.f.161.3		18	76.47	odd	18
2888.2.a.x.1.7		9	19.3	odd	18
2888.2.a.y.1.3		9	19.16	even	9
5776.2.a.cd.1.7		9	76.35	odd	18
5776.2.a.ce.1.3		9	76.3	even	18

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:	\( N \)	\(=\)	\( 152 = 2^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	152.q (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.986147 - 0.827476i) q^{3} +(-3.98739 + 1.45129i) q^{5} +(-1.68618 - 2.92055i) q^{7} +(-0.233174 - 1.32240i) q^{9} +O(q^{10})\)	\(q+(-0.986147 - 0.827476i) q^{3} +(-3.98739 + 1.45129i) q^{5} +(-1.68618 - 2.92055i) q^{7} +(-0.233174 - 1.32240i) q^{9} +(0.247839 - 0.429270i) q^{11} +(-2.70667 + 2.27116i) q^{13} +(5.13306 + 1.86828i) q^{15} +(-0.689000 + 3.90752i) q^{17} +(2.26532 - 3.72402i) q^{19} +(-0.753863 + 4.27537i) q^{21} +(-0.886425 - 0.322632i) q^{23} +(9.96280 - 8.35978i) q^{25} +(-2.79529 + 4.84159i) q^{27} +(-0.463399 - 2.62807i) q^{29} +(-3.41680 - 5.91807i) q^{31} +(-0.599617 + 0.218243i) q^{33} +(10.9620 + 9.19823i) q^{35} +6.73600 q^{37} +4.54851 q^{39} +(-1.85588 - 1.55727i) q^{41} +(-11.2724 + 4.10282i) q^{43} +(2.84894 + 4.93451i) q^{45} +(0.194129 + 1.10096i) q^{47} +(-2.18641 + 3.78698i) q^{49} +(3.91283 - 3.28326i) q^{51} +(-0.951101 - 0.346173i) q^{53} +(-0.365236 + 2.07135i) q^{55} +(-5.31547 + 1.79794i) q^{57} +(1.14470 - 6.49191i) q^{59} +(-8.89778 - 3.23853i) q^{61} +(-3.46895 + 2.91080i) q^{63} +(7.49641 - 12.9842i) q^{65} +(-1.84999 - 10.4918i) q^{67} +(0.607175 + 1.05166i) q^{69} +(-8.85275 + 3.22214i) q^{71} +(2.49328 + 2.09211i) q^{73} -16.7423 q^{75} -1.67161 q^{77} +(4.41163 + 3.70180i) q^{79} +(2.97742 - 1.08369i) q^{81} +(3.89085 + 6.73916i) q^{83} +(-2.92363 - 16.5807i) q^{85} +(-1.71768 + 2.97511i) q^{87} +(2.05797 - 1.72684i) q^{89} +(11.1970 + 4.07537i) q^{91} +(-1.52759 + 8.66341i) q^{93} +(-3.62805 + 18.1368i) q^{95} +(0.248939 - 1.41180i) q^{97} +(-0.625455 - 0.227647i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 9 q^{7} - 6 q^{9}+O(q^{10}) \) 18 * q - 9 * q^7 - 6 * q^9	\( 18 q - 9 q^{7} - 6 q^{9} - 3 q^{11} + 3 q^{13} + 33 q^{15} + 9 q^{17} - 24 q^{19} - 15 q^{21} + 6 q^{23} + 6 q^{25} - 12 q^{27} - 3 q^{29} - 6 q^{31} - 45 q^{33} - 15 q^{35} + 48 q^{37} + 12 q^{39} - 18 q^{41} - 39 q^{43} - 42 q^{45} - 27 q^{47} - 18 q^{49} + 48 q^{51} + 39 q^{53} - 27 q^{55} - 6 q^{57} + 9 q^{59} - 24 q^{61} + 3 q^{63} + 27 q^{65} + 39 q^{67} - 3 q^{69} + 12 q^{73} + 90 q^{75} + 60 q^{77} + 63 q^{79} - 6 q^{81} - 27 q^{83} - 30 q^{85} + 18 q^{87} + 66 q^{89} + 108 q^{91} + 60 q^{93} - 75 q^{95} - 81 q^{97} + 15 q^{99}+O(q^{100}) \) 18 * q - 9 * q^7 - 6 * q^9 - 3 * q^11 + 3 * q^13 + 33 * q^15 + 9 * q^17 - 24 * q^19 - 15 * q^21 + 6 * q^23 + 6 * q^25 - 12 * q^27 - 3 * q^29 - 6 * q^31 - 45 * q^33 - 15 * q^35 + 48 * q^37 + 12 * q^39 - 18 * q^41 - 39 * q^43 - 42 * q^45 - 27 * q^47 - 18 * q^49 + 48 * q^51 + 39 * q^53 - 27 * q^55 - 6 * q^57 + 9 * q^59 - 24 * q^61 + 3 * q^63 + 27 * q^65 + 39 * q^67 - 3 * q^69 + 12 * q^73 + 90 * q^75 + 60 * q^77 + 63 * q^79 - 6 * q^81 - 27 * q^83 - 30 * q^85 + 18 * q^87 + 66 * q^89 + 108 * q^91 + 60 * q^93 - 75 * q^95 - 81 * q^97 + 15 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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