LMFDB - Embedded newform 304.2.u.f.161.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [304,2,Mod(17,304)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(304, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 10]))

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

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

chi := DirichletCharacter("304.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 304 = 2^{4} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	304.u (of order $9$, degree $6$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.42745222145$
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:	no (minimal twist has level 152)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			161.3
Root			$-0.643662 - 1.11486i$ of defining polynomial
Character	$\chi$	$=$	304.161
Dual form			304.2.u.f.17.3

$q$-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 $\left(\mathbb{Z}/304\mathbb{Z}\right)^\times$.

$n$	$97$	$191$	$229$
$\chi(n)$	$e\left(\frac{4}{9}\right)$	$1$	$1$

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	$-0.601025\pi$
$3$	0.986147	−	0.827476i	0.569352	−	0.477743i	0.881431	+	0.472313i	$0.156581\pi$
$4$		0			0
$5$	−3.98739	−	1.45129i	−1.78321	−	0.649037i	−0.999614	−	0.0277715i	$-0.991159\pi$
$5$	−3.98739	−	1.45129i	−1.78321	−	0.649037i	−0.783600	−	0.621266i	$-0.786619\pi$
$6$		0			0
$7$	1.68618	−	2.92055i	0.637316	−	1.10386i	−0.348703	−	0.937233i	$-0.613378\pi$
$7$	1.68618	−	2.92055i	0.637316	−	1.10386i	0.986019	−	0.166631i	$-0.0532889\pi$
$8$		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	$-0.190475\pi$
$11$	−0.247839	−	0.429270i	−0.0747264	−	0.129430i	−0.900967	+	0.433887i	$0.857142\pi$
$12$		0			0
$13$	−2.70667	−	2.27116i	−0.750694	−	0.629907i	0.184992	−	0.982740i	$-0.440774\pi$
$13$	−2.70667	−	2.27116i	−0.750694	−	0.629907i	−0.935686	+	0.352833i	$0.885218\pi$
$14$		0			0
$15$	−5.13306	+	1.86828i	−1.32535	+	0.482388i
$16$		0			0
$17$	−0.689000	−	3.90752i	−0.167107	−	0.947712i	−0.946865	−	0.321631i	$-0.895769\pi$
$17$	−0.689000	−	3.90752i	−0.167107	−	0.947712i	0.779758	−	0.626081i	$-0.215342\pi$
$18$		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	$-0.579756\pi$
$23$	0.886425	−	0.322632i	0.184832	−	0.0672735i	0.432778	+	0.901500i	$0.357533\pi$
$24$		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	0.911074	+	0.412243i	$0.135255\pi$
$29$	−0.463399	+	2.62807i	−0.0860511	+	0.488020i	−0.997125	+	0.0757766i	$0.975856\pi$
$30$		0			0
$31$	3.41680	−	5.91807i	0.613675	−	1.06292i	−0.376940	−	0.926238i	$-0.623024\pi$
$31$	3.41680	−	5.91807i	0.613675	−	1.06292i	0.990615	−	0.136679i	$-0.0436429\pi$
$32$		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	−0.776100	−	0.630609i	$-0.782805\pi$
$41$	−1.85588	+	1.55727i	−0.289840	+	0.243205i	0.486261	+	0.873814i	$0.338361\pi$
$42$		0			0
$43$	11.2724	+	4.10282i	1.71902	+	0.625674i	0.997754	−	0.0669794i	$-0.0213362\pi$
$43$	11.2724	+	4.10282i	1.71902	+	0.625674i	0.721271	+	0.692653i	$0.243558\pi$
$44$		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	$-0.970426\pi$
$47$	−0.194129	+	1.10096i	−0.0283166	+	0.160591i	0.967371	+	0.253366i	$0.0815376\pi$
$48$		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	−0.406515	−	0.913644i	$-0.633256\pi$
$53$	−0.951101	+	0.346173i	−0.130644	+	0.0475505i	0.275871	+	0.961195i	$0.411034\pi$
$54$		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	−0.964045	−	0.265739i	$-0.914384\pi$
$59$	−1.14470	−	6.49191i	−0.149027	−	0.845175i	0.815018	−	0.579436i	$-0.196727\pi$
$60$		0			0
$61$	−8.89778	+	3.23853i	−1.13924	+	0.414651i	−0.841640	−	0.540038i	$-0.818410\pi$
$61$	−8.89778	+	3.23853i	−1.13924	+	0.414651i	−0.297604	+	0.954689i	$0.596188\pi$
$62$		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	−0.634727	−	0.772736i	$-0.718888\pi$
$67$	1.84999	−	10.4918i	0.226013	−	1.28178i	0.860740	−	0.509045i	$-0.170001\pi$
$68$		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	$-0.200064\pi$
$71$	8.85275	+	3.22214i	1.05063	+	0.382397i	0.241728	+	0.970344i	$0.422286\pi$
$72$		0			0
$73$	2.49328	−	2.09211i	0.291817	−	0.244863i	−0.485112	−	0.874452i	$-0.661221\pi$
$73$	2.49328	−	2.09211i	0.291817	−	0.244863i	0.776929	+	0.629589i	$0.216777\pi$
$74$		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	$-0.827239\pi$
$79$	−4.41163	+	3.70180i	−0.496347	+	0.416485i	0.359947	+	0.932973i	$0.382795\pi$
$80$		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	$-0.973790\pi$
$83$	−3.89085	+	6.73916i	−0.427077	+	0.739719i	0.569535	+	0.821967i	$0.307123\pi$
$84$		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	0.745311	−	0.666717i	$-0.232301\pi$
$89$	2.05797	+	1.72684i	0.218145	+	0.183045i	−0.527166	+	0.849762i	$0.676746\pi$
$90$		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	0.994834	−	0.101514i	$-0.0323687\pi$
$97$	0.248939	+	1.41180i	0.0252759	+	0.143347i	−0.969558	+	0.244861i	$0.921258\pi$
$98$		0			0
$99$	0.625455	−	0.227647i	0.0628606	−	0.0228794i
$100$		0			0
$101$	−2.85382	−	2.39464i	−0.283965	−	0.238275i	0.489668	−	0.871909i	$-0.337118\pi$
$101$	−2.85382	−	2.39464i	−0.283965	−	0.238275i	−0.773633	+	0.633634i	$0.781563\pi$
$102$		0			0
$103$	2.28192	+	3.95240i	0.224844	+	0.389442i	0.956273	−	0.292477i	$-0.0944793\pi$
$103$	2.28192	+	3.95240i	0.224844	+	0.389442i	−0.731428	+	0.681918i	$0.761146\pi$
$104$		0			0
$105$	−3.19886	+	18.1416i	−0.312177	+	1.77044i
$106$		0			0
$107$	8.64438	−	14.9725i	0.835684	−	1.44745i	−0.0577891	−	0.998329i	$-0.518405\pi$
$107$	8.64438	−	14.9725i	0.835684	−	1.44745i	0.893473	−	0.449118i	$-0.148262\pi$
$108$		0			0
$109$	8.04469	+	2.92803i	0.770542	+	0.280454i	0.697223	−	0.716854i	$-0.254419\pi$
$109$	8.04469	+	2.92803i	0.770542	+	0.280454i	0.0733187	+	0.997309i	$0.476641\pi$
$110$		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	$-0.443599\pi$
$127$	−8.59313	−	7.21049i	−0.762517	−	0.639828i	−0.938781	+	0.344515i	$0.888043\pi$
$128$		0			0
$129$	14.5112	−	5.28166i	1.27764	−	0.465024i
$130$		0			0
$131$	−0.912664	−	5.17598i	−0.0797398	−	0.452227i	−0.998368	−	0.0571044i	$-0.981813\pi$
$131$	−0.912664	−	5.17598i	−0.0797398	−	0.452227i	0.918628	−	0.395123i	$-0.129298\pi$
$132$		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	0.306393	−	0.951905i	$-0.400878\pi$
$137$	13.4952	−	4.91187i	1.15298	−	0.419649i	0.846584	+	0.532256i	$0.178656\pi$
$138$		0			0
$139$	2.84328	+	2.38580i	0.241164	+	0.202361i	0.755356	−	0.655314i	$-0.227464\pi$
$139$	2.84328	+	2.38580i	0.241164	+	0.202361i	−0.514192	+	0.857675i	$0.671908\pi$
$140$		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	−0.363238	−	0.931696i	$-0.618329\pi$
$149$	5.99620	−	5.03141i	0.491228	−	0.412189i	0.854466	+	0.519507i	$0.173884\pi$
$150$		0			0
$151$	−21.1437			−1.72065			−0.860326	−	0.509743i	$-0.829740\pi$
$151$	−21.1437			−1.72065			−0.860326	+	0.509743i	$0.829740\pi$
$152$		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	0.477953	−	0.878385i	$-0.341379\pi$
$157$	3.50177	+	1.27454i	0.279472	+	0.101719i	−0.198482	+	0.980105i	$0.563601\pi$
$158$		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	$-0.235257\pi$
$163$	−2.72987	−	4.72828i	−0.213820	−	0.370348i	−0.952907	+	0.303263i	$0.901924\pi$
$164$		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	$-0.686977\pi$
$167$	−5.73393	+	2.08698i	−0.443705	+	0.161495i	0.110499	+	0.993876i	$0.464755\pi$
$168$		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	0.682334	+	0.731041i	$0.260965\pi$
$173$	3.82988	+	21.7203i	0.291180	+	1.65137i	−0.391153	+	0.920326i	$0.627924\pi$
$174$		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	$-0.322742\pi$
$179$	−6.30040	−	10.9126i	−0.470914	−	0.815647i	−0.999447	+	0.0332660i	$0.989409\pi$
$180$		0			0
$181$	0.234375	−	1.32921i	0.0174210	−	0.0987992i	−0.974858	−	0.222829i	$-0.928471\pi$
$181$	0.234375	−	1.32921i	0.0174210	−	0.0987992i	0.992278	+	0.124030i	$0.0395819\pi$
$182$		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	$-0.212655\pi$
$191$	21.6982			1.57003			0.785014	+	0.619477i	$0.212655\pi$
$192$		0			0
$193$	−19.3246	+	16.2153i	−1.39101	+	1.16720i	−0.426087	+	0.904682i	$0.640108\pi$
$193$	−19.3246	+	16.2153i	−1.39101	+	1.16720i	−0.964927	+	0.262518i	$0.915447\pi$
$194$		0			0
$195$	18.1367	+	6.60120i	1.29879	+	0.472722i
$196$		0			0
$197$	−5.66192	+	9.80674i	−0.403395	+	0.698701i	−0.994133	−	0.108162i	$-0.965503\pi$
$197$	−5.66192	+	9.80674i	−0.403395	+	0.698701i	0.590738	+	0.806863i	$0.298837\pi$
$198$		0			0
$199$	−0.624969	+	3.54437i	−0.0443028	+	0.251254i	−0.998914	−	0.0466026i	$-0.985161\pi$
$199$	−0.624969	+	3.54437i	−0.0443028	+	0.251254i	0.954611	+	0.297856i	$0.0962717\pi$
$200$		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	0.906981	+	0.421171i	$0.138381\pi$
$211$	2.88696	+	16.3728i	0.198747	+	1.12715i	−0.708235	+	0.705977i	$0.750508\pi$
$212$		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	$-0.270922\pi$
$223$	10.1646	+	3.69962i	0.680673	+	0.247745i	0.0215367	+	0.999768i	$0.493144\pi$
$224$		0			0
$225$	−13.3780	+	11.2255i	−0.891868	+	0.748366i
$226$		0			0
$227$	9.91627			0.658166			0.329083	−	0.944301i	$-0.393260\pi$
$227$	9.91627			0.658166			0.329083	+	0.944301i	$0.393260\pi$
$228$		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	0.240538	−	0.970640i	$-0.422676\pi$
$233$	−3.03934	−	1.10623i	−0.199114	−	0.0724715i	−0.439652	+	0.898168i	$0.644898\pi$
$234$		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	$-0.217417\pi$
$239$	−2.45440	−	4.25115i	−0.158762	−	0.274984i	−0.934423	+	0.356166i	$0.884084\pi$
$240$		0			0
$241$	−9.74186	−	8.17439i	−0.627528	−	0.526559i	0.272632	−	0.962119i	$-0.412106\pi$
$241$	−9.74186	−	8.17439i	−0.627528	−	0.526559i	−0.900160	+	0.435560i	$0.856550\pi$
$242$		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	$-0.644385\pi$
$251$	−3.10677	+	1.13077i	−0.196098	+	0.0713737i	0.242104	+	0.970250i	$0.422162\pi$
$252$		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	−0.766002	−	0.642838i	$-0.777757\pi$
$257$	2.78411	−	15.7895i	0.173668	−	0.984921i	0.939670	−	0.342082i	$-0.111132\pi$
$258$		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	$-0.648163\pi$
$263$	5.72882	−	4.80705i	0.353254	−	0.296415i	0.802095	+	0.597196i	$0.203719\pi$
$264$		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	−0.328961	+	0.944343i	$0.606699\pi$
$269$	−21.5853	+	18.1123i	−1.31608	+	1.10432i	−0.987120	+	0.159980i	$0.948857\pi$
$270$		0			0
$271$	−3.62220	−	1.31837i	−0.220033	−	0.0800855i	0.229651	−	0.973273i	$-0.426241\pi$
$271$	−3.62220	−	1.31837i	−0.220033	−	0.0800855i	−0.449685	+	0.893187i	$0.648464\pi$
$272$		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	0.799938	−	0.600083i	$-0.204866\pi$
$277$	−1.99251	−	3.45112i	−0.119718	−	0.207358i	−0.919656	+	0.392725i	$0.871532\pi$
$278$		0			0
$279$	7.02932	+	5.89830i	0.420835	+	0.353122i
$280$		0			0
$281$	−5.04675	+	1.83687i	−0.301064	+	0.109578i	−0.488135	−	0.872768i	$-0.662323\pi$
$281$	−5.04675	+	1.83687i	−0.301064	+	0.109578i	0.187071	+	0.982346i	$0.440100\pi$
$282$		0			0
$283$	4.56670	+	25.8990i	0.271462	+	1.53954i	0.749980	+	0.661460i	$0.230063\pi$
$283$	4.56670	+	25.8990i	0.271462	+	1.53954i	−0.478518	+	0.878078i	$0.658826\pi$
$284$		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	0.939093	+	0.343664i	$0.111668\pi$
$293$	13.1318	+	22.7449i	0.767168	+	1.32877i	−0.171925	+	0.985110i	$0.554999\pi$
$294$		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	$-0.669598\pi$
$307$	4.41784	−	3.70701i	0.252140	−	0.211570i	0.760093	+	0.649814i	$0.225153\pi$
$308$		0			0
$309$	5.52083	+	2.00942i	0.314069	+	0.114312i
$310$		0			0
$311$	14.8857	−	25.7828i	0.844092	−	1.46201i	−0.0423147	−	0.999104i	$-0.513473\pi$
$311$	14.8857	−	25.7828i	0.844092	−	1.46201i	0.886407	−	0.462907i	$-0.153193\pi$
$312$		0			0
$313$	−0.186186	+	1.05591i	−0.0105239	+	0.0596838i	−0.989617	−	0.143727i	$-0.954091\pi$
$313$	−0.186186	+	1.05591i	−0.0105239	+	0.0596838i	0.979094	+	0.203410i	$0.0652025\pi$
$314$		0			0
$315$	−9.60765	−	16.6409i	−0.541330	−	0.937611i
$316$		0			0
$317$	8.99617	+	7.54869i	0.505275	+	0.423976i	0.859463	−	0.511198i	$-0.170798\pi$
$317$	8.99617	+	7.54869i	0.505275	+	0.423976i	−0.354188	+	0.935174i	$0.615243\pi$
$318$		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	$-0.0599986\pi$
$331$	5.98328	+	10.3633i	0.328871	+	0.569621i	−0.653417	+	0.756998i	$0.726665\pi$
$332$		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	0.467817	−	0.883825i	$-0.345041\pi$
$337$	4.73759	+	1.72434i	0.258073	+	0.0939310i	−0.209744	+	0.977756i	$0.567263\pi$
$338$		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	$-0.209388\pi$
$347$	18.7124	+	6.81076i	1.00453	+	0.365621i	0.213203	+	0.977008i	$0.431610\pi$
$348$		0			0
$349$	0.241896	−	0.418976i	0.0129484	−	0.0224273i	−0.859479	−	0.511172i	$-0.829212\pi$
$349$	0.241896	−	0.418976i	0.0129484	−	0.0224273i	0.872427	+	0.488744i	$0.162545\pi$
$350$		0			0
$351$	3.43011	−	19.4531i	0.183086	−	1.03833i
$352$		0			0
$353$	6.09193	+	10.5515i	0.324241	+	0.561601i	0.981358	−	0.192187i	$-0.0615579\pi$
$353$	6.09193	+	10.5515i	0.324241	+	0.561601i	−0.657118	+	0.753788i	$0.728225\pi$
$354$		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	$-0.0168650\pi$
$359$	0.797870	+	4.52495i	0.0421100	+	0.238818i	−0.956487	+	0.291776i	$0.905754\pi$
$360$		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	$-0.282350\pi$
$367$	−0.421581	−	0.353748i	−0.0220063	−	0.0184655i	−0.653724	+	0.756733i	$0.726794\pi$
$368$		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	−0.939282	−	0.343145i	$-0.888508\pi$
$373$	−3.33092	+	5.76932i	−0.172468	+	0.298724i	0.766814	+	0.641870i	$0.221841\pi$
$374$		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	$-0.528062\pi$
$379$	−3.42807			−0.176088			−0.0880440	+	0.996117i	$0.528062\pi$
$380$		0			0
$381$	−14.4406			−0.739815
$382$		0			0
$383$	9.15647	−	7.68319i	0.467874	−	0.392593i	−0.378144	−	0.925747i	$-0.623438\pi$
$383$	9.15647	−	7.68319i	0.467874	−	0.392593i	0.846018	+	0.533154i	$0.178993\pi$
$384$		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	−0.636041	−	0.771655i	$-0.719429\pi$
$389$	4.44881	−	25.2304i	0.225564	−	1.27923i	0.861605	−	0.507580i	$-0.169460\pi$
$390$		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	0.785149	+	0.619307i	$0.212586\pi$
$397$	5.16384	+	29.2856i	0.259166	+	1.46980i	−0.525983	+	0.850495i	$0.676302\pi$
$398$		0			0
$399$	−14.2138	+	12.4925i	−0.711582	+	0.625405i
$400$		0			0
$401$	−1.75709	−	9.96495i	−0.0877449	−	0.497626i	−0.996730	−	0.0807983i	$-0.974253\pi$
$401$	−1.75709	−	9.96495i	−0.0877449	−	0.497626i	0.908986	−	0.416827i	$-0.136858\pi$
$402$		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	0.750069	+	0.661360i	$0.230020\pi$
$409$	−3.65977	+	20.7556i	−0.180964	+	1.02630i	−0.931032	+	0.364937i	$0.881091\pi$
$410$		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	$-0.310716\pi$
$419$	22.9349			1.12044			0.560221	+	0.828343i	$0.310716\pi$
$420$		0			0
$421$	9.77997	−	8.20637i	0.476646	−	0.399954i	−0.372566	−	0.928006i	$-0.621522\pi$
$421$	9.77997	−	8.20637i	0.476646	−	0.399954i	0.849212	+	0.528052i	$0.177077\pi$
$422$		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	$-0.296819\pi$
$431$	−1.90160	−	1.59563i	−0.0915969	−	0.0768590i	−0.687436	+	0.726245i	$0.741264\pi$
$432$		0			0
$433$	−21.6702	+	7.88731i	−1.04140	+	0.379040i	−0.805412	−	0.592715i	$-0.798056\pi$
$433$	−21.6702	+	7.88731i	−1.04140	+	0.379040i	−0.235991	+	0.971755i	$0.575834\pi$
$434$		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	0.973794	+	0.227433i	$0.0730332\pi$
$439$	2.86028	+	16.2214i	0.136513	+	0.774207i	−0.837280	+	0.546774i	$0.815856\pi$
$440$		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	$-0.0790862\pi$
$443$	18.8468	+	15.8143i	0.895437	+	0.751360i	−0.0738565	+	0.997269i	$0.523531\pi$
$444$		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	−0.872633	−	0.488377i	$-0.837589\pi$
$449$	−0.283288	+	0.490669i	−0.0133692	+	0.0231561i	0.859263	+	0.511533i	$0.170922\pi$
$450$		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	0.891774	−	0.452481i	$-0.149461\pi$
$461$	27.5700	+	10.0347i	1.28406	+	0.467361i	0.392290	+	0.919842i	$0.371683\pi$
$462$		0			0
$463$	−8.73762	+	15.1340i	−0.406072	+	0.703337i	−0.994446	−	0.105252i	$-0.966435\pi$
$463$	−8.73762	+	15.1340i	−0.406072	+	0.703337i	0.588374	+	0.808589i	$0.299768\pi$
$464$		0			0
$465$	−6.48202	+	36.7614i	−0.300596	+	1.70477i
$466$		0			0
$467$	−14.5703	−	25.2366i	−0.674235	−	1.16781i	−0.976692	−	0.214646i	$-0.931140\pi$
$467$	−14.5703	−	25.2366i	−0.674235	−	1.16781i	0.302457	−	0.953163i	$-0.402193\pi$
$468$		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	$-0.794346\pi$
$479$	−22.3916	+	8.14988i	−1.02310	+	0.372378i	−0.224650	+	0.974440i	$0.572124\pi$
$480$		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	−0.369561	−	0.929206i	$-0.620492\pi$
$487$	13.6808	−	23.6958i	0.619936	−	1.07376i	0.989497	−	0.144554i	$-0.0461747\pi$
$488$		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	$-0.785116\pi$
$491$	−6.66429	+	5.59200i	−0.300755	+	0.252364i	0.479903	+	0.877321i	$0.340672\pi$
$492$		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	$-0.457703\pi$
$499$	−9.00548	−	3.27773i	−0.403141	−	0.146731i	−0.535629	+	0.844453i	$0.679926\pi$
$500$		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	$-0.906243\pi$
$503$	0.932555	−	5.28878i	0.0415806	−	0.235815i	0.998514	+	0.0544916i	$0.0173538\pi$
$504$		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	−0.945984	−	0.324215i	$-0.894900\pi$
$509$	−32.9898	+	12.0073i	−1.46225	+	0.532215i	−0.516264	+	0.856429i	$0.672678\pi$
$510$		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	0.936063	+	0.351834i	$0.114442\pi$
$521$	17.6378	+	30.5496i	0.772728	+	1.33840i	−0.163334	+	0.986571i	$0.552225\pi$
$522$		0			0
$523$	−4.15379	+	23.5573i	−0.181632	+	1.03009i	0.748574	+	0.663051i	$0.230739\pi$
$523$	−4.15379	+	23.5573i	−0.181632	+	1.03009i	−0.930206	+	0.367037i	$0.880372\pi$
$524$		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	−0.668533	−	0.743682i	$-0.733078\pi$
$541$	4.97837	−	28.2337i	0.214037	−	1.21386i	0.882570	−	0.470181i	$-0.155811\pi$
$542$		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	$-0.734642\pi$
$547$	−16.6333	+	6.05403i	−0.711189	+	0.258852i	−0.0390083	+	0.999239i	$0.512420\pi$
$548$		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	0.810721	−	0.585432i	$-0.199075\pi$
$557$	8.84945	+	7.42557i	0.374963	+	0.314631i	−0.435758	+	0.900064i	$0.643520\pi$
$558$		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	$-0.789479\pi$
$563$	3.25866	−	5.64417i	0.137336	−	0.237873i	0.926488	+	0.376325i	$0.122813\pi$
$564$		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	$-0.510436\pi$
$571$	−1.56658			−0.0655595			−0.0327797	+	0.999463i	$0.510436\pi$
$572$		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	0.421452	+	0.906851i	$0.361521\pi$
$577$	−13.8031	+	23.9076i	−0.574630	+	0.995288i	−0.996082	+	0.0884375i	$0.971813\pi$
$578$		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	−0.920237	−	0.391361i	$-0.872004\pi$
$587$	−4.58760	−	26.0176i	−0.189350	−	1.07386i	0.730887	−	0.682499i	$-0.239107\pi$
$588$		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	0.483483	−	0.875354i	$-0.339372\pi$
$593$	34.4945	−	12.5550i	1.41652	−	0.515571i	0.933036	+	0.359783i	$0.117149\pi$
$594$		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	−0.928118	−	0.372286i	$-0.878574\pi$
$599$	1.74643	−	9.90447i	0.0713570	−	0.404686i	0.999475	−	0.0323995i	$-0.0103149\pi$
$600$		0			0
$601$	14.6079	−	25.3017i	0.595870	−	1.03208i	−0.397553	−	0.917579i	$-0.630141\pi$
$601$	14.6079	−	25.3017i	0.595870	−	1.03208i	0.993423	−	0.114498i	$-0.0365260\pi$
$602$		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	$-0.625992\pi$
$607$	−18.9985			−0.771124			−0.385562	+	0.922682i	$0.625992\pi$
$608$		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	0.583693	−	0.811974i	$-0.301607\pi$
$613$	12.5998	+	4.58595i	0.508901	+	0.185225i	−0.0747923	+	0.997199i	$0.523829\pi$
$614$		0			0
$615$	6.61693	−	11.4609i	0.266821	−	0.462147i
$616$		0			0
$617$	5.26775	−	29.8749i	0.212072	−	1.20272i	−0.673845	−	0.738873i	$-0.735358\pi$
$617$	5.26775	−	29.8749i	0.212072	−	1.20272i	0.885916	−	0.463845i	$-0.153531\pi$
$618$		0			0
$619$	15.4667	+	26.7891i	0.621659	+	1.07675i	0.989177	+	0.146729i	$0.0468744\pi$
$619$	15.4667	+	26.7891i	0.621659	+	1.07675i	−0.367518	+	0.930017i	$0.619792\pi$
$620$		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	$-0.590588\pi$
$631$	3.04173	−	1.10710i	0.121089	−	0.0440729i	0.401854	+	0.915704i	$0.368366\pi$
$632$		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	0.955200	−	0.295961i	$-0.0956399\pi$
$641$	37.8930	+	13.7919i	1.49669	+	0.544749i	0.541485	+	0.840710i	$0.317862\pi$
$642$		0			0
$643$	−1.80428	+	1.51397i	−0.0711538	+	0.0597052i	−0.677671	−	0.735365i	$-0.737011\pi$
$643$	−1.80428	+	1.51397i	−0.0711538	+	0.0597052i	0.606517	+	0.795070i	$0.292566\pi$
$644$		0			0
$645$	−65.5271			−2.58013
$646$		0			0
$647$	24.9858			0.982293			0.491147	−	0.871077i	$-0.336578\pi$
$647$	24.9858			0.982293			0.491147	+	0.871077i	$0.336578\pi$
$648$		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	−0.763555	−	0.645742i	$-0.776548\pi$
$653$	4.53457	−	7.85411i	0.177452	−	0.307355i	0.941007	+	0.338387i	$0.109881\pi$
$654$		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	$-0.243583\pi$
$659$	4.21698	+	3.53847i	0.164270	+	0.137839i	−0.556947	+	0.830548i	$0.688027\pi$
$660$		0			0
$661$	15.0888	−	5.49187i	0.586886	−	0.213609i	−0.0314734	−	0.999505i	$-0.510020\pi$
$661$	15.0888	−	5.49187i	0.586886	−	0.213609i	0.618359	+	0.785896i	$0.287798\pi$
$662$		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	0.984787	−	0.173765i	$-0.0555934\pi$
$673$	8.86987	+	15.3631i	0.341909	+	0.592203i	−0.642879	+	0.765968i	$0.722260\pi$
$674$		0			0
$675$	−12.6257	+	71.6038i	−0.485963	+	2.75603i
$676$		0			0
$677$	−11.5028	+	19.9235i	−0.442089	+	0.765721i	−0.997844	−	0.0656249i	$-0.979096\pi$
$677$	−11.5028	+	19.9235i	−0.442089	+	0.765721i	0.555755	+	0.831346i	$0.312429\pi$
$678$		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	$-0.721796\pi$
$683$	−33.5439			−1.28352			−0.641760	+	0.766905i	$0.721796\pi$
$684$		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	−0.435568	−	0.900156i	$-0.643452\pi$
$691$	14.7673	−	25.5777i	0.561774	−	0.973021i	0.997342	−	0.0728654i	$-0.0232143\pi$
$692$		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	−0.702525	−	0.711659i	$-0.747944\pi$
$701$	−7.56614	−	42.9097i	−0.285769	−	1.62068i	0.416755	−	0.909019i	$-0.363167\pi$
$702$		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	0.680757	−	0.732510i	$-0.261651\pi$
$709$	2.06593	+	1.73352i	0.0775875	+	0.0651036i	−0.603169	+	0.797613i	$0.706096\pi$
$710$		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	$-0.668620\pi$
$719$	6.88537	−	5.77751i	0.256781	−	0.215465i	0.762086	+	0.647476i	$0.224175\pi$
$720$		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	$-0.477265\pi$
$727$	−13.8891	−	5.05524i	−0.515120	−	0.187488i	−0.586482	+	0.809962i	$0.699488\pi$
$728$		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	0.783433	−	0.621477i	$-0.213467\pi$
$733$	−3.96628	−	6.86981i	−0.146498	−	0.253742i	−0.929931	+	0.367734i	$0.880134\pi$
$734$		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	−0.493545	−	0.869720i	$-0.664299\pi$
$739$	−8.89550	−	50.4489i	−0.327226	−	1.85579i	0.166318	−	0.986072i	$-0.446812\pi$
$740$		0			0
$741$	10.3038	+	16.9387i	0.378520	+	0.622260i
$742$		0			0
$743$	3.26954	+	18.5425i	0.119948	+	0.680257i	0.984181	+	0.177166i	$0.0566929\pi$
$743$	3.26954	+	18.5425i	0.119948	+	0.680257i	−0.864233	+	0.503091i	$0.832196\pi$
$744$		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	−0.720312	−	0.693650i	$-0.756001\pi$
$751$	5.31103	−	30.1203i	0.193802	−	1.09911i	0.914114	−	0.405457i	$-0.132888\pi$
$752$		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	−0.497418	−	0.867511i	$-0.665718\pi$
$757$	7.44350	−	6.24584i	0.270539	−	0.227009i	0.767956	+	0.640502i	$0.221274\pi$
$758$		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	0.837790	+	0.545992i	$0.183847\pi$
$769$	−3.77737	+	21.4225i	−0.136216	+	0.772517i	−0.974006	+	0.226524i	$0.927264\pi$
$770$		0			0
$771$	−10.3199	−	17.8745i	−0.371661	−	0.643736i
$772$		0			0
$773$	−5.40500	−	4.53533i	−0.194404	−	0.163125i	0.540390	−	0.841415i	$-0.318277\pi$
$773$	−5.40500	−	4.53533i	−0.194404	−	0.163125i	−0.734794	+	0.678290i	$0.762721\pi$
$774$		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	$-0.200567\pi$
$787$	−2.98205	−	5.16507i	−0.106299	−	0.184115i	−0.914268	+	0.405110i	$0.867233\pi$
$788$		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	0.931669	−	0.363307i	$-0.118353\pi$
$809$	4.30060	+	7.44886i	0.151201	+	0.261888i	−0.780468	+	0.625196i	$0.785019\pi$
$810$		0			0
$811$	−18.5790	−	15.5896i	−0.652395	−	0.547425i	0.255401	−	0.966835i	$-0.417792\pi$
$811$	−18.5790	−	15.5896i	−0.652395	−	0.547425i	−0.907797	+	0.419410i	$0.862237\pi$
$812$		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	−0.751679	−	0.659529i	$-0.770756\pi$
$821$	−25.8899	+	9.42314i	−0.903563	+	0.328870i	−0.151883	+	0.988398i	$0.548534\pi$
$822$		0			0
$823$	−42.9391	−	36.0302i	−1.49676	−	1.25593i	−0.885618	−	0.464415i	$-0.846265\pi$
$823$	−42.9391	−	36.0302i	−1.49676	−	1.25593i	−0.611146	−	0.791518i	$-0.709291\pi$
$824$		0			0
$825$	−4.14940	−	7.18698i	−0.144464	−	0.250218i
$826$		0			0
$827$	−7.98839	+	45.3044i	−0.277784	+	1.57539i	0.452195	+	0.891919i	$0.350641\pi$
$827$	−7.98839	+	45.3044i	−0.277784	+	1.57539i	−0.729979	+	0.683470i	$0.760470\pi$
$828$		0			0
$829$	5.57204	−	9.65105i	0.193525	−	0.335195i	−0.752891	−	0.658145i	$-0.771341\pi$
$829$	5.57204	−	9.65105i	0.193525	−	0.335195i	0.946416	+	0.322950i	$0.104675\pi$
$830$		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	$-0.606874\pi$
$839$	15.7318	−	13.2005i	0.543120	−	0.455732i	0.872603	+	0.488429i	$0.162430\pi$
$840$		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	0.972170	−	0.234275i	$-0.0752717\pi$
$853$	−0.627868	−	3.56082i	−0.0214978	−	0.121920i	−0.993668	+	0.112355i	$0.964161\pi$
$854$		0			0
$855$	−24.8300	+	0.568703i	−0.849167	+	0.0194492i
$856$		0			0
$857$	3.72296	+	21.1139i	0.127174	+	0.721238i	0.979993	+	0.199032i	$0.0637797\pi$
$857$	3.72296	+	21.1139i	0.127174	+	0.721238i	−0.852819	+	0.522206i	$0.825109\pi$
$858$		0			0
$859$	31.7422	−	11.5532i	1.08303	−	0.394191i	0.261996	−	0.965069i	$-0.415619\pi$
$859$	31.7422	−	11.5532i	1.08303	−	0.394191i	0.821035	+	0.570878i	$0.193397\pi$
$860$		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	$-0.0836144\pi$
$863$	7.57823	+	13.1259i	0.257966	+	0.446810i	−0.707731	+	0.706482i	$0.750281\pi$
$864$		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	−0.873241	−	0.487289i	$-0.837986\pi$
$877$	−16.1395	+	13.5426i	−0.544991	+	0.457302i	0.328249	+	0.944591i	$0.393541\pi$
$878$		0			0
$879$	31.7708	+	11.5636i	1.07160	+	0.390031i
$880$		0			0
$881$	−17.0362	+	29.5076i	−0.573966	+	0.994138i	0.422187	+	0.906509i	$0.361262\pi$
$881$	−17.0362	+	29.5076i	−0.573966	+	0.994138i	−0.996153	+	0.0876292i	$0.972071\pi$
$882$		0			0
$883$	2.20860	−	12.5256i	0.0743253	−	0.421520i	−0.924828	−	0.380385i	$-0.875792\pi$
$883$	2.20860	−	12.5256i	0.0743253	−	0.421520i	0.999154	−	0.0411349i	$-0.0130973\pi$
$884$		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	$-0.0688035\pi$
$887$	27.8503	+	23.3692i	0.935122	+	0.784661i	−0.0416076	+	0.999134i	$0.513248\pi$
$888$		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	$-0.640671\pi$
$907$	−40.2460	−	14.6483i	−1.33635	−	0.486390i	−0.908660	+	0.417537i	$0.862893\pi$
$908$		0			0
$909$	3.83210	−	3.21551i	0.127103	−	0.106652i
$910$		0			0
$911$	−59.2711			−1.96374			−0.981870	−	0.189555i	$-0.939295\pi$
$911$	−59.2711			−1.96374			−0.981870	+	0.189555i	$0.939295\pi$
$912$		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	$-0.965696\pi$
$919$	−12.2457	+	21.2102i	−0.403949	+	0.699660i	0.590249	+	0.807221i	$0.299029\pi$
$920$		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	−0.830849	−	0.556497i	$-0.812145\pi$
$929$	−7.32848	−	41.5619i	−0.240440	−	1.36360i	0.590410	−	0.807104i	$-0.298966\pi$
$930$		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	0.376370	−	0.926469i	$-0.377172\pi$
$937$	−14.4074	−	12.0892i	−0.470668	−	0.394938i	−0.847038	+	0.531532i	$0.821617\pi$
$938$		0			0
$939$	0.690137	+	1.19535i	0.0225218	+	0.0390088i
$940$		0			0
$941$	5.38617	−	30.5465i	0.175584	−	0.995788i	−0.761883	−	0.647714i	$-0.775725\pi$
$941$	5.38617	−	30.5465i	0.175584	−	0.995788i	0.937467	−	0.348073i	$-0.113164\pi$
$942$		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	$-0.525574\pi$
$947$	27.3095	−	22.9154i	0.887440	−	0.744650i	0.967695	+	0.252124i	$0.0811291\pi$
$948$		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	−0.841986	−	0.539500i	$-0.818613\pi$
$953$	−14.1046	+	11.8351i	−0.456892	+	0.383378i	0.385094	+	0.922877i	$0.374169\pi$
$954$		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	0.972412	+	0.233268i	$0.0749420\pi$
$967$	4.30458	+	24.4125i	0.138426	+	0.785053i	−0.833986	+	0.551785i	$0.813947\pi$
$968$		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	$-0.0618591\pi$
$971$	−0.214298	−	1.21534i	−0.00687714	−	0.0390022i	−0.988053	+	0.154113i	$0.950748\pi$
$972$		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	−0.945245	−	0.326363i	$-0.894177\pi$
$977$	−23.6072	−	40.8888i	−0.755261	−	1.30815i	0.189984	−	0.981787i	$-0.439156\pi$
$978$		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	$-0.545246\pi$
$983$	−27.7941	−	10.1162i	−0.886493	−	0.322657i	−0.744827	+	0.667258i	$0.767468\pi$
$984$		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	$-0.865644\pi$
$991$	−21.0034	+	17.6239i	−0.667195	+	0.559843i	0.245039	+	0.969513i	$0.421199\pi$
$992$		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	−0.992111	−	0.125359i	$-0.959992\pi$
$997$	−0.535399	+	3.03640i	−0.0169563	+	0.0961638i	0.975155	+	0.221523i	$0.0711028\pi$
$998$		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	304.2.u.f.161.3		18
4.3	odd	2		152.2.q.c.9.1	✓	18
19.6	even	9		5776.2.a.cd.1.7		9
19.13	odd	18		5776.2.a.ce.1.3		9
19.17	even	9	inner	304.2.u.f.17.3		18
76.51	even	18		2888.2.a.x.1.7		9
76.55	odd	18		152.2.q.c.17.1	yes	18
76.63	odd	18		2888.2.a.y.1.3		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.2.q.c.9.1	✓	18	4.3	odd	2
152.2.q.c.17.1	yes	18	76.55	odd	18
304.2.u.f.17.3		18	19.17	even	9	inner
304.2.u.f.161.3		18	1.1	even	1	trivial
2888.2.a.x.1.7		9	76.51	even	18
2888.2.a.y.1.3		9	76.63	odd	18
5776.2.a.cd.1.7		9	19.6	even	9
5776.2.a.ce.1.3		9	19.13	odd	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:	\( N \)	\(=\)	\( 304 = 2^{4} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	304.u (of order \(9\), degree \(6\), not 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

Groups

Database

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