LMFDB - Embedded newform 1148.2.n.c.141.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1148,2,Mod(57,1148)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1148, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("1148.57");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1148 = 2^{2} \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1148.n (of order $5$, degree $4$, 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:	$9.16682615204$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 12 x^{14} - 19 x^{13} + 49 x^{12} - 91 x^{11} + 269 x^{10} - 367 x^{9} + 1058 x^{8} + \cdots + 1 $ x^16 - 3x^15 + 12x^14 - 19x^13 + 49x^12 - 91x^11 + 269x^10 - 367x^9 + 1058x^8 - 1675x^7 + 2755x^6 - 2800x^5 + 4032x^4 - 2186x^3 + 2189x^2 + 76*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			141.4
Root			$-1.67741 + 1.21871i$ of defining polynomial
Character	$\chi$	$=$	1148.141
Dual form			1148.2.n.c.57.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.07339 q^{3} +(-2.15094 + 1.56275i) q^{5} +(-0.309017 + 0.951057i) q^{7} +1.29895 q^{9} +O(q^{10})$	\(q+2.07339 q^{3} +(-2.15094 + 1.56275i) q^{5} +(-0.309017 + 0.951057i) q^{7} +1.29895 q^{9} +(0.978799 + 0.711139i) q^{11} +(1.50683 + 4.63753i) q^{13} +(-4.45975 + 3.24020i) q^{15} +(-4.06409 - 2.95273i) q^{17} +(-0.500524 + 1.54045i) q^{19} +(-0.640713 + 1.97191i) q^{21} +(1.09860 + 3.38115i) q^{23} +(0.639280 - 1.96750i) q^{25} -3.52694 q^{27} +(-0.0761582 + 0.0553321i) q^{29} +(-2.98750 - 2.17055i) q^{31} +(2.02943 + 1.47447i) q^{33} +(-0.821587 - 2.52859i) q^{35} +(-6.15009 + 4.46830i) q^{37} +(3.12424 + 9.61542i) q^{39} +(5.39630 - 3.44672i) q^{41} +(3.06649 + 9.43767i) q^{43} +(-2.79398 + 2.02994i) q^{45} +(2.59676 + 7.99201i) q^{47} +(-0.809017 - 0.587785i) q^{49} +(-8.42644 - 6.12217i) q^{51} +(4.13499 - 3.00425i) q^{53} -3.21668 q^{55} +(-1.03778 + 3.19396i) q^{57} +(-2.23821 - 6.88850i) q^{59} +(-2.09856 + 6.45870i) q^{61} +(-0.401399 + 1.23538i) q^{63} +(-10.4884 - 7.62028i) q^{65} +(-11.8851 + 8.63501i) q^{67} +(2.27783 + 7.01044i) q^{69} +(9.09080 + 6.60486i) q^{71} +4.58657 q^{73} +(1.32548 - 4.07940i) q^{75} +(-0.978799 + 0.711139i) q^{77} +12.0411 q^{79} -11.2096 q^{81} +0.731917 q^{83} +13.3560 q^{85} +(-0.157906 + 0.114725i) q^{87} +(2.78534 - 8.57239i) q^{89} -4.87619 q^{91} +(-6.19426 - 4.50040i) q^{93} +(-1.33075 - 4.09562i) q^{95} +(6.31745 - 4.58989i) q^{97} +(1.27141 + 0.923737i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{3} - 13 q^{5} + 4 q^{7} + 2 q^{9}+O(q^{10}) $ 16 * q - 2 * q^3 - 13 * q^5 + 4 * q^7 + 2 * q^9	$ 16 q - 2 q^{3} - 13 q^{5} + 4 q^{7} + 2 q^{9} - q^{11} - 6 q^{13} - q^{17} + 15 q^{19} + 2 q^{21} + 27 q^{23} - 3 q^{25} + 28 q^{27} - q^{29} - 14 q^{31} - 13 q^{33} - 12 q^{35} - 16 q^{37} + 10 q^{39} + 26 q^{41} + 5 q^{43} - 9 q^{45} - 14 q^{47} - 4 q^{49} + 4 q^{51} - 20 q^{53} + 10 q^{55} - 13 q^{57} - 47 q^{61} + 3 q^{63} - 29 q^{65} - 27 q^{67} + 15 q^{69} - 11 q^{71} + 70 q^{73} + 14 q^{75} + q^{77} + 30 q^{79} - 72 q^{81} - 78 q^{83} + 72 q^{85} + 21 q^{87} + 17 q^{89} - 24 q^{91} - 7 q^{93} + 27 q^{95} - 17 q^{97} + 13 q^{99}+O(q^{100}) $ 16 * q - 2 * q^3 - 13 * q^5 + 4 * q^7 + 2 * q^9 - q^11 - 6 * q^13 - q^17 + 15 * q^19 + 2 * q^21 + 27 * q^23 - 3 * q^25 + 28 * q^27 - q^29 - 14 * q^31 - 13 * q^33 - 12 * q^35 - 16 * q^37 + 10 * q^39 + 26 * q^41 + 5 * q^43 - 9 * q^45 - 14 * q^47 - 4 * q^49 + 4 * q^51 - 20 * q^53 + 10 * q^55 - 13 * q^57 - 47 * q^61 + 3 * q^63 - 29 * q^65 - 27 * q^67 + 15 * q^69 - 11 * q^71 + 70 * q^73 + 14 * q^75 + q^77 + 30 * q^79 - 72 * q^81 - 78 * q^83 + 72 * q^85 + 21 * q^87 + 17 * q^89 - 24 * q^91 - 7 * q^93 + 27 * q^95 - 17 * q^97 + 13 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times$.

$n$	$493$	$575$	$785$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	2.07339			1.19707			0.598537	−	0.801095i	$-0.295749\pi$
$3$	2.07339			1.19707			0.598537	+	0.801095i	$0.295749\pi$
$4$		0			0
$5$	−2.15094	+	1.56275i	−0.961931	+	0.698884i	−0.953598	−	0.301081i	$-0.902652\pi$
$5$	−2.15094	+	1.56275i	−0.961931	+	0.698884i	−0.00833287	+	0.999965i	$0.502652\pi$
$6$		0			0
$7$	−0.309017	+	0.951057i	−0.116797	+	0.359466i
$7$	−0.309017	+	0.951057i	−0.116797	+	0.359466i
$8$		0			0
$9$	1.29895			0.432984
$10$		0			0
$11$	0.978799	+	0.711139i	0.295119	+	0.214417i	0.725485	−	0.688238i	$-0.241615\pi$
$11$	0.978799	+	0.711139i	0.295119	+	0.214417i	−0.430366	+	0.902654i	$0.641615\pi$
$12$		0			0
$13$	1.50683	+	4.63753i	0.417918	+	1.28622i	0.909615	+	0.415453i	$0.136377\pi$
$13$	1.50683	+	4.63753i	0.417918	+	1.28622i	−0.491696	+	0.870767i	$0.663623\pi$
$14$		0			0
$15$	−4.45975	+	3.24020i	−1.15150	+	0.836615i
$16$		0			0
$17$	−4.06409	−	2.95273i	−0.985686	−	0.716142i	−0.0267135	−	0.999643i	$-0.508504\pi$
$17$	−4.06409	−	2.95273i	−0.985686	−	0.716142i	−0.958972	+	0.283501i	$0.908504\pi$
$18$		0			0
$19$	−0.500524	+	1.54045i	−0.114828	+	0.353404i	−0.991911	−	0.126934i	$-0.959486\pi$
$19$	−0.500524	+	1.54045i	−0.114828	+	0.353404i	0.877083	+	0.480339i	$0.159486\pi$
$20$		0			0
$21$	−0.640713	+	1.97191i	−0.139815	+	0.430307i
$22$		0			0
$23$	1.09860	+	3.38115i	0.229074	+	0.705018i	0.997852	+	0.0655024i	$0.0208650\pi$
$23$	1.09860	+	3.38115i	0.229074	+	0.705018i	−0.768778	+	0.639516i	$0.779135\pi$
$24$		0			0
$25$	0.639280	−	1.96750i	0.127856	−	0.393500i
$26$		0			0
$27$	−3.52694			−0.678759
$28$		0			0
$29$	−0.0761582	+	0.0553321i	−0.0141422	+	0.0102749i	−0.594834	−	0.803849i	$-0.702782\pi$
$29$	−0.0761582	+	0.0553321i	−0.0141422	+	0.0102749i	0.580692	+	0.814124i	$0.302782\pi$
$30$		0			0
$31$	−2.98750	−	2.17055i	−0.536571	−	0.389842i	0.286239	−	0.958158i	$-0.407595\pi$
$31$	−2.98750	−	2.17055i	−0.536571	−	0.389842i	−0.822810	+	0.568316i	$0.807595\pi$
$32$		0			0
$33$	2.02943	+	1.47447i	0.353279	+	0.256672i
$34$		0			0
$35$	−0.821587	−	2.52859i	−0.138874	−	0.427409i
$36$		0			0
$37$	−6.15009	+	4.46830i	−1.01107	+	0.734584i	−0.964433	−	0.264328i	$-0.914850\pi$
$37$	−6.15009	+	4.46830i	−1.01107	+	0.734584i	−0.0466355	+	0.998912i	$0.514850\pi$
$38$		0			0
$39$	3.12424	+	9.61542i	0.500279	+	1.53970i
$40$		0			0
$41$	5.39630	−	3.44672i	0.842761	−	0.538288i
$41$	5.39630	−	3.44672i	0.842761	−	0.538288i
$42$		0			0
$43$	3.06649	+	9.43767i	0.467635	+	1.43923i	0.855639	+	0.517574i	$0.173165\pi$
$43$	3.06649	+	9.43767i	0.467635	+	1.43923i	−0.388004	+	0.921658i	$0.626835\pi$
$44$		0			0
$45$	−2.79398	+	2.02994i	−0.416501	+	0.302606i
$46$		0			0
$47$	2.59676	+	7.99201i	0.378777	+	1.16575i	0.940895	+	0.338698i	$0.109987\pi$
$47$	2.59676	+	7.99201i	0.378777	+	1.16575i	−0.562118	+	0.827057i	$0.690013\pi$
$48$		0			0
$49$	−0.809017	−	0.587785i	−0.115574	−	0.0839693i
$50$		0			0
$51$	−8.42644	−	6.12217i	−1.17994	−	0.857275i
$52$		0			0
$53$	4.13499	−	3.00425i	0.567984	−	0.412665i	−0.266388	−	0.963866i	$-0.585830\pi$
$53$	4.13499	−	3.00425i	0.567984	−	0.412665i	0.834372	+	0.551201i	$0.185830\pi$
$54$		0			0
$55$	−3.21668			−0.433737
$56$		0			0
$57$	−1.03778	+	3.19396i	−0.137458	+	0.423051i
$58$		0			0
$59$	−2.23821	−	6.88850i	−0.291390	−	0.896806i	−0.984410	−	0.175888i	$-0.943720\pi$
$59$	−2.23821	−	6.88850i	−0.291390	−	0.896806i	0.693020	−	0.720918i	$-0.256280\pi$
$60$		0			0
$61$	−2.09856	+	6.45870i	−0.268693	+	0.826952i	0.722127	+	0.691761i	$0.243165\pi$
$61$	−2.09856	+	6.45870i	−0.268693	+	0.826952i	−0.990820	+	0.135191i	$0.956835\pi$
$62$		0			0
$63$	−0.401399	+	1.23538i	−0.0505715	+	0.155643i
$64$		0			0
$65$	−10.4884	−	7.62028i	−1.30093	−	0.945179i
$66$		0			0
$67$	−11.8851	+	8.63501i	−1.45199	+	1.05493i	−0.466631	+	0.884452i	$0.654533\pi$
$67$	−11.8851	+	8.63501i	−1.45199	+	1.05493i	−0.985361	+	0.170482i	$0.945467\pi$
$68$		0			0
$69$	2.27783	+	7.01044i	0.274219	+	0.843958i
$70$		0			0
$71$	9.09080	+	6.60486i	1.07888	+	0.783852i	0.977487	−	0.210994i	$-0.0676702\pi$
$71$	9.09080	+	6.60486i	1.07888	+	0.783852i	0.101393	+	0.994846i	$0.467670\pi$
$72$		0			0
$73$	4.58657			0.536817			0.268408	−	0.963305i	$-0.413502\pi$
$73$	4.58657			0.536817			0.268408	+	0.963305i	$0.413502\pi$
$74$		0			0
$75$	1.32548	−	4.07940i	0.153053	−	0.471049i
$76$		0			0
$77$	−0.978799	+	0.711139i	−0.111544	+	0.0810418i
$78$		0			0
$79$	12.0411			1.35473			0.677366	−	0.735646i	$-0.263121\pi$
$79$	12.0411			1.35473			0.677366	+	0.735646i	$0.263121\pi$
$80$		0			0
$81$	−11.2096			−1.24551
$82$		0			0
$83$	0.731917			0.0803383			0.0401692	−	0.999193i	$-0.487210\pi$
$83$	0.731917			0.0803383			0.0401692	+	0.999193i	$0.487210\pi$
$84$		0			0
$85$	13.3560			1.44866
$86$		0			0
$87$	−0.157906	+	0.114725i	−0.0169293	+	0.0122998i
$88$		0			0
$89$	2.78534	−	8.57239i	0.295245	−	0.908672i	−0.687894	−	0.725811i	$-0.741464\pi$
$89$	2.78534	−	8.57239i	0.295245	−	0.908672i	0.983139	−	0.182860i	$-0.0585355\pi$
$90$		0			0
$91$	−4.87619			−0.511164
$92$		0			0
$93$	−6.19426	−	4.50040i	−0.642315	−	0.466669i
$94$		0			0
$95$	−1.33075	−	4.09562i	−0.136532	−	0.420202i
$96$		0			0
$97$	6.31745	−	4.58989i	0.641440	−	0.466033i	−0.218905	−	0.975746i	$-0.570248\pi$
$97$	6.31745	−	4.58989i	0.641440	−	0.466033i	0.860344	+	0.509713i	$0.170248\pi$
$98$		0			0
$99$	1.27141	+	0.923737i	0.127782	+	0.0928390i
$100$		0			0
$101$	3.30459	−	10.1705i	0.328819	−	1.01200i	−0.640868	−	0.767651i	$-0.721425\pi$
$101$	3.30459	−	10.1705i	0.328819	−	1.01200i	0.969687	−	0.244350i	$-0.0785746\pi$
$102$		0			0
$103$	4.56977	−	14.0643i	0.450273	−	1.38580i	−0.426323	−	0.904571i	$-0.640191\pi$
$103$	4.56977	−	14.0643i	0.450273	−	1.38580i	0.876596	−	0.481226i	$-0.159809\pi$
$104$		0			0
$105$	−1.70347	−	5.24275i	−0.166242	−	0.511640i
$106$		0			0
$107$	3.65554	−	11.2506i	0.353394	−	1.08764i	−0.603541	−	0.797332i	$-0.706244\pi$
$107$	3.65554	−	11.2506i	0.353394	−	1.08764i	0.956935	−	0.290303i	$-0.0937562\pi$
$108$		0			0
$109$	−3.10817			−0.297709			−0.148854	−	0.988859i	$-0.547559\pi$
$109$	−3.10817			−0.297709			−0.148854	+	0.988859i	$0.547559\pi$
$110$		0			0
$111$	−12.7515	+	9.26454i	−1.21032	+	0.879351i
$112$		0			0
$113$	15.4891	+	11.2535i	1.45710	+	1.05864i	0.984108	+	0.177573i	$0.0568246\pi$
$113$	15.4891	+	11.2535i	1.45710	+	1.05864i	0.472988	+	0.881069i	$0.343175\pi$
$114$		0			0
$115$	−7.64693	−	5.55582i	−0.713079	−	0.518083i
$116$		0			0
$117$	1.95730	+	6.02394i	0.180952	+	0.556913i
$118$		0			0
$119$	4.06409	−	2.95273i	0.372554	−	0.270676i
$120$		0			0
$121$	−2.94686	−	9.06950i	−0.267896	−	0.824500i
$122$		0			0
$123$	11.1887	−	7.14641i	1.00885	−	0.644370i
$124$		0			0
$125$	−2.40827	−	7.41191i	−0.215403	−	0.662941i
$126$		0			0
$127$	6.86734	−	4.98942i	0.609378	−	0.442739i	−0.239817	−	0.970818i	$-0.577087\pi$
$127$	6.86734	−	4.98942i	0.609378	−	0.442739i	0.849195	+	0.528079i	$0.177087\pi$
$128$		0			0
$129$	6.35803	+	19.5680i	0.559793	+	1.72287i
$130$		0			0
$131$	6.52880	+	4.74345i	0.570424	+	0.414437i	0.835259	−	0.549856i	$-0.185318\pi$
$131$	6.52880	+	4.74345i	0.570424	+	0.414437i	−0.264835	+	0.964294i	$0.585318\pi$
$132$		0			0
$133$	−1.31039	−	0.952052i	−0.113625	−	0.0825534i
$134$		0			0
$135$	7.58624	−	5.51173i	0.652920	−	0.474374i
$136$		0			0
$137$	1.46554			0.125209			0.0626047	−	0.998038i	$-0.480059\pi$
$137$	1.46554			0.125209			0.0626047	+	0.998038i	$0.480059\pi$
$138$		0			0
$139$	0.0229614	−	0.0706680i	0.00194756	−	0.00599398i	−0.950078	−	0.312012i	$-0.898997\pi$
$139$	0.0229614	−	0.0706680i	0.00194756	−	0.00599398i	0.952026	+	0.306018i	$0.0989969\pi$
$140$		0			0
$141$	5.38411	+	16.5706i	0.453423	+	1.39549i
$142$		0			0
$143$	−1.82305	+	5.61077i	−0.152451	+	0.469196i
$144$		0			0
$145$	0.0773415	−	0.238033i	0.00642286	−	0.0197675i
$146$		0			0
$147$	−1.67741	−	1.21871i	−0.138350	−	0.100517i
$148$		0			0
$149$	−10.3796	+	7.54121i	−0.850329	+	0.617800i	−0.925237	−	0.379390i	$-0.876134\pi$
$149$	−10.3796	+	7.54121i	−0.850329	+	0.617800i	0.0749079	+	0.997190i	$0.476134\pi$
$150$		0			0
$151$	0.951876	+	2.92957i	0.0774626	+	0.238405i	0.982288	−	0.187378i	$-0.0599988\pi$
$151$	0.951876	+	2.92957i	0.0774626	+	0.238405i	−0.904825	+	0.425783i	$0.859999\pi$
$152$		0			0
$153$	−5.27906	−	3.83546i	−0.426787	−	0.310079i
$154$		0			0
$155$	9.81798			0.788599
$156$		0			0
$157$	−4.13354	+	12.7217i	−0.329893	+	1.01531i	0.639291	+	0.768965i	$0.279228\pi$
$157$	−4.13354	+	12.7217i	−0.329893	+	1.01531i	−0.969183	+	0.246340i	$0.920772\pi$
$158$		0			0
$159$	8.57345	−	6.22898i	0.679919	−	0.493990i
$160$		0			0
$161$	−3.55515			−0.280185
$162$		0			0
$163$	−17.6568			−1.38299			−0.691493	−	0.722383i	$-0.743047\pi$
$163$	−17.6568			−1.38299			−0.691493	+	0.722383i	$0.743047\pi$
$164$		0			0
$165$	−6.66943			−0.519214
$166$		0			0
$167$	−15.3511			−1.18791			−0.593954	−	0.804499i	$-0.702434\pi$
$167$	−15.3511			−1.18791			−0.593954	+	0.804499i	$0.702434\pi$
$168$		0			0
$169$	−8.71895	+	6.33469i	−0.670689	+	0.487284i
$170$		0			0
$171$	−0.650157	+	2.00098i	−0.0497187	+	0.153019i
$172$		0			0
$173$	10.5820			0.804532			0.402266	−	0.915523i	$-0.368223\pi$
$173$	10.5820			0.804532			0.402266	+	0.915523i	$0.368223\pi$
$174$		0			0
$175$	1.67366	+	1.21598i	0.126517	+	0.0919197i
$176$		0			0
$177$	−4.64068	−	14.2826i	−0.348815	−	1.07354i
$178$		0			0
$179$	7.81579	−	5.67850i	0.584179	−	0.424431i	−0.256049	−	0.966664i	$-0.582421\pi$
$179$	7.81579	−	5.67850i	0.584179	−	0.424431i	0.840228	+	0.542233i	$0.182421\pi$
$180$		0			0
$181$	7.65356	+	5.56064i	0.568885	+	0.413319i	0.834700	−	0.550705i	$-0.185641\pi$
$181$	7.65356	+	5.56064i	0.568885	+	0.413319i	−0.265815	+	0.964024i	$0.585641\pi$
$182$		0			0
$183$	−4.35113	+	13.3914i	−0.321645	+	0.989922i
$184$		0			0
$185$	6.24565	−	19.2221i	0.459189	−	1.41324i
$186$		0			0
$187$	−1.87812	−	5.78026i	−0.137342	−	0.422695i
$188$		0			0
$189$	1.08988	−	3.35432i	0.0792773	−	0.243991i
$190$		0			0
$191$	5.63899			0.408023			0.204012	−	0.978968i	$-0.434602\pi$
$191$	5.63899			0.408023			0.204012	+	0.978968i	$0.434602\pi$
$192$		0			0
$193$	−13.8235	+	10.0434i	−0.995040	+	0.722939i	−0.961019	−	0.276482i	$-0.910831\pi$
$193$	−13.8235	+	10.0434i	−0.995040	+	0.722939i	−0.0340213	+	0.999421i	$0.510831\pi$
$194$		0			0
$195$	−21.7466	−	15.7998i	−1.55731	−	1.13145i
$196$		0			0
$197$	13.7292	+	9.97483i	0.978164	+	0.710677i	0.957297	−	0.289105i	$-0.0933576\pi$
$197$	13.7292	+	9.97483i	0.978164	+	0.710677i	0.0208662	+	0.999782i	$0.493358\pi$
$198$		0			0
$199$	−6.69075	−	20.5920i	−0.474294	−	1.45973i	−0.846907	−	0.531741i	$-0.821538\pi$
$199$	−6.69075	−	20.5920i	−0.474294	−	1.45973i	0.372613	−	0.927987i	$-0.378462\pi$
$200$		0			0
$201$	−24.6424	+	17.9038i	−1.73814	+	1.26283i
$202$		0			0
$203$	−0.0290898	−	0.0895293i	−0.00204171	−	0.00628372i
$204$		0			0
$205$	−6.22077	+	15.8468i	−0.434477	+	1.10679i
$206$		0			0
$207$	1.42703	+	4.39195i	0.0991856	+	0.305262i
$208$		0			0
$209$	−1.58539	+	1.15185i	−0.109664	+	0.0796753i
$210$		0			0
$211$	−3.24595	−	9.99001i	−0.223461	−	0.687741i	−0.998444	−	0.0557596i	$-0.982242\pi$
$211$	−3.24595	−	9.99001i	−0.223461	−	0.687741i	0.774984	−	0.631981i	$-0.217758\pi$
$212$		0			0
$213$	18.8488	+	13.6945i	1.29150	+	0.938328i
$214$		0			0
$215$	−21.3446	−	15.5077i	−1.45569	−	1.05762i
$216$		0			0
$217$	2.98750	−	2.17055i	0.202805	−	0.147346i
$218$		0			0
$219$	9.50975			0.642609
$220$		0			0
$221$	7.56952	−	23.2966i	0.509181	−	1.56710i
$222$		0			0
$223$	0.446264	+	1.37346i	0.0298840	+	0.0919736i	0.964886	−	0.262669i	$-0.0846026\pi$
$223$	0.446264	+	1.37346i	0.0298840	+	0.0919736i	−0.935002	+	0.354642i	$0.884603\pi$
$224$		0			0
$225$	0.830395	−	2.55569i	0.0553597	−	0.170380i
$226$		0			0
$227$	1.23275	−	3.79402i	0.0818205	−	0.251818i	−0.901775	−	0.432206i	$-0.857735\pi$
$227$	1.23275	−	3.79402i	0.0818205	−	0.251818i	0.983596	+	0.180388i	$0.0577354\pi$
$228$		0			0
$229$	23.5219	+	17.0896i	1.55437	+	1.12932i	0.940442	+	0.339953i	$0.110411\pi$
$229$	23.5219	+	17.0896i	1.55437	+	1.12932i	0.613927	+	0.789363i	$0.289589\pi$
$230$		0			0
$231$	−2.02943	+	1.47447i	−0.133527	+	0.0970130i
$232$		0			0
$233$	1.22215	+	3.76140i	0.0800658	+	0.246417i	0.983075	−	0.183204i	$-0.0586470\pi$
$233$	1.22215	+	3.76140i	0.0800658	+	0.246417i	−0.903009	+	0.429622i	$0.858647\pi$
$234$		0			0
$235$	−18.0750	−	13.1323i	−1.17908	−	0.856655i
$236$		0			0
$237$	24.9660			1.62171
$238$		0			0
$239$	3.21338	−	9.88975i	0.207856	−	0.639715i	−0.791728	−	0.610874i	$-0.790818\pi$
$239$	3.21338	−	9.88975i	0.207856	−	0.639715i	0.999584	−	0.0288412i	$-0.00918170\pi$
$240$		0			0
$241$	−3.94915	+	2.86923i	−0.254387	+	0.184823i	−0.707669	−	0.706544i	$-0.750253\pi$
$241$	−3.94915	+	2.86923i	−0.254387	+	0.184823i	0.453282	+	0.891367i	$0.350253\pi$
$242$		0			0
$243$	−12.6610			−0.812206
$244$		0			0
$245$	2.65871			0.169859
$246$		0			0
$247$	−7.89810			−0.502544
$248$		0			0
$249$	1.51755			0.0961709
$250$		0			0
$251$	3.24518	−	2.35776i	0.204834	−	0.148821i	−0.480639	−	0.876918i	$-0.659595\pi$
$251$	3.24518	−	2.35776i	0.204834	−	0.148821i	0.685473	+	0.728098i	$0.259595\pi$
$252$		0			0
$253$	−1.32916	+	4.09072i	−0.0835633	+	0.257181i
$254$		0			0
$255$	27.6922			1.73416
$256$		0			0
$257$	−8.49050	−	6.16871i	−0.529623	−	0.384794i	0.290594	−	0.956847i	$-0.406147\pi$
$257$	−8.49050	−	6.16871i	−0.529623	−	0.384794i	−0.820217	+	0.572053i	$0.806147\pi$
$258$		0			0
$259$	−2.34913	−	7.22986i	−0.145968	−	0.449242i
$260$		0			0
$261$	−0.0989259	+	0.0718739i	−0.00612336	+	0.00444888i
$262$		0			0
$263$	12.8568	+	9.34098i	0.792782	+	0.575990i	0.908788	−	0.417259i	$-0.137009\pi$
$263$	12.8568	+	9.34098i	0.792782	+	0.575990i	−0.116006	+	0.993249i	$0.537009\pi$
$264$		0			0
$265$	−4.19924	+	12.9239i	−0.257957	+	0.793910i
$266$		0			0
$267$	5.77510	−	17.7739i	0.353430	−	1.08775i
$268$		0			0
$269$	8.96442	+	27.5896i	0.546570	+	1.68217i	0.717227	+	0.696839i	$0.245411\pi$
$269$	8.96442	+	27.5896i	0.546570	+	1.68217i	−0.170657	+	0.985330i	$0.554589\pi$
$270$		0			0
$271$	6.72735	−	20.7047i	0.408658	−	1.25772i	−0.509145	−	0.860681i	$-0.670038\pi$
$271$	6.72735	−	20.7047i	0.408658	−	1.25772i	0.917802	−	0.397038i	$-0.129962\pi$
$272$		0			0
$273$	−10.1103			−0.611900
$274$		0			0
$275$	2.02489	−	1.47117i	0.122106	−	0.0887150i
$276$		0			0
$277$	18.2547	+	13.2628i	1.09682	+	0.796887i	0.980538	−	0.196329i	$-0.0629022\pi$
$277$	18.2547	+	13.2628i	1.09682	+	0.796887i	0.116283	+	0.993216i	$0.462902\pi$
$278$		0			0
$279$	−3.88063	−	2.81944i	−0.232327	−	0.168795i
$280$		0			0
$281$	−0.889222	−	2.73674i	−0.0530465	−	0.163260i	0.921024	−	0.389507i	$-0.127355\pi$
$281$	−0.889222	−	2.73674i	−0.0530465	−	0.163260i	−0.974070	+	0.226246i	$0.927355\pi$
$282$		0			0
$283$	−8.51035	+	6.18313i	−0.505888	+	0.367549i	−0.811261	−	0.584684i	$-0.801219\pi$
$283$	−8.51035	+	6.18313i	−0.505888	+	0.367549i	0.305374	+	0.952233i	$0.401219\pi$
$284$		0			0
$285$	−2.75916	−	8.49183i	−0.163439	−	0.503013i
$286$		0			0
$287$	1.61048	+	6.19729i	0.0950636	+	0.365814i
$288$		0			0
$289$	2.54488	+	7.83234i	0.149699	+	0.460726i
$290$		0			0
$291$	13.0985	−	9.51665i	0.767850	−	0.557876i
$292$		0			0
$293$	−0.503378	−	1.54924i	−0.0294077	−	0.0905075i	0.935275	−	0.353921i	$-0.115152\pi$
$293$	−0.503378	−	1.54924i	−0.0294077	−	0.0905075i	−0.964683	+	0.263413i	$0.915152\pi$
$294$		0			0
$295$	15.5793	+	11.3190i	0.907060	+	0.659018i
$296$		0			0
$297$	−3.45216	−	2.50814i	−0.200315	−	0.145537i
$298$		0			0
$299$	−14.0248	+	10.1896i	−0.811074	+	0.589280i
$300$		0			0
$301$	−9.92336			−0.571973
$302$		0			0
$303$	6.85171	−	21.0874i	0.393621	−	1.21144i
$304$		0			0
$305$	−5.57946	−	17.1718i	−0.319479	−	0.983256i
$306$		0			0
$307$	5.48514	−	16.8815i	0.313053	−	0.963479i	−0.663495	−	0.748181i	$-0.730928\pi$
$307$	5.48514	−	16.8815i	0.313053	−	0.963479i	0.976548	−	0.215298i	$-0.0690723\pi$
$308$		0			0
$309$	9.47492	−	29.1608i	0.539010	−	1.65890i
$310$		0			0
$311$	−14.2421	−	10.3475i	−0.807596	−	0.586753i	0.105537	−	0.994415i	$-0.466344\pi$
$311$	−14.2421	−	10.3475i	−0.807596	−	0.586753i	−0.913133	+	0.407663i	$0.866344\pi$
$312$		0			0
$313$	−0.982709	+	0.713980i	−0.0555460	+	0.0403565i	−0.615212	−	0.788362i	$-0.710930\pi$
$313$	−0.982709	+	0.713980i	−0.0555460	+	0.0403565i	0.559666	+	0.828718i	$0.310930\pi$
$314$		0			0
$315$	−1.06720	−	3.28452i	−0.0601301	−	0.185061i
$316$		0			0
$317$	−15.6587	−	11.3767i	−0.879480	−	0.638980i	0.0536337	−	0.998561i	$-0.482920\pi$
$317$	−15.6587	−	11.3767i	−0.879480	−	0.638980i	−0.933114	+	0.359581i	$0.882920\pi$
$318$		0			0
$319$	−0.113892			−0.00637675
$320$		0			0
$321$	7.57936	−	23.3269i	0.423039	−	1.30198i
$322$		0			0
$323$	6.58271	−	4.78262i	0.366272	−	0.266112i
$324$		0			0
$325$	10.0876			0.559561
$326$		0			0
$327$	−6.44446			−0.356379
$328$		0			0
$329$	−8.40330			−0.463289
$330$		0			0
$331$	21.5799			1.18614			0.593068	−	0.805152i	$-0.297917\pi$
$331$	21.5799			1.18614			0.593068	+	0.805152i	$0.297917\pi$
$332$		0			0
$333$	−7.98868	+	5.80412i	−0.437777	+	0.318064i
$334$		0			0
$335$	12.0697	−	37.1468i	0.659440	−	2.02955i
$336$		0			0
$337$	−11.0314			−0.600919			−0.300460	−	0.953795i	$-0.597140\pi$
$337$	−11.0314			−0.600919			−0.300460	+	0.953795i	$0.597140\pi$
$338$		0			0
$339$	32.1151	+	23.3330i	1.74425	+	1.26727i
$340$		0			0
$341$	−1.38060	−	4.24906i	−0.0747639	−	0.230100i
$342$		0			0
$343$	0.809017	−	0.587785i	0.0436828	−	0.0317374i
$344$		0			0
$345$	−15.8551	−	11.5194i	−0.853608	−	0.620183i
$346$		0			0
$347$	6.66258	−	20.5053i	0.357666	−	1.10078i	−0.596781	−	0.802404i	$-0.703554\pi$
$347$	6.66258	−	20.5053i	0.357666	−	1.10078i	0.954447	−	0.298379i	$-0.0964460\pi$
$348$		0			0
$349$	−6.63119	+	20.4087i	−0.354960	+	1.09245i	0.601073	+	0.799194i	$0.294740\pi$
$349$	−6.63119	+	20.4087i	−0.354960	+	1.09245i	−0.956033	+	0.293259i	$0.905260\pi$
$350$		0			0
$351$	−5.31448	−	16.3563i	−0.283666	−	0.873033i
$352$		0			0
$353$	4.41981	−	13.6028i	0.235243	−	0.724003i	−0.761846	−	0.647758i	$-0.775707\pi$
$353$	4.41981	−	13.6028i	0.235243	−	0.724003i	0.997089	−	0.0762448i	$-0.0242931\pi$
$354$		0			0
$355$	−29.8756			−1.58563
$356$		0			0
$357$	8.42644	−	6.12217i	0.445975	−	0.324020i
$358$		0			0
$359$	6.14169	+	4.46220i	0.324146	+	0.235506i	0.737942	−	0.674864i	$-0.235798\pi$
$359$	6.14169	+	4.46220i	0.324146	+	0.235506i	−0.413797	+	0.910369i	$0.635798\pi$
$360$		0			0
$361$	13.2489	+	9.62585i	0.697308	+	0.506624i
$362$		0			0
$363$	−6.10999	−	18.8046i	−0.320691	−	0.986987i
$364$		0			0
$365$	−9.86544	+	7.16767i	−0.516381	+	0.375173i
$366$		0			0
$367$	7.81715	+	24.0587i	0.408052	+	1.25586i	0.918320	+	0.395839i	$0.129546\pi$
$367$	7.81715	+	24.0587i	0.408052	+	1.25586i	−0.510268	+	0.860016i	$0.670454\pi$
$368$		0			0
$369$	7.00955	−	4.47713i	0.364902	−	0.233070i
$370$		0			0
$371$	1.57943	+	4.86097i	0.0819997	+	0.252369i
$372$		0			0
$373$	−12.8946	+	9.36846i	−0.667656	+	0.485081i	−0.869240	−	0.494391i	$-0.835391\pi$
$373$	−12.8946	+	9.36846i	−0.667656	+	0.485081i	0.201584	+	0.979471i	$0.435391\pi$
$374$		0			0
$375$	−4.99330	−	15.3678i	−0.257853	−	0.793589i
$376$		0			0
$377$	−0.371362	−	0.269810i	−0.0191261	−	0.0138959i
$378$		0			0
$379$	18.8391	+	13.6874i	0.967702	+	0.703077i	0.954927	−	0.296842i	$-0.0959334\pi$
$379$	18.8391	+	13.6874i	0.967702	+	0.703077i	0.0127753	+	0.999918i	$0.495933\pi$
$380$		0			0
$381$	14.2387	−	10.3450i	0.729470	−	0.529991i
$382$		0			0
$383$	−1.33830			−0.0683840			−0.0341920	−	0.999415i	$-0.510886\pi$
$383$	−1.33830			−0.0683840			−0.0341920	+	0.999415i	$0.510886\pi$
$384$		0			0
$385$	0.994008	−	3.05924i	0.0506593	−	0.155913i
$386$		0			0
$387$	3.98322	+	12.2591i	0.202479	+	0.623165i
$388$		0			0
$389$	1.61729	−	4.97750i	0.0819997	−	0.252369i	−0.901649	−	0.432470i	$-0.857642\pi$
$389$	1.61729	−	4.97750i	0.0819997	−	0.252369i	0.983648	+	0.180101i	$0.0576423\pi$
$390$		0			0
$391$	5.51881	−	16.9851i	0.279098	−	0.858976i
$392$		0			0
$393$	13.5368	+	9.83503i	0.682839	+	0.496112i
$394$		0			0
$395$	−25.8998	+	18.8173i	−1.30316	+	0.946801i
$396$		0			0
$397$	−4.48930	−	13.8167i	−0.225312	−	0.693438i	−0.998260	−	0.0589687i	$-0.981219\pi$
$397$	−4.48930	−	13.8167i	−0.225312	−	0.693438i	0.772948	−	0.634469i	$-0.218781\pi$
$398$		0			0
$399$	−2.71695	−	1.97398i	−0.136017	−	0.0988225i
$400$		0			0
$401$	29.8150			1.48889			0.744445	−	0.667684i	$-0.232714\pi$
$401$	29.8150			1.48889			0.744445	+	0.667684i	$0.232714\pi$
$402$		0			0
$403$	5.56434	−	17.1253i	0.277179	−	0.853071i
$404$		0			0
$405$	24.1112	−	17.5178i	1.19809	−	0.870466i
$406$		0			0
$407$	−9.19729			−0.455893
$408$		0			0
$409$	−4.26735			−0.211007			−0.105503	−	0.994419i	$-0.533645\pi$
$409$	−4.26735			−0.211007			−0.105503	+	0.994419i	$0.533645\pi$
$410$		0			0
$411$	3.03864			0.149885
$412$		0			0
$413$	7.24299			0.356404
$414$		0			0
$415$	−1.57431	+	1.14380i	−0.0772800	+	0.0561472i
$416$		0			0
$417$	0.0476080	−	0.146522i	0.00233137	−	0.00717523i
$418$		0			0
$419$	−34.9188			−1.70590			−0.852948	−	0.521996i	$-0.825187\pi$
$419$	−34.9188			−1.70590			−0.852948	+	0.521996i	$0.825187\pi$
$420$		0			0
$421$	15.0506	+	10.9349i	0.733519	+	0.532933i	0.890675	−	0.454641i	$-0.150232\pi$
$421$	15.0506	+	10.9349i	0.733519	+	0.532933i	−0.157156	+	0.987574i	$0.550232\pi$
$422$		0			0
$423$	3.37307	+	10.3813i	0.164004	+	0.504754i
$424$		0			0
$425$	−8.40759	+	6.10848i	−0.407828	+	0.296305i
$426$		0			0
$427$	−5.49410	−	3.99170i	−0.265878	−	0.193172i
$428$		0			0
$429$	−3.77990	+	11.6333i	−0.182495	+	0.561663i
$430$		0			0
$431$	−7.68988	+	23.6670i	−0.370408	+	1.14000i	0.576116	+	0.817368i	$0.304568\pi$
$431$	−7.68988	+	23.6670i	−0.370408	+	1.14000i	−0.946525	+	0.322632i	$0.895432\pi$
$432$		0			0
$433$	6.13466	+	18.8805i	0.294813	+	0.907341i	0.983284	+	0.182078i	$0.0582822\pi$
$433$	6.13466	+	18.8805i	0.294813	+	0.907341i	−0.688471	+	0.725264i	$0.741718\pi$
$434$		0			0
$435$	0.160359	−	0.493535i	0.00768864	−	0.0236632i
$436$		0			0
$437$	−5.75837			−0.275460
$438$		0			0
$439$	16.7789	−	12.1906i	0.800813	−	0.581825i	−0.110339	−	0.993894i	$-0.535194\pi$
$439$	16.7789	−	12.1906i	0.800813	−	0.581825i	0.911153	+	0.412069i	$0.135194\pi$
$440$		0			0
$441$	−1.05088	−	0.763506i	−0.0500417	−	0.0363574i
$442$		0			0
$443$	−7.16941	−	5.20888i	−0.340629	−	0.247482i	0.404298	−	0.914627i	$-0.367516\pi$
$443$	−7.16941	−	5.20888i	−0.340629	−	0.247482i	−0.744927	+	0.667146i	$0.767516\pi$
$444$		0			0
$445$	7.40541	+	22.7915i	0.351050	+	1.08042i
$446$		0			0
$447$	−21.5209	+	15.6359i	−1.01791	+	0.739552i
$448$		0			0
$449$	5.79030	+	17.8207i	0.273261	+	0.841011i	0.989674	+	0.143335i	$0.0457826\pi$
$449$	5.79030	+	17.8207i	0.273261	+	0.841011i	−0.716413	+	0.697676i	$0.754217\pi$
$450$		0			0
$451$	7.73300	+	0.463872i	0.364133	+	0.0218429i
$452$		0			0
$453$	1.97361	+	6.07415i	0.0927284	+	0.285389i
$454$		0			0
$455$	10.4884	−	7.62028i	0.491704	−	0.357244i
$456$		0			0
$457$	3.13428	+	9.64632i	0.146615	+	0.451236i	0.997215	−	0.0745779i	$-0.0237610\pi$
$457$	3.13428	+	9.64632i	0.146615	+	0.451236i	−0.850600	+	0.525814i	$0.823761\pi$
$458$		0			0
$459$	14.3338	+	10.4141i	0.669043	+	0.486088i
$460$		0			0
$461$	−19.3889	−	14.0869i	−0.903031	−	0.656091i	0.0362116	−	0.999344i	$-0.488471\pi$
$461$	−19.3889	−	14.0869i	−0.903031	−	0.656091i	−0.939243	+	0.343254i	$0.888471\pi$
$462$		0			0
$463$	−15.7106	+	11.4144i	−0.730134	+	0.530473i	−0.889606	−	0.456729i	$-0.849021\pi$
$463$	−15.7106	+	11.4144i	−0.730134	+	0.530473i	0.159472	+	0.987202i	$0.449021\pi$
$464$		0			0
$465$	20.3565			0.944011
$466$		0			0
$467$	7.92767	−	24.3989i	0.366849	−	1.12904i	−0.581967	−	0.813213i	$-0.697717\pi$
$467$	7.92767	−	24.3989i	0.366849	−	1.12904i	0.948815	−	0.315831i	$-0.102283\pi$
$468$		0			0
$469$	−4.53969	−	13.9717i	−0.209624	−	0.645155i
$470$		0			0
$471$	−8.57046	+	26.3772i	−0.394906	+	1.21540i
$472$		0			0
$473$	−3.71002	+	11.4183i	−0.170587	+	0.525013i
$474$		0			0
$475$	2.71087	+	1.96956i	0.124383	+	0.0903697i
$476$		0			0
$477$	5.37116	−	3.90237i	0.245928	−	0.178677i
$478$		0			0
$479$	1.97174	+	6.06840i	0.0900912	+	0.277272i	0.985943	−	0.167080i	$-0.0534339\pi$
$479$	1.97174	+	6.06840i	0.0900912	+	0.277272i	−0.895852	+	0.444352i	$0.853434\pi$
$480$		0			0
$481$	−29.9890	−	21.7883i	−1.36738	−	0.993460i
$482$		0			0
$483$	−7.37122			−0.335402
$484$		0			0
$485$	−6.41561	+	19.7452i	−0.291318	+	0.896584i
$486$		0			0
$487$	−2.98602	+	2.16947i	−0.135310	+	0.0983082i	−0.653381	−	0.757029i	$-0.726650\pi$
$487$	−2.98602	+	2.16947i	−0.135310	+	0.0983082i	0.518072	+	0.855337i	$0.326650\pi$
$488$		0			0
$489$	−36.6094			−1.65554
$490$		0			0
$491$	−28.6915			−1.29483			−0.647414	−	0.762139i	$-0.724149\pi$
$491$	−28.6915			−1.29483			−0.647414	+	0.762139i	$0.724149\pi$
$492$		0			0
$493$	0.472894			0.0212981
$494$		0			0
$495$	−4.17831			−0.187801
$496$		0			0
$497$	−9.09080	+	6.60486i	−0.407778	+	0.296268i
$498$		0			0
$499$	−6.22333	+	19.1534i	−0.278594	+	0.857426i	0.709651	+	0.704553i	$0.248852\pi$
$499$	−6.22333	+	19.1534i	−0.278594	+	0.857426i	−0.988246	+	0.152873i	$0.951148\pi$
$500$		0			0
$501$	−31.8289			−1.42201
$502$		0			0
$503$	−26.3187	−	19.1216i	−1.17349	−	0.852592i	−0.182069	−	0.983286i	$-0.558279\pi$
$503$	−26.3187	−	19.1216i	−1.17349	−	0.852592i	−0.991423	+	0.130694i	$0.958279\pi$
$504$		0			0
$505$	8.78596	+	27.0404i	0.390970	+	1.20328i
$506$		0			0
$507$	−18.0778	+	13.1343i	−0.802864	+	0.583315i
$508$		0			0
$509$	−5.45107	−	3.96044i	−0.241615	−	0.175543i	0.460388	−	0.887718i	$-0.347710\pi$
$509$	−5.45107	−	3.96044i	−0.241615	−	0.175543i	−0.702002	+	0.712175i	$0.747710\pi$
$510$		0			0
$511$	−1.41733	+	4.36208i	−0.0626988	+	0.192967i
$512$		0			0
$513$	1.76531	−	5.43308i	0.0779405	−	0.239876i
$514$		0			0
$515$	12.1497	+	37.3930i	0.535380	+	1.64773i
$516$		0			0
$517$	−3.14172	+	9.66923i	−0.138173	+	0.425252i
$518$		0			0
$519$	21.9406			0.963083
$520$		0			0
$521$	−17.7191	+	12.8737i	−0.776288	+	0.564006i	−0.903863	−	0.427823i	$-0.859281\pi$
$521$	−17.7191	+	12.8737i	−0.776288	+	0.564006i	0.127575	+	0.991829i	$0.459281\pi$
$522$		0			0
$523$	5.39094	+	3.91675i	0.235729	+	0.171267i	0.699379	−	0.714751i	$-0.253460\pi$
$523$	5.39094	+	3.91675i	0.235729	+	0.171267i	−0.463649	+	0.886019i	$0.653460\pi$
$524$		0			0
$525$	3.47015	+	2.52121i	0.151450	+	0.110035i
$526$		0			0
$527$	5.73242	+	17.6426i	0.249708	+	0.768523i
$528$		0			0
$529$	8.38216	−	6.09000i	0.364442	−	0.264782i
$530$		0			0
$531$	−2.90733	−	8.94784i	−0.126167	−	0.388303i
$532$		0			0
$533$	24.1156	+	19.8319i	1.04456	+	0.859016i
$534$		0			0
$535$	9.71903	+	29.9121i	0.420190	+	1.29321i
$536$		0			0
$537$	16.2052	−	11.7738i	0.699305	−	0.508075i
$538$		0			0
$539$	−0.373868	−	1.15065i	−0.0161036	−	0.0495619i
$540$		0			0
$541$	−21.9991	−	15.9833i	−0.945815	−	0.687175i	0.00399866	−	0.999992i	$-0.498727\pi$
$541$	−21.9991	−	15.9833i	−0.945815	−	0.687175i	−0.949813	+	0.312817i	$0.898727\pi$
$542$		0			0
$543$	15.8688	+	11.5294i	0.680997	+	0.494773i
$544$		0			0
$545$	6.68551	−	4.85730i	0.286376	−	0.208064i
$546$		0			0
$547$	14.3516			0.613631			0.306815	−	0.951769i	$-0.400737\pi$
$547$	14.3516			0.613631			0.306815	+	0.951769i	$0.400737\pi$
$548$		0			0
$549$	−2.72593	+	8.38955i	−0.116340	+	0.358057i
$550$		0			0
$551$	−0.0471176	−	0.145013i	−0.00200728	−	0.00617777i
$552$		0			0
$553$	−3.72091	+	11.4518i	−0.158229	+	0.486980i
$554$		0			0
$555$	12.9497	−	39.8550i	0.549683	−	1.69175i
$556$		0			0
$557$	28.4051	+	20.6375i	1.20356	+	0.874438i	0.994630	−	0.103492i	$-0.0330017\pi$
$557$	28.4051	+	20.6375i	1.20356	+	0.874438i	0.208931	+	0.977930i	$0.433002\pi$
$558$		0			0
$559$	−39.1468	+	28.4418i	−1.65574	+	1.20296i
$560$		0			0
$561$	−3.89408	−	11.9847i	−0.164408	−	0.505996i
$562$		0			0
$563$	−15.1906	−	11.0366i	−0.640209	−	0.465139i	0.219713	−	0.975565i	$-0.429488\pi$
$563$	−15.1906	−	11.0366i	−0.640209	−	0.465139i	−0.859922	+	0.510426i	$0.829488\pi$
$564$		0			0
$565$	−50.9027			−2.14149
$566$		0			0
$567$	3.46395	−	10.6609i	0.145472	−	0.447718i
$568$		0			0
$569$	15.5881	−	11.3254i	0.653487	−	0.474786i	−0.210970	−	0.977492i	$-0.567662\pi$
$569$	15.5881	−	11.3254i	0.653487	−	0.474786i	0.864457	+	0.502706i	$0.167662\pi$
$570$		0			0
$571$	5.94797			0.248915			0.124457	−	0.992225i	$-0.460281\pi$
$571$	5.94797			0.248915			0.124457	+	0.992225i	$0.460281\pi$
$572$		0			0
$573$	11.6918			0.488434
$574$		0			0
$575$	7.35473			0.306713
$576$		0			0
$577$	8.08366			0.336527			0.168264	−	0.985742i	$-0.446184\pi$
$577$	8.08366			0.336527			0.168264	+	0.985742i	$0.446184\pi$
$578$		0			0
$579$	−28.6616	+	20.8239i	−1.19114	+	0.865411i
$580$		0			0
$581$	−0.226175	+	0.696094i	−0.00938331	+	0.0288789i
$582$		0			0
$583$	6.18376			0.256105
$584$		0			0
$585$	−13.6240	−	9.89838i	−0.563281	−	0.409248i
$586$		0			0
$587$	7.38098	+	22.7163i	0.304646	+	0.937603i	0.979809	+	0.199935i	$0.0640731\pi$
$587$	7.38098	+	22.7163i	0.304646	+	0.937603i	−0.675163	+	0.737668i	$0.735927\pi$
$588$		0			0
$589$	4.83894	−	3.51570i	0.199385	−	0.144862i
$590$		0			0
$591$	28.4660	+	20.6817i	1.17093	+	0.850733i
$592$		0			0
$593$	−4.34823	+	13.3825i	−0.178561	+	0.549553i	−0.999778	−	0.0210623i	$-0.993295\pi$
$593$	−4.34823	+	13.3825i	−0.178561	+	0.549553i	0.821218	+	0.570615i	$0.193295\pi$
$594$		0			0
$595$	−4.12723	+	12.7023i	−0.169200	+	0.520744i
$596$		0			0
$597$	−13.8725	−	42.6953i	−0.567765	−	1.74740i
$598$		0			0
$599$	−4.23566	+	13.0360i	−0.173064	+	0.532637i	−0.999540	−	0.0303357i	$-0.990342\pi$
$599$	−4.23566	+	13.0360i	−0.173064	+	0.532637i	0.826476	+	0.562973i	$0.190342\pi$
$600$		0			0
$601$	−13.2318			−0.539737			−0.269868	−	0.962897i	$-0.586980\pi$
$601$	−13.2318			−0.539737			−0.269868	+	0.962897i	$0.586980\pi$
$602$		0			0
$603$	−15.4382	+	11.2165i	−0.628690	+	0.456770i
$604$		0			0
$605$	20.5119	+	14.9028i	0.833927	+	0.605884i
$606$		0			0
$607$	−13.4413	−	9.76566i	−0.545565	−	0.396376i	0.280583	−	0.959830i	$-0.409472\pi$
$607$	−13.4413	−	9.76566i	−0.545565	−	0.396376i	−0.826148	+	0.563454i	$0.809472\pi$
$608$		0			0
$609$	−0.0603146	−	0.185629i	−0.00244407	−	0.00752208i
$610$		0			0
$611$	−33.1503	+	24.0851i	−1.34112	+	0.974380i
$612$		0			0
$613$	12.0874	+	37.2011i	0.488204	+	1.50254i	0.827286	+	0.561781i	$0.189883\pi$
$613$	12.0874	+	37.2011i	0.488204	+	1.50254i	−0.339082	+	0.940757i	$0.610117\pi$
$614$		0			0
$615$	−12.8981	+	32.8566i	−0.520101	+	1.32491i
$616$		0			0
$617$	−1.64479	−	5.06214i	−0.0662167	−	0.203794i	0.912474	−	0.409135i	$-0.134170\pi$
$617$	−1.64479	−	5.06214i	−0.0662167	−	0.203794i	−0.978690	+	0.205341i	$0.934170\pi$
$618$		0			0
$619$	−15.0651	+	10.9454i	−0.605516	+	0.439933i	−0.847833	−	0.530264i	$-0.822093\pi$
$619$	−15.0651	+	10.9454i	−0.605516	+	0.439933i	0.242316	+	0.970197i	$0.422093\pi$
$620$		0			0
$621$	−3.87470	−	11.9251i	−0.155486	−	0.478537i
$622$		0			0
$623$	7.29211	+	5.29803i	0.292152	+	0.212261i
$624$		0			0
$625$	25.1313	+	18.2590i	1.00525	+	0.730359i
$626$		0			0
$627$	−3.28713	+	2.38824i	−0.131275	+	0.0953771i
$628$		0			0
$629$	38.1882			1.52266
$630$		0			0
$631$	−9.26378	+	28.5110i	−0.368785	+	1.13500i	0.578792	+	0.815475i	$0.303524\pi$
$631$	−9.26378	+	28.5110i	−0.368785	+	1.13500i	−0.947577	+	0.319528i	$0.896476\pi$
$632$		0			0
$633$	−6.73013	−	20.7132i	−0.267499	−	0.823276i
$634$		0			0
$635$	−6.97405	+	21.4639i	−0.276757	+	0.851769i
$636$		0			0
$637$	1.50683	−	4.63753i	0.0597026	−	0.183746i
$638$		0			0
$639$	11.8085	+	8.57940i	0.467138	+	0.339396i
$640$		0			0
$641$	−1.33459	+	0.969637i	−0.0527132	+	0.0382984i	−0.613830	−	0.789438i	$-0.710372\pi$
$641$	−1.33459	+	0.969637i	−0.0527132	+	0.0382984i	0.561117	+	0.827737i	$0.310372\pi$
$642$		0			0
$643$	6.51070	+	20.0379i	0.256757	+	0.790216i	0.993478	+	0.114020i	$0.0363728\pi$
$643$	6.51070	+	20.0379i	0.256757	+	0.790216i	−0.736722	+	0.676196i	$0.763627\pi$
$644$		0			0
$645$	−44.2557	−	32.1536i	−1.74257	−	1.26605i
$646$		0			0
$647$	−6.04163			−0.237521			−0.118760	−	0.992923i	$-0.537892\pi$
$647$	−6.04163			−0.237521			−0.118760	+	0.992923i	$0.537892\pi$
$648$		0			0
$649$	2.70792	−	8.33413i	0.106295	−	0.327143i
$650$		0			0
$651$	6.19426	−	4.50040i	0.242772	−	0.176384i
$652$		0			0
$653$	23.9878			0.938715			0.469358	−	0.883008i	$-0.344485\pi$
$653$	23.9878			0.938715			0.469358	+	0.883008i	$0.344485\pi$
$654$		0			0
$655$	−21.4559			−0.838352
$656$		0			0
$657$	5.95773			0.232433
$658$		0			0
$659$	16.0486			0.625164			0.312582	−	0.949891i	$-0.398806\pi$
$659$	16.0486			0.625164			0.312582	+	0.949891i	$0.398806\pi$
$660$		0			0
$661$	−11.1098	+	8.07171i	−0.432119	+	0.313953i	−0.782496	−	0.622656i	$-0.786054\pi$
$661$	−11.1098	+	8.07171i	−0.432119	+	0.313953i	0.350376	+	0.936609i	$0.386054\pi$
$662$		0			0
$663$	15.6946	−	48.3029i	0.609527	−	1.87593i
$664$		0			0
$665$	4.30639			0.166995
$666$		0			0
$667$	−0.270754	−	0.196714i	−0.0104836	−	0.00761680i
$668$		0			0
$669$	0.925279	+	2.84772i	0.0357734	+	0.110099i
$670$		0			0
$671$	−6.64710	+	4.82940i	−0.256608	+	0.186437i
$672$		0			0
$673$	0.581325	+	0.422358i	0.0224084	+	0.0162807i	0.598933	−	0.800799i	$-0.295592\pi$
$673$	0.581325	+	0.422358i	0.0224084	+	0.0162807i	−0.576525	+	0.817080i	$0.695592\pi$
$674$		0			0
$675$	−2.25470	+	6.93925i	−0.0867835	+	0.267092i
$676$		0			0
$677$	−2.18645	+	6.72920i	−0.0840321	+	0.258624i	−0.984240	−	0.176835i	$-0.943414\pi$
$677$	−2.18645	+	6.72920i	−0.0840321	+	0.258624i	0.900208	+	0.435459i	$0.143414\pi$
$678$		0			0
$679$	2.41305	+	7.42660i	0.0926044	+	0.285007i
$680$		0			0
$681$	2.55597	−	7.86648i	0.0979452	−	0.301444i
$682$		0			0
$683$	22.5554			0.863060			0.431530	−	0.902099i	$-0.357974\pi$
$683$	22.5554			0.863060			0.431530	+	0.902099i	$0.357974\pi$
$684$		0			0
$685$	−3.15229	+	2.29027i	−0.120443	+	0.0875069i
$686$		0			0
$687$	48.7701	+	35.4335i	1.86069	+	1.35187i
$688$		0			0
$689$	20.1630	+	14.6493i	0.768149	+	0.558093i
$690$		0			0
$691$	−2.97175	−	9.14611i	−0.113051	−	0.347934i	0.878485	−	0.477770i	$-0.158555\pi$
$691$	−2.97175	−	9.14611i	−0.113051	−	0.347934i	−0.991535	+	0.129836i	$0.958555\pi$
$692$		0			0
$693$	−1.27141	+	0.923737i	−0.0482970	+	0.0350899i
$694$		0			0
$695$	0.0610478	+	0.187886i	0.00231568	+	0.00712692i
$696$		0			0
$697$	−32.1083	−	1.92605i	−1.21619	−	0.0729544i
$698$		0			0
$699$	2.53400	+	7.79885i	0.0958447	+	0.294980i
$700$		0			0
$701$	−30.6367	+	22.2589i	−1.15713	+	0.840707i	−0.989413	−	0.145128i	$-0.953641\pi$
$701$	−30.6367	+	22.2589i	−1.15713	+	0.840707i	−0.167720	+	0.985835i	$0.553641\pi$
$702$		0			0
$703$	−3.80494	−	11.7104i	−0.143506	−	0.441667i
$704$		0			0
$705$	−37.4766	−	27.2283i	−1.41145	−	1.02548i
$706$		0			0
$707$	8.65153	+	6.28571i	0.325374	+	0.236398i
$708$		0			0
$709$	36.9208	−	26.8245i	1.38659	−	1.00742i	0.390360	−	0.920662i	$-0.372351\pi$
$709$	36.9208	−	26.8245i	1.38659	−	1.00742i	0.996230	−	0.0867537i	$-0.0276493\pi$
$710$		0			0
$711$	15.6409			0.586578
$712$		0			0
$713$	4.05687	−	12.4858i	0.151931	−	0.467595i
$714$		0			0
$715$	−4.84697	−	14.9174i	−0.181266	−	0.557880i
$716$		0			0
$717$	6.66259	−	20.5053i	0.248819	−	0.765786i
$718$		0			0
$719$	−1.75246	+	5.39350i	−0.0653556	+	0.201144i	−0.978402	−	0.206712i	$-0.933724\pi$
$719$	−1.75246	+	5.39350i	−0.0653556	+	0.201144i	0.913046	+	0.407856i	$0.133724\pi$
$720$		0			0
$721$	11.9638	+	8.69222i	0.445556	+	0.323715i
$722$		0			0
$723$	−8.18813	+	5.94903i	−0.304520	+	0.221247i
$724$		0			0
$725$	0.0601797	+	0.185214i	0.00223502	+	0.00687868i
$726$		0			0
$727$	−43.0384	−	31.2693i	−1.59621	−	1.15971i	−0.894323	−	0.447422i	$-0.852342\pi$
$727$	−43.0384	−	31.2693i	−1.59621	−	1.15971i	−0.701885	−	0.712290i	$-0.747658\pi$
$728$		0			0
$729$	7.37744			0.273238
$730$		0			0
$731$	15.4044	−	47.4100i	0.569754	−	1.75352i
$732$		0			0
$733$	−28.9549	+	21.0370i	−1.06948	+	0.777019i	−0.975818	−	0.218585i	$-0.929856\pi$
$733$	−28.9549	+	21.0370i	−1.06948	+	0.777019i	−0.0936573	+	0.995604i	$0.529856\pi$
$734$		0			0
$735$	5.51255			0.203334
$736$		0			0
$737$	−17.7738			−0.654706
$738$		0			0
$739$	46.2076			1.69977			0.849887	−	0.526965i	$-0.176670\pi$
$739$	46.2076			1.69977			0.849887	+	0.526965i	$0.176670\pi$
$740$		0			0
$741$	−16.3759			−0.601582
$742$		0			0
$743$	−19.3000	+	14.0223i	−0.708048	+	0.514427i	−0.882543	−	0.470231i	$-0.844171\pi$
$743$	−19.3000	+	14.0223i	−0.708048	+	0.514427i	0.174495	+	0.984658i	$0.444171\pi$
$744$		0			0
$745$	10.5409	−	32.4414i	0.386187	−	1.18856i
$746$		0			0
$747$	0.950726			0.0347852
$748$		0			0
$749$	9.57032	+	6.95325i	0.349692	+	0.254066i
$750$		0			0
$751$	3.92443	+	12.0782i	0.143205	+	0.440739i	0.996776	−	0.0802378i	$-0.0255680\pi$
$751$	3.92443	+	12.0782i	0.143205	+	0.440739i	−0.853571	+	0.520976i	$0.825568\pi$
$752$		0			0
$753$	6.72854	−	4.88857i	0.245202	−	0.178149i
$754$		0			0
$755$	−6.62563	−	4.81380i	−0.241131	−	0.175192i
$756$		0			0
$757$	−1.58652	+	4.88280i	−0.0576630	+	0.177468i	−0.975739	−	0.218935i	$-0.929742\pi$
$757$	−1.58652	+	4.88280i	−0.0576630	+	0.177468i	0.918076	+	0.396403i	$0.129742\pi$
$758$		0			0
$759$	−2.75586	+	8.48167i	−0.100031	+	0.307865i
$760$		0			0
$761$	−3.73711	−	11.5017i	−0.135470	−	0.416935i	0.860193	−	0.509969i	$-0.170343\pi$
$761$	−3.73711	−	11.5017i	−0.135470	−	0.416935i	−0.995663	+	0.0930348i	$0.970343\pi$
$762$		0			0
$763$	0.960478	−	2.95605i	0.0347716	−	0.107016i
$764$		0			0
$765$	17.3488			0.627248
$766$		0			0
$767$	28.5730	−	20.7595i	1.03171	−	0.749583i
$768$		0			0
$769$	33.0231	+	23.9927i	1.19084	+	0.865199i	0.993353	−	0.115106i	$-0.0367207\pi$
$769$	33.0231	+	23.9927i	1.19084	+	0.865199i	0.197491	+	0.980305i	$0.436721\pi$
$770$		0			0
$771$	−17.6041	−	12.7902i	−0.633997	−	0.460626i
$772$		0			0
$773$	−8.47035	−	26.0691i	−0.304657	−	0.937639i	−0.979805	−	0.199956i	$-0.935920\pi$
$773$	−8.47035	−	26.0691i	−0.304657	−	0.937639i	0.675147	−	0.737683i	$-0.264080\pi$
$774$		0			0
$775$	−6.18041	+	4.49033i	−0.222007	+	0.161297i
$776$		0			0
$777$	−4.87066	−	14.9903i	−0.174734	−	0.537775i
$778$		0			0
$779$	2.60854	+	10.0379i	0.0934606	+	0.359646i
$780$		0			0
$781$	4.20110	+	12.9297i	0.150327	+	0.462659i
$782$		0			0
$783$	0.268605	−	0.195153i	0.00959916	−	0.00697420i
$784$		0			0
$785$	−10.9899	−	33.8235i	−0.392247	−	1.20721i
$786$		0			0
$787$	18.5673	+	13.4900i	0.661854	+	0.480865i	0.867289	−	0.497806i	$-0.165861\pi$
$787$	18.5673	+	13.4900i	0.661854	+	0.480865i	−0.205435	+	0.978671i	$0.565861\pi$
$788$		0			0
$789$	26.6571	+	19.3675i	0.949018	+	0.689502i
$790$		0			0
$791$	−15.4891	+	11.2535i	−0.550730	+	0.400129i
$792$		0			0
$793$	−33.1146			−1.17593
$794$		0			0
$795$	−8.70667	+	26.7964i	−0.308794	+	0.950369i
$796$		0			0
$797$	−15.9129	−	48.9750i	−0.563666	−	1.73478i	−0.671883	−	0.740657i	$-0.734514\pi$
$797$	−15.9129	−	48.9750i	−0.563666	−	1.73478i	0.108218	−	0.994127i	$-0.465486\pi$
$798$		0			0
$799$	13.0448	−	40.1478i	0.461492	−	1.42033i
$800$		0			0
$801$	3.61802	−	11.1351i	0.127837	−	0.393441i
$802$		0			0
$803$	4.48933	+	3.26169i	0.158425	+	0.115102i
$804$		0			0
$805$	7.64693	−	5.55582i	0.269519	−	0.195817i
$806$		0			0
$807$	18.5867	+	57.2041i	0.654284	+	2.01368i
$808$		0			0
$809$	−43.3619	−	31.5043i	−1.52452	−	1.10763i	−0.959188	−	0.282770i	$-0.908747\pi$
$809$	−43.3619	−	31.5043i	−1.52452	−	1.10763i	−0.565336	−	0.824861i	$-0.691253\pi$
$810$		0			0
$811$	42.9584			1.50847			0.754237	−	0.656603i	$-0.228007\pi$
$811$	42.9584			1.50847			0.754237	+	0.656603i	$0.228007\pi$
$812$		0			0
$813$	13.9484	−	42.9289i	0.489193	−	1.50558i
$814$		0			0
$815$	37.9788	−	27.5932i	1.33034	−	0.966547i
$816$		0			0
$817$	−16.0731			−0.562328
$818$		0			0
$819$	−6.33394			−0.221326
$820$		0			0
$821$	−45.5436			−1.58948			−0.794742	−	0.606947i	$-0.792394\pi$
$821$	−45.5436			−1.58948			−0.794742	+	0.606947i	$0.792394\pi$
$822$		0			0
$823$	24.4586			0.852572			0.426286	−	0.904588i	$-0.359822\pi$
$823$	24.4586			0.852572			0.426286	+	0.904588i	$0.359822\pi$
$824$		0			0
$825$	4.19840	−	3.05032i	0.146170	−	0.106198i
$826$		0			0
$827$	−14.2768	+	43.9394i	−0.496453	+	1.52792i	0.318228	+	0.948014i	$0.396912\pi$
$827$	−14.2768	+	43.9394i	−0.496453	+	1.52792i	−0.814681	+	0.579910i	$0.803088\pi$
$828$		0			0
$829$	−37.2775			−1.29470			−0.647350	−	0.762193i	$-0.724123\pi$
$829$	−37.2775			−1.29470			−0.647350	+	0.762193i	$0.724123\pi$
$830$		0			0
$831$	37.8492	+	27.4991i	1.31297	+	0.953932i
$832$		0			0
$833$	1.55234	+	4.77762i	0.0537855	+	0.165535i
$834$		0			0
$835$	33.0195	−	23.9900i	1.14269	−	0.830210i
$836$		0			0
$837$	10.5367	+	7.65538i	0.364203	+	0.264609i
$838$		0			0
$839$	4.05830	−	12.4902i	0.140108	−	0.431208i	−0.856242	−	0.516576i	$-0.827206\pi$
$839$	4.05830	−	12.4902i	0.140108	−	0.431208i	0.996350	+	0.0853677i	$0.0272065\pi$
$840$		0			0
$841$	−8.95875	+	27.5722i	−0.308923	+	0.950766i
$842$		0			0
$843$	−1.84371	−	5.67434i	−0.0635006	−	0.195435i
$844$		0			0
$845$	8.85443	−	27.2511i	0.304602	−	0.937467i
$846$		0			0
$847$	9.53623			0.327669
$848$		0			0
$849$	−17.6453	+	12.8201i	−0.605585	+	0.439983i
$850$		0			0
$851$	−21.8645	−	15.8855i	−0.749505	−	0.544547i
$852$		0			0
$853$	41.5065	+	30.1563i	1.42116	+	1.03253i	0.991579	+	0.129501i	$0.0413376\pi$
$853$	41.5065	+	30.1563i	1.42116	+	1.03253i	0.429578	+	0.903030i	$0.358662\pi$
$854$		0			0
$855$	−1.72858	−	5.32002i	−0.0591162	−	0.181941i
$856$		0			0
$857$	16.8664	−	12.2542i	0.576146	−	0.418594i	−0.261187	−	0.965288i	$-0.584114\pi$
$857$	16.8664	−	12.2542i	0.576146	−	0.418594i	0.837333	+	0.546694i	$0.184114\pi$
$858$		0			0
$859$	−2.54122	−	7.82109i	−0.0867055	−	0.266852i	0.898298	−	0.439387i	$-0.144804\pi$
$859$	−2.54122	−	7.82109i	−0.0867055	−	0.266852i	−0.985003	+	0.172535i	$0.944804\pi$
$860$		0			0
$861$	3.33916	+	12.8494i	0.113798	+	0.437906i
$862$		0			0
$863$	−11.5387	−	35.5124i	−0.392781	−	1.20886i	−0.930676	−	0.365845i	$-0.880780\pi$
$863$	−11.5387	−	35.5124i	−0.392781	−	1.20886i	0.537894	−	0.843012i	$-0.319220\pi$
$864$		0			0
$865$	−22.7612	+	16.5370i	−0.773904	+	0.562274i
$866$		0			0
$867$	5.27654	+	16.2395i	0.179201	+	0.551523i
$868$		0			0
$869$	11.7858	+	8.56292i	0.399807	+	0.290477i
$870$		0			0
$871$	−57.9538	−	42.1059i	−1.96369	−	1.42671i
$872$		0			0
$873$	8.20607	−	5.96206i	0.277733	−	0.201785i
$874$		0			0
$875$	7.79334			0.263463
$876$		0			0
$877$	−2.19770	+	6.76381i	−0.0742109	+	0.228398i	−0.981281	−	0.192582i	$-0.938314\pi$
$877$	−2.19770	+	6.76381i	−0.0742109	+	0.228398i	0.907070	+	0.420980i	$0.138314\pi$
$878$		0			0
$879$	−1.04370	−	3.21218i	−0.0352031	−	0.108344i
$880$		0			0
$881$	12.6898	−	39.0552i	0.427531	−	1.31580i	−0.473019	−	0.881052i	$-0.656836\pi$
$881$	12.6898	−	39.0552i	0.427531	−	1.31580i	0.900550	−	0.434753i	$-0.143164\pi$
$882$		0			0
$883$	14.5915	−	44.9080i	0.491043	−	1.51127i	−0.331991	−	0.943282i	$-0.607720\pi$
$883$	14.5915	−	44.9080i	0.491043	−	1.51127i	0.823034	−	0.567992i	$-0.192280\pi$
$884$		0			0
$885$	32.3019	+	23.4687i	1.08582	+	0.788893i
$886$		0			0
$887$	−0.131343	+	0.0954264i	−0.00441007	+	0.00320411i	−0.589988	−	0.807412i	$-0.700868\pi$
$887$	−0.131343	+	0.0954264i	−0.00441007	+	0.00320411i	0.585578	+	0.810616i	$0.300868\pi$
$888$		0			0
$889$	2.62309	+	8.07305i	0.0879757	+	0.270761i
$890$		0			0
$891$	−10.9719	−	7.97157i	−0.367573	−	0.267058i
$892$		0			0
$893$	−13.6111			−0.455477
$894$		0			0
$895$	−7.93723	+	24.4283i	−0.265312	+	0.816547i
$896$		0			0
$897$	−29.0789	+	21.1270i	−0.970915	+	0.705411i
$898$		0			0
$899$	0.347624			0.0115939
$900$		0			0
$901$	−25.6757			−0.855381
$902$		0			0
$903$	−20.5750			−0.684693
$904$		0			0
$905$	−25.1523			−0.836090
$906$		0			0
$907$	−17.3995	+	12.6415i	−0.577742	+	0.419754i	−0.837909	−	0.545809i	$-0.816222\pi$
$907$	−17.3995	+	12.6415i	−0.577742	+	0.419754i	0.260167	+	0.965564i	$0.416222\pi$
$908$		0			0
$909$	4.29251	−	13.2110i	0.142374	−	0.438181i
$910$		0			0
$911$	32.7756			1.08590			0.542952	−	0.839764i	$-0.317307\pi$
$911$	32.7756			1.08590			0.542952	+	0.839764i	$0.317307\pi$
$912$		0			0
$913$	0.716400	+	0.520495i	0.0237094	+	0.0172259i
$914$		0			0
$915$	−11.5684	−	35.6039i	−0.382440	−	1.17703i
$916$		0			0
$917$	−6.52880	+	4.74345i	−0.215600	+	0.156643i
$918$		0			0
$919$	7.95450	+	5.77928i	0.262395	+	0.190641i	0.711202	−	0.702988i	$-0.248151\pi$
$919$	7.95450	+	5.77928i	0.262395	+	0.190641i	−0.448807	+	0.893629i	$0.648151\pi$
$920$		0			0
$921$	11.3728	−	35.0020i	0.374748	−	1.15335i
$922$		0			0
$923$	−16.9320	+	52.1112i	−0.557323	+	1.71526i
$924$		0			0
$925$	4.85976	+	14.9568i	0.159788	+	0.491777i
$926$		0			0
$927$	5.93592	−	18.2689i	0.194961	−	0.600029i
$928$		0			0
$929$	−10.0832			−0.330818			−0.165409	−	0.986225i	$-0.552894\pi$
$929$	−10.0832			−0.330818			−0.165409	+	0.986225i	$0.552894\pi$
$930$		0			0
$931$	1.31039	−	0.952052i	0.0429462	−	0.0312023i
$932$		0			0
$933$	−29.5295	−	21.4544i	−0.966752	−	0.702386i
$934$		0			0
$935$	13.0728	+	9.49798i	0.427528	+	0.310617i
$936$		0			0
$937$	9.64873	+	29.6957i	0.315210	+	0.970117i	0.975668	+	0.219254i	$0.0703624\pi$
$937$	9.64873	+	29.6957i	0.315210	+	0.970117i	−0.660458	+	0.750863i	$0.729638\pi$
$938$		0			0
$939$	−2.03754	+	1.48036i	−0.0664926	+	0.0483097i
$940$		0			0
$941$	7.76564	+	23.9002i	0.253153	+	0.779123i	0.994188	+	0.107658i	$0.0343350\pi$
$941$	7.76564	+	23.9002i	0.253153	+	0.779123i	−0.741036	+	0.671466i	$0.765665\pi$
$942$		0			0
$943$	17.5823	+	14.4591i	0.572557	+	0.470854i
$944$		0			0
$945$	2.89769	+	8.91816i	0.0942617	+	0.290108i
$946$		0			0
$947$	42.4945	−	30.8741i	1.38089	−	1.00327i	0.384089	−	0.923296i	$-0.374516\pi$
$947$	42.4945	−	30.8741i	1.38089	−	1.00327i	0.996797	−	0.0799757i	$-0.0254843\pi$
$948$		0			0
$949$	6.91115	+	21.2703i	0.224346	+	0.690464i
$950$		0			0
$951$	−32.4666	−	23.5884i	−1.05280	−	0.764906i
$952$		0			0
$953$	−9.00782	−	6.54457i	−0.291792	−	0.211999i	0.432252	−	0.901753i	$-0.357719\pi$
$953$	−9.00782	−	6.54457i	−0.291792	−	0.211999i	−0.724044	+	0.689753i	$0.757719\pi$
$954$		0			0
$955$	−12.1292	+	8.81235i	−0.392490	+	0.285161i
$956$		0			0
$957$	−0.236144			−0.00763344
$958$		0			0
$959$	−0.452876	+	1.39381i	−0.0146241	+	0.0450085i
$960$		0			0
$961$	−5.36563	−	16.5137i	−0.173085	−	0.532701i
$962$		0			0
$963$	4.74837	−	14.6140i	0.153014	−	0.470929i
$964$		0			0
$965$	14.0383	−	43.2055i	0.451910	−	1.39084i
$966$		0			0
$967$	−22.0628	−	16.0295i	−0.709491	−	0.515475i	0.173518	−	0.984831i	$-0.444486\pi$
$967$	−22.0628	−	16.0295i	−0.709491	−	0.515475i	−0.883009	+	0.469355i	$0.844486\pi$
$968$		0			0
$969$	13.6485	−	9.91625i	0.438454	−	0.318556i
$970$		0			0
$971$	14.3335	+	44.1138i	0.459982	+	1.41568i	0.865185	+	0.501453i	$0.167201\pi$
$971$	14.3335	+	44.1138i	0.459982	+	1.41568i	−0.405202	+	0.914227i	$0.632799\pi$
$972$		0			0
$973$	0.0601138	+	0.0436752i	0.00192716	+	0.00140016i
$974$		0			0
$975$	20.9156			0.669836
$976$		0			0
$977$	−7.94350	+	24.4476i	−0.254135	+	0.782147i	0.739864	+	0.672757i	$0.234890\pi$
$977$	−7.94350	+	24.4476i	−0.254135	+	0.782147i	−0.993999	+	0.109391i	$0.965110\pi$
$978$		0			0
$979$	8.82245	−	6.40988i	0.281967	−	0.204861i
$980$		0			0
$981$	−4.03737			−0.128903
$982$		0			0
$983$	−30.6330			−0.977039			−0.488520	−	0.872553i	$-0.662463\pi$
$983$	−30.6330			−0.977039			−0.488520	+	0.872553i	$0.662463\pi$
$984$		0			0
$985$	−45.1189			−1.43761
$986$		0			0
$987$	−17.4233			−0.554591
$988$		0			0
$989$	−28.5413	+	20.7365i	−0.907561	+	0.659382i
$990$		0			0
$991$	3.34713	−	10.3014i	0.106325	−	0.327235i	−0.883714	−	0.468027i	$-0.844965\pi$
$991$	3.34713	−	10.3014i	0.106325	−	0.327235i	0.990039	+	0.140792i	$0.0449649\pi$
$992$		0			0
$993$	44.7435			1.41989
$994$		0			0
$995$	46.5716	+	33.8363i	1.47642	+	1.07268i
$996$		0			0
$997$	−10.0727	−	31.0007i	−0.319007	−	0.981803i	−0.974074	−	0.226232i	$-0.927359\pi$
$997$	−10.0727	−	31.0007i	−0.319007	−	0.981803i	0.655066	−	0.755571i	$-0.272641\pi$
$998$		0			0
$999$	21.6910	−	15.7594i	0.686272	−	0.498606i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.n.c.141.4	yes	16
41.16	even	5	inner	1148.2.n.c.57.4	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.n.c.57.4	✓	16	41.16	even	5	inner
1148.2.n.c.141.4	yes	16	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1148.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+2.07339 q^{3} +(-2.15094 + 1.56275i) q^{5} +(-0.309017 + 0.951057i) q^{7} +1.29895 q^{9} +O(q^{10})\)	\(q+2.07339 q^{3} +(-2.15094 + 1.56275i) q^{5} +(-0.309017 + 0.951057i) q^{7} +1.29895 q^{9} +(0.978799 + 0.711139i) q^{11} +(1.50683 + 4.63753i) q^{13} +(-4.45975 + 3.24020i) q^{15} +(-4.06409 - 2.95273i) q^{17} +(-0.500524 + 1.54045i) q^{19} +(-0.640713 + 1.97191i) q^{21} +(1.09860 + 3.38115i) q^{23} +(0.639280 - 1.96750i) q^{25} -3.52694 q^{27} +(-0.0761582 + 0.0553321i) q^{29} +(-2.98750 - 2.17055i) q^{31} +(2.02943 + 1.47447i) q^{33} +(-0.821587 - 2.52859i) q^{35} +(-6.15009 + 4.46830i) q^{37} +(3.12424 + 9.61542i) q^{39} +(5.39630 - 3.44672i) q^{41} +(3.06649 + 9.43767i) q^{43} +(-2.79398 + 2.02994i) q^{45} +(2.59676 + 7.99201i) q^{47} +(-0.809017 - 0.587785i) q^{49} +(-8.42644 - 6.12217i) q^{51} +(4.13499 - 3.00425i) q^{53} -3.21668 q^{55} +(-1.03778 + 3.19396i) q^{57} +(-2.23821 - 6.88850i) q^{59} +(-2.09856 + 6.45870i) q^{61} +(-0.401399 + 1.23538i) q^{63} +(-10.4884 - 7.62028i) q^{65} +(-11.8851 + 8.63501i) q^{67} +(2.27783 + 7.01044i) q^{69} +(9.09080 + 6.60486i) q^{71} +4.58657 q^{73} +(1.32548 - 4.07940i) q^{75} +(-0.978799 + 0.711139i) q^{77} +12.0411 q^{79} -11.2096 q^{81} +0.731917 q^{83} +13.3560 q^{85} +(-0.157906 + 0.114725i) q^{87} +(2.78534 - 8.57239i) q^{89} -4.87619 q^{91} +(-6.19426 - 4.50040i) q^{93} +(-1.33075 - 4.09562i) q^{95} +(6.31745 - 4.58989i) q^{97} +(1.27141 + 0.923737i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{3} - 13 q^{5} + 4 q^{7} + 2 q^{9}+O(q^{10}) \) 16 * q - 2 * q^3 - 13 * q^5 + 4 * q^7 + 2 * q^9	\( 16 q - 2 q^{3} - 13 q^{5} + 4 q^{7} + 2 q^{9} - q^{11} - 6 q^{13} - q^{17} + 15 q^{19} + 2 q^{21} + 27 q^{23} - 3 q^{25} + 28 q^{27} - q^{29} - 14 q^{31} - 13 q^{33} - 12 q^{35} - 16 q^{37} + 10 q^{39} + 26 q^{41} + 5 q^{43} - 9 q^{45} - 14 q^{47} - 4 q^{49} + 4 q^{51} - 20 q^{53} + 10 q^{55} - 13 q^{57} - 47 q^{61} + 3 q^{63} - 29 q^{65} - 27 q^{67} + 15 q^{69} - 11 q^{71} + 70 q^{73} + 14 q^{75} + q^{77} + 30 q^{79} - 72 q^{81} - 78 q^{83} + 72 q^{85} + 21 q^{87} + 17 q^{89} - 24 q^{91} - 7 q^{93} + 27 q^{95} - 17 q^{97} + 13 q^{99}+O(q^{100}) \) 16 * q - 2 * q^3 - 13 * q^5 + 4 * q^7 + 2 * q^9 - q^11 - 6 * q^13 - q^17 + 15 * q^19 + 2 * q^21 + 27 * q^23 - 3 * q^25 + 28 * q^27 - q^29 - 14 * q^31 - 13 * q^33 - 12 * q^35 - 16 * q^37 + 10 * q^39 + 26 * q^41 + 5 * q^43 - 9 * q^45 - 14 * q^47 - 4 * q^49 + 4 * q^51 - 20 * q^53 + 10 * q^55 - 13 * q^57 - 47 * q^61 + 3 * q^63 - 29 * q^65 - 27 * q^67 + 15 * q^69 - 11 * q^71 + 70 * q^73 + 14 * q^75 + q^77 + 30 * q^79 - 72 * q^81 - 78 * q^83 + 72 * q^85 + 21 * q^87 + 17 * q^89 - 24 * q^91 - 7 * q^93 + 27 * q^95 - 17 * q^97 + 13 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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