LMFDB - Embedded newform 129.2.n.b.98.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [129,2,Mod(5,129)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(129, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([21, 25]))

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

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

chi := DirichletCharacter("129.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 129 = 3 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	129.n (of order $42$, degree $12$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.03007018607$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$12$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			98.5
Character	$\chi$	$=$	129.98
Dual form			129.2.n.b.104.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.697042 + 0.335678i) q^{2} +(0.634997 - 1.61145i) q^{3} +(-0.873791 + 1.09570i) q^{4} +(-2.42009 - 2.24551i) q^{5} +(0.0983093 + 1.33640i) q^{6} +(3.51626 - 2.03011i) q^{7} +(0.585578 - 2.56558i) q^{8} +(-2.19356 - 2.04653i) q^{9} +O(q^{10})$	\(q+(-0.697042 + 0.335678i) q^{2} +(0.634997 - 1.61145i) q^{3} +(-0.873791 + 1.09570i) q^{4} +(-2.42009 - 2.24551i) q^{5} +(0.0983093 + 1.33640i) q^{6} +(3.51626 - 2.03011i) q^{7} +(0.585578 - 2.56558i) q^{8} +(-2.19356 - 2.04653i) q^{9} +(2.44067 + 0.752848i) q^{10} +(1.58659 - 1.26526i) q^{11} +(1.21081 + 2.10384i) q^{12} +(-4.52234 + 1.39496i) q^{13} +(-1.76952 + 2.59540i) q^{14} +(-5.15529 + 2.47396i) q^{15} +(-0.170668 - 0.747745i) q^{16} +(1.47041 + 1.58472i) q^{17} +(2.21598 + 0.690192i) q^{18} +(5.06067 - 1.98617i) q^{19} +(4.57506 - 0.689579i) q^{20} +(-1.03862 - 6.95539i) q^{21} +(-0.681199 + 1.41452i) q^{22} +(1.02161 + 6.77797i) q^{23} +(-3.76248 - 2.57277i) q^{24} +(0.440844 + 5.88266i) q^{25} +(2.68401 - 2.49040i) q^{26} +(-4.69080 + 2.23527i) q^{27} +(-0.848082 + 5.62665i) q^{28} +(-0.531288 - 0.362226i) q^{29} +(2.76300 - 3.45497i) q^{30} +(0.106494 - 1.42107i) q^{31} +(3.65147 + 4.57880i) q^{32} +(-1.03143 - 3.36015i) q^{33} +(-1.55689 - 0.611035i) q^{34} +(-13.0683 - 2.98275i) q^{35} +(4.15910 - 0.615237i) q^{36} +(5.94578 + 3.43280i) q^{37} +(-2.86079 + 3.08320i) q^{38} +(-0.623765 + 8.17334i) q^{39} +(-7.17820 + 4.89402i) q^{40} +(0.589213 + 1.22351i) q^{41} +(3.05873 + 4.49956i) q^{42} +(-2.12269 - 6.20437i) q^{43} +2.84400i q^{44} +(0.713083 + 9.87846i) q^{45} +(-2.98732 - 4.38160i) q^{46} +(2.74171 + 2.18644i) q^{47} +(-1.31333 - 0.199792i) q^{48} +(4.74270 - 8.21460i) q^{49} +(-2.28197 - 3.95248i) q^{50} +(3.48741 - 1.36320i) q^{51} +(2.42313 - 6.17403i) q^{52} +(0.842656 - 2.73182i) q^{53} +(2.51935 - 3.13267i) q^{54} +(-6.68085 - 0.500661i) q^{55} +(-3.14938 - 10.2100i) q^{56} +(0.0128961 - 9.41624i) q^{57} +(0.491922 + 0.0741452i) q^{58} +(9.41118 - 2.14804i) q^{59} +(1.79392 - 7.81037i) q^{60} +(0.681166 - 0.0510463i) q^{61} +(0.402790 + 1.02629i) q^{62} +(-11.8678 - 2.74297i) q^{63} +(-2.70019 - 1.30034i) q^{64} +(14.0769 + 6.77906i) q^{65} +(1.84688 + 1.99594i) q^{66} +(0.172940 + 0.440643i) q^{67} +(-3.02121 + 0.226408i) q^{68} +(11.5711 + 2.65770i) q^{69} +(10.1104 - 2.30763i) q^{70} +(-7.95534 - 1.19907i) q^{71} +(-6.53505 + 4.42935i) q^{72} +(-1.86451 - 6.04459i) q^{73} +(-5.29678 - 0.396939i) q^{74} +(9.75956 + 3.02507i) q^{75} +(-2.24573 + 7.28047i) q^{76} +(3.01023 - 7.66994i) q^{77} +(-2.30882 - 5.90654i) q^{78} +(4.55511 + 7.88969i) q^{79} +(-1.26604 + 2.19285i) q^{80} +(0.623395 + 8.97838i) q^{81} +(-0.821412 - 0.655054i) q^{82} +(-2.96496 - 4.34879i) q^{83} +(8.52856 + 4.93955i) q^{84} -7.13698i q^{85} +(3.56227 + 3.61217i) q^{86} +(-0.921077 + 0.626133i) q^{87} +(-2.31707 - 4.81144i) q^{88} +(9.67968 - 6.59949i) q^{89} +(-3.81303 - 6.64633i) q^{90} +(-13.0698 + 14.0859i) q^{91} +(-8.31930 - 4.80315i) q^{92} +(-2.22236 - 1.07399i) q^{93} +(-2.64503 - 0.603710i) q^{94} +(-16.7072 - 6.55711i) q^{95} +(9.69719 - 2.97665i) q^{96} +(2.46727 + 3.09386i) q^{97} +(-0.548404 + 7.31795i) q^{98} +(-6.06968 - 0.471582i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 14 q^{3} - 48 q^{4} - 4 q^{6} - 42 q^{7}+O(q^{10}) $ 144 * q - 14 * q^3 - 48 * q^4 - 4 * q^6 - 42 * q^7	$ 144 q - 14 q^{3} - 48 q^{4} - 4 q^{6} - 42 q^{7} - 26 q^{10} - 4 q^{12} - 48 q^{13} - 19 q^{15} - 8 q^{16} + 16 q^{18} - 10 q^{19} - 15 q^{21} + 14 q^{22} - 11 q^{24} - 16 q^{25} - 14 q^{27} - 42 q^{28} - 6 q^{30} - 36 q^{31} + 7 q^{33} + 80 q^{34} + 48 q^{36} - 6 q^{37} + 7 q^{39} + 118 q^{40} + 46 q^{43} + 78 q^{46} - 41 q^{48} - 54 q^{49} + 7 q^{51} - 4 q^{52} - 52 q^{54} - 22 q^{55} - 110 q^{57} + 18 q^{58} - 9 q^{60} - 58 q^{61} - 82 q^{63} + 72 q^{64} - 127 q^{66} + 10 q^{67} - 15 q^{69} - 196 q^{70} + 179 q^{72} + 42 q^{73} + 119 q^{75} + 4 q^{76} + 62 q^{78} - 30 q^{79} + 200 q^{81} - 28 q^{82} + 111 q^{84} - 18 q^{87} - 14 q^{88} + 131 q^{90} - 38 q^{91} + 156 q^{93} + 28 q^{94} + 304 q^{96} + 72 q^{97} + 121 q^{99}+O(q^{100}) $ 144 * q - 14 * q^3 - 48 * q^4 - 4 * q^6 - 42 * q^7 - 26 * q^10 - 4 * q^12 - 48 * q^13 - 19 * q^15 - 8 * q^16 + 16 * q^18 - 10 * q^19 - 15 * q^21 + 14 * q^22 - 11 * q^24 - 16 * q^25 - 14 * q^27 - 42 * q^28 - 6 * q^30 - 36 * q^31 + 7 * q^33 + 80 * q^34 + 48 * q^36 - 6 * q^37 + 7 * q^39 + 118 * q^40 + 46 * q^43 + 78 * q^46 - 41 * q^48 - 54 * q^49 + 7 * q^51 - 4 * q^52 - 52 * q^54 - 22 * q^55 - 110 * q^57 + 18 * q^58 - 9 * q^60 - 58 * q^61 - 82 * q^63 + 72 * q^64 - 127 * q^66 + 10 * q^67 - 15 * q^69 - 196 * q^70 + 179 * q^72 + 42 * q^73 + 119 * q^75 + 4 * q^76 + 62 * q^78 - 30 * q^79 + 200 * q^81 - 28 * q^82 + 111 * q^84 - 18 * q^87 - 14 * q^88 + 131 * q^90 - 38 * q^91 + 156 * q^93 + 28 * q^94 + 304 * q^96 + 72 * q^97 + 121 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/129\mathbb{Z}\right)^\times$.

$n$	$44$	$46$
$\chi(n)$	$-1$	$e\left(\frac{13}{42}\right)$

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 $

$2$	−0.697042	+	0.335678i	−0.492883	+	0.237360i	−0.663779	−	0.747929i	$-0.731048\pi$
$2$	−0.697042	+	0.335678i	−0.492883	+	0.237360i	0.170895	+	0.985289i	$0.445334\pi$
$3$	0.634997	−	1.61145i	0.366616	−	0.930373i
$3$	0.634997	−	1.61145i	0.366616	−	0.930373i
$4$	−0.873791	+	1.09570i	−0.436896	+	0.547850i
$5$	−2.42009	−	2.24551i	−1.08230	−	1.00422i	−0.999971	−	0.00761856i	$-0.997575\pi$
$5$	−2.42009	−	2.24551i	−1.08230	−	1.00422i	−0.0823252	−	0.996606i	$-0.526235\pi$
$6$	0.0983093	+	1.33640i	0.0401346	+	0.545585i
$7$	3.51626	−	2.03011i	1.32902	−	0.767310i	0.343872	−	0.939017i	$-0.388261\pi$
$7$	3.51626	−	2.03011i	1.32902	−	0.767310i	0.985148	+	0.171707i	$0.0549281\pi$
$8$	0.585578	−	2.56558i	0.207033	−	0.907071i
$9$	−2.19356	−	2.04653i	−0.731186	−	0.682178i
$10$	2.44067	+	0.752848i	0.771808	+	0.238071i
$11$	1.58659	−	1.26526i	0.478375	−	0.381491i	−0.354408	−	0.935091i	$-0.615318\pi$
$11$	1.58659	−	1.26526i	0.478375	−	0.381491i	0.832783	+	0.553600i	$0.186746\pi$
$12$	1.21081	+	2.10384i	0.349532	+	0.607326i
$13$	−4.52234	+	1.39496i	−1.25427	+	0.386892i	−0.849531	−	0.527539i	$-0.823115\pi$
$13$	−4.52234	+	1.39496i	−1.25427	+	0.386892i	−0.404742	+	0.914431i	$0.632639\pi$
$14$	−1.76952	+	2.59540i	−0.472923	+	0.693650i
$15$	−5.15529	+	2.47396i	−1.33109	+	0.638774i
$16$	−0.170668	−	0.747745i	−0.0426670	−	0.186936i
$17$	1.47041	+	1.58472i	0.356626	+	0.384351i	0.885726	−	0.464208i	$-0.153661\pi$
$17$	1.47041	+	1.58472i	0.356626	+	0.384351i	−0.529100	+	0.848559i	$0.677471\pi$
$18$	2.21598	+	0.690192i	0.522311	+	0.162680i
$19$	5.06067	−	1.98617i	1.16100	−	0.455658i	0.294898	−	0.955529i	$-0.404714\pi$
$19$	5.06067	−	1.98617i	1.16100	−	0.455658i	0.866100	+	0.499871i	$0.166619\pi$
$20$	4.57506	−	0.689579i	1.02301	−	0.154195i
$21$	−1.03862	−	6.95539i	−0.226645	−	1.51779i
$22$	−0.681199	+	1.41452i	−0.145232	+	0.301578i
$23$	1.02161	+	6.77797i	0.213021	+	1.41330i	0.798197	+	0.602397i	$0.205788\pi$
$23$	1.02161	+	6.77797i	0.213021	+	1.41330i	−0.585175	+	0.810907i	$0.698974\pi$
$24$	−3.76248	−	2.57277i	−0.768012	−	0.525164i
$25$	0.440844	+	5.88266i	0.0881689	+	1.17653i
$26$	2.68401	−	2.49040i	0.526377	−	0.488407i
$27$	−4.69080	+	2.23527i	−0.902744	+	0.430178i
$28$	−0.848082	+	5.62665i	−0.160272	+	1.06334i
$29$	−0.531288	−	0.362226i	−0.0986577	−	0.0672637i	0.512986	−	0.858397i	$-0.328539\pi$
$29$	−0.531288	−	0.362226i	−0.0986577	−	0.0672637i	−0.611644	+	0.791133i	$0.709492\pi$
$30$	2.76300	−	3.45497i	0.504452	−	0.630789i
$31$	0.106494	−	1.42107i	0.0191270	−	0.255232i	−0.979441	−	0.201731i	$-0.935343\pi$
$31$	0.106494	−	1.42107i	0.0191270	−	0.255232i	0.998568	−	0.0535002i	$-0.0170378\pi$
$32$	3.65147	+	4.57880i	0.645495	+	0.809425i
$33$	−1.03143	−	3.36015i	−0.179549	−	0.584927i
$34$	−1.55689	−	0.611035i	−0.267005	−	0.104792i
$35$	−13.0683	−	2.98275i	−2.20894	−	0.504177i
$36$	4.15910	−	0.615237i	0.693183	−	0.102540i
$37$	5.94578	+	3.43280i	0.977481	+	0.564349i	0.901509	−	0.432761i	$-0.142461\pi$
$37$	5.94578	+	3.43280i	0.977481	+	0.564349i	0.0759722	+	0.997110i	$0.475794\pi$
$38$	−2.86079	+	3.08320i	−0.464081	+	0.500161i
$39$	−0.623765	+	8.17334i	−0.0998823	+	1.30878i
$40$	−7.17820	+	4.89402i	−1.13497	+	0.773812i
$41$	0.589213	+	1.22351i	0.0920196	+	0.191081i	0.941899	−	0.335897i	$-0.109039\pi$
$41$	0.589213	+	1.22351i	0.0920196	+	0.191081i	−0.849879	+	0.526978i	$0.823325\pi$
$42$	3.05873	+	4.49956i	0.471972	+	0.694297i
$43$	−2.12269	−	6.20437i	−0.323707	−	0.946157i
$43$	−2.12269	−	6.20437i	−0.323707	−	0.946157i
$44$			2.84400i			0.428749i
$45$	0.713083	+	9.87846i	0.106300	+	1.47259i
$46$	−2.98732	−	4.38160i	−0.440457	−	0.646031i
$47$	2.74171	+	2.18644i	0.399920	+	0.318925i	0.802713	−	0.596366i	$-0.203389\pi$
$47$	2.74171	+	2.18644i	0.399920	+	0.318925i	−0.402793	+	0.915291i	$0.631961\pi$
$48$	−1.31333	−	0.199792i	−0.189563	−	0.0288376i
$49$	4.74270	−	8.21460i	0.677529	−	1.17351i
$50$	−2.28197	−	3.95248i	−0.322719	−	0.558965i
$51$	3.48741	−	1.36320i	0.488334	−	0.190886i
$52$	2.42313	−	6.17403i	0.336028	−	0.856185i
$53$	0.842656	−	2.73182i	0.115748	−	0.375245i	−0.879099	−	0.476640i	$-0.841855\pi$
$53$	0.842656	−	2.73182i	0.115748	−	0.375245i	0.994846	+	0.101395i	$0.0323307\pi$
$54$	2.51935	−	3.13267i	0.342840	−	0.426303i
$55$	−6.68085	−	0.500661i	−0.900846	−	0.0675091i
$56$	−3.14938	−	10.2100i	−0.420854	−	1.36437i
$57$	0.0128961	−	9.41624i	0.00170812	−	1.24721i
$58$	0.491922	+	0.0741452i	0.0645925	+	0.00973575i
$59$	9.41118	−	2.14804i	1.22523	−	0.279651i	0.439513	−	0.898236i	$-0.355151\pi$
$59$	9.41118	−	2.14804i	1.22523	−	0.279651i	0.785718	+	0.618585i	$0.212294\pi$
$60$	1.79392	−	7.81037i	0.231595	−	1.00831i
$61$	0.681166	−	0.0510463i	0.0872143	−	0.00653581i	−0.0310514	−	0.999518i	$-0.509886\pi$
$61$	0.681166	−	0.0510463i	0.0872143	−	0.00653581i	0.118266	+	0.992982i	$0.462267\pi$
$62$	0.402790	+	1.02629i	0.0511544	+	0.130339i
$63$	−11.8678	−	2.74297i	−1.49520	−	0.345582i
$64$	−2.70019	−	1.30034i	−0.337523	−	0.162543i
$65$	14.0769	+	6.77906i	1.74602	+	0.840839i
$66$	1.84688	+	1.99594i	0.227335	+	0.245683i
$67$	0.172940	+	0.440643i	0.0211279	+	0.0538331i	0.941048	−	0.338272i	$-0.109842\pi$
$67$	0.172940	+	0.440643i	0.0211279	+	0.0538331i	−0.919921	+	0.392105i	$0.871747\pi$
$68$	−3.02121	+	0.226408i	−0.366375	+	0.0274560i
$69$	11.5711	+	2.65770i	1.39300	+	0.319950i
$70$	10.1104	−	2.30763i	1.20842	−	0.275815i
$71$	−7.95534	−	1.19907i	−0.944125	−	0.142304i	−0.341101	−	0.940027i	$-0.610800\pi$
$71$	−7.95534	−	1.19907i	−0.944125	−	0.142304i	−0.603024	+	0.797723i	$0.706038\pi$
$72$	−6.53505	+	4.42935i	−0.770163	+	0.522004i
$73$	−1.86451	−	6.04459i	−0.218224	−	0.707466i	−0.996802	−	0.0799170i	$-0.974534\pi$
$73$	−1.86451	−	6.04459i	−0.218224	−	0.707466i	0.778577	−	0.627549i	$-0.215942\pi$
$74$	−5.29678	−	0.396939i	−0.615738	−	0.0461432i
$75$	9.75956	+	3.02507i	1.12694	+	0.349305i
$76$	−2.24573	+	7.28047i	−0.257603	+	0.835128i
$77$	3.01023	−	7.66994i	0.343048	−	0.874071i
$78$	−2.30882	−	5.90654i	−0.261422	−	0.668784i
$79$	4.55511	+	7.88969i	0.512490	+	0.887659i	0.999895	+	0.0144832i	$0.00461032\pi$
$79$	4.55511	+	7.88969i	0.512490	+	0.887659i	−0.487405	+	0.873176i	$0.662056\pi$
$80$	−1.26604	+	2.19285i	−0.141548	+	0.245168i
$81$	0.623395	+	8.97838i	0.0692661	+	0.997598i
$82$	−0.821412	−	0.655054i	−0.0907098	−	0.0723387i
$83$	−2.96496	−	4.34879i	−0.325446	−	0.477342i	0.628293	−	0.777977i	$-0.283754\pi$
$83$	−2.96496	−	4.34879i	−0.325446	−	0.477342i	−0.953739	+	0.300635i	$0.902801\pi$
$84$	8.52856	+	4.93955i	0.930542	+	0.538949i
$85$		−	7.13698i		−	0.774114i
$86$	3.56227	+	3.61217i	0.384130	+	0.389510i
$87$	−0.921077	+	0.626133i	−0.0987498	+	0.0671285i
$88$	−2.31707	−	4.81144i	−0.247000	−	0.512901i
$89$	9.67968	−	6.59949i	1.02604	−	0.699545i	0.0714467	−	0.997444i	$-0.477238\pi$
$89$	9.67968	−	6.59949i	1.02604	−	0.699545i	0.954597	+	0.297899i	$0.0962860\pi$
$90$	−3.81303	−	6.64633i	−0.401928	−	0.700585i
$91$	−13.0698	+	14.0859i	−1.37009	+	1.47660i
$92$	−8.31930	−	4.80315i	−0.867347	−	0.500763i
$93$	−2.22236	−	1.07399i	−0.230448	−	0.111367i
$94$	−2.64503	−	0.603710i	−0.272814	−	0.0622680i
$95$	−16.7072	−	6.55711i	−1.71413	−	0.672745i
$96$	9.69719	−	2.97665i	0.989715	−	0.303803i
$97$	2.46727	+	3.09386i	0.250513	+	0.314134i	0.891149	−	0.453711i	$-0.149900\pi$
$97$	2.46727	+	3.09386i	0.250513	+	0.314134i	−0.640635	+	0.767845i	$0.721329\pi$
$98$	−0.548404	+	7.31795i	−0.0553972	+	0.739224i
$99$	−6.06968	−	0.471582i	−0.610026	−	0.0473958i
$100$	−6.83084	−	4.65718i	−0.683084	−	0.465718i
$101$	0.847735	−	5.62436i	0.0843528	−	0.559644i	−0.906236	−	0.422772i	$-0.861057\pi$
$101$	0.847735	−	5.62436i	0.0843528	−	0.559644i	0.990589	−	0.136872i	$-0.0437049\pi$
$102$	−1.97327	+	2.12085i	−0.195383	+	0.209995i
$103$	−6.63724	+	6.15846i	−0.653987	+	0.606811i	−0.935746	−	0.352674i	$-0.885272\pi$
$103$	−6.63724	+	6.15846i	−0.653987	+	0.606811i	0.281760	+	0.959485i	$0.409082\pi$
$104$	0.930699	+	12.4193i	0.0912625	+	1.21781i
$105$	−13.1049	+	19.1649i	−1.27891	+	1.87030i
$106$	0.329646	+	2.18706i	0.0320180	+	0.212426i
$107$	−7.13899	+	14.8243i	−0.690152	+	1.43312i	0.201083	+	0.979574i	$0.435554\pi$
$107$	−7.13899	+	14.8243i	−0.690152	+	1.43312i	−0.891235	+	0.453542i	$0.850160\pi$
$108$	1.64959	−	7.09286i	0.158732	−	0.682511i
$109$	−2.81176	+	0.423804i	−0.269317	+	0.0405931i	−0.282312	−	0.959323i	$-0.591101\pi$
$109$	−2.81176	+	0.423804i	−0.269317	+	0.0405931i	0.0129952	+	0.999916i	$0.495863\pi$
$110$	4.82490	−	1.89363i	0.460036	−	0.180551i
$111$	9.30735	−	7.40153i	0.883414	−	0.702522i
$112$	−2.11812	−	2.28279i	−0.200143	−	0.215703i
$113$	0.650636	+	2.85062i	0.0612067	+	0.268164i	0.996267	−	0.0863244i	$-0.0275121\pi$
$113$	0.650636	+	2.85062i	0.0612067	+	0.268164i	−0.935060	+	0.354489i	$0.884655\pi$
$114$	3.15183	+	6.56785i	0.295196	+	0.615135i
$115$	12.7476	−	18.6973i	1.18872	−	1.74353i
$116$	0.861126	−	0.265622i	0.0799536	−	0.0246624i
$117$	12.7749	+	6.19521i	1.18104	+	0.572747i
$118$	−5.83894	+	4.65640i	−0.537518	+	0.428656i
$119$	8.38748	+	2.58720i	0.768879	+	0.237168i
$120$	3.32834	+	14.6750i	0.303834	+	1.33964i
$121$	−1.53135	+	6.70930i	−0.139214	+	0.609936i
$122$	−0.457666	+	0.264234i	−0.0414351	+	0.0239226i
$123$	2.34578	−	0.172562i	0.211512	−	0.0155594i
$124$	1.46401	+	1.35840i	0.131472	+	0.121988i
$125$	1.85080	−	2.32083i	0.165541	−	0.207582i
$126$	9.19311	−	2.07179i	0.818988	−	0.184570i
$127$	−1.26180	+	0.607651i	−0.111967	+	0.0539203i	−0.489029	−	0.872268i	$-0.662649\pi$
$127$	−1.26180	+	0.607651i	−0.111967	+	0.0539203i	0.377062	+	0.926188i	$0.376934\pi$
$128$	−9.39436			−0.830352
$129$	−11.3459	−	0.519145i	−0.998955	−	0.0457082i
$130$	−12.0878			−1.06017
$131$	17.7079	−	8.52766i	1.54714	−	0.745065i	0.551142	−	0.834411i	$-0.314192\pi$
$131$	17.7079	−	8.52766i	1.54714	−	0.745065i	0.996001	+	0.0893465i	$0.0284779\pi$
$132$	4.58297	+	1.80593i	0.398897	+	0.157186i
$133$	13.7625	−	17.2576i	1.19336	−	1.49642i
$134$	−0.268460	−	0.249095i	−0.0231914	−	0.0215185i
$135$	16.3715	+	5.12369i	1.40903	+	0.440977i
$136$	4.92677	−	2.84447i	0.422467	−	0.243912i
$137$	−4.13327	+	18.1091i	−0.353129	+	1.54716i	0.416780	+	0.909007i	$0.363159\pi$
$137$	−4.13327	+	18.1091i	−0.353129	+	1.54716i	−0.769909	+	0.638153i	$0.779699\pi$
$138$	−8.95767	+	2.03163i	−0.762528	+	0.172944i
$139$	−1.37855	−	0.425226i	−0.116927	−	0.0360672i	0.235740	−	0.971816i	$-0.424249\pi$
$139$	−1.37855	−	0.425226i	−0.116927	−	0.0360672i	−0.352666	+	0.935749i	$0.614725\pi$
$140$	14.6872	−	11.7126i	1.24129	−	0.989897i
$141$	5.26433	−	3.02975i	0.443336	−	0.255151i
$142$	5.94771	−	1.83463i	0.499121	−	0.153958i
$143$	−5.41011	+	7.93518i	−0.452417	+	0.663573i
$144$	−1.15592	+	1.98950i	−0.0963263	+	0.165792i
$145$	0.472380	+	2.06963i	0.0392291	+	0.171874i
$146$	3.32868	+	3.58746i	0.275483	+	0.296900i
$147$	−10.2258	−	12.8589i	−0.843413	−	1.06058i
$148$	−8.95669	+	3.51524i	−0.736236	+	0.288951i
$149$	−13.2771	+	2.00119i	−1.08770	+	0.163944i	−0.668325	−	0.743869i	$-0.732988\pi$
$149$	−13.2771	+	2.00119i	−1.08770	+	0.163944i	−0.419374	+	0.907814i	$0.637750\pi$
$150$	−7.81827	+	1.16747i	−0.638359	+	0.0953233i
$151$	−6.39703	+	13.2836i	−0.520583	+	1.08100i	0.460544	+	0.887637i	$0.347654\pi$
$151$	−6.39703	+	13.2836i	−0.520583	+	1.08100i	−0.981127	+	0.193365i	$0.938060\pi$
$152$	−2.13226	−	14.1466i	−0.172949	−	1.14744i
$153$	0.0177643	−	6.48541i	0.00143616	−	0.524315i
$154$	0.476372	+	6.35674i	0.0383871	+	0.512241i
$155$	−3.44876	+	3.19998i	−0.277011	+	0.257029i
$156$	−8.41048	−	7.82525i	−0.673378	−	0.626521i
$157$	−0.387407	+	2.57027i	−0.0309184	+	0.205130i	−0.998956	−	0.0456732i	$-0.985457\pi$
$157$	−0.387407	+	2.57027i	−0.0309184	+	0.205130i	0.968038	+	0.250803i	$0.0806948\pi$
$158$	−5.82350	−	3.97040i	−0.463293	−	0.315868i
$159$	−3.86712	−	3.09260i	−0.306682	−	0.245259i
$160$	1.44487	−	19.2805i	0.114227	−	1.52426i
$161$	17.3523	+	21.7591i	1.36755	+	1.71486i
$162$	−3.44838	−	6.04905i	−0.270930	−	0.475258i
$163$	−11.5355	−	4.52733i	−0.903527	−	0.354608i	−0.132330	−	0.991206i	$-0.542246\pi$
$163$	−11.5355	−	4.52733i	−0.903527	−	0.354608i	−0.771196	+	0.636598i	$0.780341\pi$
$164$	−1.85545	−	0.423495i	−0.144886	−	0.0330694i
$165$	−5.04911	+	10.4480i	−0.393073	+	0.813372i
$166$	3.52649	+	2.03602i	0.273709	+	0.158026i
$167$	8.20652	−	8.84452i	0.635039	−	0.684410i	−0.330756	−	0.943716i	$-0.607304\pi$
$167$	8.20652	−	8.84452i	0.635039	−	0.684410i	0.965795	+	0.259307i	$0.0834941\pi$
$168$	−18.4528	−	1.40827i	−1.42367	−	0.108650i
$169$	7.76459	−	5.29380i	0.597276	−	0.407216i
$170$	2.39573	+	4.97478i	0.183744	+	0.381548i
$171$	−15.1656	−	6.00007i	−1.15975	−	0.458836i
$172$	8.65291	+	3.09550i	0.659778	+	0.236029i
$173$			5.96818i			0.453752i	0.973924	+	0.226876i	$0.0728512\pi$
$173$			5.96818i			0.453752i	−0.973924	+	0.226876i	$0.927149\pi$
$174$	0.431850	−	0.745626i	0.0327385	−	0.0565258i
$175$	13.4926	+	19.7900i	1.01994	+	1.49598i
$176$	−1.21687	−	0.970425i	−0.0917253	−	0.0731485i
$177$	2.51460	−	16.5297i	0.189009	−	1.24245i
$178$	−4.53184	+	7.84938i	−0.339676	+	0.588336i
$179$	−6.51379	−	11.2822i	−0.486864	−	0.843273i	0.513022	−	0.858375i	$-0.328526\pi$
$179$	−6.51379	−	11.2822i	−0.486864	−	0.843273i	−0.999886	+	0.0151026i	$0.995192\pi$
$180$	−11.4469	−	7.85039i	−0.853202	−	0.585133i
$181$	−0.614269	+	1.56513i	−0.0456583	+	0.116335i	−0.951884	−	0.306459i	$-0.900856\pi$
$181$	−0.614269	+	1.56513i	−0.0456583	+	0.116335i	0.906225	+	0.422795i	$0.138951\pi$
$182$	4.38188	−	14.2057i	0.324806	−	1.05300i
$183$	0.350279	−	1.13008i	0.0258934	−	0.0835380i
$184$	17.9877	+	1.34799i	1.32607	+	0.0993751i
$185$	−6.68092	−	21.6590i	−0.491191	−	1.59240i
$186$	1.90959	+	0.00261529i	0.140018	+	0.000191763i
$187$	4.33802	+	0.653851i	0.317227	+	0.0478143i
$188$	−4.79137	+	1.09360i	−0.349446	+	0.0797589i
$189$	−11.9562	+	17.3826i	−0.869684	+	1.26440i
$190$	13.8467	−	1.03767i	1.00455	−	0.0752804i
$191$	1.40064	+	3.56876i	0.101346	+	0.258227i	0.972549	−	0.232696i	$-0.0747549\pi$
$191$	1.40064	+	3.56876i	0.101346	+	0.258227i	−0.871203	+	0.490923i	$0.836660\pi$
$192$	−3.81005	+	3.52551i	−0.274967	+	0.254432i
$193$	20.8223	+	10.0275i	1.49882	+	0.721794i	0.990260	−	0.139233i	$-0.0444637\pi$
$193$	20.8223	+	10.0275i	1.49882	+	0.721794i	0.508560	+	0.861027i	$0.330178\pi$
$194$	−2.75833	−	1.32834i	−0.198037	−	0.0953694i
$195$	19.8629	−	18.3795i	1.42241	−	1.31618i
$196$	4.85661	+	12.3744i	0.346900	+	0.883888i
$197$	−15.7792	+	1.18249i	−1.12422	+	0.0842487i	−0.623837	−	0.781555i	$-0.714427\pi$
$197$	−15.7792	+	1.18249i	−1.12422	+	0.0842487i	−0.500384	+	0.865803i	$0.666808\pi$
$198$	4.38912	−	1.70874i	0.311921	−	0.121435i
$199$	−4.65659	+	1.06284i	−0.330097	+	0.0753425i	−0.384357	−	0.923184i	$-0.625577\pi$
$199$	−4.65659	+	1.06284i	−0.330097	+	0.0753425i	0.0542606	+	0.998527i	$0.482720\pi$
$200$	15.3506	+	2.31373i	1.08545	+	0.163606i
$201$	0.819892	+	0.00112289i	0.0578307	+	7.92023e-5i
$202$	1.29706	+	4.20498i	0.0912611	+	0.295861i
$203$	−2.60350	−	0.195106i	−0.182730	−	0.0136937i
$204$	−1.55361	+	5.01230i	−0.108774	+	0.350931i
$205$	1.32147	−	4.28409i	0.0922953	−	0.299214i
$206$	2.55918	−	6.52068i	0.178306	−	0.454317i
$207$	11.6304	−	16.9586i	0.808367	−	1.17871i
$208$	1.81489	+	3.14349i	0.125840	+	0.217962i
$209$	5.51619	−	9.55431i	0.381563	−	0.660886i
$210$	2.70143	−	17.7578i	0.186416	−	1.22540i
$211$	−7.15600	−	5.70672i	−0.492640	−	0.392867i	0.345418	−	0.938449i	$-0.387737\pi$
$211$	−7.15600	−	5.70672i	−0.492640	−	0.392867i	−0.838057	+	0.545582i	$0.816309\pi$
$212$	2.25695	+	3.31034i	0.155008	+	0.227355i
$213$	−6.98387	+	12.0582i	−0.478527	+	0.826217i
$214$		−	12.7295i		−	0.870173i
$215$	−8.79490	+	19.7816i	−0.599808	+	1.34910i
$216$	2.98795	+	13.3436i	0.203304	+	0.907914i
$217$	−2.51047	−	5.21304i	−0.170422	−	0.353884i
$218$	1.81765	−	1.23925i	0.123107	−	0.0839328i
$219$	−10.9245	−	0.833727i	−0.738211	−	0.0563381i
$220$	6.38624	−	6.88273i	0.430560	−	0.464034i
$221$	−8.86030	−	5.11550i	−0.596008	−	0.344106i
$222$	−4.00308	+	8.28345i	−0.268669	+	0.555949i
$223$	−14.3368	−	3.27229i	−0.960065	−	0.219129i	−0.286354	−	0.958124i	$-0.592443\pi$
$223$	−14.3368	−	3.27229i	−0.960065	−	0.219129i	−0.673711	+	0.738995i	$0.735301\pi$
$224$	22.1350	+	8.68733i	1.47895	+	0.580447i
$225$	11.0720	−	13.8062i	0.738136	−	0.920411i
$226$	−1.41041	−	1.76860i	−0.0938192	−	0.117646i
$227$	−0.0159000	+	0.212170i	−0.00105532	+	0.0140822i	−0.997707	−	0.0676871i	$-0.978438\pi$
$227$	−0.0159000	+	0.212170i	−0.00105532	+	0.0140822i	0.996651	+	0.0817693i	$0.0260571\pi$
$228$	10.3061	+	8.24196i	0.682539	+	0.545837i
$229$	−17.3305	−	11.8157i	−1.14523	−	0.780805i	−0.166518	−	0.986038i	$-0.553252\pi$
$229$	−17.3305	−	11.8157i	−1.14523	−	0.780805i	−0.978713	+	0.205233i	$0.934205\pi$
$230$	−2.60935	+	17.3119i	−0.172056	+	1.14151i
$231$	−10.4483	−	9.72123i	−0.687445	−	0.639610i
$232$	−1.24043	+	1.15095i	−0.0814384	+	0.0755638i
$233$	−2.23484	−	29.8218i	−0.146409	−	1.95369i	−0.273669	−	0.961824i	$-0.588237\pi$
$233$	−2.23484	−	29.8218i	−0.146409	−	1.95369i	0.127260	−	0.991869i	$-0.459382\pi$
$234$	−10.9842	−	0.0300870i	−0.718060	−	0.00196685i
$235$	−1.72550	−	11.4479i	−0.112559	−	0.746781i
$236$	−5.86980	+	12.1888i	−0.382092	+	0.793421i
$237$	15.6063	−	2.33042i	1.01374	−	0.151377i
$238$	−6.71489	+	1.01211i	−0.435262	+	0.0656052i
$239$	−8.19678	+	3.21700i	−0.530205	+	0.208090i	−0.615315	−	0.788281i	$-0.710971\pi$
$239$	−8.19678	+	3.21700i	−0.530205	+	0.208090i	0.0851097	+	0.996372i	$0.472876\pi$
$240$	2.72974	+	3.43261i	0.176204	+	0.221574i
$241$	10.6080	+	11.4327i	0.683318	+	0.736442i	0.975519	−	0.219915i	$-0.0705781\pi$
$241$	10.6080	+	11.4327i	0.683318	+	0.736442i	−0.292201	+	0.956357i	$0.594388\pi$
$242$	−1.18475	−	5.19071i	−0.0761583	−	0.333671i
$243$	14.8641	+	4.69667i	0.953532	+	0.301292i
$244$	−0.539265	+	0.790957i	−0.0345229	+	0.0506358i
$245$	−29.9238	+	9.23026i	−1.91176	+	0.589700i
$246$	−1.57718	+	0.907709i	−0.100558	+	0.0578734i
$247$	−20.1155	+	16.0416i	−1.27992	+	1.02070i
$248$	−3.58351	−	1.10537i	−0.227553	−	0.0701909i
$249$	−8.89061	+	2.01642i	−0.563419	+	0.127785i
$250$	−0.511036	+	2.23899i	−0.0323207	+	0.141606i
$251$	17.4772	−	10.0905i	1.10315	−	0.636906i	0.166106	−	0.986108i	$-0.446881\pi$
$251$	17.4772	−	10.0905i	1.10315	−	0.636906i	0.937047	+	0.349202i	$0.113547\pi$
$252$	13.3755	−	10.6068i	0.842575	−	0.668163i
$253$	10.1968	+	9.46124i	0.641067	+	0.594823i
$254$	0.675553	−	0.847117i	0.0423880	−	0.0531528i
$255$	−11.5009	−	4.53196i	−0.720215	−	0.283802i
$256$	11.9486	−	5.75416i	0.746790	−	0.359635i
$257$	11.2101			0.699268			0.349634	−	0.936886i	$-0.386306\pi$
$257$	11.2101			0.699268			0.349634	+	0.936886i	$0.386306\pi$
$258$	8.08287	−	3.44672i	0.503217	−	0.214583i
$259$	27.8759			1.73212
$260$	−19.7281	+	9.50053i	−1.22348	+	0.589198i
$261$	0.424103	+	1.88186i	0.0262513	+	0.116484i
$262$	−9.48058	+	11.8883i	−0.585712	+	0.734460i
$263$	18.0080	+	16.7090i	1.11042	+	1.03032i	0.999333	+	0.0365088i	$0.0116237\pi$
$263$	18.0080	+	16.7090i	1.11042	+	1.03032i	0.111087	+	0.993811i	$0.464567\pi$
$264$	−9.22473	+	0.678595i	−0.567743	+	0.0417646i
$265$	−8.17364	+	4.71906i	−0.502103	+	0.289889i
$266$	−3.80003	+	16.6490i	−0.232995	+	1.02082i
$267$	−4.48821	−	19.7890i	−0.274674	−	1.21107i
$268$	−0.633926	−	0.195540i	−0.0387232	−	0.0119445i
$269$	2.69037	−	2.14550i	0.164035	−	0.130813i	−0.538032	−	0.842924i	$-0.680832\pi$
$269$	2.69037	−	2.14550i	0.164035	−	0.130813i	0.702067	+	0.712111i	$0.252261\pi$
$270$	−13.1315	+	1.92411i	−0.799158	+	0.117098i
$271$	28.8271	−	8.89198i	1.75112	−	0.540149i	0.757492	−	0.652845i	$-0.226425\pi$
$271$	28.8271	−	8.89198i	1.75112	−	0.540149i	0.993630	+	0.112695i	$0.0359484\pi$
$272$	0.934016	−	1.36995i	0.0566330	−	0.0830654i
$273$	14.3995	+	30.0059i	0.871495	+	1.81604i
$274$	−3.19774	−	14.0102i	−0.193183	−	0.846388i
$275$	8.14255	+	8.77558i	0.491014	+	0.529187i
$276$	−13.0228	+	10.3562i	−0.783879	+	0.623368i
$277$	−7.91984	+	3.10831i	−0.475857	+	0.186760i	−0.591134	−	0.806573i	$-0.701320\pi$
$277$	−7.91984	+	3.10831i	−0.475857	+	0.186760i	0.115277	+	0.993333i	$0.463224\pi$
$278$	1.10364	−	0.166348i	0.0661922	−	0.00997687i
$279$	−3.14187	+	2.89925i	−0.188099	+	0.173574i
$280$	−15.3050	+	31.7812i	−0.914649	+	1.89929i
$281$	−0.343396	−	2.27828i	−0.0204853	−	0.135911i	0.976250	−	0.216645i	$-0.0695115\pi$
$281$	−0.343396	−	2.27828i	−0.0204853	−	0.135911i	−0.996736	+	0.0807345i	$0.974273\pi$
$282$	−2.65244	+	3.87898i	−0.157950	+	0.230990i
$283$	1.53708	+	20.5109i	0.0913698	+	1.21925i	0.834846	+	0.550483i	$0.185557\pi$
$283$	1.53708	+	20.5109i	0.0913698	+	1.21925i	−0.743476	+	0.668762i	$0.766824\pi$
$284$	8.26513	−	7.66892i	0.490445	−	0.455067i
$285$	−21.1755	+	22.7592i	−1.25433	+	1.34814i
$286$	1.10741	−	7.34721i	0.0654828	−	0.434450i
$287$	4.55569	+	3.10602i	0.268914	+	0.183342i
$288$	1.36096	−	17.5167i	0.0801951	−	1.03218i
$289$	0.921165	−	12.2921i	0.0541862	−	0.723065i
$290$	−1.02400	−	1.28405i	−0.0601313	−	0.0754023i
$291$	6.55232	−	2.01130i	0.384104	−	0.117904i
$292$	8.25225	+	3.23877i	0.482926	+	0.189535i
$293$	−0.0196976	−	0.00449585i	−0.00115075	−	0.000262650i	0.221946	−	0.975059i	$-0.428759\pi$
$293$	−0.0196976	−	0.00449585i	−0.00115075	−	0.000262650i	−0.223096	+	0.974796i	$0.571616\pi$
$294$	11.4443	+	5.53060i	0.667444	+	0.322551i
$295$	−27.5993	−	15.9345i	−1.60690	−	0.927742i
$296$	12.2889	−	13.2442i	0.714275	−	0.769806i
$297$	−4.61416	+	9.48155i	−0.267741	+	0.550175i
$298$	8.58291	−	5.85173i	0.497195	−	0.338982i
$299$	−14.0751	−	29.2272i	−0.813983	−	1.69025i
$300$	−11.8424	+	8.05027i	−0.683721	+	0.464782i
$301$	−20.0595	−	17.5069i	−1.15621	−	1.00908i
$302$		−	11.4065i		−	0.656373i
$303$	−8.52507	−	4.93753i	−0.489753	−	0.283654i
$304$	−2.34884	−	3.44512i	−0.134715	−	0.197591i
$305$	−1.76311	−	1.40603i	−0.100955	−	0.0805091i
$306$	2.16463	+	4.52657i	0.123743	+	0.258767i
$307$	−4.92521	+	8.53072i	−0.281097	+	0.486874i	−0.971655	−	0.236403i	$-0.924031\pi$
$307$	−4.92521	+	8.53072i	−0.281097	+	0.486874i	0.690558	+	0.723277i	$0.257365\pi$
$308$	5.77364	+	10.0002i	0.328984	+	0.569816i
$309$	5.70944	+	14.6062i	0.324798	+	0.830917i
$310$	1.32977	−	3.38819i	0.0755257	−	0.192436i
$311$	−1.62374	+	5.26404i	−0.0920740	+	0.298496i	−0.989882	−	0.141890i	$-0.954682\pi$
$311$	−1.62374	+	5.26404i	−0.0920740	+	0.298496i	0.897809	+	0.440386i	$0.145158\pi$
$312$	20.6041	+	6.38645i	1.16648	+	0.361561i
$313$	−3.15955	−	0.236776i	−0.178588	−	0.0133834i	−0.0148643	−	0.999890i	$-0.504732\pi$
$313$	−3.15955	−	0.236776i	−0.178588	−	0.0133834i	−0.163724	+	0.986506i	$0.552351\pi$
$314$	−0.592745	−	1.92163i	−0.0334506	−	0.108444i
$315$	22.5618	+	33.2875i	1.27121	+	1.87554i
$316$	−12.6250	−	1.90291i	−0.710209	−	0.107047i
$317$	7.88762	−	1.80030i	0.443013	−	0.101115i	0.00480498	−	0.999988i	$-0.498471\pi$
$317$	7.88762	−	1.80030i	0.443013	−	0.101115i	0.438208	+	0.898874i	$0.355613\pi$
$318$	3.73366	+	0.857565i	0.209373	+	0.0480899i
$319$	−1.30125	+	0.0975150i	−0.0728559	+	0.00545979i
$320$	3.61476	+	9.21025i	0.202071	+	0.514869i
$321$	19.3554	+	20.9175i	1.08031	+	1.16750i
$322$	−19.3993	−	9.34222i	−1.08108	−	0.520621i
$323$	10.5888	+	5.09928i	0.589175	+	0.283732i
$324$	−10.3823	−	7.16218i	−0.576796	−	0.397899i
$325$	−10.1997	−	25.9885i	−0.565778	−	1.44158i
$326$	9.56042	−	0.716455i	0.529503	−	0.0396808i
$327$	−1.10252	+	4.80012i	−0.0609693	+	0.265447i
$328$	3.48405	−	0.795213i	0.192375	−	0.0439083i
$329$	14.0793	+	2.12211i	0.776216	+	0.116996i
$330$	0.0122952	−	8.97754i	0.000676830	−	0.494197i
$331$	4.57315	+	14.8258i	0.251363	+	0.814898i	0.990034	+	0.140832i	$0.0449777\pi$
$331$	4.57315	+	14.8258i	0.251363	+	0.814898i	−0.738671	+	0.674066i	$0.764546\pi$
$332$	7.35572	+	0.551235i	0.403698	+	0.0302530i
$333$	−6.01708	−	19.6983i	−0.329734	−	1.07946i
$334$	−2.75138	+	8.91975i	−0.150549	+	0.488067i
$335$	0.570941	−	1.45473i	0.0311938	−	0.0794806i
$336$	−5.02360	+	1.96368i	−0.274060	+	0.107128i
$337$	−5.65408	−	9.79315i	−0.307997	−	0.533467i	0.669927	−	0.742427i	$-0.266325\pi$
$337$	−5.65408	−	9.79315i	−0.307997	−	0.533467i	−0.977924	+	0.208960i	$0.932992\pi$
$338$	−3.63523	+	6.29640i	−0.197730	+	0.342479i
$339$	5.00680	+	0.761668i	0.271932	+	0.0413681i
$340$	7.81999	+	6.23623i	0.424098	+	0.338207i
$341$	−1.62906	−	2.38940i	−0.0882188	−	0.129393i
$342$	12.5852	−	0.908470i	0.680528	−	0.0491244i
$343$		−	10.0913i		−	0.544879i
$344$	−17.1608	+	1.81279i	−0.925250	+	0.0977391i
$345$	−22.0352	−	32.4149i	−1.18633	−	1.74516i
$346$	−2.00338	−	4.16007i	−0.107703	−	0.223647i
$347$	−12.9504	+	8.82940i	−0.695211	+	0.473987i	−0.858647	−	0.512567i	$-0.828695\pi$
$347$	−12.9504	+	8.82940i	−0.695211	+	0.473987i	0.163436	+	0.986554i	$0.447742\pi$
$348$	0.118775	−	1.55633i	0.00636699	−	0.0834282i
$349$	−1.81694	+	1.95820i	−0.0972586	+	0.104820i	−0.779805	−	0.626022i	$-0.784682\pi$
$349$	−1.81694	+	1.95820i	−0.0972586	+	0.104820i	0.682547	+	0.730842i	$0.260872\pi$
$350$	−16.0479	−	9.26529i	−0.857799	−	0.495250i
$351$	18.0953	−	16.6521i	0.965855	−	0.888825i
$352$	11.5868	+	2.64460i	0.617577	+	0.140958i
$353$	−32.8760	−	12.9029i	−1.74981	−	0.686750i	−0.999676	−	0.0254662i	$-0.991893\pi$
$353$	−32.8760	−	12.9029i	−1.74981	−	0.686750i	−0.750136	−	0.661284i	$-0.770012\pi$
$354$	3.79586	+	12.3660i	0.201748	+	0.657244i
$355$	16.5601	+	20.7657i	0.878918	+	1.10213i
$356$	−1.22696	+	16.3726i	−0.0650286	+	0.867746i
$357$	9.49517	−	11.8732i	0.502538	−	0.628395i
$358$	8.32758	+	5.67765i	0.440126	+	0.300073i
$359$	0.431893	−	2.86542i	0.0227945	−	0.151231i	−0.974538	−	0.224222i	$-0.928016\pi$
$359$	0.431893	−	2.86542i	0.0227945	−	0.151231i	0.997333	+	0.0729902i	$0.0232542\pi$
$360$	25.7616	+	3.95513i	1.35775	+	0.208454i
$361$	7.73756	−	7.17940i	0.407240	−	0.377863i
$362$	−0.0972087	−	1.29716i	−0.00510917	−	0.0681772i
$363$	9.83932	+	6.72809i	0.516430	+	0.353133i
$364$	−4.01363	−	26.6287i	−0.210371	−	1.39572i
$365$	−9.06093	+	18.8152i	−0.474271	+	0.984834i
$366$	0.135183	+	0.905295i	0.00706615	+	0.0473205i
$367$	−19.3897	+	2.92252i	−1.01213	+	0.152555i	−0.634111	−	0.773242i	$-0.718634\pi$
$367$	−19.3897	+	2.92252i	−1.01213	+	0.152555i	−0.378022	+	0.925797i	$0.623396\pi$
$368$	4.89384	−	1.92069i	0.255109	−	0.100123i
$369$	1.21149	−	3.88969i	0.0630676	−	0.202489i
$370$	11.9273	+	12.8546i	0.620073	+	0.668279i
$371$	−2.58291	−	11.3165i	−0.134098	−	0.587522i
$372$	3.11865	−	1.49660i	0.161694	−	0.0775953i
$373$	−1.79689	+	2.63556i	−0.0930395	+	0.136464i	−0.869936	−	0.493164i	$-0.835840\pi$
$373$	−1.79689	+	2.63556i	−0.0930395	+	0.136464i	0.776897	+	0.629628i	$0.216793\pi$
$374$	−3.24327	+	1.00041i	−0.167705	+	0.0517302i
$375$	−2.56466	−	4.45620i	−0.132438	−	0.230117i
$376$	7.21498	−	5.75376i	0.372084	−	0.296727i
$377$	2.90796	+	0.896986i	0.149767	+	0.0461972i
$378$	2.49900	−	16.1298i	0.128535	−	0.829630i
$379$	4.38859	−	19.2277i	0.225427	−	0.987659i	−0.727892	−	0.685692i	$-0.759500\pi$
$379$	4.38859	−	19.2277i	0.225427	−	0.987659i	0.953318	−	0.301967i	$-0.0976432\pi$
$380$	21.7833	−	12.5766i	1.11746	−	0.645165i
$381$	0.177962	+	2.41919i	0.00911725	+	0.123939i
$382$	−2.17426	−	2.01742i	−0.111245	−	0.103220i
$383$	−16.6288	+	20.8518i	−0.849690	+	1.06548i	0.147387	+	0.989079i	$0.452914\pi$
$383$	−16.6288	+	20.8518i	−0.849690	+	1.06548i	−0.997077	+	0.0763991i	$0.975658\pi$
$384$	−5.96539	+	15.1386i	−0.304420	+	0.772537i
$385$	−24.5080	+	11.8024i	−1.24904	+	0.601507i
$386$	−17.8800			−0.910068
$387$	−8.04122	+	17.9538i	−0.408758	+	0.912643i
$388$	−5.54582			−0.281546
$389$	11.7981	−	5.68166i	0.598187	−	0.288072i	−0.110185	−	0.993911i	$-0.535144\pi$
$389$	11.7981	−	5.68166i	0.598187	−	0.288072i	0.708372	+	0.705839i	$0.249430\pi$
$390$	−7.67568	+	19.4788i	−0.388673	+	0.986349i
$391$	−9.23900	+	11.5853i	−0.467236	+	0.585896i
$392$	−18.2980	−	16.9781i	−0.924190	−	0.857523i
$393$	−2.49748	−	33.9504i	−0.125981	−	1.71257i
$394$	10.6018	−	6.12097i	0.534112	−	0.308370i
$395$	6.69263	−	29.3223i	0.336743	−	1.47537i
$396$	5.82035	−	6.23848i	0.292483	−	0.313496i
$397$	2.83658	+	0.874971i	0.142364	+	0.0439135i	0.365118	−	0.930961i	$-0.381029\pi$
$397$	2.83658	+	0.874971i	0.142364	+	0.0439135i	−0.222754	+	0.974875i	$0.571505\pi$
$398$	2.88907	−	2.30396i	0.144816	−	0.115487i
$399$	−19.0707	−	33.1361i	−0.954728	−	1.65888i
$400$	4.32349	−	1.33362i	0.216175	−	0.0666810i
$401$	−3.75170	+	5.50274i	−0.187351	+	0.274794i	−0.908410	−	0.418080i	$-0.862703\pi$
$401$	−3.75170	+	5.50274i	−0.187351	+	0.274794i	0.721059	+	0.692874i	$0.243656\pi$
$402$	−0.571876	+	0.274437i	−0.0285226	+	0.0136877i
$403$	1.50073	+	6.57512i	0.0747566	+	0.327530i
$404$	5.42186	+	5.84338i	0.269748	+	0.290719i
$405$	18.6524	−	23.1283i	0.926846	−	1.14926i
$406$	1.88025	−	0.737942i	0.0933150	−	0.0366234i
$407$	13.7769	−	2.07654i	0.682896	−	0.102930i
$408$	−1.45525	−	9.74549i	−0.0720455	−	0.482474i
$409$	5.68304	−	11.8010i	0.281008	−	0.583520i	−0.711917	−	0.702264i	$-0.752173\pi$
$409$	5.68304	−	11.8010i	0.281008	−	0.583520i	0.992925	+	0.118744i	$0.0378869\pi$
$410$	0.516956	+	3.42978i	0.0255307	+	0.169385i
$411$	26.5573	+	18.1598i	1.30997	+	0.895755i
$412$	−0.948258	−	12.6536i	−0.0467173	−	0.623400i
$413$	28.7314	−	26.6588i	1.41378	−	1.31179i
$414$	−2.41422	+	15.7249i	−0.118653	+	0.772839i
$415$	−2.58982	+	17.1823i	−0.127129	+	0.843446i
$416$	−22.9004	−	15.6133i	−1.12279	−	0.765503i
$417$	−1.56060	+	1.95145i	−0.0764231	+	0.0955628i
$418$	−0.637843	+	8.51142i	−0.0311979	+	0.416307i
$419$	−14.0995	−	17.6802i	−0.688806	−	0.863736i	0.307326	−	0.951604i	$-0.400566\pi$
$419$	−14.0995	−	17.6802i	−0.688806	−	0.863736i	−0.996132	+	0.0878688i	$0.971994\pi$
$420$	−9.54803	−	31.1051i	−0.465896	−	1.51778i
$421$	26.8526	+	10.5389i	1.30872	+	0.513633i	0.914203	−	0.405257i	$-0.132818\pi$
$421$	26.8526	+	10.5389i	1.30872	+	0.513633i	0.394513	+	0.918890i	$0.370913\pi$
$422$	6.90366	+	1.57571i	0.336065	+	0.0767046i
$423$	−1.53948	−	10.4071i	−0.0748518	−	0.506010i
$424$	−6.51528	−	3.76160i	−0.316410	−	0.182679i
$425$	−8.67415	+	9.34851i	−0.420758	+	0.453470i
$426$	0.820365	−	10.7494i	0.0397468	−	0.520812i
$427$	2.29152	−	1.56233i	0.110895	−	0.0756067i
$428$	−10.0050	−	20.7755i	−0.483608	−	1.00422i
$429$	9.35176	+	13.7570i	0.451507	+	0.664192i
$430$	−0.509839	−	16.7409i	−0.0245866	−	0.807317i
$431$			8.59287i			0.413904i	0.978351	+	0.206952i	$0.0663544\pi$
$431$			8.59287i			0.413904i	−0.978351	+	0.206952i	$0.933646\pi$
$432$	2.47198	+	3.12603i	0.118933	+	0.150401i
$433$	−19.7948	−	29.0337i	−0.951279	−	1.39527i	−0.918331	−	0.395813i	$-0.870463\pi$
$433$	−19.7948	−	29.0337i	−0.951279	−	1.39527i	−0.0329480	−	0.999457i	$-0.510490\pi$
$434$	3.49980	+	2.79100i	0.167996	+	0.133972i
$435$	3.63508	+	0.552992i	0.174289	+	0.0265139i
$436$	1.99253	−	3.45116i	0.0954247	−	0.165280i
$437$	18.6322	+	32.2720i	0.891301	+	1.54378i
$438$	7.89472	−	3.08598i	0.377224	−	0.147454i
$439$	1.23587	−	3.14895i	0.0589849	−	0.150291i	−0.898343	−	0.439294i	$-0.855229\pi$
$439$	1.23587	−	3.14895i	0.0589849	−	0.150291i	0.957328	+	0.289003i	$0.0933238\pi$
$440$	−5.19664	+	16.8471i	−0.247740	+	0.803154i
$441$	−27.2149	+	8.31311i	−1.29595	+	0.395862i
$442$	7.89316	+	0.591511i	0.375440	+	0.0281353i
$443$	7.75328	+	25.1355i	0.368369	+	1.19422i	0.930225	+	0.366989i	$0.119611\pi$
$443$	7.75328	+	25.1355i	0.368369	+	1.19422i	−0.561856	+	0.827235i	$0.689912\pi$
$444$	−0.0228243	+	16.6655i	−0.00108319	+	0.790907i
$445$	−38.2449	−	5.76449i	−1.81298	−	0.273263i
$446$	11.0918	−	2.53163i	0.525212	−	0.119876i
$447$	−5.20606	+	22.6661i	−0.246238	+	1.07207i
$448$	−12.1344	+	0.909347i	−0.573296	+	0.0429626i
$449$	14.7072	+	37.4734i	0.694078	+	1.76848i	0.637977	+	0.770056i	$0.279772\pi$
$449$	14.7072	+	37.4734i	0.694078	+	1.76848i	0.0561007	+	0.998425i	$0.482133\pi$
$450$	−3.08326	+	13.3401i	−0.145346	+	0.628859i
$451$	2.48290	+	1.19570i	0.116915	+	0.0563035i
$452$	−3.69195	−	1.77795i	−0.173655	−	0.0836277i
$453$	17.3437	+	18.7435i	0.814880	+	0.880648i
$454$	−0.0601379	−	0.153229i	−0.00282241	−	0.00719138i
$455$	63.2601	−	4.74069i	2.96568	−	0.222247i
$456$	−24.1506	−	5.54703i	−1.13096	−	0.259763i
$457$	28.5372	−	6.51344i	1.33492	−	0.304686i	0.505263	−	0.862965i	$-0.331396\pi$
$457$	28.5372	−	6.51344i	1.33492	−	0.304686i	0.829653	+	0.558280i	$0.188538\pi$
$458$	16.0464	+	2.41860i	0.749797	+	0.113014i
$459$	−10.4397	−	4.14684i	−0.487281	−	0.193558i
$460$	9.34789	+	30.3051i	0.435848	+	1.41298i
$461$	−30.0459	−	2.25163i	−1.39938	−	0.104869i	−0.646441	−	0.762964i	$-0.723743\pi$
$461$	−30.0459	−	2.25163i	−1.39938	−	0.104869i	−0.752935	+	0.658095i	$0.771362\pi$
$462$	10.5461	+	3.26886i	0.490648	+	0.152081i
$463$	−8.98573	+	29.1310i	−0.417602	+	1.35383i	0.465664	+	0.884962i	$0.345816\pi$
$463$	−8.98573	+	29.1310i	−0.417602	+	1.35383i	−0.883266	+	0.468872i	$0.844661\pi$
$464$	−0.180179	+	0.459089i	−0.00836460	+	0.0213127i
$465$	2.96666	+	7.58948i	0.137576	+	0.351954i
$466$	11.5683	+	20.0369i	0.535891	+	0.928191i
$467$	−7.98700	+	13.8339i	−0.369594	+	0.640156i	−0.989502	−	0.144519i	$-0.953837\pi$
$467$	−7.98700	+	13.8339i	−0.369594	+	0.640156i	0.619908	+	0.784675i	$0.287170\pi$
$468$	−17.9506	+	8.58409i	−0.829769	+	0.396799i
$469$	1.50266	+	1.19833i	0.0693862	+	0.0553336i
$470$	5.04556	+	7.40048i	0.232734	+	0.341359i
$471$	3.89587	+	2.25640i	0.179512	+	0.103970i
$472$		−	25.4030i		−	1.16927i
$473$	−11.2180	−	7.15803i	−0.515804	−	0.329127i
$474$	−10.0960	+	6.86311i	−0.463725	+	0.315233i
$475$	13.9149	+	28.8946i	0.638460	+	1.32578i
$476$	−10.1637	+	6.92949i	−0.465853	+	0.317613i
$477$	−7.43918	+	4.26789i	−0.340617	+	0.195413i
$478$	4.63362	−	4.99386i	0.211937	−	0.228414i
$479$	8.13708	+	4.69794i	0.371793	+	0.214655i	0.674241	−	0.738511i	$-0.264471\pi$
$479$	8.13708	+	4.69794i	0.371793	+	0.214655i	−0.302449	+	0.953166i	$0.597804\pi$
$480$	−30.1521	−	14.5714i	−1.37625	−	0.665091i
$481$	−31.6775	−	7.23018i	−1.44437	−	0.329668i
$482$	−11.2319	−	4.40819i	−0.511598	−	0.200787i
$483$	46.0824	−	14.1454i	2.09682	−	0.643640i
$484$	−6.01330	−	7.54043i	−0.273332	−	0.342747i
$485$	0.976291	−	13.0277i	0.0443311	−	0.591557i
$486$	−11.9375	+	1.71577i	−0.541495	+	0.0778288i
$487$	−33.6135	−	22.9173i	−1.52317	−	1.03848i	−0.980031	−	0.198843i	$-0.936282\pi$
$487$	−33.6135	−	22.9173i	−1.52317	−	1.03848i	−0.543144	−	0.839640i	$-0.682766\pi$
$488$	0.267912	−	1.77748i	0.0121278	−	0.0804627i
$489$	−14.6206	+	15.7140i	−0.661164	+	0.710611i
$490$	17.7597	−	16.4786i	0.802303	−	0.744428i
$491$	−0.660242	−	8.81032i	−0.0297963	−	0.397604i	−0.992085	−	0.125572i	$-0.959923\pi$
$491$	−0.660242	−	8.81032i	−0.0297963	−	0.397604i	0.962288	−	0.272032i	$-0.0876957\pi$
$492$	−1.86065	+	2.72105i	−0.0838845	+	0.122675i
$493$	−0.207182	−	1.37456i	−0.00933101	−	0.0619072i
$494$	8.63654	−	17.9340i	0.388576	−	0.806887i
$495$	13.6302	+	14.7708i	0.612633	+	0.663899i
$496$	−1.08077	+	0.162900i	−0.0485282	+	0.00731444i
$497$	−30.4073	+	11.9340i	−1.36395	+	0.535312i
$498$	5.52026	−	4.38991i	0.247369	−	0.196716i
$499$	21.0602	+	22.6975i	0.942784	+	1.01608i	0.999843	+	0.0177091i	$0.00563728\pi$
$499$	21.0602	+	22.6975i	0.942784	+	1.01608i	−0.0570588	+	0.998371i	$0.518172\pi$
$500$	0.925721	+	4.05585i	0.0413995	+	0.181383i
$501$	−9.04141	−	18.8407i	−0.403941	−	0.841738i
$502$	−8.79521	+	12.9002i	−0.392550	+	0.575765i
$503$	19.2108	−	5.92574i	0.856566	−	0.264216i	0.164791	−	0.986328i	$-0.447305\pi$
$503$	19.2108	−	5.92574i	0.856566	−	0.264216i	0.691775	+	0.722113i	$0.256829\pi$
$504$	−13.9868	+	28.8416i	−0.623024	+	1.28471i
$505$	−14.6812	+	11.7078i	−0.653303	+	0.520992i
$506$	−10.2835	−	3.17205i	−0.457158	−	0.141015i
$507$	−3.60023	−	15.8738i	−0.159892	−	0.704981i
$508$	0.436747	−	1.91352i	0.0193775	−	0.0848985i
$509$	−3.19083	+	1.84222i	−0.141431	+	0.0816551i	−0.569046	−	0.822306i	$-0.692687\pi$
$509$	−3.19083	+	1.84222i	−0.141431	+	0.0816551i	0.427615	+	0.903961i	$0.359354\pi$
$510$	9.53789	−	0.701632i	0.422345	−	0.0310688i
$511$	−18.8273	−	17.4692i	−0.832870	−	0.772790i
$512$	5.31742	−	6.66783i	0.234999	−	0.294679i
$513$	−19.2990	+	20.6287i	−0.852070	+	0.910779i
$514$	−7.81393	+	3.76299i	−0.344658	+	0.165978i
$515$	29.8916			1.31718
$516$	10.4828	−	11.9781i	0.461480	−	0.527308i
$517$	7.11639			0.312979
$518$	−19.4307	+	9.35731i	−0.853734	+	0.411137i
$519$	9.61743	+	3.78977i	0.422158	+	0.166353i
$520$	25.6354	−	32.1457i	1.12418	−	1.40968i
$521$	12.2072	+	11.3267i	0.534809	+	0.496230i	0.900708	−	0.434424i	$-0.143048\pi$
$521$	12.2072	+	11.3267i	0.534809	+	0.496230i	−0.365900	+	0.930654i	$0.619239\pi$
$522$	−0.927318	−	1.16938i	−0.0405876	−	0.0511822i
$523$	2.35915	−	1.36206i	0.103159	−	0.0595586i	−0.447533	−	0.894267i	$-0.647697\pi$
$523$	2.35915	−	1.36206i	0.103159	−	0.0595586i	0.550692	+	0.834709i	$0.314364\pi$
$524$	−6.12923	+	26.8539i	−0.267756	+	1.17312i
$525$	40.4583	−	9.17607i	1.76575	−	0.400477i
$526$	−18.1612	−	5.60198i	−0.791864	−	0.244258i
$527$	2.40859	−	1.92079i	0.104920	−	0.0836707i
$528$	−2.33650	+	1.34472i	−0.101683	+	0.0585214i
$529$	−22.9190	+	7.06957i	−0.996477	+	0.307373i
$530$	4.11329	−	6.03309i	0.178670	−	0.262061i
$531$	−25.0400	−	14.5485i	−1.08664	−	0.631349i
$532$	6.88362	+	30.1591i	0.298443	+	1.30756i
$533$	−4.37137	−	4.71122i	−0.189345	−	0.204066i
$534$	9.77120	+	12.2872i	0.422841	+	0.531718i
$535$	50.5651	−	19.8453i	2.18612	−	0.857988i
$536$	1.23178	−	0.185660i	0.0532046	−	0.00801931i
$537$	−22.3170	+	3.33249i	−0.963050	+	0.143808i
$538$	−1.15510	+	2.39860i	−0.0498001	+	0.103411i
$539$	−2.86891	−	19.0340i	−0.123573	−	0.819851i
$540$	−19.9193	+	13.4612i	−0.857189	+	0.579277i
$541$	−0.821353	−	10.9602i	−0.0353127	−	0.471216i	−0.986627	−	0.162994i	$-0.947885\pi$
$541$	−0.821353	−	10.9602i	−0.0353127	−	0.471216i	0.951314	−	0.308222i	$-0.0997340\pi$
$542$	−17.1089	+	15.8747i	−0.734889	+	0.681877i
$543$	2.13208	+	1.98372i	0.0914962	+	0.0851295i
$544$	−1.88697	+	12.5193i	−0.0809033	+	0.536758i
$545$	7.75635	+	5.28819i	0.332246	+	0.226521i
$546$	−20.1093	−	16.0818i	−0.860600	−	0.688236i
$547$	−3.19488	+	42.6327i	−0.136603	+	1.82284i	0.336331	+	0.941744i	$0.390814\pi$
$547$	−3.19488	+	42.6327i	−0.136603	+	1.82284i	−0.472934	+	0.881098i	$0.656805\pi$
$548$	−16.2305	−	20.3524i	−0.693331	−	0.869410i
$549$	−1.59864	−	1.28206i	−0.0682285	−	0.0547168i
$550$	−8.62147	−	3.38368i	−0.367621	−	0.144280i
$551$	−3.40812	−	0.777881i	−0.145191	−	0.0331388i
$552$	13.5943	−	28.1303i	0.578614	−	1.19731i
$553$	32.0339	+	18.4948i	1.36222	+	0.786478i
$554$	4.47707	−	4.82513i	0.190212	−	0.205000i
$555$	−39.1448	−	2.98742i	−1.66161	−	0.126809i
$556$	1.67048	−	1.13892i	0.0708443	−	0.0483008i
$557$	16.0746	+	33.3792i	0.681102	+	1.41432i	0.898823	+	0.438311i	$0.144423\pi$
$557$	16.0746	+	33.3792i	0.681102	+	1.41432i	−0.217721	+	0.976011i	$0.569862\pi$
$558$	1.21680	−	3.07556i	0.0515113	−	0.130199i
$559$	18.2544	+	25.0972i	0.772077	+	1.06150i
$560$			10.2808i			0.434444i
$561$	3.80828	−	6.57532i	0.160786	−	0.277610i
$562$	1.00413	+	1.47279i	0.0423567	+	0.0621258i
$563$	4.65441	+	3.71177i	0.196160	+	0.156432i	0.716644	−	0.697439i	$-0.245677\pi$
$563$	4.65441	+	3.71177i	0.196160	+	0.156432i	−0.520484	+	0.853871i	$0.674249\pi$
$564$	−1.28022	+	8.41549i	−0.0539070	+	0.354356i
$565$	4.82652	−	8.35977i	0.203053	−	0.351698i
$566$	−7.95646	−	13.7810i	−0.334435	−	0.579258i
$567$	20.4191	+	30.3047i	0.857523	+	1.27268i
$568$	−7.73480	+	19.7079i	−0.324545	+	0.826927i
$569$	5.39029	−	17.4749i	0.225973	−	0.732586i	−0.769594	−	0.638533i	$-0.779542\pi$
$569$	5.39029	−	17.4749i	0.225973	−	0.732586i	0.995567	−	0.0940527i	$-0.0299822\pi$
$570$	7.12047	−	22.9723i	0.298244	−	0.962202i
$571$	6.56950	+	0.492316i	0.274925	+	0.0206028i	0.211479	−	0.977383i	$-0.432172\pi$
$571$	6.56950	+	0.492316i	0.274925	+	0.0206028i	0.0634458	+	0.997985i	$0.479791\pi$
$572$	−3.96726	−	12.8616i	−0.165880	−	0.537769i
$573$	6.64029	+	0.00909424i	0.277402	+	0.000379917i
$574$	−4.21813	−	0.635781i	−0.176061	−	0.0265370i
$575$	−39.4221	+	8.99784i	−1.64402	+	0.375236i
$576$	3.26182	+	8.37840i	0.135909	+	0.349100i
$577$	29.8042	−	2.23351i	1.24076	−	0.0929824i	0.561874	−	0.827223i	$-0.310080\pi$
$577$	29.8042	−	2.23351i	1.24076	−	0.0929824i	0.678890	+	0.734240i	$0.262461\pi$
$578$	3.48409	+	8.87733i	0.144919	+	0.369248i
$579$	29.3809	−	27.1867i	1.22103	−	1.12984i
$580$	−2.68046	−	1.29084i	−0.111300	−	0.0535993i
$581$	−19.2541	−	9.27227i	−0.798793	−	0.384679i
$582$	−3.89209	+	3.60143i	−0.161332	+	0.149284i
$583$	−2.11953	−	5.40046i	−0.0877818	−	0.223664i
$584$	−16.5997	+	1.24398i	−0.686901	+	0.0514761i
$585$	−17.0048	−	43.6791i	−0.703064	−	1.80591i
$586$	0.0152392	−	0.00347825i	0.000629526	−	0.000143685i
$587$	−31.9920	−	4.82201i	−1.32045	−	0.199026i	−0.549271	−	0.835644i	$-0.685095\pi$
$587$	−31.9920	−	4.82201i	−1.32045	−	0.199026i	−0.771179	+	0.636618i	$0.780333\pi$
$588$	23.0247	+	0.0315336i	0.949524	+	0.00130043i
$589$	−2.28355	−	7.40308i	−0.0940920	−	0.305039i
$590$	24.5868	+	1.84252i	1.01222	+	0.0758555i
$591$	−8.11421	+	26.1783i	−0.333774	+	1.07683i
$592$	1.55210	−	5.03180i	0.0637911	−	0.206806i
$593$	−8.43528	+	21.4928i	−0.346396	+	0.882602i	0.646424	+	0.762979i	$0.276264\pi$
$593$	−8.43528	+	21.4928i	−0.346396	+	0.882602i	−0.992819	+	0.119623i	$0.961831\pi$
$594$	0.0335183	−	8.15791i	0.00137527	−	0.334723i
$595$	−14.4889	−	25.0954i	−0.593986	−	1.02881i
$596$	9.40867	−	16.2963i	0.385394	−	0.667522i
$597$	−1.24421	+	8.17877i	−0.0509221	+	0.334735i
$598$	19.6218	+	15.6479i	0.802397	+	0.639890i
$599$	−13.9430	−	20.4506i	−0.569695	−	0.835590i	0.427976	−	0.903790i	$-0.359227\pi$
$599$	−13.9430	−	20.4506i	−0.569695	−	0.835590i	−0.997672	+	0.0682004i	$0.978274\pi$
$600$	13.4761	−	23.2676i	0.550158	−	0.949894i
$601$			41.5210i			1.69368i	0.531850	+	0.846839i	$0.321497\pi$
$601$			41.5210i			1.69368i	−0.531850	+	0.846839i	$0.678503\pi$
$602$	19.8590	+	5.46950i	0.809391	+	0.222920i
$603$	0.522438	−	1.32050i	0.0212753	−	0.0537751i
$604$	−8.96513	−	18.6163i	−0.364786	−	0.757486i
$605$	18.7718	−	12.7984i	0.763184	−	0.520330i
$606$	7.59975	+	0.579991i	0.308719	+	0.0235605i
$607$	29.1352	−	31.4003i	1.18256	−	1.27450i	0.228959	−	0.973436i	$-0.426468\pi$
$607$	29.1352	−	31.4003i	1.18256	−	1.27450i	0.953604	−	0.301064i	$-0.0973418\pi$
$608$	27.5731	+	15.9194i	1.11824	+	0.645615i
$609$	−1.96762	+	4.07153i	−0.0797320	+	0.164987i
$610$	1.70093	+	0.388227i	0.0688687	+	0.0157188i
$611$	−15.4490	−	6.06327i	−0.624998	−	0.245294i
$612$	7.09054	+	5.68636i	0.286618	+	0.229858i
$613$	20.9365	+	26.2535i	0.845617	+	1.06037i	0.997408	+	0.0719578i	$0.0229247\pi$
$613$	20.9365	+	26.2535i	0.845617	+	1.06037i	−0.151790	+	0.988413i	$0.548504\pi$
$614$	0.569508	−	7.59955i	0.0229835	−	0.306693i
$615$	−6.06449	−	4.84987i	−0.244544	−	0.195566i
$616$	−17.9152	−	12.2143i	−0.721822	−	0.492130i
$617$	3.76947	−	25.0088i	0.151753	−	1.00682i	−0.775220	−	0.631691i	$-0.782361\pi$
$617$	3.76947	−	25.0088i	0.151753	−	1.00682i	0.926974	−	0.375126i	$-0.122401\pi$
$618$	−8.88269	−	8.26460i	−0.357314	−	0.332451i
$619$	20.6257	−	19.1378i	0.829016	−	0.769215i	−0.146484	−	0.989213i	$-0.546796\pi$
$619$	20.6257	−	19.1378i	0.829016	−	0.769215i	0.975500	+	0.219998i	$0.0706052\pi$
$620$	−0.492722	−	6.57492i	−0.0197882	−	0.264055i
$621$	−19.9428	−	29.5105i	−0.800276	−	1.18421i
$622$	−0.635206	−	4.21431i	−0.0254694	−	0.168979i
$623$	20.6385	−	42.8563i	0.826865	−	1.71700i
$624$	6.21803	−	0.928510i	0.248920	−	0.0371701i
$625$	19.4758	−	2.93550i	0.779030	−	0.117420i
$626$	2.28182	−	0.895549i	0.0911999	−	0.0357933i
$627$	−11.8936	−	14.9560i	−0.474983	−	0.597286i
$628$	−2.47774	−	2.67036i	−0.0988725	−	0.106559i
$629$	3.30269	+	14.4700i	0.131687	+	0.576957i
$630$	−26.9004	−	15.6293i	−1.07174	−	0.622688i
$631$	14.5126	−	21.2861i	0.577737	−	0.847385i	−0.420466	−	0.907308i	$-0.638133\pi$
$631$	14.5126	−	21.2861i	0.577737	−	0.847385i	0.998203	+	0.0599236i	$0.0190857\pi$
$632$	22.9090	−	7.06650i	0.911272	−	0.281090i
$633$	−13.7402	+	7.90781i	−0.546122	+	0.314307i
$634$	−4.89368	+	3.90258i	−0.194353	+	0.154991i
$635$	4.41816	+	1.36282i	0.175329	+	0.0540819i
$636$	6.76761	−	1.53492i	0.268353	−	0.0608634i
$637$	−9.98911	+	43.7651i	−0.395783	+	1.73404i
$638$	0.874291	−	0.504772i	0.0346135	−	0.0199841i
$639$	14.9966	+	18.9111i	0.593254	+	0.748112i
$640$	22.7352	+	21.0952i	0.898687	+	0.833860i
$641$	10.1238	−	12.6949i	0.399868	−	0.501418i	−0.540610	−	0.841273i	$-0.681807\pi$
$641$	10.1238	−	12.6949i	0.399868	−	0.501418i	0.940478	+	0.339855i	$0.110378\pi$
$642$	−20.5130	−	8.08322i	−0.809585	−	0.319019i
$643$	−21.9073	+	10.5500i	−0.863938	+	0.416051i	−0.812732	−	0.582637i	$-0.802021\pi$
$643$	−21.9073	+	10.5500i	−0.863938	+	0.416051i	−0.0512060	+	0.998688i	$0.516306\pi$
$644$	−39.0037			−1.53696
$645$	26.2924	+	26.7338i	1.03526	+	1.05264i
$646$	−9.09253			−0.357741
$647$	−23.8507	+	11.4859i	−0.937668	+	0.451557i	−0.839346	−	0.543597i	$-0.817062\pi$
$647$	−23.8507	+	11.4859i	−0.937668	+	0.451557i	−0.0983223	+	0.995155i	$0.531348\pi$
$648$	23.3998	+	3.65817i	0.919233	+	0.143706i
$649$	12.2138	−	15.3157i	0.479435	−	0.601193i
$650$	15.8334	+	14.6912i	0.621036	+	0.576237i
$651$	−9.99471	+	0.735236i	−0.391723	+	0.0288162i
$652$	15.0402	−	8.68345i	0.589019	−	0.340070i
$653$	9.79570	−	42.9178i	0.383335	−	1.67950i	−0.303613	−	0.952796i	$-0.598193\pi$
$653$	9.79570	−	42.9178i	0.383335	−	1.67950i	0.686948	−	0.726707i	$-0.258950\pi$
$654$	−0.842795	−	3.71598i	−0.0329559	−	0.145306i
$655$	−62.0035	−	19.1256i	−2.42268	−	0.747297i
$656$	0.814316	−	0.649395i	0.0317937	−	0.0253546i
$657$	−8.28055	+	17.0749i	−0.323055	+	0.666157i
$658$	−10.5262	+	3.24690i	−0.410354	+	0.126577i
$659$	−6.98671	+	10.2476i	−0.272163	+	0.399191i	−0.937850	−	0.347041i	$-0.887186\pi$
$659$	−6.98671	+	10.2476i	−0.272163	+	0.399191i	0.665686	+	0.746232i	$0.268139\pi$
$660$	−7.03595	−	14.6616i	−0.273874	−	0.570704i
$661$	−2.54626	−	11.1559i	−0.0990380	−	0.433914i	−1.00000		1.58961e-5i	$-0.999995\pi$
$661$	−2.54626	−	11.1559i	−0.0990380	−	0.433914i	0.900962	−	0.433898i	$-0.142862\pi$
$662$	−8.16436	−	8.79909i	−0.317317	−	0.341986i
$663$	−13.8696	+	11.0296i	−0.538652	+	0.428355i
$664$	−12.8934	+	5.06029i	−0.500361	+	0.196377i
$665$	−72.0586	+	10.8611i	−2.79431	+	0.421175i
$666$	10.8064	+	11.7107i	0.418741	+	0.453782i
$667$	1.91239	−	3.97111i	0.0740479	−	0.153762i
$668$	2.52016	+	16.7201i	0.0975078	+	0.646922i
$669$	−14.3770	+	21.0252i	−0.555846	+	0.812882i
$670$	0.0903519	+	1.20566i	0.00349060	+	0.0465788i
$671$	1.01614	−	0.942843i	0.0392278	−	0.0363981i
$672$	28.0549	−	30.1530i	1.08224	−	1.16318i
$673$	−5.01265	+	33.2567i	−0.193223	+	1.28195i	0.656339	+	0.754466i	$0.272104\pi$
$673$	−5.01265	+	33.2567i	−0.193223	+	1.28195i	−0.849563	+	0.527487i	$0.823134\pi$
$674$	7.22847	+	4.92829i	0.278430	+	0.189831i
$675$	−15.2173	−	26.6089i	−0.585712	−	1.02418i
$676$	−0.984207	+	13.1333i	−0.0378541	+	0.505128i
$677$	19.2117	+	24.0907i	0.738365	+	0.925880i	0.999220	−	0.0394981i	$-0.0125759\pi$
$677$	19.2117	+	24.0907i	0.738365	+	0.925880i	−0.260855	+	0.965378i	$0.584004\pi$
$678$	−3.74562	+	1.14976i	−0.143850	+	0.0441561i
$679$	14.9564	+	5.86997i	0.573975	+	0.225269i
$680$	−18.3105	−	4.17926i	−0.702176	−	0.160267i
$681$	0.331806	+	0.160349i	0.0127148	+	0.00614460i
$682$	1.93759	+	1.11867i	0.0741943	+	0.0428361i
$683$	22.6738	−	24.4366i	0.867590	−	0.935040i	−0.130820	−	0.991406i	$-0.541761\pi$
$683$	22.6738	−	24.4366i	0.867590	−	0.935040i	0.998410	+	0.0563661i	$0.0179514\pi$
$684$	19.8259	−	11.3742i	0.758061	−	0.434903i
$685$	50.6670	−	34.5442i	1.93589	−	1.31987i
$686$	3.38743	+	7.03407i	0.129333	+	0.268562i
$687$	−30.0453	+	20.4243i	−1.14630	+	0.779236i
$688$	−4.27701	+	2.64612i	−0.163060	+	0.100882i
$689$			13.5297i			0.515441i
$690$	26.2404	+	15.1979i	0.998955	+	0.578573i
$691$	−8.33547	−	12.2259i	−0.317096	−	0.465095i	0.634290	−	0.773095i	$-0.281293\pi$
$691$	−8.33547	−	12.2259i	−0.317096	−	0.465095i	−0.951386	+	0.308000i	$0.900340\pi$
$692$	−6.53933	−	5.21494i	−0.248588	−	0.198242i
$693$	−22.2999	+	10.6639i	−0.847104	+	0.405089i
$694$	6.06311	−	10.5016i	0.230152	−	0.398636i
$695$	2.38136	+	4.12463i	0.0903300	+	0.156456i
$696$	1.06704	+	2.72975i	0.0404459	+	0.103471i
$697$	−1.07254	+	2.73280i	−0.0406255	+	0.103512i
$698$	0.609161	−	1.97485i	0.0230571	−	0.0747492i
$699$	−49.4756	−	15.3354i	−1.87134	−	0.580039i
$700$	−33.4736	−	2.50850i	−1.26518	−	0.0948123i
$701$	7.93188	+	25.7145i	0.299583	+	0.971225i	0.972774	+	0.231756i	$0.0744470\pi$
$701$	7.93188	+	25.7145i	0.299583	+	0.971225i	−0.673191	+	0.739469i	$0.735077\pi$
$702$	−7.02342	+	17.6814i	−0.265082	+	0.667342i
$703$	36.9078	+	5.56295i	1.39200	+	0.209811i
$704$	−5.92936	+	1.35334i	−0.223471	+	0.0510059i
$705$	−19.5435	−	4.48884i	−0.736050	−	0.169060i
$706$	27.2471	−	2.04189i	1.02546	−	0.0768476i
$707$	−8.43721	−	21.4977i	−0.317314	−	0.808503i
$708$	15.9143	+	17.1987i	0.598097	+	0.646368i
$709$	−26.9022	−	12.9554i	−1.01033	−	0.486550i	−0.145900	−	0.989299i	$-0.546608\pi$
$709$	−26.9022	−	12.9554i	−1.01033	−	0.486550i	−0.864433	+	0.502749i	$0.832322\pi$
$710$	−18.5137	−	8.91571i	−0.694805	−	0.334600i
$711$	6.15461	−	26.6287i	0.230816	−	0.998654i
$712$	−11.2633	−	28.6985i	−0.422112	−	1.07552i
$713$	9.74076	−	0.729969i	0.364794	−	0.0273376i
$714$	−2.63297	+	11.4634i	−0.0985365	+	0.429008i
$715$	30.9115	−	7.05535i	1.15602	−	0.263855i
$716$	18.0536	+	2.72115i	0.674696	+	0.101694i
$717$	−0.0208878	+	15.2515i	−0.000780068	+	0.569578i
$718$	0.660812	+	2.14230i	0.0246613	+	0.0799499i
$719$	−22.7332	−	1.70362i	−0.847805	−	0.0635342i	−0.356260	−	0.934387i	$-0.615948\pi$
$719$	−22.7332	−	1.70362i	−0.847805	−	0.0635342i	−0.491544	+	0.870853i	$0.663567\pi$
$720$	7.26487	−	2.21914i	0.270746	−	0.0827025i
$721$	−10.8359	+	35.1290i	−0.403549	+	1.30827i
$722$	−2.98344	+	7.60167i	−0.111032	+	0.282905i
$723$	25.1592	−	9.83451i	0.935680	−	0.365749i
$724$	−1.17817	−	2.04065i	−0.0437864	−	0.0758403i
$725$	1.89664	−	3.28507i	0.0704394	−	0.122005i
$726$	−9.11689	−	1.38692i	−0.338359	−	0.0514735i
$727$	−9.49193	−	7.56956i	−0.352036	−	0.280739i	0.431465	−	0.902130i	$-0.357997\pi$
$727$	−9.49193	−	7.56956i	−0.352036	−	0.280739i	−0.783501	+	0.621390i	$0.786568\pi$
$728$	28.4852	+	41.7800i	1.05573	+	1.54847i
$729$	17.0071	−	20.9704i	0.629893	−	0.776682i
$730$		−	16.1566i		−	0.597981i
$731$	6.71098	−	12.4868i	0.248215	−	0.461841i
$732$	0.932158	+	1.37126i	0.0344535	+	0.0506831i
$733$	−6.13926	−	12.7483i	−0.226759	−	0.470869i	0.756285	−	0.654243i	$-0.227013\pi$
$733$	−6.13926	−	12.7483i	−0.226759	−	0.470869i	−0.983043	+	0.183374i	$0.941298\pi$
$734$	12.5344	−	8.54581i	0.462653	−	0.315432i
$735$	−4.12737	+	54.0819i	−0.152240	+	1.99484i
$736$	−27.3045	+	29.4273i	−1.00646	+	1.08470i
$737$	0.831914	+	0.480306i	0.0306439	+	0.0176923i
$738$	0.461224	+	3.11795i	0.0169779	+	0.114773i
$739$	−10.8418	−	2.47456i	−0.398821	−	0.0910283i	0.0184061	−	0.999831i	$-0.494141\pi$
$739$	−10.8418	−	2.47456i	−0.398821	−	0.0910283i	−0.417227	+	0.908802i	$0.636998\pi$
$740$	29.5695	+	11.6052i	1.08700	+	0.426615i
$741$	13.0769	+	42.6015i	0.480394	+	1.56500i
$742$	5.59909	+	7.02103i	0.205549	+	0.257750i
$743$	2.19634	−	29.3081i	0.0805758	−	1.07521i	−0.799591	−	0.600545i	$-0.794950\pi$
$743$	2.19634	−	29.3081i	0.0805758	−	1.07521i	0.880167	−	0.474665i	$-0.157431\pi$
$744$	−4.05677	+	5.07276i	−0.148728	+	0.185976i
$745$	36.6254	+	24.9707i	1.34185	+	0.914857i
$746$	0.367812	−	2.44027i	0.0134665	−	0.0893446i
$747$	−2.39615	+	15.6072i	−0.0876704	+	0.571038i
$748$	−4.50695	+	4.18184i	−0.164790	+	0.152903i
$749$	4.99239	+	66.6189i	0.182418	+	2.43420i
$750$	3.28352	+	2.24526i	0.119897	+	0.0819854i
$751$	−4.57509	−	30.3537i	−0.166947	−	1.10762i	−0.902668	−	0.430338i	$-0.858394\pi$
$751$	−4.57509	−	30.3537i	−0.166947	−	1.10762i	0.735720	−	0.677285i	$-0.236844\pi$
$752$	1.16698	−	2.42326i	0.0425553	−	0.0883671i
$753$	−5.16235	−	34.5711i	−0.188126	−	1.25984i
$754$	−2.32807	+	0.350900i	−0.0847832	+	0.0127790i
$755$	45.3098	−	17.7828i	1.64899	−	0.647182i
$756$	−8.59893	−	28.2892i	−0.312740	−	1.02887i
$757$	−35.9963	−	38.7948i	−1.30831	−	1.41002i	−0.854966	−	0.518684i	$-0.826422\pi$
$757$	−35.9963	−	38.7948i	−1.30831	−	1.41002i	−0.453342	−	0.891337i	$-0.649768\pi$
$758$	3.39527	+	14.8756i	0.123322	+	0.540308i
$759$	21.7213	−	10.4238i	0.788432	−	0.378360i
$760$	−26.6062	+	39.0241i	−0.965108	+	1.41555i
$761$	−27.1970	+	8.38917i	−0.985891	+	0.304107i	−0.745454	−	0.666557i	$-0.767767\pi$
$761$	−27.1970	+	8.38917i	−0.985891	+	0.304107i	−0.240438	+	0.970665i	$0.577291\pi$
$762$	−0.936115	−	1.62654i	−0.0339119	−	0.0589233i
$763$	−9.02648	+	7.19838i	−0.326781	+	0.260599i
$764$	−5.13416	−	1.58368i	−0.185747	−	0.0572954i
$765$	−14.6061	+	15.6554i	−0.528084	+	0.566022i
$766$	4.59146	−	20.1165i	0.165896	−	0.726839i
$767$	−39.5642	+	22.8424i	−1.42858	+	0.824791i
$768$	−1.68521	−	22.9085i	−0.0608098	−	0.826641i
$769$	−1.86836	−	1.73358i	−0.0673747	−	0.0625146i	0.645767	−	0.763535i	$-0.276538\pi$
$769$	−1.86836	−	1.73358i	−0.0673747	−	0.0625146i	−0.713141	+	0.701020i	$0.752728\pi$
$770$	13.1213	−	16.4536i	0.472858	−	0.592945i
$771$	7.11839	−	18.0646i	0.256363	−	0.650580i
$772$	−29.1814	+	14.0530i	−1.05026	+	0.505780i
$773$	42.3762			1.52417			0.762083	−	0.647480i	$-0.224177\pi$
$773$	42.3762			1.52417			0.762083	+	0.647480i	$0.224177\pi$
$774$	−0.421624	−	15.2138i	−0.0151550	−	0.546849i
$775$	8.40662			0.301975
$776$	9.38234	−	4.51829i	0.336806	−	0.162197i
$777$	17.7011	−	44.9206i	0.635023	−	1.61152i
$778$	−6.31656	+	7.92072i	−0.226460	+	0.283971i
$779$	5.41191	+	5.02152i	0.193902	+	0.179915i
$780$	2.78240	+	37.8236i	0.0996260	+	1.35430i
$781$	−14.1390	+	8.16316i	−0.505933	+	0.292101i
$782$	2.55103	−	11.1768i	0.0912247	−	0.399681i
$783$	3.30184	+	0.511555i	0.117998	+	0.0182815i
$784$	−6.95186	−	2.14436i	−0.248281	−	0.0765844i
$785$	6.70914	−	5.35036i	0.239460	−	0.190963i
$786$	13.1372	+	22.8265i	0.468590	+	0.814195i
$787$	−3.08247	+	0.950815i	−0.109878	+	0.0338929i	−0.349207	−	0.937046i	$-0.613549\pi$
$787$	−3.08247	+	0.950815i	−0.109878	+	0.0338929i	0.239329	+	0.970939i	$0.423073\pi$
$788$	12.4921	−	18.3225i	0.445012	−	0.652712i
$789$	38.3607	−	18.4089i	1.36568	−	0.655373i
$790$	5.17781	+	22.6855i	0.184218	+	0.807112i
$791$	8.07489	+	8.70266i	0.287110	+	0.309431i
$792$	−4.76415	+	15.2961i	−0.169287	+	0.543524i
$793$	−3.00926	+	1.18105i	−0.106862	+	0.0419402i
$794$	−2.27093	+	0.342287i	−0.0805922	+	0.0121473i
$795$	2.41430	+	16.1680i	0.0856263	+	0.573421i
$796$	2.90434	−	6.03092i	0.102942	−	0.213760i
$797$	2.73989	+	18.1780i	0.0970517	+	0.643896i	0.983478	+	0.181027i	$0.0579420\pi$
$797$	2.73989	+	18.1780i	0.0970517	+	0.643896i	−0.886426	+	0.462869i	$0.846820\pi$
$798$	24.4161	+	16.6957i	0.864321	+	0.591020i
$799$	0.566529	+	7.55980i	0.0200424	+	0.267447i
$800$	−25.3258	+	23.4989i	−0.895401	+	0.830811i
$801$	−34.7390	−	5.33342i	−1.22744	−	0.188447i
$802$	0.767948	−	5.09500i	0.0271172	−	0.179911i
$803$	−10.6062	−	7.23119i	−0.374285	−	0.255183i
$804$	−0.717645	+	0.897374i	−0.0253094	+	0.0316479i
$805$	6.86624	−	91.6237i	0.242003	−	3.22931i
$806$	−3.25319	−	4.07938i	−0.114589	−	0.143690i
$807$	−1.74899	−	5.69778i	−0.0615674	−	0.200571i
$808$	−13.9333	−	5.46843i	−0.490173	−	0.192379i
$809$	−19.9107	−	4.54449i	−0.700024	−	0.159776i	−0.142326	−	0.989820i	$-0.545458\pi$
$809$	−19.9107	−	4.54449i	−0.700024	−	0.159776i	−0.557698	+	0.830044i	$0.688315\pi$
$810$	−5.23785	+	22.3826i	−0.184039	+	0.786445i
$811$	−15.3464	−	8.86025i	−0.538885	−	0.311125i	0.205742	−	0.978606i	$-0.434039\pi$
$811$	−15.3464	−	8.86025i	−0.538885	−	0.311125i	−0.744627	+	0.667481i	$0.767373\pi$
$812$	2.48870	−	2.68218i	0.0873362	−	0.0941260i
$813$	3.97611	−	52.0999i	0.139448	−	1.82722i
$814$	−8.90604	+	6.07204i	−0.312157	+	0.212825i
$815$	17.7506	+	36.8596i	0.621777	+	1.29113i
$816$	−1.61451	−	2.37504i	−0.0565192	−	0.0831429i
$817$	−23.0651	−	27.1823i	−0.806947	−	0.950987i
$818$			10.1334i			0.354307i
$819$	57.4966	−	4.15043i	2.00909	−	0.145028i
$820$	3.53939	+	5.19134i	0.123601	+	0.181289i
$821$	−19.8132	−	15.8005i	−0.691484	−	0.551440i	0.213470	−	0.976950i	$-0.431523\pi$
$821$	−19.8132	−	15.8005i	−0.691484	−	0.551440i	−0.904954	+	0.425510i	$0.860095\pi$
$822$	−24.6074	−	3.74344i	−0.858280	−	0.130567i
$823$	−14.8357	+	25.6962i	−0.517141	+	0.895714i	0.482661	+	0.875807i	$0.339670\pi$
$823$	−14.8357	+	25.6962i	−0.517141	+	0.895714i	−0.999802	+	0.0199068i	$0.993663\pi$
$824$	11.9134	+	20.6346i	0.415024	+	0.718842i
$825$	19.3119	−	7.54887i	0.672355	−	0.262818i
$826$	−11.0782	+	28.2268i	−0.385460	+	0.982136i
$827$	−4.93587	+	16.0017i	−0.171637	+	0.556434i	−0.999993	−	0.00376853i	$-0.998800\pi$
$827$	−4.93587	+	16.0017i	−0.171637	+	0.556434i	0.828356	+	0.560202i	$0.189277\pi$
$828$	8.41905	+	27.5617i	0.292582	+	0.957836i
$829$	41.2398	+	3.09050i	1.43232	+	0.107337i	0.768161	−	0.640256i	$-0.221172\pi$
$829$	41.2398	+	3.09050i	1.43232	+	0.107337i	0.664156	+	0.747594i	$0.268791\pi$
$830$	−3.96251	−	12.8461i	−0.137541	−	0.445896i
$831$	−0.0201820	+	14.7362i	−0.000700107	+	0.511193i
$832$	14.0251	+	2.11394i	0.486233	+	0.0732878i
$833$	19.9916	−	4.56294i	0.692666	−	0.158097i
$834$	0.432749	−	1.88410i	0.0149849	−	0.0652411i
$835$	−39.7210	+	2.97668i	−1.37460	+	0.103012i
$836$	5.64866	+	14.3926i	0.195363	+	0.497777i
$837$	2.67693	+	6.90399i	0.0925284	+	0.238637i
$838$	15.7628	+	7.59097i	0.544517	+	0.262226i
$839$	−18.5065	−	8.91228i	−0.638916	−	0.307686i	0.0862356	−	0.996275i	$-0.472516\pi$
$839$	−18.5065	−	8.91228i	−0.638916	−	0.307686i	−0.725152	+	0.688589i	$0.758231\pi$
$840$	41.4952	+	44.8442i	1.43172	+	1.54727i
$841$	−10.4438	−	26.6104i	−0.360132	−	0.917602i
$842$	−22.2551	+	1.66779i	−0.766960	+	0.0574757i
$843$	−3.88940	−	0.893336i	−0.133958	−	0.0307681i
$844$	12.5057	−	2.85435i	0.430464	−	0.0982507i
$845$	−30.6783	−	4.62401i	−1.05537	−	0.159071i
$846$	4.56651	+	6.73742i	0.157000	+	0.231637i
$847$	8.23600	+	26.7004i	0.282992	+	0.917438i
$848$	−2.18652	−	0.163857i	−0.0750855	−	0.00562688i
$849$	34.0284	+	10.5474i	1.16785	+	0.361986i
$850$	2.90816	−	9.42803i	0.0997491	−	0.323379i
$851$	−17.1931	+	43.8073i	−0.589372	+	1.50170i
$852$	−7.10977	−	18.1886i	−0.243577	−	0.623132i
$853$	−6.71632	−	11.6330i	−0.229962	−	0.398306i	0.727834	−	0.685753i	$-0.240527\pi$
$853$	−6.71632	−	11.6330i	−0.229962	−	0.398306i	−0.957797	+	0.287447i	$0.907194\pi$
$854$	−1.07285	+	1.85823i	−0.0367121	+	0.0635872i
$855$	23.2290	+	48.5753i	0.794413	+	1.66124i
$856$	33.8525	+	26.9964i	1.15705	+	0.922719i
$857$	−23.8982	−	35.0523i	−0.816348	−	1.19736i	−0.977605	−	0.210450i	$-0.932507\pi$
$857$	−23.8982	−	35.0523i	−0.816348	−	1.19736i	0.161256	−	0.986913i	$-0.448445\pi$
$858$	−11.1365	−	6.45000i	−0.380193	−	0.220199i
$859$			32.1479i			1.09687i	0.836192	+	0.548437i	$0.184777\pi$
$859$			32.1479i			1.09687i	−0.836192	+	0.548437i	$0.815223\pi$
$860$	−13.9898	−	26.9216i	−0.477049	−	0.918019i
$861$	7.89805	−	5.36897i	0.269165	−	0.182974i
$862$	−2.88444	−	5.98959i	−0.0982443	−	0.204006i
$863$	−31.3019	+	21.3413i	−1.06553	+	0.726466i	−0.963336	−	0.268298i	$-0.913539\pi$
$863$	−31.3019	+	21.3413i	−1.06553	+	0.726466i	−0.102195	+	0.994764i	$0.532586\pi$
$864$	−27.3632	−	13.3162i	−0.930913	−	0.453025i
$865$	13.4016	−	14.4435i	0.455669	−	0.491094i
$866$	23.5438	+	13.5930i	0.800051	+	0.461910i
$867$	−19.2232	−	9.28986i	−0.652854	−	0.315500i
$868$	7.90555	+	1.80439i	0.268332	+	0.0612450i
$869$	17.2096	+	6.75428i	0.583797	+	0.229123i
$870$	−2.71943	+	0.834756i	−0.0921973	+	0.0283009i
$871$	−1.39677	−	1.75150i	−0.0473278	−	0.0593472i
$872$	−0.559197	+	7.46196i	−0.0189368	+	0.252694i
$873$	0.919588	−	11.8359i	0.0311233	−	0.400585i
$874$	−23.8204	−	16.2405i	−0.805738	−	0.549343i
$875$	1.79635	−	11.9180i	0.0607276	−	0.402901i
$876$	10.4593	−	11.2415i	0.353386	−	0.379815i
$877$	−14.2452	+	13.2176i	−0.481026	+	0.446327i	−0.883034	−	0.469309i	$-0.844503\pi$
$877$	−14.2452	+	13.2176i	−0.481026	+	0.446327i	0.402008	+	0.915636i	$0.368313\pi$
$878$	0.195578	+	2.60980i	0.00660043	+	0.0880766i
$879$	−0.0197528	+	0.0288869i	−0.000666244	+	0.000974331i
$880$	0.765841	+	5.08102i	0.0258165	+	0.171281i
$881$	−1.39836	+	2.90372i	−0.0471120	+	0.0978290i	−0.923196	−	0.384329i	$-0.874433\pi$
$881$	−1.39836	+	2.90372i	−0.0471120	+	0.0978290i	0.876084	+	0.482158i	$0.160147\pi$
$882$	16.1794	−	14.9300i	0.544788	−	0.502720i
$883$	−30.1506	+	4.54447i	−1.01465	+	0.152934i	−0.635255	−	0.772302i	$-0.719105\pi$
$883$	−30.1506	+	4.54447i	−1.01465	+	0.152934i	−0.379392	+	0.925236i	$0.623867\pi$
$884$	13.3471	−	5.23835i	0.448912	−	0.176185i
$885$	−43.2032	+	34.3567i	−1.45226	+	1.15489i
$886$	−13.8418	−	14.9179i	−0.465024	−	0.501177i
$887$	−10.5461	−	46.2054i	−0.354103	−	1.55143i	−0.767605	−	0.640923i	$-0.778552\pi$
$887$	−10.5461	−	46.2054i	−0.354103	−	1.55143i	0.413502	−	0.910503i	$-0.364305\pi$
$888$	−13.5391	−	28.2130i	−0.454342	−	0.946765i
$889$	−3.20321	+	4.69825i	−0.107432	+	0.157574i
$890$	28.5933	−	8.81988i	0.958451	−	0.295643i
$891$	12.3491	+	13.4563i	0.413710	+	0.450801i
$892$	16.1128	−	12.8496i	0.539498	−	0.430235i
$893$	18.2175	+	5.61937i	0.609627	+	0.188045i
$894$	−3.97966	−	17.5468i	−0.133100	−	0.586852i
$895$	−9.57042	+	41.9308i	−0.319904	+	1.40159i
$896$	−33.0330	+	19.0716i	−1.10355	+	0.637137i
$897$	−56.0359	+	4.12214i	−1.87098	+	0.137634i
$898$	−22.8306	−	21.1837i	−0.761866	−	0.706908i
$899$	−0.571328	+	0.716423i	−0.0190549	+	0.0238940i
$900$	5.45275	+	24.1953i	0.181758	+	0.806511i
$901$	5.56822	−	2.68151i	0.185504	−	0.0893342i
$902$	−2.13206			−0.0709898
$903$	−40.9492	+	21.2081i	−1.36270	+	0.705761i
$904$	7.69451			0.255916
$905$	5.00111	−	2.40841i	0.166243	−	0.0800582i
$906$	−18.3811	−	7.24312i	−0.610671	−	0.240637i
$907$	19.8878	−	24.9385i	0.660364	−	0.828071i	−0.333019	−	0.942920i	$-0.608067\pi$
$907$	19.8878	−	24.9385i	0.660364	−	0.828071i	0.993383	+	0.114850i	$0.0366386\pi$
$908$	−0.218581	−	0.202814i	−0.00725388	−	0.00673062i
$909$	−13.3700	+	10.6024i	−0.443455	+	0.351660i
$910$	−42.5036	+	24.5395i	−1.40898	+	0.813476i
$911$	−3.38040	+	14.8105i	−0.111998	+	0.490694i	0.887553	+	0.460706i	$0.152404\pi$
$911$	−3.38040	+	14.8105i	−0.111998	+	0.490694i	−0.999550	+	0.0299874i	$0.990453\pi$
$912$	−7.04315	+	1.59741i	−0.233222	+	0.0528955i
$913$	−10.2065	−	3.14830i	−0.337787	−	0.104193i
$914$	−17.7052	+	14.1195i	−0.585637	+	0.467030i
$915$	−3.38532	+	1.94834i	−0.111915	+	0.0644100i
$916$	28.0897	−	8.66453i	0.928110	−	0.286284i
$917$	44.9533	−	65.9343i	1.48449	−	2.17734i
$918$	8.66888	−	0.613836i	0.286116	−	0.0202596i
$919$	−3.39290	−	14.8652i	−0.111921	−	0.490359i	−0.999556	−	0.0298102i	$-0.990510\pi$
$919$	−3.39290	−	14.8652i	−0.111921	−	0.490359i	0.887634	−	0.460549i	$-0.152347\pi$
$920$	−40.5048	−	43.6538i	−1.33540	−	1.43922i
$921$	10.6194	+	13.3537i	0.349920	+	0.440020i
$922$	21.6991	−	8.51625i	0.714620	−	0.280468i
$923$	37.6494	−	5.67474i	1.23925	−	0.186786i
$924$	19.7812	−	2.95383i	0.650752	−	0.0971738i
$925$	−17.5728	+	36.4904i	−0.577791	+	1.19980i
$926$	−3.51520	−	23.3219i	−0.115517	−	0.766404i
$927$	27.1627	+	0.0744016i	0.892139	+	0.00244367i
$928$	−0.281422	−	3.75532i	−0.00923814	−	0.123274i
$929$	24.0898	−	22.3520i	0.790359	−	0.733346i	−0.177696	−	0.984086i	$-0.556864\pi$
$929$	24.0898	−	22.3520i	0.790359	−	0.733346i	0.968055	+	0.250739i	$0.0806737\pi$
$930$	−4.61551	−	4.29435i	−0.151349	−	0.140817i
$931$	7.68569	−	50.9912i	0.251888	−	1.67117i
$932$	34.6286	+	23.6094i	1.13430	+	0.773350i
$933$	7.45168	+	5.95923i	0.243957	+	0.195097i
$934$	0.923546	−	12.3239i	0.0302193	−	0.403249i
$935$	−9.03016	−	11.3235i	−0.295318	−	0.370317i
$936$	23.3750	−	29.1472i	0.764036	−	0.952706i
$937$	−14.6570	−	5.75244i	−0.478822	−	0.187924i	0.113640	−	0.993522i	$-0.463749\pi$
$937$	−14.6570	−	5.75244i	−0.478822	−	0.187924i	−0.592463	+	0.805598i	$0.701844\pi$
$938$	−1.44967	−	0.330877i	−0.0473333	−	0.0108035i
$939$	−2.38786	+	4.94112i	−0.0779248	+	0.161247i
$940$	14.0512	+	8.11248i	0.458300	+	0.264600i
$941$	−27.5104	+	29.6492i	−0.896815	+	0.966537i	−0.999603	−	0.0281667i	$-0.991033\pi$
$941$	−27.5104	+	29.6492i	−0.896815	+	0.966537i	0.102788	+	0.994703i	$0.467224\pi$
$942$	−3.47301	−	0.265050i	−0.113157	−	0.00863579i
$943$	−7.69098	+	5.24362i	−0.250453	+	0.170756i
$944$	−3.21237	−	6.67056i	−0.104554	−	0.217108i
$945$	67.9679	−	15.2197i	2.21100	−	0.495097i
$946$	10.2222	+	1.22382i	0.332353	+	0.0397897i
$947$		−	17.8882i		−	0.581287i	−0.956831	−	0.290644i	$-0.906131\pi$
$947$		−	17.8882i		−	0.581287i	0.956831	−	0.290644i	$-0.0938694\pi$
$948$	−11.0832	+	19.1362i	−0.359967	+	0.621514i
$949$	16.8639	+	24.7348i	0.547426	+	0.802926i
$950$	−19.3986	−	15.4698i	−0.629373	−	0.501908i
$951$	2.10752	−	13.8537i	0.0683410	−	0.449237i
$952$	11.5492	−	20.0038i	0.374311	−	0.648326i
$953$	−21.9140	−	37.9561i	−0.709863	−	1.22952i	−0.964908	−	0.262589i	$-0.915424\pi$
$953$	−21.9140	−	37.9561i	−0.709863	−	1.22952i	0.255045	−	0.966929i	$-0.417910\pi$
$954$	3.75279	−	5.47207i	0.121501	−	0.177165i
$955$	4.62404	−	11.7819i	0.149630	−	0.381252i
$956$	3.63741	−	11.7922i	0.117642	−	0.381387i
$957$	−0.669147	+	2.15882i	−0.0216305	+	0.0697848i
$958$	−7.24888	−	0.543228i	−0.234201	−	0.0175509i
$959$	22.2297	+	72.0671i	0.717836	+	2.32717i
$960$	17.1372	+	0.0234704i	0.553102	+	0.000757503i
$961$	28.6457	+	4.31764i	0.924053	+	0.139279i
$962$	24.5076	−	5.59369i	0.790156	−	0.180348i
$963$	45.9982	−	17.9077i	1.48227	−	0.577068i
$964$	−21.7959	+	1.63338i	−0.701998	+	0.0526075i
$965$	−27.8749	−	71.0241i	−0.897324	−	2.28635i
$966$	−27.3730	+	25.3288i	−0.880713	+	0.814941i
$967$	14.2790	+	6.87640i	0.459181	+	0.221130i	0.649151	−	0.760660i	$-0.275125\pi$
$967$	14.2790	+	6.87640i	0.459181	+	0.221130i	−0.189969	+	0.981790i	$0.560839\pi$
$968$	16.3165	+	7.85764i	0.524434	+	0.252554i
$969$	14.9411	−	13.8253i	0.479977	−	0.444131i
$970$	3.69259	+	9.40858i	0.118562	+	0.302091i
$971$	−60.3441	+	4.52216i	−1.93653	+	0.145123i	−0.986139	−	0.165924i	$-0.946939\pi$
$971$	−60.3441	+	4.52216i	−1.93653	+	0.145123i	−0.950394	+	0.311047i	$0.899320\pi$
$972$	−18.1343	+	12.1827i	−0.581657	+	0.390759i
$973$	−5.71058	+	1.30340i	−0.183073	+	0.0417852i
$974$	31.1229	+	4.69102i	0.997242	+	0.150310i
$975$	−48.3559	−	0.0662261i	−1.54863	−	0.00212093i
$976$	−0.154423	−	0.500626i	−0.00494295	−	0.0160247i
$977$	41.7114	+	3.12584i	1.33447	+	0.100004i	0.722770	−	0.691089i	$-0.242869\pi$
$977$	41.7114	+	3.12584i	1.33447	+	0.100004i	0.611696	+	0.791093i	$0.290488\pi$
$978$	4.91631	−	15.8611i	0.157206	−	0.507182i
$979$	7.00758	−	22.7180i	0.223963	−	0.726071i
$980$	16.0335	−	40.8528i	0.512172	−	1.30499i
$981$	7.03508	+	4.82471i	0.224613	+	0.154041i
$982$	3.41764	+	5.91953i	0.109061	+	0.188900i
$983$	−9.43246	+	16.3375i	−0.300849	+	0.521086i	−0.976328	−	0.216293i	$-0.930603\pi$
$983$	−9.43246	+	16.3375i	−0.300849	+	0.521086i	0.675480	+	0.737379i	$0.263937\pi$
$984$	0.930916	−	6.11935i	0.0296765	−	0.195078i
$985$	40.8423	+	32.5707i	1.30134	+	1.03779i
$986$	0.605825	+	0.888582i	0.0192934	+	0.0282982i
$987$	12.3600	−	21.3406i	0.393422	−	0.679277i
$988$		−	36.0575i		−	1.14714i
$989$	39.8844	−	20.7260i	1.26825	−	0.659048i
$990$	−14.4591	−	5.72052i	−0.459539	−	0.181810i
$991$	−13.6776	−	28.4018i	−0.434482	−	0.902212i	−0.997144	−	0.0755247i	$-0.975937\pi$
$991$	−13.6776	−	28.4018i	−0.434482	−	0.902212i	0.562662	−	0.826687i	$-0.309777\pi$
$992$	6.89565	−	4.70138i	0.218937	−	0.149269i
$993$	26.7950	+	2.04491i	0.850312	+	0.0648933i
$994$	17.1892	−	18.5255i	0.545208	−	0.587594i
$995$	13.6560	+	7.88428i	0.432923	+	0.249948i
$996$	5.55915	−	11.5034i	0.176148	−	0.364498i
$997$	21.5125	+	4.91008i	0.681307	+	0.155504i	0.549148	−	0.835725i	$-0.314952\pi$
$997$	21.5125	+	4.91008i	0.681307	+	0.155504i	0.132158	+	0.991229i	$0.457809\pi$
$998$	−22.2989	−	8.75167i	−0.705859	−	0.277029i
$999$	−35.5637	−	2.81212i	−1.12519	−	0.0889714i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	129.2.n.b.98.5	✓	144
3.2	odd	2	inner	129.2.n.b.98.8	yes	144
43.18	odd	42	inner	129.2.n.b.104.8	yes	144
129.104	even	42	inner	129.2.n.b.104.5	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
129.2.n.b.98.5	✓	144	1.1	even	1	trivial
129.2.n.b.98.8	yes	144	3.2	odd	2	inner
129.2.n.b.104.5	yes	144	129.104	even	42	inner
129.2.n.b.104.8	yes	144	43.18	odd	42	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 129 = 3 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	129.n (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.697042 + 0.335678i) q^{2} +(0.634997 - 1.61145i) q^{3} +(-0.873791 + 1.09570i) q^{4} +(-2.42009 - 2.24551i) q^{5} +(0.0983093 + 1.33640i) q^{6} +(3.51626 - 2.03011i) q^{7} +(0.585578 - 2.56558i) q^{8} +(-2.19356 - 2.04653i) q^{9} +O(q^{10})\)	\(q+(-0.697042 + 0.335678i) q^{2} +(0.634997 - 1.61145i) q^{3} +(-0.873791 + 1.09570i) q^{4} +(-2.42009 - 2.24551i) q^{5} +(0.0983093 + 1.33640i) q^{6} +(3.51626 - 2.03011i) q^{7} +(0.585578 - 2.56558i) q^{8} +(-2.19356 - 2.04653i) q^{9} +(2.44067 + 0.752848i) q^{10} +(1.58659 - 1.26526i) q^{11} +(1.21081 + 2.10384i) q^{12} +(-4.52234 + 1.39496i) q^{13} +(-1.76952 + 2.59540i) q^{14} +(-5.15529 + 2.47396i) q^{15} +(-0.170668 - 0.747745i) q^{16} +(1.47041 + 1.58472i) q^{17} +(2.21598 + 0.690192i) q^{18} +(5.06067 - 1.98617i) q^{19} +(4.57506 - 0.689579i) q^{20} +(-1.03862 - 6.95539i) q^{21} +(-0.681199 + 1.41452i) q^{22} +(1.02161 + 6.77797i) q^{23} +(-3.76248 - 2.57277i) q^{24} +(0.440844 + 5.88266i) q^{25} +(2.68401 - 2.49040i) q^{26} +(-4.69080 + 2.23527i) q^{27} +(-0.848082 + 5.62665i) q^{28} +(-0.531288 - 0.362226i) q^{29} +(2.76300 - 3.45497i) q^{30} +(0.106494 - 1.42107i) q^{31} +(3.65147 + 4.57880i) q^{32} +(-1.03143 - 3.36015i) q^{33} +(-1.55689 - 0.611035i) q^{34} +(-13.0683 - 2.98275i) q^{35} +(4.15910 - 0.615237i) q^{36} +(5.94578 + 3.43280i) q^{37} +(-2.86079 + 3.08320i) q^{38} +(-0.623765 + 8.17334i) q^{39} +(-7.17820 + 4.89402i) q^{40} +(0.589213 + 1.22351i) q^{41} +(3.05873 + 4.49956i) q^{42} +(-2.12269 - 6.20437i) q^{43} +2.84400i q^{44} +(0.713083 + 9.87846i) q^{45} +(-2.98732 - 4.38160i) q^{46} +(2.74171 + 2.18644i) q^{47} +(-1.31333 - 0.199792i) q^{48} +(4.74270 - 8.21460i) q^{49} +(-2.28197 - 3.95248i) q^{50} +(3.48741 - 1.36320i) q^{51} +(2.42313 - 6.17403i) q^{52} +(0.842656 - 2.73182i) q^{53} +(2.51935 - 3.13267i) q^{54} +(-6.68085 - 0.500661i) q^{55} +(-3.14938 - 10.2100i) q^{56} +(0.0128961 - 9.41624i) q^{57} +(0.491922 + 0.0741452i) q^{58} +(9.41118 - 2.14804i) q^{59} +(1.79392 - 7.81037i) q^{60} +(0.681166 - 0.0510463i) q^{61} +(0.402790 + 1.02629i) q^{62} +(-11.8678 - 2.74297i) q^{63} +(-2.70019 - 1.30034i) q^{64} +(14.0769 + 6.77906i) q^{65} +(1.84688 + 1.99594i) q^{66} +(0.172940 + 0.440643i) q^{67} +(-3.02121 + 0.226408i) q^{68} +(11.5711 + 2.65770i) q^{69} +(10.1104 - 2.30763i) q^{70} +(-7.95534 - 1.19907i) q^{71} +(-6.53505 + 4.42935i) q^{72} +(-1.86451 - 6.04459i) q^{73} +(-5.29678 - 0.396939i) q^{74} +(9.75956 + 3.02507i) q^{75} +(-2.24573 + 7.28047i) q^{76} +(3.01023 - 7.66994i) q^{77} +(-2.30882 - 5.90654i) q^{78} +(4.55511 + 7.88969i) q^{79} +(-1.26604 + 2.19285i) q^{80} +(0.623395 + 8.97838i) q^{81} +(-0.821412 - 0.655054i) q^{82} +(-2.96496 - 4.34879i) q^{83} +(8.52856 + 4.93955i) q^{84} -7.13698i q^{85} +(3.56227 + 3.61217i) q^{86} +(-0.921077 + 0.626133i) q^{87} +(-2.31707 - 4.81144i) q^{88} +(9.67968 - 6.59949i) q^{89} +(-3.81303 - 6.64633i) q^{90} +(-13.0698 + 14.0859i) q^{91} +(-8.31930 - 4.80315i) q^{92} +(-2.22236 - 1.07399i) q^{93} +(-2.64503 - 0.603710i) q^{94} +(-16.7072 - 6.55711i) q^{95} +(9.69719 - 2.97665i) q^{96} +(2.46727 + 3.09386i) q^{97} +(-0.548404 + 7.31795i) q^{98} +(-6.06968 - 0.471582i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 14 q^{3} - 48 q^{4} - 4 q^{6} - 42 q^{7}+O(q^{10}) \) 144 * q - 14 * q^3 - 48 * q^4 - 4 * q^6 - 42 * q^7	\( 144 q - 14 q^{3} - 48 q^{4} - 4 q^{6} - 42 q^{7} - 26 q^{10} - 4 q^{12} - 48 q^{13} - 19 q^{15} - 8 q^{16} + 16 q^{18} - 10 q^{19} - 15 q^{21} + 14 q^{22} - 11 q^{24} - 16 q^{25} - 14 q^{27} - 42 q^{28} - 6 q^{30} - 36 q^{31} + 7 q^{33} + 80 q^{34} + 48 q^{36} - 6 q^{37} + 7 q^{39} + 118 q^{40} + 46 q^{43} + 78 q^{46} - 41 q^{48} - 54 q^{49} + 7 q^{51} - 4 q^{52} - 52 q^{54} - 22 q^{55} - 110 q^{57} + 18 q^{58} - 9 q^{60} - 58 q^{61} - 82 q^{63} + 72 q^{64} - 127 q^{66} + 10 q^{67} - 15 q^{69} - 196 q^{70} + 179 q^{72} + 42 q^{73} + 119 q^{75} + 4 q^{76} + 62 q^{78} - 30 q^{79} + 200 q^{81} - 28 q^{82} + 111 q^{84} - 18 q^{87} - 14 q^{88} + 131 q^{90} - 38 q^{91} + 156 q^{93} + 28 q^{94} + 304 q^{96} + 72 q^{97} + 121 q^{99}+O(q^{100}) \) 144 * q - 14 * q^3 - 48 * q^4 - 4 * q^6 - 42 * q^7 - 26 * q^10 - 4 * q^12 - 48 * q^13 - 19 * q^15 - 8 * q^16 + 16 * q^18 - 10 * q^19 - 15 * q^21 + 14 * q^22 - 11 * q^24 - 16 * q^25 - 14 * q^27 - 42 * q^28 - 6 * q^30 - 36 * q^31 + 7 * q^33 + 80 * q^34 + 48 * q^36 - 6 * q^37 + 7 * q^39 + 118 * q^40 + 46 * q^43 + 78 * q^46 - 41 * q^48 - 54 * q^49 + 7 * q^51 - 4 * q^52 - 52 * q^54 - 22 * q^55 - 110 * q^57 + 18 * q^58 - 9 * q^60 - 58 * q^61 - 82 * q^63 + 72 * q^64 - 127 * q^66 + 10 * q^67 - 15 * q^69 - 196 * q^70 + 179 * q^72 + 42 * q^73 + 119 * q^75 + 4 * q^76 + 62 * q^78 - 30 * q^79 + 200 * q^81 - 28 * q^82 + 111 * q^84 - 18 * q^87 - 14 * q^88 + 131 * q^90 - 38 * q^91 + 156 * q^93 + 28 * q^94 + 304 * q^96 + 72 * q^97 + 121 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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