LMFDB - Embedded newform 403.2.bs.a.4.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(4,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([5, 18]))

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

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

chi := DirichletCharacter("403.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.bs (of order $30$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$36$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			4.14
Character	$\chi$	$=$	403.4
Dual form			403.2.bs.a.101.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.129772 + 0.610527i) q^{2} +(-0.324888 - 0.360825i) q^{3} +(1.47119 + 0.655015i) q^{4} -0.658726i q^{5} +(0.262455 - 0.151528i) q^{6} +(0.662294 - 1.48754i) q^{7} +(-1.32458 + 1.82312i) q^{8} +(0.288943 - 2.74911i) q^{9} +O(q^{10})$	\(q+(-0.129772 + 0.610527i) q^{2} +(-0.324888 - 0.360825i) q^{3} +(1.47119 + 0.655015i) q^{4} -0.658726i q^{5} +(0.262455 - 0.151528i) q^{6} +(0.662294 - 1.48754i) q^{7} +(-1.32458 + 1.82312i) q^{8} +(0.288943 - 2.74911i) q^{9} +(0.402170 + 0.0854839i) q^{10} +(5.05103 - 0.530885i) q^{11} +(-0.241626 - 0.743648i) q^{12} +(-2.95551 - 2.06518i) q^{13} +(0.822235 + 0.597389i) q^{14} +(-0.237685 + 0.214012i) q^{15} +(1.21398 + 1.34827i) q^{16} +(-0.107385 + 1.02170i) q^{17} +(1.64091 + 0.533164i) q^{18} +(0.567301 + 0.510800i) q^{19} +(0.431475 - 0.969109i) q^{20} +(-0.751913 + 0.244311i) q^{21} +(-0.331361 + 3.15269i) q^{22} +(0.219261 - 0.0976215i) q^{23} +(1.08817 - 0.114371i) q^{24} +4.56608 q^{25} +(1.64439 - 1.53642i) q^{26} +(-2.26425 + 1.64507i) q^{27} +(1.94872 - 1.75463i) q^{28} +(-2.09348 - 0.444983i) q^{29} +(-0.0998157 - 0.172886i) q^{30} +(5.43726 + 1.19842i) q^{31} +(-4.88387 + 2.81971i) q^{32} +(-1.83258 - 1.65006i) q^{33} +(-0.609840 - 0.198149i) q^{34} +(-0.979879 - 0.436270i) q^{35} +(2.22580 - 3.85520i) q^{36} +(-1.53842 - 0.888208i) q^{37} +(-0.385477 + 0.280065i) q^{38} +(0.215041 + 1.73738i) q^{39} +(1.20094 + 0.872532i) q^{40} +(-1.66059 + 7.81245i) q^{41} +(-0.0515818 - 0.490768i) q^{42} +(4.29507 - 4.77016i) q^{43} +(7.77875 + 2.52747i) q^{44} +(-1.81091 - 0.190334i) q^{45} +(0.0311467 + 0.146534i) q^{46} +(-9.11802 - 2.96263i) q^{47} +(0.0920789 - 0.876072i) q^{48} +(2.90978 + 3.23164i) q^{49} +(-0.592547 + 2.78772i) q^{50} +(0.403543 - 0.293191i) q^{51} +(-2.99538 - 4.97417i) q^{52} +(8.85394 + 6.43276i) q^{53} +(-0.710527 - 1.59587i) q^{54} +(-0.349707 - 3.32724i) q^{55} +(1.83470 + 3.17780i) q^{56} -0.370649i q^{57} +(0.543349 - 1.22038i) q^{58} +(2.58037 + 12.1397i) q^{59} +(-0.489860 + 0.159165i) q^{60} +(-7.30070 - 12.6452i) q^{61} +(-1.43727 + 3.16408i) q^{62} +(-3.89804 - 2.25053i) q^{63} +(0.0335616 + 0.103292i) q^{64} +(-1.36039 + 1.94687i) q^{65} +(1.24522 - 0.904708i) q^{66} +(-10.8793 - 6.28118i) q^{67} +(-0.827212 + 1.43277i) q^{68} +(-0.106460 - 0.0473989i) q^{69} +(0.393515 - 0.541627i) q^{70} +(-2.53248 - 0.266175i) q^{71} +(4.62923 + 4.16818i) q^{72} +(3.80354 + 5.23513i) q^{73} +(0.741918 - 0.823984i) q^{74} +(-1.48347 - 1.64756i) q^{75} +(0.500024 + 1.12307i) q^{76} +(2.55556 - 7.86520i) q^{77} +(-1.08862 - 0.0941737i) q^{78} +(-8.00324 - 5.81469i) q^{79} +(0.888137 - 0.799682i) q^{80} +(-6.78233 - 1.44163i) q^{81} +(-4.55422 - 2.02767i) q^{82} +(-13.8860 + 4.51183i) q^{83} +(-1.26623 - 0.133086i) q^{84} +(0.673020 + 0.0707372i) q^{85} +(2.35493 + 3.24129i) q^{86} +(0.519586 + 0.899950i) q^{87} +(-5.72260 + 9.91184i) q^{88} +(-13.8329 + 1.45389i) q^{89} +(0.351209 - 1.08091i) q^{90} +(-5.02945 + 3.02867i) q^{91} +0.386518 q^{92} +(-1.33408 - 2.35125i) q^{93} +(2.99202 - 5.18234i) q^{94} +(0.336477 - 0.373696i) q^{95} +(2.60413 + 0.846135i) q^{96} +(-0.893245 + 2.00626i) q^{97} +(-2.35061 + 1.35713i) q^{98} -14.0392i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 9 q^{2} - q^{3} - 39 q^{4} - 42 q^{6} - 15 q^{7} + 31 q^{9}+O(q^{10}) $ 288 * q - 9 * q^2 - q^3 - 39 * q^4 - 42 * q^6 - 15 * q^7 + 31 * q^9	$ 288 q - 9 q^{2} - q^{3} - 39 q^{4} - 42 q^{6} - 15 q^{7} + 31 q^{9} + 3 q^{10} - 18 q^{11} - 46 q^{12} - q^{13} - 32 q^{14} + 18 q^{15} + 21 q^{16} - 15 q^{17} - 15 q^{19} + 51 q^{20} - 10 q^{22} - 4 q^{23} - 51 q^{24} - 296 q^{25} - 6 q^{26} - 52 q^{27} + 21 q^{28} + q^{29} + 60 q^{30} + 138 q^{32} + 69 q^{33} - 10 q^{35} + 128 q^{36} - 18 q^{37} + 32 q^{38} - 14 q^{39} + 60 q^{40} - 15 q^{41} - 49 q^{42} - 36 q^{43} + 6 q^{45} - 69 q^{46} + 21 q^{48} - 23 q^{49} + 117 q^{50} + 8 q^{51} + 26 q^{52} - 48 q^{53} + 75 q^{54} + 46 q^{55} - 98 q^{56} - 21 q^{58} - 105 q^{59} - 74 q^{61} - 3 q^{62} - 90 q^{63} + 90 q^{64} + 89 q^{65} - 8 q^{66} + 6 q^{67} - 182 q^{68} + 29 q^{69} + 3 q^{71} - 183 q^{72} - 53 q^{74} - 38 q^{75} + 144 q^{76} - 128 q^{78} - 72 q^{79} - 72 q^{80} + 11 q^{81} - 11 q^{82} - 33 q^{84} + 72 q^{85} - 18 q^{87} - 14 q^{88} + 81 q^{89} - 34 q^{90} - 48 q^{91} + 8 q^{92} + 72 q^{93} - 6 q^{94} + 141 q^{97} + 96 q^{98}+O(q^{100}) $ 288 * q - 9 * q^2 - q^3 - 39 * q^4 - 42 * q^6 - 15 * q^7 + 31 * q^9 + 3 * q^10 - 18 * q^11 - 46 * q^12 - q^13 - 32 * q^14 + 18 * q^15 + 21 * q^16 - 15 * q^17 - 15 * q^19 + 51 * q^20 - 10 * q^22 - 4 * q^23 - 51 * q^24 - 296 * q^25 - 6 * q^26 - 52 * q^27 + 21 * q^28 + q^29 + 60 * q^30 + 138 * q^32 + 69 * q^33 - 10 * q^35 + 128 * q^36 - 18 * q^37 + 32 * q^38 - 14 * q^39 + 60 * q^40 - 15 * q^41 - 49 * q^42 - 36 * q^43 + 6 * q^45 - 69 * q^46 + 21 * q^48 - 23 * q^49 + 117 * q^50 + 8 * q^51 + 26 * q^52 - 48 * q^53 + 75 * q^54 + 46 * q^55 - 98 * q^56 - 21 * q^58 - 105 * q^59 - 74 * q^61 - 3 * q^62 - 90 * q^63 + 90 * q^64 + 89 * q^65 - 8 * q^66 + 6 * q^67 - 182 * q^68 + 29 * q^69 + 3 * q^71 - 183 * q^72 - 53 * q^74 - 38 * q^75 + 144 * q^76 - 128 * q^78 - 72 * q^79 - 72 * q^80 + 11 * q^81 - 11 * q^82 - 33 * q^84 + 72 * q^85 - 18 * q^87 - 14 * q^88 + 81 * q^89 - 34 * q^90 - 48 * q^91 + 8 * q^92 + 72 * q^93 - 6 * q^94 + 141 * q^97 + 96 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{5}\right)$

Coefficient data

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

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

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

$2$	−0.129772	+	0.610527i	−0.0917624	+	0.431708i	0.908152	+	0.418640i	$0.137493\pi$
$2$	−0.129772	+	0.610527i	−0.0917624	+	0.431708i	−0.999915	+	0.0130679i	$0.995840\pi$
$3$	−0.324888	−	0.360825i	−0.187574	−	0.208322i	0.642022	−	0.766687i	$-0.278096\pi$
$3$	−0.324888	−	0.360825i	−0.187574	−	0.208322i	−0.829596	+	0.558364i	$0.811429\pi$
$4$	1.47119	+	0.655015i	0.735594	+	0.327508i
$5$		−	0.658726i		−	0.294591i	−0.989093	−	0.147296i	$-0.952943\pi$
$5$		−	0.658726i		−	0.294591i	0.989093	−	0.147296i	$-0.0470568\pi$
$6$	0.262455	−	0.151528i	0.107147	−	0.0618612i
$7$	0.662294	−	1.48754i	0.250324	−	0.562236i	−0.744055	−	0.668118i	$-0.767100\pi$
$7$	0.662294	−	1.48754i	0.250324	−	0.562236i	0.994379	+	0.105882i	$0.0337666\pi$
$8$	−1.32458	+	1.82312i	−0.468308	+	0.644571i
$9$	0.288943	−	2.74911i	0.0963144	−	0.916370i
$10$	0.402170	+	0.0854839i	0.127177	+	0.0270324i
$11$	5.05103	−	0.530885i	1.52294	−	0.160068i	0.694235	−	0.719749i	$-0.255743\pi$
$11$	5.05103	−	0.530885i	1.52294	−	0.160068i	0.828708	+	0.559681i	$0.189076\pi$
$12$	−0.241626	−	0.743648i	−0.0697514	−	0.214673i
$13$	−2.95551	−	2.06518i	−0.819710	−	0.572778i
$13$	−2.95551	−	2.06518i	−0.819710	−	0.572778i
$14$	0.822235	+	0.597389i	0.219752	+	0.159659i
$15$	−0.237685	+	0.214012i	−0.0613700	+	0.0552578i
$16$	1.21398	+	1.34827i	0.303496	+	0.337066i
$17$	−0.107385	+	1.02170i	−0.0260447	+	0.247799i	0.973752	+	0.227613i	$0.0730922\pi$
$17$	−0.107385	+	1.02170i	−0.0260447	+	0.247799i	−0.999796	+	0.0201851i	$0.993574\pi$
$18$	1.64091	+	0.533164i	0.386766	+	0.125668i
$19$	0.567301	+	0.510800i	0.130148	+	0.117186i	0.731634	−	0.681697i	$-0.238758\pi$
$19$	0.567301	+	0.510800i	0.130148	+	0.117186i	−0.601486	+	0.798883i	$0.705425\pi$
$20$	0.431475	−	0.969109i	0.0964808	−	0.216699i
$21$	−0.751913	+	0.244311i	−0.164081	+	0.0533131i
$22$	−0.331361	+	3.15269i	−0.0706463	+	0.672155i
$23$	0.219261	−	0.0976215i	0.0457192	−	0.0203555i	−0.383750	−	0.923437i	$-0.625367\pi$
$23$	0.219261	−	0.0976215i	0.0457192	−	0.0203555i	0.429469	+	0.903082i	$0.358701\pi$
$24$	1.08817	−	0.114371i	0.222121	−	0.0233459i
$25$	4.56608			0.913216
$26$	1.64439	−	1.53642i	0.322492	−	0.301316i
$27$	−2.26425	+	1.64507i	−0.435755	+	0.316594i
$28$	1.94872	−	1.75463i	0.368273	−	0.331595i
$29$	−2.09348	−	0.444983i	−0.388750	−	0.0826313i	0.00939050	−	0.999956i	$-0.497011\pi$
$29$	−2.09348	−	0.444983i	−0.388750	−	0.0826313i	−0.398140	+	0.917325i	$0.630344\pi$
$30$	−0.0998157	−	0.172886i	−0.0182238	−	0.0315645i
$31$	5.43726	+	1.19842i	0.976561	+	0.215242i
$31$	5.43726	+	1.19842i	0.976561	+	0.215242i
$32$	−4.88387	+	2.81971i	−0.863355	+	0.498458i
$33$	−1.83258	−	1.65006i	−0.319011	−	0.287239i
$34$	−0.609840	−	0.198149i	−0.104587	−	0.0339823i
$35$	−0.979879	−	0.436270i	−0.165630	−	0.0737431i
$36$	2.22580	−	3.85520i	0.370966	−	0.642533i
$37$	−1.53842	−	0.888208i	−0.252915	−	0.146020i	0.368183	−	0.929753i	$-0.379980\pi$
$37$	−1.53842	−	0.888208i	−0.252915	−	0.146020i	−0.621098	+	0.783733i	$0.713313\pi$
$38$	−0.385477	+	0.280065i	−0.0625326	+	0.0454326i
$39$	0.215041	+	1.73738i	0.0344341	+	0.278203i
$40$	1.20094	+	0.872532i	0.189885	+	0.137959i
$41$	−1.66059	+	7.81245i	−0.259340	+	1.22010i	0.634929	+	0.772570i	$0.281029\pi$
$41$	−1.66059	+	7.81245i	−0.259340	+	1.22010i	−0.894269	+	0.447529i	$0.852304\pi$
$42$	−0.0515818	−	0.490768i	−0.00795924	−	0.0757271i
$43$	4.29507	−	4.77016i	0.654992	−	0.727442i	−0.320556	−	0.947230i	$-0.603870\pi$
$43$	4.29507	−	4.77016i	0.654992	−	0.727442i	0.975548	+	0.219787i	$0.0705364\pi$
$44$	7.77875	+	2.52747i	1.17269	+	0.381030i
$45$	−1.81091	−	0.190334i	−0.269954	−	0.0283734i
$46$	0.0311467	+	0.146534i	0.00459233	+	0.0216052i
$47$	−9.11802	−	2.96263i	−1.33000	−	0.432143i	−0.444083	−	0.895986i	$-0.646470\pi$
$47$	−9.11802	−	2.96263i	−1.33000	−	0.432143i	−0.885918	+	0.463842i	$0.846470\pi$
$48$	0.0920789	−	0.876072i	0.0132904	−	0.126450i
$49$	2.90978	+	3.23164i	0.415683	+	0.461663i
$50$	−0.592547	+	2.78772i	−0.0837989	+	0.394243i
$51$	0.403543	−	0.293191i	0.0565073	−	0.0410550i
$52$	−2.99538	−	4.97417i	−0.415385	−	0.689794i
$53$	8.85394	+	6.43276i	1.21618	+	0.883608i	0.995777	−	0.0918009i	$-0.0292623\pi$
$53$	8.85394	+	6.43276i	1.21618	+	0.883608i	0.220404	+	0.975409i	$0.429262\pi$
$54$	−0.710527	−	1.59587i	−0.0966904	−	0.217170i
$55$	−0.349707	−	3.32724i	−0.0471545	−	0.448645i
$56$	1.83470	+	3.17780i	0.245172	+	0.424651i
$57$		−	0.370649i		−	0.0490937i
$58$	0.543349	−	1.22038i	0.0713452	−	0.160244i
$59$	2.58037	+	12.1397i	0.335936	+	1.58045i	0.744435	+	0.667695i	$0.232719\pi$
$59$	2.58037	+	12.1397i	0.335936	+	1.58045i	−0.408499	+	0.912759i	$0.633948\pi$
$60$	−0.489860	+	0.159165i	−0.0632407	+	0.0205482i
$61$	−7.30070	−	12.6452i	−0.934758	−	1.61905i	−0.775064	−	0.631883i	$-0.782282\pi$
$61$	−7.30070	−	12.6452i	−0.934758	−	1.61905i	−0.159694	−	0.987167i	$-0.551051\pi$
$62$	−1.43727	+	3.16408i	−0.182533	+	0.401838i
$63$	−3.89804	−	2.25053i	−0.491107	−	0.283541i
$64$	0.0335616	+	0.103292i	0.00419520	+	0.0129115i
$65$	−1.36039	+	1.94687i	−0.168735	+	0.241479i
$66$	1.24522	−	0.904708i	0.153276	−	0.111362i
$67$	−10.8793	−	6.28118i	−1.32912	−	0.767368i	−0.343957	−	0.938985i	$-0.611767\pi$
$67$	−10.8793	−	6.28118i	−1.32912	−	0.767368i	−0.985164	+	0.171617i	$0.945101\pi$
$68$	−0.827212	+	1.43277i	−0.100314	+	0.173749i
$69$	−0.106460	−	0.0473989i	−0.0128162	−	0.00570616i
$70$	0.393515	−	0.541627i	0.0470341	−	0.0647369i
$71$	−2.53248	−	0.266175i	−0.300550	−	0.0315891i	−0.0469469	−	0.998897i	$-0.514949\pi$
$71$	−2.53248	−	0.266175i	−0.300550	−	0.0315891i	−0.253603	+	0.967308i	$0.581616\pi$
$72$	4.62923	+	4.16818i	0.545560	+	0.491225i
$73$	3.80354	+	5.23513i	0.445171	+	0.612726i	0.971351	−	0.237647i	$-0.0763763\pi$
$73$	3.80354	+	5.23513i	0.445171	+	0.612726i	−0.526180	+	0.850373i	$0.676376\pi$
$74$	0.741918	−	0.823984i	0.0862462	−	0.0957862i
$75$	−1.48347	−	1.64756i	−0.171296	−	0.190243i
$76$	0.500024	+	1.12307i	0.0573567	+	0.128825i
$77$	2.55556	−	7.86520i	0.291233	−	0.896322i
$78$	−1.08862	−	0.0941737i	−0.123262	−	0.0106631i
$79$	−8.00324	−	5.81469i	−0.900435	−	0.654204i	0.0381430	−	0.999272i	$-0.487856\pi$
$79$	−8.00324	−	5.81469i	−0.900435	−	0.654204i	−0.938578	+	0.345068i	$0.887856\pi$
$80$	0.888137	−	0.799682i	0.0992968	−	0.0894072i
$81$	−6.78233	−	1.44163i	−0.753592	−	0.160181i
$82$	−4.55422	−	2.02767i	−0.502929	−	0.223918i
$83$	−13.8860	+	4.51183i	−1.52418	+	0.495237i	−0.946961	−	0.321350i	$-0.895864\pi$
$83$	−13.8860	+	4.51183i	−1.52418	+	0.495237i	−0.577223	+	0.816587i	$0.695864\pi$
$84$	−1.26623	−	0.133086i	−0.138157	−	0.0145209i
$85$	0.673020	+	0.0707372i	0.0729992	+	0.00767253i
$86$	2.35493	+	3.24129i	0.253939	+	0.349517i
$87$	0.519586	+	0.899950i	0.0557055	+	0.0964848i
$88$	−5.72260	+	9.91184i	−0.610031	+	1.05661i
$89$	−13.8329	+	1.45389i	−1.46628	+	0.154112i	−0.803771	−	0.594939i	$-0.797176\pi$
$89$	−13.8329	+	1.45389i	−1.46628	+	0.154112i	−0.662512	+	0.749052i	$0.730509\pi$
$90$	0.351209	−	1.08091i	0.0370207	−	0.113938i
$91$	−5.02945	+	3.02867i	−0.527230	+	0.317491i
$92$	0.386518			0.0402973
$93$	−1.33408	−	2.35125i	−0.138338	−	0.243813i
$94$	2.99202	−	5.18234i	0.308604	−	0.534517i
$95$	0.336477	−	0.373696i	0.0345218	−	0.0383404i
$96$	2.60413	+	0.846135i	0.265783	+	0.0863582i
$97$	−0.893245	+	2.00626i	−0.0906953	+	0.203705i	−0.953198	−	0.302348i	$-0.902229\pi$
$97$	−0.893245	+	2.00626i	−0.0906953	+	0.203705i	0.862502	+	0.506053i	$0.168896\pi$
$98$	−2.35061	+	1.35713i	−0.237448	+	0.137090i
$99$		−	14.0392i		−	1.41100i
$100$	6.71756	+	2.99085i	0.671756	+	0.299085i
$101$	−0.631089	+	0.280979i	−0.0627957	+	0.0279585i	−0.437894	−	0.899027i	$-0.644276\pi$
$101$	−0.631089	+	0.280979i	−0.0627957	+	0.0279585i	0.375098	+	0.926985i	$0.377609\pi$
$102$	0.126633	+	0.284422i	0.0125385	+	0.0281620i
$103$	−1.28737	−	3.96212i	−0.126848	−	0.390399i	0.867385	−	0.497638i	$-0.165799\pi$
$103$	−1.28737	−	3.96212i	−0.126848	−	0.390399i	−0.994233	+	0.107239i	$0.965799\pi$
$104$	7.67987	−	2.65276i	0.753073	−	0.260125i
$105$	0.160934	+	0.495304i	0.0157056	+	0.0483367i
$106$	−5.07637	+	4.57078i	−0.493060	+	0.443953i
$107$	−5.92767	+	2.63917i	−0.573049	+	0.255138i	−0.672738	−	0.739881i	$-0.734882\pi$
$107$	−5.92767	+	2.63917i	−0.573049	+	0.255138i	0.0996889	+	0.995019i	$0.468215\pi$
$108$	−4.40868	+	0.937094i	−0.424226	+	0.0901719i
$109$	5.98724	+	1.94537i	0.573473	+	0.186333i	0.581375	−	0.813636i	$-0.302515\pi$
$109$	5.98724	+	1.94537i	0.573473	+	0.186333i	−0.00790121	+	0.999969i	$0.502515\pi$
$110$	2.07676	+	0.218276i	0.198011	+	0.0208118i
$111$	0.179327	+	0.843669i	0.0170210	+	0.0800775i
$112$	2.80961	−	0.912898i	0.265483	−	0.0862607i
$113$	6.29778	+	2.80395i	0.592445	+	0.263774i	0.680983	−	0.732299i	$-0.261553\pi$
$113$	6.29778	+	2.80395i	0.592445	+	0.263774i	−0.0885377	+	0.996073i	$0.528219\pi$
$114$	0.226291	+	0.0480997i	0.0211941	+	0.00450495i
$115$	−0.0643058	−	0.144433i	−0.00599654	−	0.0134685i
$116$	−2.78843	−	2.02591i	−0.258899	−	0.188101i
$117$	−6.53139	+	7.52829i	−0.603827	+	0.695991i
$118$	−7.74647			−0.713121
$119$	1.44870	+	0.836405i	0.132802	+	0.0766731i
$120$	−0.0753391	−	0.716804i	−0.00687749	−	0.0654349i
$121$	14.4714	−	3.07600i	1.31559	−	0.279636i
$122$	8.66765	−	2.81629i	0.784732	−	0.254975i
$123$	3.35843	−	1.93899i	0.302820	−	0.174833i
$124$	7.21425	+	5.32458i	0.647859	+	0.478162i
$125$		−	6.30142i		−	0.563616i
$126$	1.87987	−	2.08780i	0.167472	−	0.185996i
$127$	−8.61680	−	9.56993i	−0.764618	−	0.849194i	0.227594	−	0.973756i	$-0.426914\pi$
$127$	−8.61680	−	9.56993i	−0.764618	−	0.849194i	−0.992212	+	0.124562i	$0.960247\pi$
$128$	−11.2845	+	1.18604i	−0.997414	+	0.104832i
$129$	−3.11661			−0.274402
$130$	−1.01208	−	1.08320i	−0.0887650	−	0.0950031i
$131$	8.82497	−	6.41171i	0.771041	−	0.560194i	−0.131236	−	0.991351i	$-0.541895\pi$
$131$	8.82497	−	6.41171i	0.771041	−	0.560194i	0.902277	+	0.431157i	$0.141895\pi$
$132$	−1.61525	−	3.62792i	−0.140590	−	0.315770i
$133$	1.13555	−	0.505581i	0.0984650	−	0.0438394i
$134$	5.24666	−	5.82700i	0.453242	−	0.503377i
$135$	1.08365	+	1.49152i	0.0932659	+	0.128369i
$136$	−1.72044	−	1.54909i	−0.147527	−	0.132834i
$137$	3.34135	+	15.7198i	0.285471	+	1.34303i	0.853958	+	0.520342i	$0.174196\pi$
$137$	3.34135	+	15.7198i	0.285471	+	1.34303i	−0.568487	+	0.822692i	$0.692471\pi$
$138$	0.0427538	−	0.0588456i	0.00363944	−	0.00500927i
$139$	−11.6033	+	2.46636i	−0.984179	+	0.209194i	−0.671775	−	0.740755i	$-0.734468\pi$
$139$	−11.6033	+	2.46636i	−0.984179	+	0.209194i	−0.312404	+	0.949949i	$0.601134\pi$
$140$	−1.15582	−	1.28367i	−0.0976848	−	0.108490i
$141$	1.89335	+	4.25253i	0.159449	+	0.358128i
$142$	0.491151	−	1.51161i	0.0412165	−	0.126851i
$143$	−16.0247	−	8.86226i	−1.34006	−	0.741100i
$144$	4.05730	−	2.94780i	0.338109	−	0.245650i
$145$	−0.293122	+	1.37903i	−0.0243424	+	0.114522i
$146$	−3.68978	+	1.64280i	−0.305369	+	0.135959i
$147$	0.220703	−	2.09984i	0.0182032	−	0.173192i
$148$	−1.68152	−	2.31441i	−0.138220	−	0.190243i
$149$	−1.28858	+	0.743960i	−0.105564	+	0.0609476i	−0.551853	−	0.833942i	$-0.686079\pi$
$149$	−1.28858	+	0.743960i	−0.105564	+	0.0609476i	0.446288	+	0.894889i	$0.352746\pi$
$150$	1.19839	−	0.691891i	0.0978481	−	0.0564926i
$151$	1.27805	+	1.75909i	0.104006	+	0.143153i	0.857848	−	0.513904i	$-0.171801\pi$
$151$	1.27805	+	1.75909i	0.104006	+	0.143153i	−0.753841	+	0.657057i	$0.771801\pi$
$152$	−1.68268	+	0.357665i	−0.136484	+	0.0290105i
$153$	2.77774	+	0.590426i	0.224567	+	0.0477331i
$154$	4.47028	+	2.58092i	0.360225	+	0.207976i
$155$	0.789428	−	3.58166i	0.0634084	−	0.287686i
$156$	−0.821642	+	2.69686i	−0.0657840	+	0.215922i
$157$	4.92416	+	15.1550i	0.392991	+	1.20950i	0.930515	+	0.366253i	$0.119359\pi$
$157$	4.92416	+	15.1550i	0.392991	+	1.20950i	−0.537525	+	0.843248i	$0.680641\pi$
$158$	4.58862	−	4.13161i	0.365051	−	0.328694i
$159$	−0.555439	−	5.28465i	−0.0440492	−	0.419100i
$160$	1.85741	+	3.21713i	0.146841	+	0.254337i
$161$		−	0.390814i		−	0.0308004i
$162$	1.76031	−	3.95372i	0.138303	−	0.310633i
$163$	15.8336	+	1.66417i	1.24018	+	0.130348i	0.701813	−	0.712362i	$-0.252374\pi$
$163$	15.8336	+	1.66417i	1.24018	+	0.130348i	0.538368	+	0.842710i	$0.319041\pi$
$164$	−7.56031	+	10.4059i	−0.590361	+	0.812562i
$165$	−1.08694	+	1.20717i	−0.0846180	+	0.0939778i
$166$	−0.952588	−	9.06327i	−0.0739352	−	0.703446i
$167$	−2.49155	+	11.7218i	−0.192802	+	0.907061i	0.770249	+	0.637743i	$0.220132\pi$
$167$	−2.49155	+	11.7218i	−0.192802	+	0.907061i	−0.963051	+	0.269318i	$0.913202\pi$
$168$	0.550556	−	1.69444i	0.0424763	−	0.130729i
$169$	4.47005	+	12.2073i	0.343850	+	0.939025i
$170$	−0.130526	+	0.401717i	−0.0100109	+	0.0308103i
$171$	1.56816	−	1.41198i	0.119920	−	0.107977i
$172$	9.44338	−	4.20446i	0.720051	−	0.320587i
$173$	22.7474	−	4.83510i	1.72945	−	0.367606i	0.767546	−	0.640994i	$-0.221478\pi$
$173$	22.7474	−	4.83510i	1.72945	−	0.367606i	0.961904	+	0.273388i	$0.0881442\pi$
$174$	−0.616872	+	0.200434i	−0.0467649	+	0.0151948i
$175$	3.02409	−	6.79221i	0.228600	−	0.513443i
$176$	6.84764	+	6.16565i	0.516161	+	0.464753i
$177$	3.54197	−	4.87511i	0.266231	−	0.366436i
$178$	0.907473	−	8.63403i	0.0680179	−	0.647148i
$179$	−1.64431	−	15.6446i	−0.122902	−	1.16933i	−0.865963	−	0.500109i	$-0.833293\pi$
$179$	−1.64431	−	15.6446i	−0.122902	−	1.16933i	0.743061	−	0.669224i	$-0.233373\pi$
$180$	−2.53952	−	1.46619i	−0.189284	−	0.109283i
$181$	12.5101			0.929869			0.464934	−	0.885345i	$-0.346078\pi$
$181$	12.5101			0.929869			0.464934	+	0.885345i	$0.346078\pi$
$182$	−1.19641	−	3.46365i	−0.0886835	−	0.256743i
$183$	−2.19079	+	6.74255i	−0.161948	+	0.498423i
$184$	−0.112452	+	0.529047i	−0.00829010	+	0.0390019i
$185$	−0.585085	+	1.01340i	−0.0430163	+	0.0745064i
$186$	1.60863	−	0.509369i	0.117950	−	0.0373488i
$187$			5.21764i			0.381552i
$188$	−11.4738	−	10.3310i	−0.836810	−	0.753467i
$189$	0.947508	+	4.45767i	0.0689211	+	0.324248i
$190$	0.184486	+	0.253923i	0.0133840	+	0.0184215i
$191$	9.63881	+	16.6949i	0.697440	+	1.20800i	0.969351	+	0.245679i	$0.0790109\pi$
$191$	9.63881	+	16.6949i	0.697440	+	1.20800i	−0.271911	+	0.962322i	$0.587656\pi$
$192$	0.0263666	−	0.0456683i	0.00190284	−	0.00329582i
$193$	8.28006	−	0.870270i	0.596012	−	0.0626434i	0.198281	−	0.980145i	$-0.436464\pi$
$193$	8.28006	−	0.870270i	0.596012	−	0.0626434i	0.397731	+	0.917502i	$0.369798\pi$
$194$	−1.10896	−	0.805706i	−0.0796187	−	0.0578464i
$195$	1.14445	−	0.141653i	0.0819560	−	0.0101440i
$196$	2.16406	+	6.66030i	0.154576	+	0.475736i
$197$	−6.75441	+	0.709917i	−0.481232	+	0.0505795i	−0.342039	−	0.939686i	$-0.611117\pi$
$197$	−6.75441	+	0.709917i	−0.481232	+	0.0505795i	−0.139193	+	0.990265i	$0.544451\pi$
$198$	8.57134	+	1.82189i	0.609138	+	0.129476i
$199$	1.70296	−	0.361974i	0.120719	−	0.0256597i	−0.147156	−	0.989113i	$-0.547012\pi$
$199$	1.70296	−	0.361974i	0.120719	−	0.0256597i	0.267875	+	0.963454i	$0.413679\pi$
$200$	−6.04812	+	8.32452i	−0.427666	+	0.588632i
$201$	1.26816	+	5.96622i	0.0894490	+	0.420824i
$202$	−0.0896479	−	0.421760i	−0.00630761	−	0.0296750i
$203$	−2.04843	+	2.81942i	−0.143772	+	0.197885i
$204$	0.785732	−	0.167013i	0.0550123	−	0.0116932i
$205$	5.14626	+	1.09387i	0.359430	+	0.0763993i
$206$	2.58604	−	0.271804i	0.180178	−	0.0189375i
$207$	−0.205018	−	0.630981i	−0.0142497	−	0.0438562i
$208$	−0.803525	−	6.49191i	−0.0557144	−	0.450133i
$209$	3.13663	+	2.27889i	0.216965	+	0.157634i
$210$	−0.323281	+	0.0339782i	−0.0223085	+	0.00234472i
$211$	−12.9645	+	22.4551i	−0.892511	+	1.54588i	−0.0556568	+	0.998450i	$0.517725\pi$
$211$	−12.9645	+	22.4551i	−0.892511	+	1.54588i	−0.836855	+	0.547425i	$0.815608\pi$
$212$	8.81225	+	15.2633i	0.605228	+	1.04829i
$213$	0.726732	+	1.00026i	0.0497948	+	0.0685367i
$214$	−0.842041	−	3.96149i	−0.0575607	−	0.270802i
$215$	−3.14223	−	2.82927i	−0.214298	−	0.192955i
$216$		−	6.30702i		−	0.429138i
$217$	5.38375	−	7.29442i	0.365473	−	0.495178i
$218$	−1.96468	+	3.40292i	−0.133065	+	0.230475i
$219$	0.653239	−	3.07325i	0.0441418	−	0.207671i
$220$	1.66491	−	5.12407i	0.112248	−	0.345464i
$221$	2.42737	−	2.79787i	0.163283	−	0.188205i
$222$	−0.538355			−0.0361320
$223$	−3.13036	−	1.80731i	−0.209624	−	0.121027i	0.391512	−	0.920173i	$-0.371952\pi$
$223$	−3.13036	−	1.80731i	−0.209624	−	0.121027i	−0.601137	+	0.799146i	$0.705285\pi$
$224$	0.959856	+	9.13242i	0.0641331	+	0.610185i
$225$	1.31934	−	12.5527i	0.0879558	−	0.836844i
$226$	−2.52916	+	3.48109i	−0.168237	+	0.231559i
$227$	−5.96890	−	5.37442i	−0.396170	−	0.356713i	0.446837	−	0.894615i	$-0.352550\pi$
$227$	−5.96890	−	5.37442i	−0.396170	−	0.356713i	−0.843007	+	0.537902i	$0.819217\pi$
$228$	0.242781	−	0.545295i	0.0160786	−	0.0361130i
$229$	−23.9079	+	7.76816i	−1.57988	+	0.513335i	−0.962026	−	0.272957i	$-0.911998\pi$
$229$	−23.9079	+	7.76816i	−1.57988	+	0.513335i	−0.617855	+	0.786292i	$0.711998\pi$
$230$	0.0965254	−	0.0205171i	0.00636470	−	0.00135286i
$231$	−3.66823	+	1.63320i	−0.241352	+	0.107457i
$232$	3.58423	−	3.22726i	0.235316	−	0.211880i
$233$	−1.28779	+	3.96341i	−0.0843658	+	0.259651i	−0.984337	−	0.176299i	$-0.943588\pi$
$233$	−1.28779	+	3.96341i	−0.0843658	+	0.259651i	0.899971	+	0.435950i	$0.143588\pi$
$234$	−3.74864	−	4.96455i	−0.245056	−	0.324543i
$235$	−1.95156	+	6.00628i	−0.127306	+	0.391806i
$236$	−4.15547	+	19.5500i	−0.270498	+	1.27259i
$237$	0.502072	+	4.77690i	0.0326131	+	0.310293i
$238$	−0.698647	+	0.775927i	−0.0452866	+	0.0502958i
$239$	10.5718	−	14.5509i	0.683834	−	0.941217i	−0.316138	−	0.948713i	$-0.602386\pi$
$239$	10.5718	−	14.5509i	0.683834	−	0.941217i	0.999972	+	0.00749624i	$0.00238615\pi$
$240$	−0.577091	−	0.0606547i	−0.0372511	−	0.00391525i
$241$	3.41489	−	7.66996i	0.219972	−	0.494066i	−0.769525	−	0.638617i	$-0.779507\pi$
$241$	3.41489	−	7.66996i	0.219972	−	0.494066i	0.989497	+	0.144551i	$0.0461737\pi$
$242$			9.23439i			0.593609i
$243$	5.88147	+	10.1870i	0.377297	+	0.653497i
$244$	−2.45792	−	23.3855i	−0.157352	−	1.49710i
$245$	2.12876	−	1.91675i	0.136002	−	0.122457i
$246$	0.747978	+	2.30204i	0.0476894	+	0.146773i
$247$	−0.621767	−	2.68125i	−0.0395621	−	0.170604i
$248$	−9.38692	+	8.32539i	−0.596070	+	0.528663i
$249$	6.13937	+	3.54457i	0.389067	+	0.224628i
$250$	3.84719	+	0.817746i	0.243318	+	0.0517188i
$251$	20.5917	−	4.37690i	1.29974	−	0.276267i	0.494477	−	0.869191i	$-0.335360\pi$
$251$	20.5917	−	4.37690i	1.29974	−	0.276267i	0.805259	+	0.592924i	$0.202026\pi$
$252$	−4.26061	−	5.86423i	−0.268393	−	0.369412i
$253$	1.05567	−	0.609491i	0.0663694	−	0.0383184i
$254$	6.96092	−	4.01889i	0.436767	−	0.252167i
$255$	−0.193133	−	0.265824i	−0.0120944	−	0.0166466i
$256$	0.717584	−	6.82736i	0.0448490	−	0.426710i
$257$	−4.41611	+	1.96618i	−0.275469	+	0.122647i	−0.539822	−	0.841779i	$-0.681508\pi$
$257$	−4.41611	+	1.96618i	−0.275469	+	0.122647i	0.264352	+	0.964426i	$0.414842\pi$
$258$	0.404447	−	1.90278i	0.0251798	−	0.118462i
$259$	−2.34013	+	1.70020i	−0.145409	+	0.105645i
$260$	−3.27662	+	1.97314i	−0.203207	+	0.122369i
$261$	−1.82820	+	5.62663i	−0.113163	+	0.348280i
$262$	2.76930	+	6.21994i	0.171088	+	0.384269i
$263$	−16.6972	−	18.5442i	−1.02960	−	1.14348i	−0.989536	−	0.144285i	$-0.953912\pi$
$263$	−16.6972	−	18.5442i	−1.02960	−	1.14348i	−0.0400598	−	0.999197i	$-0.512755\pi$
$264$	5.43565	−	1.15538i	0.334541	−	0.0711089i
$265$	4.23743	−	5.83232i	0.260303	−	0.358276i
$266$	0.161308	+	0.758896i	0.00989045	+	0.0465309i
$267$	5.01874	+	4.51890i	0.307142	+	0.276552i
$268$	−11.8913	−	16.3669i	−0.726374	−	0.999769i
$269$	1.31246	−	1.45764i	0.0800222	−	0.0888737i	−0.701804	−	0.712370i	$-0.747622\pi$
$269$	1.31246	−	1.45764i	0.0800222	−	0.0888737i	0.781826	+	0.623496i	$0.214288\pi$
$270$	−1.05124	+	0.468042i	−0.0639764	+	0.0284841i
$271$	4.17446	+	9.37599i	0.253580	+	0.569551i	0.994816	−	0.101694i	$-0.0324264\pi$
$271$	4.17446	+	9.37599i	0.253580	+	0.569551i	−0.741235	+	0.671245i	$0.765760\pi$
$272$	−1.50789	+	1.09554i	−0.0914290	+	0.0664271i
$273$	2.72683	+	0.830772i	0.165035	+	0.0502806i
$274$	−10.0310			−0.605994
$275$	23.0634	−	2.42406i	1.39078	−	0.146176i
$276$	−0.125575	−	0.139465i	−0.00755874	−	0.00839484i
$277$	18.1849	−	20.1964i	1.09263	−	1.21348i	0.117211	−	0.993107i	$-0.462605\pi$
$277$	18.1849	−	20.1964i	1.09263	−	1.21348i	0.975415	−	0.220376i	$-0.0707286\pi$
$278$		−	7.40420i		−	0.444074i
$279$	4.86564	−	14.6014i	0.291298	−	0.874160i
$280$	2.09330	−	1.20857i	0.125098	−	0.0722256i
$281$	−5.38199	+	1.74872i	−0.321063	+	0.104320i	−0.465114	−	0.885251i	$-0.653987\pi$
$281$	−5.38199	+	1.74872i	−0.321063	+	0.104320i	0.144052	+	0.989570i	$0.453987\pi$
$282$	−2.84199	+	0.604084i	−0.169238	+	0.0359727i
$283$	0.0519544	+	0.494313i	0.00308837	+	0.0293838i	0.995958	−	0.0898251i	$-0.0286308\pi$
$283$	0.0519544	+	0.494313i	0.00308837	+	0.0293838i	−0.992869	+	0.119209i	$0.961964\pi$
$284$	−3.55141	−	2.05041i	−0.210737	−	0.121669i
$285$	−0.244156			−0.0144626
$286$	7.49021	−	8.63347i	0.442905	−	0.510508i
$287$	10.5215	+	7.64432i	0.621065	+	0.451230i
$288$	6.34052	+	14.2410i	0.373619	+	0.839161i
$289$	15.5962	+	3.31507i	0.917422	+	0.195004i
$290$	−0.803896	−	0.357918i	−0.0472064	−	0.0210176i
$291$	1.01411	−	0.329506i	0.0594485	−	0.0193160i
$292$	2.16664	+	10.1932i	0.126793	+	0.596514i
$293$	−14.2000	−	1.49248i	−0.829572	−	0.0871915i	−0.319783	−	0.947491i	$-0.603610\pi$
$293$	−14.2000	−	1.49248i	−0.829572	−	0.0871915i	−0.509789	+	0.860299i	$0.670277\pi$
$294$	1.25337	+	0.407245i	0.0730981	+	0.0237510i
$295$	7.99673	−	1.69976i	0.465588	−	0.0989637i
$296$	3.65706	−	1.62823i	0.212563	−	0.0946389i
$297$	−10.5634	+	9.51137i	−0.612953	+	0.551905i
$298$	−0.286987	−	0.883256i	−0.0166247	−	0.0511657i
$299$	−0.849635	−	0.164294i	−0.0491356	−	0.00950135i
$300$	−1.10328	−	3.39556i	−0.0636981	−	0.196043i
$301$	−4.25119	−	9.54832i	−0.245034	−	0.550356i
$302$	−1.23983	+	0.552006i	−0.0713440	+	0.0317644i
$303$	0.306418	+	0.136426i	0.0176033	+	0.00783747i
$304$			1.38497i			0.0794337i
$305$	−8.32970	+	4.80916i	−0.476957	+	0.275372i
$306$	−0.720942	+	1.61926i	−0.0412135	+	0.0925671i
$307$	20.8463	+	6.77338i	1.18976	+	0.386577i	0.835985	−	0.548752i	$-0.184897\pi$
$307$	20.8463	+	6.77338i	1.18976	+	0.386577i	0.353778	+	0.935329i	$0.384897\pi$
$308$	8.91153	−	9.89726i	0.507781	−	0.563948i
$309$	−1.01138	+	1.75176i	−0.0575354	+	0.0996542i
$310$	2.08426	+	0.946765i	0.118378	+	0.0537727i
$311$	4.87721			0.276561			0.138281	−	0.990393i	$-0.455842\pi$
$311$	4.87721			0.276561			0.138281	+	0.990393i	$0.455842\pi$
$312$	−3.45228	−	1.90924i	−0.195447	−	0.108089i
$313$	−3.84872	+	11.8451i	−0.217543	+	0.669527i	0.781421	+	0.624004i	$0.214495\pi$
$313$	−3.84872	+	11.8451i	−0.217543	+	0.669527i	−0.998963	+	0.0455226i	$0.985505\pi$
$314$	−9.89156	+	1.03964i	−0.558213	+	0.0586705i
$315$	−1.48248	+	2.56774i	−0.0835285	+	0.144676i
$316$	−7.96556	−	13.7967i	−0.448098	−	0.776128i
$317$	0.0986553	+	0.135787i	0.00554103	+	0.00762658i	0.811779	−	0.583965i	$-0.198500\pi$
$317$	0.0986553	+	0.135787i	0.00554103	+	0.00762658i	−0.806237	+	0.591592i	$0.798500\pi$
$318$	3.29850	+	0.346687i	0.184971	+	0.0194412i
$319$	−10.8105	−	1.13623i	−0.605270	−	0.0636164i
$320$	0.0680411	−	0.0221079i	0.00380361	−	0.00123587i
$321$	2.87811	+	1.28142i	0.160640	+	0.0715217i
$322$	0.238602	+	0.0507165i	0.0132968	+	0.00282632i
$323$	−0.582803	+	0.524759i	−0.0324280	+	0.0291983i
$324$	−9.03379	−	6.56344i	−0.501877	−	0.364635i
$325$	−13.4951	−	9.42979i	−0.748573	−	0.523070i
$326$	−3.07077	+	9.45086i	−0.170074	+	0.523435i
$327$	−1.24325	−	2.79238i	−0.0687516	−	0.154419i
$328$	−12.0435	−	13.3756i	−0.664989	−	0.738545i
$329$	−10.4458	+	11.6013i	−0.575897	+	0.639599i
$330$	−0.595954	−	0.820261i	−0.0328062	−	0.0451539i
$331$	−19.5292	−	17.5842i	−1.07342	−	0.966513i	−0.0738948	−	0.997266i	$-0.523543\pi$
$331$	−19.5292	−	17.5842i	−1.07342	−	0.966513i	−0.999527	+	0.0307527i	$0.990210\pi$
$332$	−23.3842	−	2.45778i	−1.28337	−	0.134888i
$333$	−2.88630	+	3.97265i	−0.158168	+	0.217700i
$334$	−6.83315	−	3.04232i	−0.373894	−	0.166468i
$335$	−4.13758	+	7.16649i	−0.226060	+	0.391547i
$336$	−1.24221	−	0.717188i	−0.0677679	−	0.0391258i
$337$	−13.7728	+	10.0065i	−0.750252	+	0.545090i	−0.895905	−	0.444246i	$-0.853472\pi$
$337$	−13.7728	+	10.0065i	−0.750252	+	0.545090i	0.145653	+	0.989336i	$0.453472\pi$
$338$	−8.03299	+	1.14492i	−0.436937	+	0.0622756i
$339$	−1.03434	−	3.18337i	−0.0561776	−	0.172897i
$340$	0.943805	+	0.544906i	0.0511850	+	0.0295517i
$341$	28.1000	+	3.16668i	1.52170	+	0.171485i
$342$	0.658549	+	1.14064i	0.0356103	+	0.0616788i
$343$	17.5746	−	5.71034i	0.948941	−	0.308330i
$344$	3.00743	+	14.1489i	0.162150	+	0.762856i
$345$	−0.0312229	+	0.0701278i	−0.00168098	+	0.00377555i
$346$			14.5153i			0.780350i
$347$	−11.5611	−	20.0245i	−0.620635	−	1.07497i	−0.989368	−	0.145435i	$-0.953542\pi$
$347$	−11.5611	−	20.0245i	−0.620635	−	1.07497i	0.368733	−	0.929535i	$-0.379792\pi$
$348$	0.174928	+	1.66433i	0.00937715	+	0.0892176i
$349$	−4.76853	−	10.7103i	−0.255254	−	0.573309i	0.739780	−	0.672849i	$-0.234930\pi$
$349$	−4.76853	−	10.7103i	−0.255254	−	0.573309i	−0.995034	+	0.0995397i	$0.968263\pi$
$350$	3.75439	+	2.72772i	0.200681	+	0.145803i
$351$	10.0894	−	0.185940i	0.538531	−	0.00992476i
$352$	−23.1717	+	16.8352i	−1.23505	+	0.897319i
$353$	0.391557	−	1.84213i	0.0208405	−	0.0980468i	−0.966498	−	0.256674i	$-0.917373\pi$
$353$	0.391557	−	1.84213i	0.0208405	−	0.0980468i	0.987339	+	0.158627i	$0.0507067\pi$
$354$	2.51674	+	2.79512i	0.133763	+	0.148559i
$355$	−0.175336	+	1.66821i	−0.00930588	+	0.0885395i
$356$	−21.3031	−	6.92179i	−1.12906	−	0.366854i
$357$	−0.168869	−	0.794464i	−0.00893747	−	0.0420475i
$358$	9.76484	+	1.02633i	0.516088	+	0.0542430i
$359$	15.9823	+	5.19298i	0.843515	+	0.274075i	0.698727	−	0.715388i	$-0.253750\pi$
$359$	15.9823	+	5.19298i	0.843515	+	0.274075i	0.144788	+	0.989463i	$0.453750\pi$
$360$	2.74569	−	3.04940i	0.144710	−	0.160717i
$361$	−1.92513	−	18.3164i	−0.101322	−	0.964019i
$362$	−1.62346	+	7.63776i	−0.0853269	+	0.401432i
$363$	−5.81150	−	4.22231i	−0.305025	−	0.221614i
$364$	−9.38309	+	1.16138i	−0.491808	+	0.0608726i
$365$	3.44852	−	2.50549i	0.180504	−	0.131143i
$366$	−3.83221	−	2.21253i	−0.200313	−	0.115651i
$367$	−6.41590	+	11.1127i	−0.334907	+	0.580076i	−0.983467	−	0.181088i	$-0.942038\pi$
$367$	−6.41590	+	11.1127i	−0.334907	+	0.580076i	0.648560	+	0.761164i	$0.275372\pi$
$368$	0.397799	+	0.177112i	0.0207367	+	0.00923259i
$369$	20.9975	+	6.82249i	1.09308	+	0.355165i
$370$	−0.542779	−	0.488721i	−0.0282178	−	0.0254074i
$371$	15.4329	−	8.91018i	0.801235	−	0.462593i
$372$	−0.422583	−	4.33298i	−0.0219099	−	0.224654i
$373$	3.88330	+	6.72608i	0.201070	+	0.348263i	0.948873	−	0.315657i	$-0.102225\pi$
$373$	3.88330	+	6.72608i	0.201070	+	0.348263i	−0.747804	+	0.663920i	$0.768891\pi$
$374$	−3.18551	−	0.677102i	−0.164719	−	0.0350121i
$375$	−2.27371	+	2.04726i	−0.117414	+	0.105720i
$376$	17.4787	−	12.6990i	0.901397	−	0.654903i
$377$	5.26833	+	5.63857i	0.271333	+	0.290401i
$378$	−2.84449			−0.146305
$379$	−33.4216	+	3.51275i	−1.71675	+	0.180438i	−0.911166	−	0.412040i	$-0.864817\pi$
$379$	−33.4216	+	3.51275i	−1.71675	+	0.180438i	−0.805587	+	0.592478i	$0.798150\pi$
$380$	0.739797	−	0.329379i	0.0379508	−	0.0168968i
$381$	−0.653572	+	6.21832i	−0.0334835	+	0.318574i
$382$	−11.4435	+	3.71823i	−0.585503	+	0.190241i
$383$	−1.60901	+	3.61391i	−0.0822168	+	0.184662i	−0.949976	−	0.312323i	$-0.898893\pi$
$383$	−1.60901	+	3.61391i	−0.0822168	+	0.184662i	0.867759	+	0.496985i	$0.165560\pi$
$384$	4.09414	+	3.68638i	0.208928	+	0.188120i
$385$	−5.18101	−	1.68341i	−0.264049	−	0.0857946i
$386$	−0.543193	+	5.16814i	−0.0276478	+	0.263051i
$387$	−11.8727	−	13.1859i	−0.603521	−	0.670278i
$388$	−2.62826	+	2.36650i	−0.133430	+	0.120141i
$389$	−13.2266	−	9.60969i	−0.670615	−	0.487230i	0.199616	−	0.979874i	$-0.436031\pi$
$389$	−13.2266	−	9.60969i	−0.670615	−	0.487230i	−0.870231	+	0.492644i	$0.836031\pi$
$390$	−0.0620347	+	0.717103i	−0.00314125	+	0.0363119i
$391$	0.0761944	+	0.234502i	0.00385332	+	0.0118593i
$392$	−9.74589	+	1.02433i	−0.492242	+	0.0517367i
$393$	−5.18064	−	1.10118i	−0.261329	−	0.0555471i
$394$	0.443107	−	4.21588i	0.0223234	−	0.212393i
$395$	−3.83029	+	5.27194i	−0.192723	+	0.265260i
$396$	9.19591	−	20.6544i	0.462112	−	1.03792i
$397$	−30.6658	+	17.7049i	−1.53907	+	0.888583i	−0.540177	+	0.841551i	$0.681643\pi$
$397$	−30.6658	+	17.7049i	−1.53907	+	0.888583i	−0.998893	+	0.0470317i	$0.985024\pi$
$398$			1.08668i			0.0544701i
$399$	−0.551355	−	0.245479i	−0.0276023	−	0.0122893i
$400$	5.54315	+	6.15629i	0.277157	+	0.307814i
$401$	−5.58439	+	26.2725i	−0.278871	+	1.31199i	0.586131	+	0.810217i	$0.300651\pi$
$401$	−5.58439	+	26.2725i	−0.278871	+	1.31199i	−0.865002	+	0.501769i	$0.832683\pi$
$402$	−3.80711			−0.189881
$403$	−13.5949	−	14.7709i	−0.677211	−	0.735789i
$404$	−1.11250			−0.0553488
$405$	−0.949638	+	4.46770i	−0.0471879	+	0.222002i
$406$	−1.45551	−	1.61650i	−0.0722355	−	0.0802257i
$407$	−8.24215	−	3.66964i	−0.408548	−	0.181897i
$408$			1.12406i			0.0556493i
$409$	12.8757	−	7.43378i	0.636662	−	0.367577i	−0.146666	−	0.989186i	$-0.546854\pi$
$409$	12.8757	−	7.43378i	0.636662	−	0.367577i	0.783327	+	0.621609i	$0.213521\pi$
$410$	−1.33568	+	2.99998i	−0.0659644	+	0.148158i
$411$	4.58654	−	6.31283i	0.226237	−	0.311389i
$412$	0.701283	−	6.67227i	0.0345498	−	0.328719i
$413$	19.7672	+	4.20165i	0.972681	+	0.206750i
$414$	0.411836	−	0.0432858i	0.0202407	−	0.00212738i
$415$	2.97206	+	9.14705i	0.145892	+	0.449011i
$416$	20.2575	+	1.75243i	0.993207	+	0.0859197i
$417$	4.65970	+	3.38547i	0.228187	+	0.165787i
$418$	−1.79837	+	1.61926i	−0.0879613	+	0.0792007i
$419$	−18.6181	−	20.6775i	−0.909554	−	1.01016i	−0.999898	−	0.0142514i	$-0.995463\pi$
$419$	−18.6181	−	20.6775i	−0.909554	−	1.01016i	0.0903445	−	0.995911i	$-0.471203\pi$
$420$	−0.0876674	+	0.834100i	−0.00427773	+	0.0406999i
$421$	33.5097	+	10.8880i	1.63316	+	0.530647i	0.974996	−	0.222223i	$-0.0713313\pi$
$421$	33.5097	+	10.8880i	1.63316	+	0.530647i	0.658169	+	0.752870i	$0.271331\pi$
$422$	−12.0271	−	10.8292i	−0.585468	−	0.527157i
$423$	−10.7792	+	24.2104i	−0.524101	+	1.17715i
$424$	−23.4554	+	7.62112i	−1.13910	+	0.370114i
$425$	−0.490328	+	4.66516i	−0.0237844	+	0.226294i
$426$	−0.704996	+	0.313884i	−0.0341571	+	0.0152077i
$427$	−23.6454	+	2.48523i	−1.14428	+	0.120269i
$428$	−10.4494			−0.505091
$429$	2.00852	+	8.66137i	0.0969724	+	0.418175i
$430$	2.13512	−	1.55126i	0.102965	−	0.0748082i
$431$	0.920323	−	0.828663i	0.0443304	−	0.0399153i	−0.646668	−	0.762772i	$-0.723838\pi$
$431$	0.920323	−	0.828663i	0.0443304	−	0.0399153i	0.690998	+	0.722857i	$0.257171\pi$
$432$	−4.96676	−	1.05572i	−0.238963	−	0.0507932i
$433$	−4.54503	−	7.87223i	−0.218420	−	0.378315i	0.735905	−	0.677085i	$-0.236757\pi$
$433$	−4.54503	−	7.87223i	−0.218420	−	0.378315i	−0.954325	+	0.298770i	$0.903424\pi$
$434$	3.75479	+	4.23354i	0.180235	+	0.203216i
$435$	0.592820	−	0.342265i	0.0284236	−	0.0164104i
$436$	7.53411	+	6.78374i	0.360818	+	0.324882i
$437$	0.174252	+	0.0566180i	0.00833561	+	0.00270840i
$438$	1.79153	+	0.797640i	0.0856026	+	0.0381127i
$439$	−16.8009	+	29.1001i	−0.801865	+	1.38887i	0.116523	+	0.993188i	$0.462825\pi$
$439$	−16.8009	+	29.1001i	−0.801865	+	1.38887i	−0.918387	+	0.395682i	$0.870508\pi$
$440$	6.52918	+	3.76963i	0.311267	+	0.179710i
$441$	9.72489	−	7.06555i	0.463090	−	0.336455i
$442$	1.39317	+	1.84506i	0.0662665	+	0.0877606i
$443$	−11.0367	−	8.01864i	−0.524370	−	0.380977i	0.293878	−	0.955843i	$-0.405054\pi$
$443$	−11.0367	−	8.01864i	−0.524370	−	0.380977i	−0.818248	+	0.574866i	$0.805054\pi$
$444$	−0.288792	+	1.35866i	−0.0137054	+	0.0644791i
$445$	0.957718	+	9.11207i	0.0454002	+	0.431954i
$446$	1.50965	−	1.67663i	0.0714838	−	0.0793908i
$447$	0.687083	+	0.223247i	0.0324979	+	0.0105592i
$448$	0.175878	+	0.0184856i	0.00830947	+	0.000873361i
$449$	0.111614	+	0.525105i	0.00526741	+	0.0247812i	0.980703	−	0.195504i	$-0.0626344\pi$
$449$	0.111614	+	0.525105i	0.00526741	+	0.0247812i	−0.975435	+	0.220286i	$0.929301\pi$
$450$	7.49253	+	2.43447i	0.353201	+	0.114762i
$451$	−4.24017	+	40.3425i	−0.199662	+	1.89965i
$452$	7.42859	+	8.25028i	0.349411	+	0.388061i
$453$	0.219499	−	1.03266i	0.0103130	−	0.0485187i
$454$	4.05583	−	2.94673i	0.190349	−	0.138297i
$455$	1.99506	+	3.31303i	0.0935300	+	0.155317i
$456$	0.675739	+	0.490953i	0.0316444	+	0.0229910i
$457$	6.85505	+	15.3967i	0.320666	+	0.720227i	0.999906	−	0.0136886i	$-0.00435736\pi$
$457$	6.85505	+	15.3967i	0.320666	+	0.720227i	−0.679241	+	0.733916i	$0.737691\pi$
$458$	−1.64010	−	15.6045i	−0.0766370	−	0.729152i
$459$	−1.43762	−	2.49004i	−0.0671025	−	0.116225i
$460$		−	0.254610i		−	0.0118712i
$461$	−2.89985	+	6.51318i	−0.135060	+	0.303349i	−0.968396	−	0.249417i	$-0.919761\pi$
$461$	−2.89985	+	6.51318i	−0.135060	+	0.303349i	0.833336	+	0.552766i	$0.186428\pi$
$462$	−0.521082	−	2.45150i	−0.0242429	−	0.114054i
$463$	14.5994	−	4.74363i	0.678491	−	0.220455i	0.0505563	−	0.998721i	$-0.483901\pi$
$463$	14.5994	−	4.74363i	0.678491	−	0.220455i	0.627935	+	0.778266i	$0.283901\pi$
$464$	−1.94150	−	3.36277i	−0.0901317	−	0.156113i
$465$	−1.54883	+	0.878796i	−0.0718253	+	0.0407532i
$466$	−2.25265	−	1.30057i	−0.104352	−	0.0602476i
$467$	−4.43923	−	13.6625i	−0.205423	−	0.632227i	−0.999696	−	0.0246657i	$-0.992148\pi$
$467$	−4.43923	−	13.6625i	−0.205423	−	0.632227i	0.794273	−	0.607561i	$-0.207852\pi$
$468$	−14.5400	+	6.79738i	−0.672114	+	0.314209i
$469$	−16.5488	+	12.0234i	−0.764153	+	0.555189i
$470$	−3.41374	−	1.97092i	−0.157464	−	0.0909119i
$471$	3.86850	−	6.70044i	0.178251	−	0.308740i
$472$	−25.5500	−	11.3756i	−1.17604	−	0.523605i
$473$	19.1621	−	26.3744i	0.881075	−	1.21270i
$474$	−2.98158	−	0.313377i	−0.136949	−	0.0143939i
$475$	2.59034	+	2.33235i	0.118853	+	0.107016i
$476$	1.58345	+	2.17943i	0.0725771	+	0.0998938i
$477$	20.2427	−	22.4817i	0.926847	−	1.02937i
$478$	7.51178	+	8.34267i	0.343581	+	0.381585i
$479$	−3.56132	−	7.99885i	−0.162721	−	0.365477i	0.813722	−	0.581255i	$-0.197438\pi$
$479$	−3.56132	−	7.99885i	−0.162721	−	0.365477i	−0.976442	+	0.215778i	$0.930771\pi$
$480$	0.557371	−	1.71541i	0.0254404	−	0.0782974i
$481$	2.71250	+	5.80222i	0.123680	+	0.264559i
$482$	4.23957	+	3.08023i	0.193107	+	0.140300i
$483$	−0.141015	+	0.126971i	−0.00641642	+	0.00577737i
$484$	23.3050	+	4.95364i	1.05932	+	0.225165i
$485$	1.32158	+	0.588404i	0.0600097	+	0.0267180i
$486$	−6.98269	+	2.26881i	−0.316741	+	0.102916i
$487$	29.8656	+	3.13900i	1.35334	+	0.142241i	0.753272	−	0.657709i	$-0.228474\pi$
$487$	29.8656	+	3.13900i	1.35334	+	0.142241i	0.600066	+	0.799951i	$0.295141\pi$
$488$	32.7240	+	3.43943i	1.48135	+	0.155696i
$489$	−4.54367	−	6.25382i	−0.205472	−	0.282808i
$490$	0.893974	+	1.54841i	0.0403856	+	0.0699499i
$491$	8.64673	−	14.9766i	0.390222	−	0.675884i	−0.602257	−	0.798302i	$-0.705732\pi$
$491$	8.64673	−	14.9766i	0.390222	−	0.675884i	0.992479	+	0.122419i	$0.0390651\pi$
$492$	6.21096	−	0.652798i	0.280011	−	0.0294304i
$493$	0.679447	−	2.09112i	0.0306008	−	0.0941795i
$494$	1.71766	−	0.0316554i	0.0772814	−	0.00142424i
$495$	−9.24800			−0.415667
$496$	4.98496	+	8.78573i	0.223831	+	0.394491i
$497$	−2.07319	+	3.59088i	−0.0929954	+	0.161073i
$498$	−2.96077	+	3.28827i	−0.132675	+	0.147351i
$499$	−3.84109	−	1.24805i	−0.171951	−	0.0558703i	0.221776	−	0.975098i	$-0.428815\pi$
$499$	−3.84109	−	1.24805i	−0.171951	−	0.0558703i	−0.393727	+	0.919227i	$0.628815\pi$
$500$	4.12753	−	9.27058i	0.184589	−	0.414593i
$501$	5.03900	−	2.90927i	0.225126	−	0.129977i
$502$			13.1398i			0.586457i
$503$	8.63338	+	3.84383i	0.384943	+	0.171388i	0.590079	−	0.807346i	$-0.299097\pi$
$503$	8.63338	+	3.84383i	0.384943	+	0.171388i	−0.205135	+	0.978734i	$0.565763\pi$
$504$	9.26624	−	4.12560i	0.412751	−	0.183769i
$505$	0.185088	+	0.415715i	0.00823632	+	0.0184991i
$506$	0.235115	+	0.723610i	0.0104521	+	0.0321684i
$507$	2.95244	−	5.57892i	0.131123	−	0.247769i
$508$	−6.40849	−	19.7233i	−0.284331	−	0.875080i
$509$	23.7536	−	21.3878i	1.05286	−	0.947998i	0.0541362	−	0.998534i	$-0.482759\pi$
$509$	23.7536	−	21.3878i	1.05286	−	0.947998i	0.998722	+	0.0505356i	$0.0160928\pi$
$510$	0.187356	−	0.0834163i	0.00829626	−	0.00369373i
$511$	10.3065	−	2.19072i	0.455933	−	0.0969116i
$512$	−17.5074	−	5.68849i	−0.773724	−	0.251398i
$513$	−2.12481	−	0.223327i	−0.0938127	−	0.00986012i
$514$	−0.627321	−	2.95131i	−0.0276699	−	0.130177i
$515$	−2.60995	+	0.848024i	−0.115008	+	0.0373684i
$516$	−4.58512	−	2.04143i	−0.201849	−	0.0898688i
$517$	−47.6282	−	10.1237i	−2.09469	−	0.445240i
$518$	−0.734338	−	1.64935i	−0.0322650	−	0.0724683i
$519$	−9.13498	−	6.63695i	−0.400981	−	0.291330i
$520$	−1.74744	−	5.05893i	−0.0766304	−	0.221849i
$521$	38.3099			1.67839			0.839193	−	0.543834i	$-0.183028\pi$
$521$	38.3099			1.67839			0.839193	+	0.543834i	$0.183028\pi$
$522$	−3.19796	−	1.84635i	−0.139971	−	0.0808123i
$523$	−2.94980	−	28.0654i	−0.128986	−	1.22722i	−0.847154	−	0.531347i	$-0.821686\pi$
$523$	−2.94980	−	28.0654i	−0.128986	−	1.22722i	0.718169	−	0.695869i	$-0.244981\pi$
$524$	17.1830	−	3.65235i	0.750641	−	0.159554i
$525$	−3.43329	+	1.11554i	−0.149841	+	0.0486864i
$526$	13.4885	−	7.78762i	0.588129	−	0.339556i
$527$	−1.80830	+	5.42655i	−0.0787708	+	0.236384i
$528$		−	4.47395i		−	0.194704i
$529$	−15.3515	+	17.0495i	−0.667455	+	0.741284i
$530$	3.01089	+	3.34393i	0.130785	+	0.145251i
$531$	34.1189	−	3.58604i	1.48064	−	0.155621i
$532$	2.00178			0.0867880
$533$	21.0420	−	19.6603i	0.911430	−	0.851583i
$534$	−3.41020	+	2.47766i	−0.147574	+	0.107219i
$535$	1.73849	+	3.90471i	0.0751614	+	0.168815i
$536$	25.8618	−	11.5144i	1.11706	−	0.497348i
$537$	−5.11075	+	5.67606i	−0.220545	+	0.244940i
$538$	0.719607	+	0.990453i	0.0310244	+	0.0427015i
$539$	16.4130	+	14.7784i	0.706959	+	0.636549i
$540$	0.617288	+	2.90411i	0.0265639	+	0.124973i
$541$	14.4511	−	19.8903i	0.621302	−	0.855150i	−0.376144	−	0.926561i	$-0.622750\pi$
$541$	14.4511	−	19.8903i	0.621302	−	0.855150i	0.997447	+	0.0714115i	$0.0227504\pi$
$542$	−6.26603	+	1.33189i	−0.269149	+	0.0572094i
$543$	−4.06439	−	4.51396i	−0.174420	−	0.193713i
$544$	−2.35644	−	5.29264i	−0.101031	−	0.226920i
$545$	1.28147	−	3.94395i	0.0548920	−	0.168940i
$546$	−0.861074	+	1.55699i	−0.0368506	+	0.0666332i
$547$	24.5023	−	17.8020i	1.04764	−	0.761157i	0.0758797	−	0.997117i	$-0.475823\pi$
$547$	24.5023	−	17.8020i	1.04764	−	0.761157i	0.971763	+	0.235960i	$0.0758235\pi$
$548$	−5.38096	+	25.3154i	−0.229863	+	1.08142i
$549$	−36.8725	+	16.4167i	−1.57368	+	0.700647i
$550$	−1.51302	+	14.3954i	−0.0645154	+	0.613823i
$551$	−0.960336	−	1.32179i	−0.0409117	−	0.0563101i
$552$	0.227428	−	0.131306i	0.00967998	−	0.00558874i
$553$	−13.9501	+	8.05408i	−0.593217	+	0.342494i
$554$	9.97056	+	13.7233i	0.423609	+	0.583047i
$555$	0.555747	−	0.118128i	0.0235901	−	0.00501424i
$556$	−18.6861	−	3.97186i	−0.792469	−	0.168444i
$557$	−22.5110	−	12.9968i	−0.953823	−	0.550690i	−0.0595568	−	0.998225i	$-0.518969\pi$
$557$	−22.5110	−	12.9968i	−0.953823	−	0.550690i	−0.894267	+	0.447535i	$0.852302\pi$
$558$	8.28310	+	4.86544i	0.350652	+	0.205971i
$559$	−22.5453	+	5.22814i	−0.953567	+	0.221127i
$560$	−0.601349	−	1.85076i	−0.0254116	−	0.0782090i
$561$	1.88266	−	1.69515i	0.0794859	−	0.0715694i
$562$	−0.369209	−	3.51279i	−0.0155741	−	0.148178i
$563$	−5.82972	−	10.0974i	−0.245693	−	0.425553i	0.716633	−	0.697450i	$-0.245682\pi$
$563$	−5.82972	−	10.0974i	−0.245693	−	0.425553i	−0.962326	+	0.271897i	$0.912349\pi$
$564$			7.49645i			0.315658i
$565$	1.84704	−	4.14851i	0.0777054	−	0.174529i
$566$	−0.308534	−	0.0324282i	−0.0129686	−	0.00136306i
$567$	−6.63637	+	9.13419i	−0.278702	+	0.383600i
$568$	3.83973	−	4.26446i	0.161112	−	0.178933i
$569$	3.24477	+	30.8720i	0.136028	+	1.29422i	0.823211	+	0.567736i	$0.192180\pi$
$569$	3.24477	+	30.8720i	0.136028	+	1.29422i	−0.687183	+	0.726484i	$0.741153\pi$
$570$	0.0316845	−	0.149064i	0.00132712	−	0.00624361i
$571$	4.54880	−	13.9998i	0.190362	−	0.585873i	−0.809638	−	0.586930i	$-0.800337\pi$
$571$	4.54880	−	13.9998i	0.190362	−	0.585873i	0.999999	+	0.00105715i	$0.000336503\pi$
$572$	−17.7705	−	23.5345i	−0.743021	−	0.984027i
$573$	2.89241	−	8.90191i	0.120832	−	0.371883i
$574$	−6.03246	+	5.43165i	−0.251790	+	0.226713i
$575$	1.00117	−	0.445747i	0.0417515	−	0.0185890i
$576$	0.293659	−	0.0624191i	0.0122358	−	0.00260079i
$577$	16.9810	−	5.51748i	0.706930	−	0.229696i	0.0665828	−	0.997781i	$-0.478790\pi$
$577$	16.9810	−	5.51748i	0.706930	−	0.229696i	0.640347	+	0.768085i	$0.278790\pi$
$578$	−4.04788	+	9.09169i	−0.168370	+	0.378164i
$579$	−3.00411	−	2.70491i	−0.124847	−	0.112412i
$580$	−1.33452	+	1.83681i	−0.0554130	+	0.0762695i
$581$	−2.48509	+	23.6441i	−0.103099	+	0.980921i
$582$	0.0695691	+	0.661905i	0.00288373	+	0.0274369i
$583$	48.1366	+	27.7917i	1.99361	+	1.15101i
$584$	−14.5824			−0.603422
$585$	4.95908	+	4.30239i	0.205033	+	0.177882i
$586$	2.75395	−	8.47579i	0.113765	−	0.350132i
$587$	8.17440	−	38.4575i	0.337394	−	1.58731i	−0.403040	−	0.915182i	$-0.632046\pi$
$587$	8.17440	−	38.4575i	0.337394	−	1.58731i	0.740433	−	0.672130i	$-0.234620\pi$
$588$	1.70012	−	2.94470i	0.0701120	−	0.121437i
$589$	2.47241	+	3.45721i	0.101874	+	0.142452i
$590$			5.10280i			0.210079i
$591$	2.45059	+	2.20652i	0.100804	+	0.0907640i
$592$	−0.670078	−	3.15247i	−0.0275400	−	0.129566i
$593$	−0.481132	−	0.662222i	−0.0197577	−	0.0271942i	0.799024	−	0.601299i	$-0.205350\pi$
$593$	−0.481132	−	0.662222i	−0.0197577	−	0.0271942i	−0.818782	+	0.574105i	$0.805350\pi$
$594$	−4.43611	−	7.68357i	−0.182016	−	0.315261i
$595$	0.550961	−	0.954293i	0.0225872	−	0.0391222i
$596$	−2.38304	+	0.250468i	−0.0976133	+	0.0102596i
$597$	−0.683880	−	0.496868i	−0.0279894	−	0.0203355i
$598$	0.210564	−	0.497405i	0.00861061	−	0.0203404i
$599$	−2.32431	−	7.15349i	−0.0949688	−	0.292284i	0.892277	−	0.451489i	$-0.149107\pi$
$599$	−2.32431	−	7.15349i	−0.0949688	−	0.292284i	−0.987246	+	0.159205i	$0.949107\pi$
$600$	4.96866	−	0.522227i	0.202845	−	0.0213198i
$601$	1.41817	+	0.301441i	0.0578483	+	0.0122960i	0.236745	−	0.971572i	$-0.423919\pi$
$601$	1.41817	+	0.301441i	0.0578483	+	0.0122960i	−0.178897	+	0.983868i	$0.557253\pi$
$602$	6.38119	−	1.35636i	0.260078	−	0.0552813i
$603$	−20.4112	+	28.0935i	−0.831207	+	1.14406i
$604$	0.728026	+	3.42509i	0.0296230	+	0.139365i
$605$	−2.02624	−	9.53272i	−0.0823784	−	0.387560i
$606$	−0.123056	+	0.169372i	−0.00499882	+	0.00688028i
$607$	−7.26463	+	1.54414i	−0.294862	+	0.0626749i	−0.352968	−	0.935636i	$-0.614827\pi$
$607$	−7.26463	+	1.54414i	−0.294862	+	0.0626749i	0.0581054	+	0.998310i	$0.481494\pi$
$608$	−4.21093	−	0.895061i	−0.170776	−	0.0362995i
$609$	1.68283	−	0.176872i	0.0681917	−	0.00716723i
$610$	−1.85516	−	5.70960i	−0.0751133	−	0.231175i
$611$	20.8300	+	27.5864i	0.842693	+	1.11603i
$612$	3.69983	+	2.68809i	0.149557	+	0.108659i
$613$	37.0345	−	3.89248i	1.49581	−	0.157216i	0.679005	−	0.734133i	$-0.262411\pi$
$613$	37.0345	−	3.89248i	1.49581	−	0.157216i	0.816802	+	0.576918i	$0.195745\pi$
$614$	−6.84060	+	11.8483i	−0.276064	+	0.478157i
$615$	−1.27726	−	2.21229i	−0.0515043	−	0.0892080i
$616$	10.9542	+	15.0771i	0.441357	+	0.607475i
$617$	6.03806	+	28.4068i	0.243083	+	1.14362i	0.915146	+	0.403122i	$0.132075\pi$
$617$	6.03806	+	28.4068i	0.243083	+	1.14362i	−0.672063	+	0.740494i	$0.734592\pi$
$618$	−0.938250	−	0.844804i	−0.0377419	−	0.0339830i
$619$		−	20.8939i		−	0.839796i	−0.907571	−	0.419898i	$-0.862066\pi$
$619$		−	20.8939i		−	0.839796i	0.907571	−	0.419898i	$-0.137934\pi$
$620$	3.50744	−	4.75221i	0.140862	−	0.190853i
$621$	−0.335868	+	0.581740i	−0.0134779	+	0.0233444i
$622$	−0.632923	+	2.97767i	−0.0253779	+	0.119394i
$623$	−6.99871	+	21.5398i	−0.280398	+	0.862975i
$624$	−2.08139	+	2.39908i	−0.0833222	+	0.0960400i
$625$	18.6795			0.747180
$626$	−6.73233	−	3.88691i	−0.269078	−	0.155352i
$627$	−0.196772	−	1.87216i	−0.00785832	−	0.0747669i
$628$	−2.68239	+	25.5213i	−0.107039	+	1.01841i
$629$	1.07268	−	1.47642i	0.0427707	−	0.0588689i
$630$	−1.37529	−	1.23832i	−0.0547929	−	0.0493357i
$631$	7.04936	−	15.8331i	0.280631	−	0.630307i	−0.717148	−	0.696921i	$-0.754553\pi$
$631$	7.04936	−	15.8331i	0.280631	−	0.630307i	0.997779	+	0.0666140i	$0.0212196\pi$
$632$	21.2018	−	6.88888i	0.843362	−	0.274025i
$633$	12.3144	−	2.61750i	0.489453	−	0.104036i
$634$	−0.0957045	+	0.0426104i	−0.00380091	+	0.00169228i
$635$	−6.30396	+	5.67611i	−0.250165	+	0.225250i
$636$	2.64437	−	8.13854i	0.104856	−	0.322714i
$637$	−1.92596	−	15.5604i	−0.0763092	−	0.616524i
$638$	2.09659	−	6.45264i	0.0830047	−	0.255462i
$639$	−1.46349	+	6.88516i	−0.0578946	+	0.272373i
$640$	0.781278	+	7.43336i	0.0308827	+	0.293829i
$641$	−0.110778	+	0.123031i	−0.00437545	+	0.00485943i	−0.745329	−	0.666697i	$-0.767707\pi$
$641$	−0.110778	+	0.123031i	−0.00437545	+	0.00485943i	0.740953	+	0.671557i	$0.234374\pi$
$642$	−1.15584	+	1.59087i	−0.0456172	+	0.0627867i
$643$	−24.3390	−	2.55813i	−0.959837	−	0.100883i	−0.388366	−	0.921505i	$-0.626960\pi$
$643$	−24.3390	−	2.55813i	−0.959837	−	0.100883i	−0.571471	+	0.820622i	$0.693627\pi$
$644$	0.255989	−	0.574960i	0.0100874	−	0.0226566i
$645$			2.05299i			0.0808365i
$646$	−0.244748	−	0.423916i	−0.00962948	−	0.0166788i
$647$	−1.15450	−	10.9843i	−0.0453880	−	0.431838i	−0.993494	−	0.113884i	$-0.963671\pi$
$647$	−1.15450	−	10.9843i	−0.0453880	−	0.431838i	0.948106	−	0.317954i	$-0.102996\pi$
$648$	11.6120	−	10.4555i	0.456161	−	0.410729i
$649$	19.4783	+	59.9481i	0.764591	+	2.35317i
$650$	7.50842	−	7.01540i	0.294504	−	0.275167i
$651$	−4.38113	+	0.427279i	−0.171710	+	0.0167464i
$652$	22.2041	+	12.8195i	0.869579	+	0.502052i
$653$	−10.3710	−	2.20442i	−0.405848	−	0.0862657i	0.000464224	−	1.00000i	$-0.499852\pi$
$653$	−10.3710	−	2.20442i	−0.405848	−	0.0862657i	−0.406313	+	0.913734i	$0.633186\pi$
$654$	1.86616	−	0.396664i	0.0729726	−	0.0155108i
$655$	−4.22356	−	5.81323i	−0.165028	−	0.227142i
$656$	−12.5492	+	7.24527i	−0.489963	+	0.282880i
$657$	15.4910	−	8.94371i	0.604360	−	0.348927i
$658$	−5.72732	−	7.88298i	−0.223274	−	0.307311i
$659$	−3.63858	+	34.6188i	−0.141739	+	1.34856i	0.660172	+	0.751114i	$0.270483\pi$
$659$	−3.63858	+	34.6188i	−0.141739	+	1.34856i	−0.801911	+	0.597443i	$0.796183\pi$
$660$	−2.38980	+	1.06401i	−0.0930229	+	0.0414165i
$661$	4.06312	−	19.1155i	0.158037	−	0.743507i	−0.825731	−	0.564064i	$-0.809237\pi$
$661$	4.06312	−	19.1155i	0.158037	−	0.743507i	0.983768	−	0.179443i	$-0.0574295\pi$
$662$	13.2700	−	9.64118i	0.515751	−	0.374715i
$663$	−1.79817	+	0.0331390i	−0.0698350	+	0.00128701i
$664$	10.1674	−	31.2921i	0.394572	−	1.21437i
$665$	−0.333039	−	0.748018i	−0.0129147	−	0.0290069i
$666$	−2.05085	−	2.27770i	−0.0794688	−	0.0882590i
$667$	−0.502459	+	0.106801i	−0.0194553	+	0.00413535i
$668$	−11.3435	+	15.6130i	−0.438893	+	0.604085i
$669$	0.364893	+	1.71669i	0.0141076	+	0.0663710i
$670$	−3.83840	−	3.45611i	−0.148290	−	0.133521i
$671$	−43.5892	−	59.9954i	−1.68274	−	2.31609i
$672$	2.98336	−	3.31336i	0.115086	−	0.127816i
$673$	6.49373	−	2.89120i	0.250315	−	0.111447i	−0.277744	−	0.960655i	$-0.589587\pi$
$673$	6.49373	−	2.89120i	0.250315	−	0.111447i	0.528059	+	0.849208i	$0.322920\pi$
$674$	−4.32194	−	9.70723i	−0.166475	−	0.373909i
$675$	−10.3387	+	7.51153i	−0.397938	+	0.289119i
$676$	−1.41970	+	20.8872i	−0.0546037	+	0.803354i
$677$	−19.9070			−0.765088			−0.382544	−	0.923937i	$-0.624952\pi$
$677$	−19.9070			−0.765088			−0.382544	+	0.923937i	$0.624952\pi$
$678$	2.07776	−	0.218382i	0.0797960	−	0.00838689i
$679$	2.39280	+	2.65747i	0.0918272	+	0.101984i
$680$	−1.02043	+	1.13330i	−0.0391316	+	0.0434601i
$681$			3.89982i			0.149441i
$682$	−5.57992	+	16.7449i	−0.213666	+	0.641194i
$683$	6.06194	−	3.49987i	0.231954	−	0.133919i	−0.379519	−	0.925184i	$-0.623911\pi$
$683$	6.06194	−	3.49987i	0.231954	−	0.133919i	0.611473	+	0.791265i	$0.290577\pi$
$684$	3.23193	−	1.05012i	0.123576	−	0.0401522i
$685$	10.3550	−	2.20103i	0.395646	−	0.0840971i
$686$	1.20563	+	11.4708i	0.0460313	+	0.437958i
$687$	10.5704	+	6.10280i	0.403285	+	0.232836i
$688$	11.6456			0.443984
$689$	−12.8831	−	37.2971i	−0.490805	−	1.42090i
$690$	−0.0387631	−	0.0281630i	−0.00147569	−	0.00107215i
$691$	−6.96709	−	15.6483i	−0.265040	−	0.595291i	0.731177	−	0.682188i	$-0.238971\pi$
$691$	−6.96709	−	15.6483i	−0.265040	−	0.595291i	−0.996217	+	0.0868974i	$0.972305\pi$
$692$	36.6327	+	7.78652i	1.39257	+	0.295999i
$693$	−20.8839	−	9.29810i	−0.793313	−	0.353206i
$694$	13.7258	−	4.45978i	0.521024	−	0.169291i
$695$	1.62465	+	7.64339i	0.0616266	+	0.289930i
$696$	−2.32895	−	0.244782i	−0.0882786	−	0.00927846i
$697$	−7.80365	−	2.53556i	−0.295584	−	0.0960412i
$698$	7.15775	−	1.52143i	0.270925	−	0.0575869i
$699$	1.84848	−	0.822998i	0.0699161	−	0.0311286i
$700$	8.89801	−	8.01180i	0.336313	−	0.302818i
$701$	−7.81922	−	24.0651i	−0.295328	−	0.908926i	−0.983111	−	0.183010i	$-0.941416\pi$
$701$	−7.81922	−	24.0651i	−0.295328	−	0.908926i	0.687783	−	0.725916i	$-0.258584\pi$
$702$	−1.19579	+	6.18397i	−0.0451323	+	0.233399i
$703$	−0.419051	−	1.28971i	−0.0158048	−	0.0486422i
$704$	0.224357	+	0.503914i	0.00845577	+	0.0189920i
$705$	2.80125	−	1.24720i	0.105501	−	0.0469722i
$706$	1.07386	+	0.478113i	0.0404152	+	0.0179940i
$707$			1.12486i			0.0423047i
$708$	8.40418	−	4.85216i	0.315848	−	0.182355i
$709$	−3.80276	+	8.54115i	−0.142816	+	0.320770i	−0.970764	−	0.240035i	$-0.922841\pi$
$709$	−3.80276	+	8.54115i	−0.142816	+	0.320770i	0.827949	+	0.560804i	$0.189508\pi$
$710$	−0.995735	−	0.323534i	−0.0373693	−	0.0121420i
$711$	−18.2977	+	20.3217i	−0.686218	+	0.762122i
$712$	15.6721	−	27.1448i	0.587335	−	1.01729i
$713$	1.30917	−	0.268027i	0.0490289	−	0.0100377i
$714$	0.506956			0.0189724
$715$	−5.83780	+	10.5559i	−0.218321	+	0.394768i
$716$	7.82836	−	24.0932i	0.292559	−	0.900405i
$717$	−8.68498	+	0.912828i	−0.324346	+	0.0340902i
$718$	−5.24451	+	9.08375i	−0.195723	+	0.339003i
$719$	4.12017	+	7.13634i	0.153656	+	0.266141i	0.932569	−	0.360992i	$-0.117562\pi$
$719$	4.12017	+	7.13634i	0.153656	+	0.266141i	−0.778913	+	0.627132i	$0.784228\pi$
$720$	−1.94179	−	2.67265i	−0.0723664	−	0.0996038i
$721$	−6.74641	−	0.709077i	−0.251250	−	0.0264074i
$722$	11.4325	+	1.20160i	0.425472	+	0.0447189i
$723$	−3.87697	+	1.25971i	−0.144186	+	0.0468489i
$724$	18.4047	+	8.19431i	0.684006	+	0.304539i
$725$	−9.55900	−	2.03183i	−0.355012	−	0.0754602i
$726$	3.33200	−	3.00015i	0.123662	−	0.111346i
$727$	−13.4188	−	9.74934i	−0.497676	−	0.361583i	0.310452	−	0.950589i	$-0.399519\pi$
$727$	−13.4188	−	9.74934i	−0.497676	−	0.361583i	−0.808129	+	0.589006i	$0.799519\pi$
$728$	1.14025	−	13.1810i	0.0422606	−	0.488520i
$729$	−4.66313	+	14.3516i	−0.172708	+	0.531542i
$730$	1.08215	+	2.43055i	0.0400523	+	0.0899589i
$731$	4.41244	+	4.90051i	0.163200	+	0.181252i
$732$	−7.63953	+	8.48456i	−0.282365	+	0.313598i
$733$	−29.7835	−	40.9935i	−1.10008	−	1.51413i	−0.835280	−	0.549825i	$-0.814694\pi$
$733$	−29.7835	−	40.9935i	−1.10008	−	1.51413i	−0.264799	−	0.964304i	$-0.585306\pi$
$734$	−5.95198	−	5.35919i	−0.219692	−	0.197811i
$735$	−1.38322	−	0.145382i	−0.0510209	−	0.00536251i
$736$	−0.795581	+	1.09502i	−0.0293255	+	0.0403631i
$737$	−58.2864	−	25.9508i	−2.14701	−	0.955909i
$738$	−6.89019	+	11.9342i	−0.253631	+	0.439302i
$739$	4.44710	+	2.56753i	0.163589	+	0.0944482i	0.579559	−	0.814930i	$-0.303225\pi$
$739$	4.44710	+	2.56753i	0.163589	+	0.0944482i	−0.415970	+	0.909378i	$0.636558\pi$
$740$	−1.52456	+	1.10766i	−0.0560440	+	0.0407183i
$741$	−0.765458	+	1.09546i	−0.0281198	+	0.0402426i
$742$	3.43716	+	10.5785i	0.126182	+	0.388348i
$743$	16.6885	+	9.63511i	0.612242	+	0.353478i	0.773842	−	0.633378i	$-0.218332\pi$
$743$	16.6885	+	9.63511i	0.612242	+	0.353478i	−0.161600	+	0.986856i	$0.551666\pi$
$744$	6.05371	+	0.682212i	0.221940	+	0.0250111i
$745$	0.490066	+	0.848819i	0.0179546	+	0.0310983i
$746$	−4.61040	+	1.49801i	−0.168799	+	0.0548460i
$747$	8.39125	+	39.4777i	0.307020	+	1.44441i
$748$	−3.41764	+	7.67614i	−0.124961	+	0.280667i
$749$			10.5655i			0.386056i
$750$	−0.954845	−	1.65384i	−0.0348660	−	0.0603897i
$751$	0.866871	+	8.24773i	0.0316326	+	0.300964i	0.998887	+	0.0471570i	$0.0150161\pi$
$751$	0.866871	+	8.24773i	0.0316326	+	0.300964i	−0.967255	+	0.253807i	$0.918317\pi$
$752$	−7.07473	−	15.8901i	−0.257989	−	0.579452i
$753$	−8.26929	−	6.00799i	−0.301350	−	0.218943i
$754$	−4.12618	+	2.48473i	−0.150267	+	0.0904886i
$755$	1.15876	−	0.841886i	0.0421715	−	0.0306394i
$756$	−1.52588	+	7.17871i	−0.0554958	+	0.261087i
$757$	16.1762	+	17.9655i	0.587935	+	0.652968i	0.961555	−	0.274614i	$-0.0885501\pi$
$757$	16.1762	+	17.9655i	0.587935	+	0.652968i	−0.373620	+	0.927582i	$0.621883\pi$
$758$	2.19254	−	20.8607i	0.0796368	−	0.757693i
$759$	−0.562895	−	0.182896i	−0.0204318	−	0.00663869i
$760$	0.235603	+	1.10843i	0.00854623	+	0.0402068i
$761$	−1.02499	−	0.107730i	−0.0371557	−	0.00390522i	0.0859324	−	0.996301i	$-0.472613\pi$
$761$	−1.02499	−	0.107730i	−0.0371557	−	0.00390522i	−0.123088	+	0.992396i	$0.539280\pi$
$762$	−3.71164	−	1.20598i	−0.134458	−	0.0436882i
$763$	6.85913	−	7.61783i	0.248317	−	0.275784i
$764$	3.24508	+	30.8749i	0.117403	+	1.11702i
$765$	0.388929	−	1.82977i	0.0140618	−	0.0661553i
$766$	−1.99758	−	1.45133i	−0.0721756	−	0.0524387i
$767$	17.4444	−	41.2079i	0.629880	−	1.48793i
$768$	−2.69662	+	1.95921i	−0.0973058	+	0.0706968i
$769$	0.466567	+	0.269372i	0.0168248	+	0.00971382i	0.508389	−	0.861128i	$-0.330241\pi$
$769$	0.466567	+	0.269372i	0.0168248	+	0.00971382i	−0.491564	+	0.870841i	$0.663575\pi$
$770$	1.70012	−	2.94469i	0.0612679	−	0.106119i
$771$	2.14419	+	0.954655i	0.0772211	+	0.0343811i
$772$	12.7516	+	4.14324i	0.458939	+	0.149118i
$773$	29.9893	+	27.0025i	1.07864	+	0.971211i	0.999671	−	0.0256664i	$-0.00817077\pi$
$773$	29.9893	+	27.0025i	1.07864	+	0.971211i	0.0789682	+	0.996877i	$0.474837\pi$
$774$	9.59110	−	5.53742i	0.344745	−	0.199039i
$775$	24.8270	+	5.47206i	0.891811	+	0.196562i
$776$	−2.47449	−	4.28594i	−0.0888290	−	0.153856i
$777$	1.37376	+	0.292001i	0.0492832	+	0.0104755i
$778$	7.58341	−	6.82814i	0.271879	−	0.244801i
$779$	−4.93265	+	3.58378i	−0.176730	+	0.128402i
$780$	1.77649	+	0.541237i	0.0636086	+	0.0193794i
$781$	−12.9330			−0.462778
$782$	−0.153058	+	0.0160870i	−0.00547334	+	0.000575271i
$783$	5.47219	−	2.43638i	0.195560	−	0.0870689i
$784$	−0.824681	+	7.84632i	−0.0294529	+	0.280226i
$785$	9.98299	−	3.24367i	0.356308	−	0.115772i
$786$	1.34460	−	3.02002i	0.0479603	−	0.107721i
$787$	−7.11781	−	6.40890i	−0.253722	−	0.228453i	0.532448	−	0.846463i	$-0.321272\pi$
$787$	−7.11781	−	6.40890i	−0.253722	−	0.228453i	−0.786170	+	0.618010i	$0.787939\pi$
$788$	−10.4020	−	3.37982i	−0.370556	−	0.120401i
$789$	−1.26646	+	12.0496i	−0.0450872	+	0.428976i
$790$	−2.72160	−	3.02264i	−0.0968302	−	0.107541i
$791$	8.34197	−	7.51114i	0.296606	−	0.267065i
$792$	25.5952	+	18.5960i	0.909487	+	0.660781i
$793$	−4.53733	+	52.4502i	−0.161125	+	1.86256i
$794$	−6.82977	−	21.0199i	−0.242380	−	0.745968i
$795$	−3.48114	+	0.365882i	−0.123463	+	0.0129765i
$796$	2.74247	+	0.582929i	0.0972042	+	0.0206614i
$797$	1.10015	−	10.4672i	0.0389693	−	0.370768i	−0.957606	−	0.288081i	$-0.906983\pi$
$797$	1.10015	−	10.4672i	0.0389693	−	0.370768i	0.996575	−	0.0826878i	$-0.0263504\pi$
$798$	0.221422	−	0.304761i	0.00783824	−	0.0107884i
$799$	4.00605	−	8.99774i	0.141724	−	0.318317i
$800$	−22.3002	+	12.8750i	−0.788430	+	0.455200i
$801$			38.4482i			1.35850i
$802$	−15.3154	−	6.81884i	−0.540805	−	0.240782i
$803$	21.9911	+	24.4236i	0.776048	+	0.861889i
$804$	−2.04226	+	9.60809i	−0.0720250	+	0.338851i
$805$	−0.257439			−0.00907353
$806$	10.7822	−	6.38323i	0.379788	−	0.224840i
$807$	−0.952355			−0.0335245
$808$	0.323666	−	1.52273i	0.0113865	−	0.0535695i
$809$	−28.8602	−	32.0525i	−1.01467	−	1.12691i	−0.991881	−	0.127166i	$-0.959412\pi$
$809$	−28.8602	−	32.0525i	−1.01467	−	1.12691i	−0.0227893	−	0.999740i	$-0.507255\pi$
$810$	−2.60441	−	1.15956i	−0.0915098	−	0.0407428i
$811$			2.16524i			0.0760317i	0.999277	+	0.0380159i	$0.0121037\pi$
$811$			2.16524i			0.0760317i	−0.999277	+	0.0380159i	$0.987896\pi$
$812$	−4.86039	+	2.80615i	−0.170566	+	0.0984764i
$813$	2.02686	−	4.55240i	0.0710851	−	0.159660i
$814$	3.31001	−	4.55584i	0.116016	−	0.159682i
$815$	1.09623	−	10.4300i	0.0383994	−	0.365346i
$816$	0.885194	+	0.188154i	0.0309880	+	0.00658670i
$817$	4.87319	−	0.512193i	0.170491	−	0.0179194i
$818$	2.86763	+	8.82565i	0.100264	+	0.308582i
$819$	6.87292	+	14.7016i	0.240159	+	0.513716i
$820$	6.85461	+	4.98017i	0.239373	+	0.173915i
$821$	−26.9252	+	24.2435i	−0.939694	+	0.846105i	−0.988270	−	0.152715i	$-0.951198\pi$
$821$	−26.9252	+	24.2435i	−0.939694	+	0.846105i	0.0485760	+	0.998819i	$0.484532\pi$
$822$	3.25895	+	3.61943i	0.113669	+	0.126242i
$823$	−4.26550	+	40.5835i	−0.148686	+	1.41465i	0.624773	+	0.780807i	$0.285192\pi$
$823$	−4.26550	+	40.5835i	−0.148686	+	1.41465i	−0.773459	+	0.633847i	$0.781475\pi$
$824$	8.92864	+	2.90109i	0.311044	+	0.101064i
$825$	−8.36770	−	7.53431i	−0.291326	−	0.262311i
$826$	−5.13044	+	11.5232i	−0.178511	+	0.400942i
$827$	−16.5919	+	5.39103i	−0.576956	+	0.187464i	−0.582936	−	0.812518i	$-0.698096\pi$
$827$	−16.5919	+	5.39103i	−0.576956	+	0.187464i	0.00598054	+	0.999982i	$0.498096\pi$
$828$	0.111682	−	1.06258i	0.00388121	−	0.0369272i
$829$	10.4863	−	4.66881i	0.364205	−	0.162155i	−0.216471	−	0.976289i	$-0.569455\pi$
$829$	10.4863	−	4.66881i	0.364205	−	0.162155i	0.580676	+	0.814134i	$0.302788\pi$
$830$	−5.97021	+	0.627494i	−0.207229	+	0.0217806i
$831$	−13.1954			−0.457745
$832$	0.114125	−	0.374591i	0.00395658	−	0.0129866i
$833$	−3.61423	+	2.62589i	−0.125226	+	0.0909818i
$834$	−2.67162	+	2.40554i	−0.0925106	+	0.0832970i
$835$	7.72146	+	1.64125i	0.267212	+	0.0567977i
$836$	3.12186	+	5.40722i	0.107972	+	0.187013i
$837$	−14.2828	+	6.23118i	−0.493685	+	0.215381i
$838$	15.0403	−	8.68351i	0.519558	−	0.299967i
$839$	−40.3916	−	36.3688i	−1.39447	−	1.25559i	−0.928773	−	0.370648i	$-0.879136\pi$
$839$	−40.3916	−	36.3688i	−1.39447	−	1.25559i	−0.465701	−	0.884942i	$-0.654198\pi$
$840$	−1.11617	−	0.362665i	−0.0385115	−	0.0125131i
$841$	−22.3082	−	9.93224i	−0.769247	−	0.342491i
$842$	−10.9960	+	19.0457i	−0.378948	+	0.656357i
$843$	2.37953	+	1.37382i	0.0819553	+	0.0473169i
$844$	−33.7816	+	24.5438i	−1.16281	+	0.844832i
$845$	8.04128	−	2.94454i	0.276628	−	0.101295i
$846$	−13.3823	−	9.72280i	−0.460093	−	0.334277i
$847$	5.00869	−	23.5640i	0.172101	−	0.809670i
$848$	2.07546	+	19.7467i	0.0712717	+	0.678105i
$849$	0.161481	−	0.179343i	0.00554202	−	0.00615503i
$850$	−2.78458	−	0.904764i	−0.0955102	−	0.0310332i
$851$	−0.424024	−	0.0445668i	−0.0145354	−	0.00152773i
$852$	0.413973	+	1.94759i	0.0141825	+	0.0667234i
$853$	4.65301	+	1.51186i	0.159316	+	0.0517650i	0.387589	−	0.921832i	$-0.373308\pi$
$853$	4.65301	+	1.51186i	0.159316	+	0.0517650i	−0.228273	+	0.973597i	$0.573308\pi$
$854$	1.55120	−	14.7587i	0.0530809	−	0.505031i
$855$	−0.930107	−	1.03299i	−0.0318090	−	0.0353275i
$856$	3.04012	−	14.3026i	0.103909	−	0.488854i
$857$	30.8148	−	22.3883i	1.05261	−	0.764769i	0.0799067	−	0.996802i	$-0.474538\pi$
$857$	30.8148	−	22.3883i	1.05261	−	0.764769i	0.972708	+	0.232033i	$0.0745378\pi$
$858$	−5.54865	+	0.102258i	−0.189428	+	0.00349103i
$859$	20.8257	+	15.1307i	0.710563	+	0.516254i	0.883355	−	0.468704i	$-0.155279\pi$
$859$	20.8257	+	15.1307i	0.710563	+	0.516254i	−0.172792	+	0.984958i	$0.555279\pi$
$860$	−2.76959	−	6.22060i	−0.0944422	−	0.212121i
$861$	−0.660052	−	6.27998i	−0.0224945	−	0.214021i
$862$	0.386489	+	0.669419i	0.0131639	+	0.0228005i
$863$		−	28.9494i		−	0.985448i	−0.870186	−	0.492724i	$-0.836001\pi$
$863$		−	28.9494i		−	0.985448i	0.870186	−	0.492724i	$-0.163999\pi$
$864$	6.41968	−	14.4188i	0.218402	−	0.490539i
$865$	−3.18501	−	14.9843i	−0.108293	−	0.509481i
$866$	5.39602	−	1.75327i	0.183364	−	0.0595787i
$867$	−3.87086	−	6.70452i	−0.131461	−	0.227697i
$868$	12.6985	−	7.20503i	0.431014	−	0.244555i
$869$	−43.5115	−	25.1214i	−1.47603	−	0.852185i
$870$	0.132031	+	0.406349i	0.00447627	+	0.0137765i
$871$	19.1821	+	41.0319i	0.649962	+	1.39031i
$872$	−11.4772	+	8.33867i	−0.388667	+	0.282383i
$873$	5.25734	+	3.03533i	0.177934	+	0.102730i
$874$	−0.0571798	+	0.0990383i	−0.00193413	+	0.00335002i
$875$	−9.37360	−	4.17340i	−0.316886	−	0.141087i
$876$	2.97406	−	4.09344i	0.100484	−	0.138305i
$877$	−40.8887	−	4.29758i	−1.38071	−	0.145119i	−0.615115	−	0.788438i	$-0.710890\pi$
$877$	−40.8887	−	4.29758i	−1.38071	−	0.145119i	−0.765598	+	0.643319i	$0.777557\pi$
$878$	−15.5861	−	14.0338i	−0.526005	−	0.473617i
$879$	4.07488	+	5.60860i	0.137442	+	0.189173i
$880$	4.06147	−	4.51072i	0.136912	−	0.152056i
$881$	17.7077	+	19.6663i	0.596586	+	0.662576i	0.963509	−	0.267675i	$-0.0862554\pi$
$881$	17.7077	+	19.6663i	0.596586	+	0.662576i	−0.366923	+	0.930251i	$0.619589\pi$
$882$	3.05170	+	6.85422i	0.102756	+	0.230794i
$883$	−15.3493	+	47.2403i	−0.516545	+	1.58976i	0.263908	+	0.964548i	$0.414989\pi$
$883$	−15.3493	+	47.2403i	−0.516545	+	1.58976i	−0.780453	+	0.625215i	$0.785011\pi$
$884$	5.40377	−	2.52623i	0.181748	−	0.0849663i
$885$	−3.21136	−	2.33319i	−0.107949	−	0.0784293i
$886$	6.32785	−	5.69762i	0.212588	−	0.191415i
$887$	−11.9783	−	2.54607i	−0.402193	−	0.0854888i	0.00237375	−	0.999997i	$-0.499244\pi$
$887$	−11.9783	−	2.54607i	−0.402193	−	0.0854888i	−0.404567	+	0.914508i	$0.632578\pi$
$888$	−1.77564	−	0.790568i	−0.0595867	−	0.0265297i
$889$	−19.9425	+	6.47970i	−0.668849	+	0.217322i
$890$	−5.68745	−	0.597776i	−0.190644	−	0.0200375i
$891$	−35.0231	−	3.68108i	−1.17332	−	0.123321i
$892$	−3.42153	−	4.70933i	−0.114561	−	0.157680i
$893$	−3.65935	−	6.33818i	−0.122456	−	0.212099i
$894$	−0.225462	+	0.390512i	−0.00754058	+	0.0130607i
$895$	−10.3055	+	1.08315i	−0.344475	+	0.0362058i
$896$	−5.70934	+	17.5716i	−0.190736	+	0.587024i
$897$	0.216755	+	0.359947i	0.00723724	+	0.0120183i
$898$	−0.335075			−0.0111816
$899$	−10.8495	−	4.92835i	−0.361852	−	0.164370i
$900$	10.1632	−	17.6031i	0.338772	−	0.586771i
$901$	−7.52313	+	8.35528i	−0.250632	+	0.278355i
$902$	−24.0799	−	7.82405i	−0.801774	−	0.260512i
$903$	−2.06411	+	4.63607i	−0.0686894	+	0.154279i
$904$	−13.4538	+	7.76757i	−0.447468	+	0.258346i
$905$		−	8.24073i		−	0.273931i
$906$	0.601983	+	0.268020i	0.0199996	+	0.00890437i
$907$	9.32371	−	4.15118i	0.309589	−	0.137838i	−0.246061	−	0.969254i	$-0.579136\pi$
$907$	9.32371	−	4.15118i	0.309589	−	0.137838i	0.555650	+	0.831417i	$0.312470\pi$
$908$	−5.26105	−	11.8165i	−0.174594	−	0.392145i
$909$	0.590093	+	1.81612i	0.0195722	+	0.0602369i
$910$	−2.28160	+	0.788103i	−0.0756342	+	0.0261254i
$911$	−9.95882	−	30.6501i	−0.329950	−	1.01548i	−0.969156	−	0.246447i	$-0.920737\pi$
$911$	−9.95882	−	30.6501i	−0.329950	−	1.01548i	0.639206	−	0.769036i	$-0.279263\pi$
$912$	0.499734	−	0.449962i	0.0165478	−	0.0148997i
$913$	−67.7432	+	30.1612i	−2.24197	+	0.998191i
$914$	−10.2897	+	2.18714i	−0.340353	+	0.0723442i
$915$	4.44149	+	1.44313i	0.146831	+	0.0477083i
$916$	−40.2613	−	4.23164i	−1.33027	−	0.139817i
$917$	−3.69294	−	17.3739i	−0.121952	−	0.573737i
$918$	1.70680	−	0.554572i	0.0563327	−	0.0183036i
$919$	−4.42872	−	1.97179i	−0.146090	−	0.0650435i	0.332389	−	0.943142i	$-0.392145\pi$
$919$	−4.42872	−	1.97179i	−0.146090	−	0.0650435i	−0.478479	+	0.878099i	$0.658812\pi$
$920$	0.348497	+	0.0740753i	0.0114896	+	0.00244219i
$921$	−4.32872	−	9.72247i	−0.142636	−	0.320366i
$922$	−3.60015	−	2.61567i	−0.118565	−	0.0861424i
$923$	6.93507	+	6.01672i	0.228271	+	0.198043i
$924$	−6.46643			−0.212730
$925$	−7.02455	−	4.05563i	−0.230966	−	0.133348i
$926$	1.00153	+	9.52891i	0.0329123	+	0.313139i
$927$	−11.2643	+	2.39430i	−0.369967	+	0.0786390i
$928$	11.4790	−	3.72976i	0.376817	−	0.122435i
$929$	23.7968	−	13.7391i	0.780749	−	0.450765i	−0.0559469	−	0.998434i	$-0.517818\pi$
$929$	23.7968	−	13.7391i	0.780749	−	0.450765i	0.836696	+	0.547668i	$0.184484\pi$
$930$	−0.335535	−	1.05965i	−0.0110026	−	0.0347472i
$931$			3.31963i			0.108796i
$932$	−4.49067	+	4.98739i	−0.147097	+	0.163368i
$933$	−1.58455	−	1.75982i	−0.0518758	−	0.0576139i
$934$	8.91744	−	0.937261i	0.291788	−	0.0306681i
$935$	3.43700			0.112402
$936$	−5.07368	−	21.8793i	−0.165839	−	0.715147i
$937$	45.2822	−	32.8995i	1.47931	−	1.07478i	0.501526	−	0.865143i	$-0.332772\pi$
$937$	45.2822	−	32.8995i	1.47931	−	1.07478i	0.977780	−	0.209635i	$-0.0672277\pi$
$938$	−5.19305	−	11.6638i	−0.169559	−	0.380836i
$939$	5.52443	−	2.45963i	0.180283	−	0.0802671i
$940$	−6.80531	+	7.55806i	−0.221965	+	0.246517i
$941$	−24.4695	−	33.6794i	−0.797684	−	1.09792i	−0.993108	−	0.117199i	$-0.962609\pi$
$941$	−24.4695	−	33.6794i	−0.797684	−	1.09792i	0.195425	−	0.980719i	$-0.437391\pi$
$942$	3.58878	+	3.23135i	0.116929	+	0.105283i
$943$	0.398560	+	1.87508i	0.0129789	+	0.0610609i
$944$	−13.2350	+	18.2164i	−0.430763	+	0.592894i
$945$	2.93639	−	0.624148i	0.0955206	−	0.0203035i
$946$	13.6156	+	15.1216i	0.442681	+	0.491647i
$947$	−8.52398	−	19.1452i	−0.276992	−	0.622135i	0.720458	−	0.693498i	$-0.243932\pi$
$947$	−8.52398	−	19.1452i	−0.276992	−	0.622135i	−0.997450	+	0.0713637i	$0.977265\pi$
$948$	−2.39030	+	7.35658i	−0.0776332	+	0.238930i
$949$	−0.429909	−	23.3275i	−0.0139554	−	0.757242i
$950$	−1.76012	+	1.27880i	−0.0571058	+	0.0414898i
$951$	0.0169435	−	0.0797130i	0.000549432	−	0.00258487i
$952$	−3.44377	+	1.53327i	−0.111613	+	0.0496935i
$953$	2.61277	−	24.8589i	0.0846360	−	0.805258i	−0.867057	−	0.498208i	$-0.833992\pi$
$953$	2.61277	−	24.8589i	0.0846360	−	0.805258i	0.951693	−	0.307050i	$-0.0993418\pi$
$954$	11.0988	+	15.2762i	0.359337	+	0.494585i
$955$	10.9974	−	6.34933i	0.355866	−	0.205460i
$956$	25.0842	−	14.4824i	0.811280	−	0.468393i
$957$	3.10222	+	4.26984i	0.100280	+	0.138024i
$958$	5.34568	−	1.13626i	0.172711	−	0.0367108i
$959$	25.5968	+	5.44076i	0.826562	+	0.175691i
$960$	−0.0300829	−	0.0173683i	−0.000970920	−	0.000560561i
$961$	28.1276	+	13.0322i	0.907342	+	0.420394i
$962$	−3.89442	+	0.903094i	−0.125561	+	0.0291169i
$963$	5.54260	+	17.0584i	0.178608	+	0.549698i
$964$	10.0479	−	9.04716i	0.323621	−	0.291389i
$965$	−0.573269	−	5.45429i	−0.0184542	−	0.175580i
$966$	−0.0592194	−	0.102571i	−0.00190535	−	0.00330017i
$967$			17.8073i			0.572643i	0.958134	+	0.286321i	$0.0924325\pi$
$967$			17.8073i			0.572643i	−0.958134	+	0.286321i	$0.907567\pi$
$968$	−13.5606	+	30.4576i	−0.435854	+	0.978944i
$969$	0.378692	+	0.0398021i	0.0121653	+	0.00127863i
$970$	−0.530740	+	0.730500i	−0.0170410	+	0.0234550i
$971$	26.7177	−	29.6731i	0.857413	−	0.952254i	−0.141878	−	0.989884i	$-0.545314\pi$
$971$	26.7177	−	29.6731i	0.857413	−	0.952254i	0.999292	+	0.0376301i	$0.0119809\pi$
$972$	1.98011	+	18.8395i	0.0635119	+	0.604276i
$973$	−4.01600	+	18.8938i	−0.128747	+	0.605707i
$974$	−5.79214	+	17.8264i	−0.185592	+	0.571194i
$975$	0.981893	+	7.93299i	0.0314457	+	0.254059i
$976$	8.18613	−	25.1943i	0.262032	−	0.806451i
$977$	−4.15410	+	3.74036i	−0.132901	+	0.119665i	−0.732901	−	0.680335i	$-0.761834\pi$
$977$	−4.15410	+	3.74036i	−0.132901	+	0.119665i	0.600000	+	0.800000i	$0.295167\pi$
$978$	4.40777	−	1.96246i	0.140945	−	0.0627527i
$979$	−69.0985	+	14.6873i	−2.20840	+	0.469409i
$980$	4.38731	−	1.42552i	0.140148	−	0.0455367i
$981$	7.07801	−	15.8975i	0.225984	−	0.507567i
$982$	8.02151	+	7.22260i	0.255977	+	0.230482i
$983$	20.0319	−	27.5716i	0.638920	−	0.879397i	−0.359638	−	0.933092i	$-0.617100\pi$
$983$	20.0319	−	27.5716i	0.638920	−	0.879397i	0.998557	+	0.0536946i	$0.0170997\pi$
$984$	−0.913479	+	8.69117i	−0.0291206	+	0.277064i
$985$	0.467641	+	4.44930i	0.0149003	+	0.141767i
$986$	1.18851	+	0.686189i	0.0378500	+	0.0218527i
$987$	7.57976			0.241266
$988$	0.841524	−	4.35189i	0.0267725	−	0.138452i
$989$	0.476073	−	1.46520i	0.0151382	−	0.0465907i
$990$	1.20013	−	5.64616i	0.0381426	−	0.179447i
$991$	−3.92258	+	6.79411i	−0.124605	+	0.215822i	−0.921578	−	0.388192i	$-0.873100\pi$
$991$	−3.92258	+	6.79411i	−0.124605	+	0.215822i	0.796973	+	0.604014i	$0.206433\pi$
$992$	−29.9341	+	9.47856i	−0.950408	+	0.300945i
$993$			12.7595i			0.404911i
$994$	−1.92329	−	1.73173i	−0.0610029	−	0.0549273i
$995$	−0.238442	−	1.12178i	−0.00755912	−	0.0355628i
$996$	6.71042	+	9.23611i	0.212628	+	0.292657i
$997$	21.8329	+	37.8157i	0.691455	+	1.19764i	0.971361	+	0.237608i	$0.0763635\pi$
$997$	21.8329	+	37.8157i	0.691455	+	1.19764i	−0.279906	+	0.960028i	$0.590303\pi$
$998$	1.26043	−	2.18313i	0.0398983	−	0.0691058i
$999$	4.94453	−	0.519691i	0.156438	−	0.0164423i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.bs.a.4.14	✓	288
13.10	even	6	inner	403.2.bs.a.283.23	yes	288
31.8	even	5	inner	403.2.bs.a.225.23	yes	288
403.101	even	30	inner	403.2.bs.a.101.14	yes	288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.bs.a.4.14	✓	288	1.1	even	1	trivial
403.2.bs.a.101.14	yes	288	403.101	even	30	inner
403.2.bs.a.225.23	yes	288	31.8	even	5	inner
403.2.bs.a.283.23	yes	288	13.10	even	6	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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.bs (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.129772 + 0.610527i) q^{2} +(-0.324888 - 0.360825i) q^{3} +(1.47119 + 0.655015i) q^{4} -0.658726i q^{5} +(0.262455 - 0.151528i) q^{6} +(0.662294 - 1.48754i) q^{7} +(-1.32458 + 1.82312i) q^{8} +(0.288943 - 2.74911i) q^{9} +O(q^{10})\)	\(q+(-0.129772 + 0.610527i) q^{2} +(-0.324888 - 0.360825i) q^{3} +(1.47119 + 0.655015i) q^{4} -0.658726i q^{5} +(0.262455 - 0.151528i) q^{6} +(0.662294 - 1.48754i) q^{7} +(-1.32458 + 1.82312i) q^{8} +(0.288943 - 2.74911i) q^{9} +(0.402170 + 0.0854839i) q^{10} +(5.05103 - 0.530885i) q^{11} +(-0.241626 - 0.743648i) q^{12} +(-2.95551 - 2.06518i) q^{13} +(0.822235 + 0.597389i) q^{14} +(-0.237685 + 0.214012i) q^{15} +(1.21398 + 1.34827i) q^{16} +(-0.107385 + 1.02170i) q^{17} +(1.64091 + 0.533164i) q^{18} +(0.567301 + 0.510800i) q^{19} +(0.431475 - 0.969109i) q^{20} +(-0.751913 + 0.244311i) q^{21} +(-0.331361 + 3.15269i) q^{22} +(0.219261 - 0.0976215i) q^{23} +(1.08817 - 0.114371i) q^{24} +4.56608 q^{25} +(1.64439 - 1.53642i) q^{26} +(-2.26425 + 1.64507i) q^{27} +(1.94872 - 1.75463i) q^{28} +(-2.09348 - 0.444983i) q^{29} +(-0.0998157 - 0.172886i) q^{30} +(5.43726 + 1.19842i) q^{31} +(-4.88387 + 2.81971i) q^{32} +(-1.83258 - 1.65006i) q^{33} +(-0.609840 - 0.198149i) q^{34} +(-0.979879 - 0.436270i) q^{35} +(2.22580 - 3.85520i) q^{36} +(-1.53842 - 0.888208i) q^{37} +(-0.385477 + 0.280065i) q^{38} +(0.215041 + 1.73738i) q^{39} +(1.20094 + 0.872532i) q^{40} +(-1.66059 + 7.81245i) q^{41} +(-0.0515818 - 0.490768i) q^{42} +(4.29507 - 4.77016i) q^{43} +(7.77875 + 2.52747i) q^{44} +(-1.81091 - 0.190334i) q^{45} +(0.0311467 + 0.146534i) q^{46} +(-9.11802 - 2.96263i) q^{47} +(0.0920789 - 0.876072i) q^{48} +(2.90978 + 3.23164i) q^{49} +(-0.592547 + 2.78772i) q^{50} +(0.403543 - 0.293191i) q^{51} +(-2.99538 - 4.97417i) q^{52} +(8.85394 + 6.43276i) q^{53} +(-0.710527 - 1.59587i) q^{54} +(-0.349707 - 3.32724i) q^{55} +(1.83470 + 3.17780i) q^{56} -0.370649i q^{57} +(0.543349 - 1.22038i) q^{58} +(2.58037 + 12.1397i) q^{59} +(-0.489860 + 0.159165i) q^{60} +(-7.30070 - 12.6452i) q^{61} +(-1.43727 + 3.16408i) q^{62} +(-3.89804 - 2.25053i) q^{63} +(0.0335616 + 0.103292i) q^{64} +(-1.36039 + 1.94687i) q^{65} +(1.24522 - 0.904708i) q^{66} +(-10.8793 - 6.28118i) q^{67} +(-0.827212 + 1.43277i) q^{68} +(-0.106460 - 0.0473989i) q^{69} +(0.393515 - 0.541627i) q^{70} +(-2.53248 - 0.266175i) q^{71} +(4.62923 + 4.16818i) q^{72} +(3.80354 + 5.23513i) q^{73} +(0.741918 - 0.823984i) q^{74} +(-1.48347 - 1.64756i) q^{75} +(0.500024 + 1.12307i) q^{76} +(2.55556 - 7.86520i) q^{77} +(-1.08862 - 0.0941737i) q^{78} +(-8.00324 - 5.81469i) q^{79} +(0.888137 - 0.799682i) q^{80} +(-6.78233 - 1.44163i) q^{81} +(-4.55422 - 2.02767i) q^{82} +(-13.8860 + 4.51183i) q^{83} +(-1.26623 - 0.133086i) q^{84} +(0.673020 + 0.0707372i) q^{85} +(2.35493 + 3.24129i) q^{86} +(0.519586 + 0.899950i) q^{87} +(-5.72260 + 9.91184i) q^{88} +(-13.8329 + 1.45389i) q^{89} +(0.351209 - 1.08091i) q^{90} +(-5.02945 + 3.02867i) q^{91} +0.386518 q^{92} +(-1.33408 - 2.35125i) q^{93} +(2.99202 - 5.18234i) q^{94} +(0.336477 - 0.373696i) q^{95} +(2.60413 + 0.846135i) q^{96} +(-0.893245 + 2.00626i) q^{97} +(-2.35061 + 1.35713i) q^{98} -14.0392i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 9 q^{2} - q^{3} - 39 q^{4} - 42 q^{6} - 15 q^{7} + 31 q^{9}+O(q^{10}) \) 288 * q - 9 * q^2 - q^3 - 39 * q^4 - 42 * q^6 - 15 * q^7 + 31 * q^9	\( 288 q - 9 q^{2} - q^{3} - 39 q^{4} - 42 q^{6} - 15 q^{7} + 31 q^{9} + 3 q^{10} - 18 q^{11} - 46 q^{12} - q^{13} - 32 q^{14} + 18 q^{15} + 21 q^{16} - 15 q^{17} - 15 q^{19} + 51 q^{20} - 10 q^{22} - 4 q^{23} - 51 q^{24} - 296 q^{25} - 6 q^{26} - 52 q^{27} + 21 q^{28} + q^{29} + 60 q^{30} + 138 q^{32} + 69 q^{33} - 10 q^{35} + 128 q^{36} - 18 q^{37} + 32 q^{38} - 14 q^{39} + 60 q^{40} - 15 q^{41} - 49 q^{42} - 36 q^{43} + 6 q^{45} - 69 q^{46} + 21 q^{48} - 23 q^{49} + 117 q^{50} + 8 q^{51} + 26 q^{52} - 48 q^{53} + 75 q^{54} + 46 q^{55} - 98 q^{56} - 21 q^{58} - 105 q^{59} - 74 q^{61} - 3 q^{62} - 90 q^{63} + 90 q^{64} + 89 q^{65} - 8 q^{66} + 6 q^{67} - 182 q^{68} + 29 q^{69} + 3 q^{71} - 183 q^{72} - 53 q^{74} - 38 q^{75} + 144 q^{76} - 128 q^{78} - 72 q^{79} - 72 q^{80} + 11 q^{81} - 11 q^{82} - 33 q^{84} + 72 q^{85} - 18 q^{87} - 14 q^{88} + 81 q^{89} - 34 q^{90} - 48 q^{91} + 8 q^{92} + 72 q^{93} - 6 q^{94} + 141 q^{97} + 96 q^{98}+O(q^{100}) \) 288 * q - 9 * q^2 - q^3 - 39 * q^4 - 42 * q^6 - 15 * q^7 + 31 * q^9 + 3 * q^10 - 18 * q^11 - 46 * q^12 - q^13 - 32 * q^14 + 18 * q^15 + 21 * q^16 - 15 * q^17 - 15 * q^19 + 51 * q^20 - 10 * q^22 - 4 * q^23 - 51 * q^24 - 296 * q^25 - 6 * q^26 - 52 * q^27 + 21 * q^28 + q^29 + 60 * q^30 + 138 * q^32 + 69 * q^33 - 10 * q^35 + 128 * q^36 - 18 * q^37 + 32 * q^38 - 14 * q^39 + 60 * q^40 - 15 * q^41 - 49 * q^42 - 36 * q^43 + 6 * q^45 - 69 * q^46 + 21 * q^48 - 23 * q^49 + 117 * q^50 + 8 * q^51 + 26 * q^52 - 48 * q^53 + 75 * q^54 + 46 * q^55 - 98 * q^56 - 21 * q^58 - 105 * q^59 - 74 * q^61 - 3 * q^62 - 90 * q^63 + 90 * q^64 + 89 * q^65 - 8 * q^66 + 6 * q^67 - 182 * q^68 + 29 * q^69 + 3 * q^71 - 183 * q^72 - 53 * q^74 - 38 * q^75 + 144 * q^76 - 128 * q^78 - 72 * q^79 - 72 * q^80 + 11 * q^81 - 11 * q^82 - 33 * q^84 + 72 * q^85 - 18 * q^87 - 14 * q^88 + 81 * q^89 - 34 * q^90 - 48 * q^91 + 8 * q^92 + 72 * q^93 - 6 * q^94 + 141 * q^97 + 96 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more