LMFDB - Embedded newform 513.2.g.c.505.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [513,2,Mod(64,513)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("513.64"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(513, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 513 = 3^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	513.g (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [32,-1,0,-17,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$4.09632562369$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 171)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			505.7
Character	$\chi$	$=$	513.505
Dual form			513.2.g.c.64.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0973467 - 0.168609i) q^{2} +(0.981047 - 1.69922i) q^{4} +1.90563 q^{5} +(1.69446 - 2.93489i) q^{7} -0.771394 q^{8} +(-0.185507 - 0.321308i) q^{10} +(0.311589 - 0.539688i) q^{11} +(-1.84489 + 3.19545i) q^{13} -0.659800 q^{14} +(-1.88700 - 3.26838i) q^{16} +(3.04830 - 5.27981i) q^{17} +(-1.14464 + 4.20592i) q^{19} +(1.86952 - 3.23810i) q^{20} -0.121329 q^{22} +(-3.92442 + 6.79729i) q^{23} -1.36856 q^{25} +0.718377 q^{26} +(-3.32469 - 5.75853i) q^{28} +1.18459 q^{29} +(-0.910124 - 1.57638i) q^{31} +(-1.13878 + 1.97243i) q^{32} -1.18697 q^{34} +(3.22902 - 5.59282i) q^{35} +5.63896 q^{37} +(0.820586 - 0.216435i) q^{38} -1.46999 q^{40} +4.03639 q^{41} +(-2.54719 - 4.41186i) q^{43} +(-0.611367 - 1.05892i) q^{44} +1.52812 q^{46} +12.8718 q^{47} +(-2.24237 - 3.88391i) q^{49} +(0.133225 + 0.230752i) q^{50} +(3.61985 + 6.26977i) q^{52} +(-1.93076 - 3.34418i) q^{53} +(0.593775 - 1.02845i) q^{55} +(-1.30709 + 2.26395i) q^{56} +(-0.115316 - 0.199733i) q^{58} -8.50437 q^{59} +3.64691 q^{61} +(-0.177195 + 0.306911i) q^{62} -7.10458 q^{64} +(-3.51569 + 6.08935i) q^{65} +(-0.523023 + 0.905902i) q^{67} +(-5.98105 - 10.3595i) q^{68} -1.25734 q^{70} +(-1.56289 + 2.70700i) q^{71} +(2.06890 - 3.58345i) q^{73} +(-0.548934 - 0.950782i) q^{74} +(6.02386 + 6.07121i) q^{76} +(-1.05595 - 1.82896i) q^{77} +(8.16729 + 14.1462i) q^{79} +(-3.59593 - 6.22834i) q^{80} +(-0.392929 - 0.680574i) q^{82} +(-5.35528 + 9.27561i) q^{83} +(5.80894 - 10.0614i) q^{85} +(-0.495921 + 0.858960i) q^{86} +(-0.240358 + 0.416312i) q^{88} +(5.25259 + 9.09775i) q^{89} +(6.25218 + 10.8291i) q^{91} +(7.70007 + 13.3369i) q^{92} +(-1.25303 - 2.17031i) q^{94} +(-2.18127 + 8.01495i) q^{95} +(-7.34332 - 12.7190i) q^{97} +(-0.436576 + 0.756171i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - q^{2} - 17 q^{4} + 6 q^{5} + q^{7} + 36 q^{8} - 8 q^{10} - 7 q^{11} - 4 q^{13} + 2 q^{14} - 11 q^{16} + 7 q^{17} + 7 q^{19} + 3 q^{20} + 16 q^{22} - 5 q^{23} + 18 q^{25} + 4 q^{26} - 10 q^{28}+ \cdots - 18 q^{98}+O(q^{100}) $ 32 * q - q^2 - 17 * q^4 + 6 * q^5 + q^7 + 36 * q^8 - 8 * q^10 - 7 * q^11 - 4 * q^13 + 2 * q^14 - 11 * q^16 + 7 * q^17 + 7 * q^19 + 3 * q^20 + 16 * q^22 - 5 * q^23 + 18 * q^25 + 4 * q^26 - 10 * q^28 + 20 * q^29 - 10 * q^31 - 17 * q^32 + 26 * q^34 + 3 * q^35 + 2 * q^37 - 38 * q^38 - 24 * q^40 + 12 * q^41 + 7 * q^43 - 20 * q^44 - 18 * q^47 - 13 * q^49 - q^50 + 19 * q^52 - 16 * q^53 + 15 * q^55 + 6 * q^56 + 74 * q^59 + 24 * q^61 - 54 * q^62 - 64 * q^64 - 54 * q^65 - 11 * q^67 + 2 * q^68 - 48 * q^70 - 9 * q^71 - 10 * q^73 - 6 * q^74 + 29 * q^76 - 46 * q^77 - 8 * q^79 + 24 * q^80 + 7 * q^82 - 3 * q^83 - 27 * q^85 - 17 * q^86 + 9 * q^88 - 30 * q^89 - q^91 + 17 * q^92 - 18 * q^94 + 6 * q^95 - 18 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/513\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.0973467	−	0.168609i	−0.0688345	−	0.119225i	0.829554	−	0.558426i	$-0.188595\pi$
$2$	−0.0973467	−	0.168609i	−0.0688345	−	0.119225i	−0.898389	+	0.439202i	$0.855261\pi$
$3$		0			0
$3$		0			0
$4$	0.981047	−	1.69922i	0.490524	−	0.849612i
$5$	1.90563			0.852225			0.426113	−	0.904670i	$-0.359883\pi$
$5$	1.90563			0.852225			0.426113	+	0.904670i	$0.359883\pi$
$6$		0			0
$7$	1.69446	−	2.93489i	0.640445	−	1.10928i	−0.344889	−	0.938644i	$-0.612083\pi$
$7$	1.69446	−	2.93489i	0.640445	−	1.10928i	0.985334	−	0.170639i	$-0.0545833\pi$
$8$	−0.771394			−0.272729
$9$		0			0
$10$	−0.185507	−	0.321308i	−0.0586625	−	0.101606i
$11$	0.311589	−	0.539688i	0.0939477	−	0.162722i	−0.815221	−	0.579150i	$-0.803385\pi$
$11$	0.311589	−	0.539688i	0.0939477	−	0.162722i	0.909169	+	0.416428i	$0.136718\pi$
$12$		0			0
$13$	−1.84489	+	3.19545i	−0.511681	+	0.886258i	0.488227	+	0.872717i	$0.337644\pi$
$13$	−1.84489	+	3.19545i	−0.511681	+	0.886258i	−0.999908	+	0.0135411i	$0.995690\pi$
$14$	−0.659800			−0.176339
$15$		0			0
$16$	−1.88700	−	3.26838i	−0.471750	−	0.817096i
$17$	3.04830	−	5.27981i	0.739321	−	1.28054i	−0.213481	−	0.976947i	$-0.568480\pi$
$17$	3.04830	−	5.27981i	0.739321	−	1.28054i	0.952802	−	0.303594i	$-0.0981866\pi$
$18$		0			0
$19$	−1.14464	+	4.20592i	−0.262599	+	0.964905i
$19$	−1.14464	+	4.20592i	−0.262599	+	0.964905i
$20$	1.86952	−	3.23810i	0.418037	−	0.724061i
$21$		0			0
$22$	−0.121329			−0.0258674
$23$	−3.92442	+	6.79729i	−0.818297	+	1.41733i	0.0886387	+	0.996064i	$0.471748\pi$
$23$	−3.92442	+	6.79729i	−0.818297	+	1.41733i	−0.906936	+	0.421269i	$0.861585\pi$
$24$		0			0
$25$	−1.36856			−0.273712
$26$	0.718377			0.140885
$27$		0			0
$28$	−3.32469	−	5.75853i	−0.628307	−	1.08826i
$29$	1.18459			0.219972			0.109986	−	0.993933i	$-0.464919\pi$
$29$	1.18459			0.219972			0.109986	+	0.993933i	$0.464919\pi$
$30$		0			0
$31$	−0.910124	−	1.57638i	−0.163463	−	0.283126i	0.772645	−	0.634838i	$-0.218933\pi$
$31$	−0.910124	−	1.57638i	−0.163463	−	0.283126i	−0.936108	+	0.351711i	$0.885600\pi$
$32$	−1.13878	+	1.97243i	−0.201310	+	0.348679i
$33$		0			0
$34$	−1.18697			−0.203563
$35$	3.22902	−	5.59282i	0.545803	−	0.945359i
$36$		0			0
$37$	5.63896			0.927039			0.463520	−	0.886087i	$-0.346586\pi$
$37$	5.63896			0.927039			0.463520	+	0.886087i	$0.346586\pi$
$38$	0.820586	−	0.216435i	0.133117	−	0.0351104i
$39$		0			0
$40$	−1.46999			−0.232426
$41$	4.03639			0.630378			0.315189	−	0.949029i	$-0.397932\pi$
$41$	4.03639			0.630378			0.315189	+	0.949029i	$0.397932\pi$
$42$		0			0
$43$	−2.54719	−	4.41186i	−0.388442	−	0.672802i	0.603798	−	0.797138i	$-0.293653\pi$
$43$	−2.54719	−	4.41186i	−0.388442	−	0.672802i	−0.992240	+	0.124335i	$0.960320\pi$
$44$	−0.611367	−	1.05892i	−0.0921671	−	0.159638i
$45$		0			0
$46$	1.52812			0.225308
$47$	12.8718			1.87754			0.938772	−	0.344539i	$-0.111965\pi$
$47$	12.8718			1.87754			0.938772	+	0.344539i	$0.111965\pi$
$48$		0			0
$49$	−2.24237	−	3.88391i	−0.320339	−	0.554844i
$50$	0.133225	+	0.230752i	0.0188408	+	0.0326333i
$51$		0			0
$52$	3.61985	+	6.26977i	0.501983	+	0.869461i
$53$	−1.93076	−	3.34418i	−0.265211	−	0.459359i	0.702408	−	0.711775i	$-0.252108\pi$
$53$	−1.93076	−	3.34418i	−0.265211	−	0.459359i	−0.967619	+	0.252416i	$0.918775\pi$
$54$		0			0
$55$	0.593775	−	1.02845i	0.0800646	−	0.138676i
$56$	−1.30709	+	2.26395i	−0.174668	+	0.302534i
$57$		0			0
$58$	−0.115316	−	0.199733i	−0.0151417	−	0.0262262i
$59$	−8.50437			−1.10717			−0.553587	−	0.832791i	$-0.686741\pi$
$59$	−8.50437			−1.10717			−0.553587	+	0.832791i	$0.686741\pi$
$60$		0			0
$61$	3.64691			0.466939			0.233469	−	0.972364i	$-0.424992\pi$
$61$	3.64691			0.466939			0.233469	+	0.972364i	$0.424992\pi$
$62$	−0.177195	+	0.306911i	−0.0225038	+	0.0389778i
$63$		0			0
$64$	−7.10458			−0.888073
$65$	−3.51569	+	6.08935i	−0.436068	+	0.755291i
$66$		0			0
$67$	−0.523023	+	0.905902i	−0.0638974	+	0.110674i	−0.896204	−	0.443641i	$-0.853686\pi$
$67$	−0.523023	+	0.905902i	−0.0638974	+	0.110674i	0.832307	+	0.554315i	$0.187020\pi$
$68$	−5.98105	−	10.3595i	−0.725309	−	1.25627i
$69$		0			0
$70$	−1.25734			−0.150280
$71$	−1.56289	+	2.70700i	−0.185481	+	0.321262i	−0.943738	−	0.330693i	$-0.892718\pi$
$71$	−1.56289	+	2.70700i	−0.185481	+	0.321262i	0.758258	+	0.651955i	$0.226051\pi$
$72$		0			0
$73$	2.06890	−	3.58345i	0.242147	−	0.419411i	−0.719179	−	0.694825i	$-0.755482\pi$
$73$	2.06890	−	3.58345i	0.242147	−	0.419411i	0.961326	+	0.275414i	$0.0888151\pi$
$74$	−0.548934	−	0.950782i	−0.0638123	−	0.110526i
$75$		0			0
$76$	6.02386	+	6.07121i	0.690984	+	0.696416i
$77$	−1.05595	−	1.82896i	−0.120337	−	0.208429i
$78$		0			0
$79$	8.16729	+	14.1462i	0.918892	+	1.59157i	0.801100	+	0.598530i	$0.204248\pi$
$79$	8.16729	+	14.1462i	0.918892	+	1.59157i	0.117792	+	0.993038i	$0.462418\pi$
$80$	−3.59593	−	6.22834i	−0.402038	−	0.696350i
$81$		0			0
$82$	−0.392929	−	0.680574i	−0.0433918	−	0.0751568i
$83$	−5.35528	+	9.27561i	−0.587818	+	1.01813i	0.406700	+	0.913562i	$0.366679\pi$
$83$	−5.35528	+	9.27561i	−0.587818	+	1.01813i	−0.994518	+	0.104569i	$0.966654\pi$
$84$		0			0
$85$	5.80894	−	10.0614i	0.630068	−	1.09131i
$86$	−0.495921	+	0.858960i	−0.0534765	+	0.0926240i
$87$		0			0
$88$	−0.240358	+	0.416312i	−0.0256222	+	0.0443790i
$89$	5.25259	+	9.09775i	0.556773	+	0.964359i	0.997763	+	0.0668472i	$0.0212940\pi$
$89$	5.25259	+	9.09775i	0.556773	+	0.964359i	−0.440990	+	0.897512i	$0.645373\pi$
$90$		0			0
$91$	6.25218	+	10.8291i	0.655407	+	1.13520i
$92$	7.70007	+	13.3369i	0.802788	+	1.39047i
$93$		0			0
$94$	−1.25303	−	2.17031i	−0.129240	−	0.223850i
$95$	−2.18127	+	8.01495i	−0.223794	+	0.822316i
$96$		0			0
$97$	−7.34332	−	12.7190i	−0.745602	−	1.29142i	−0.949913	−	0.312514i	$-0.898829\pi$
$97$	−7.34332	−	12.7190i	−0.745602	−	1.29142i	0.204312	−	0.978906i	$-0.434504\pi$
$98$	−0.436576	+	0.756171i	−0.0441008	+	0.0763848i
$99$		0			0
$100$	−1.34262	+	2.32549i	−0.134262	+	0.232549i
$101$	−8.53801			−0.849563			−0.424782	−	0.905296i	$-0.639649\pi$
$101$	−8.53801			−0.849563			−0.424782	+	0.905296i	$0.639649\pi$
$102$		0			0
$103$	6.69656	+	11.5988i	0.659832	+	1.14286i	0.980659	+	0.195725i	$0.0627059\pi$
$103$	6.69656	+	11.5988i	0.659832	+	1.14286i	−0.320827	+	0.947138i	$0.603961\pi$
$104$	1.42314	−	2.46495i	0.139550	−	0.241708i
$105$		0			0
$106$	−0.375907	+	0.651090i	−0.0365113	+	0.0632395i
$107$	−10.1943			−0.985524			−0.492762	−	0.870164i	$-0.664013\pi$
$107$	−10.1943			−0.985524			−0.492762	+	0.870164i	$0.664013\pi$
$108$		0			0
$109$	−0.945297	+	1.63730i	−0.0905431	+	0.156825i	−0.907740	−	0.419534i	$-0.862194\pi$
$109$	−0.945297	+	1.63730i	−0.0905431	+	0.156825i	0.817197	+	0.576359i	$0.195527\pi$
$110$	−0.231208			−0.0220448
$111$		0			0
$112$	−12.7898			−1.20852
$113$	4.93706	+	8.55125i	0.464440	+	0.804434i	0.999176	−	0.0405856i	$-0.0129223\pi$
$113$	4.93706	+	8.55125i	0.464440	+	0.804434i	−0.534736	+	0.845019i	$0.679589\pi$
$114$		0			0
$115$	−7.47850	+	12.9531i	−0.697374	+	1.20789i
$116$	1.16214	−	2.01288i	0.107902	−	0.186891i
$117$		0			0
$118$	0.827873	+	1.43392i	0.0762118	+	0.132003i
$119$	−10.3304	−	17.8928i	−0.946988	−	1.64023i
$120$		0			0
$121$	5.30582	+	9.18996i	0.482348	+	0.835451i
$122$	−0.355014	−	0.614903i	−0.0321415	−	0.0556707i
$123$		0			0
$124$	−3.57150			−0.320730
$125$	−12.1361			−1.08549
$126$		0			0
$127$	−4.32772	−	7.49583i	−0.384023	−	0.665148i	0.607610	−	0.794236i	$-0.292128\pi$
$127$	−4.32772	−	7.49583i	−0.384023	−	0.665148i	−0.991633	+	0.129088i	$0.958795\pi$
$128$	2.96917	+	5.14275i	0.262440	+	0.454559i
$129$		0			0
$130$	1.36896			0.120066
$131$	−2.08447			−0.182121			−0.0910604	−	0.995845i	$-0.529026\pi$
$131$	−2.08447			−0.182121			−0.0910604	+	0.995845i	$0.529026\pi$
$132$		0			0
$133$	10.4044	+	10.4862i	0.902172	+	0.909265i
$134$	0.203658			0.0175934
$135$		0			0
$136$	−2.35144	+	4.07281i	−0.201634	+	0.349241i
$137$	17.0350			1.45540			0.727700	−	0.685896i	$-0.240589\pi$
$137$	17.0350			1.45540			0.727700	+	0.685896i	$0.240589\pi$
$138$		0			0
$139$	−1.13106	+	1.95905i	−0.0959351	+	0.166164i	−0.909998	−	0.414612i	$-0.863917\pi$
$139$	−1.13106	+	1.95905i	−0.0959351	+	0.166164i	0.814063	+	0.580776i	$0.197251\pi$
$140$	−6.33563	−	10.9736i	−0.535459	−	0.927442i
$141$		0			0
$142$	0.608568			0.0510699
$143$	1.14970	+	1.99133i	0.0961425	+	0.166524i
$144$		0			0
$145$	2.25739			0.187466
$146$	−0.805604			−0.0666723
$147$		0			0
$148$	5.53209	−	9.58186i	0.454735	−	0.787624i
$149$	−2.40529			−0.197049			−0.0985246	−	0.995135i	$-0.531412\pi$
$149$	−2.40529			−0.197049			−0.0985246	+	0.995135i	$0.531412\pi$
$150$		0			0
$151$	3.86313	−	6.69114i	0.314377	−	0.544517i	−0.664928	−	0.746908i	$-0.731538\pi$
$151$	3.86313	−	6.69114i	0.314377	−	0.544517i	0.979305	+	0.202391i	$0.0648710\pi$
$152$	0.882971	−	3.24442i	0.0716184	−	0.263157i
$153$		0			0
$154$	−0.205586	+	0.356086i	−0.0165666	+	0.0286942i
$155$	−1.73436	−	3.00401i	−0.139307	−	0.241288i
$156$		0			0
$157$	−5.43874			−0.434058			−0.217029	−	0.976165i	$-0.569637\pi$
$157$	−5.43874			−0.434058			−0.217029	+	0.976165i	$0.569637\pi$
$158$	1.59012	−	2.75417i	0.126503	−	0.219110i
$159$		0			0
$160$	−2.17010	+	3.75872i	−0.171561	+	0.297153i
$161$	13.2995	+	23.0354i	1.04815	+	1.81545i
$162$		0			0
$163$	−7.27424			−0.569763			−0.284881	−	0.958563i	$-0.591954\pi$
$163$	−7.27424			−0.569763			−0.284881	+	0.958563i	$0.591954\pi$
$164$	3.95989	−	6.85873i	0.309216	−	0.535577i
$165$		0			0
$166$	2.08527			0.161849
$167$	−2.23165	+	3.86534i	−0.172691	+	0.299109i	−0.939360	−	0.342934i	$-0.888579\pi$
$167$	−2.23165	+	3.86534i	−0.172691	+	0.299109i	0.766669	+	0.642042i	$0.221913\pi$
$168$		0			0
$169$	−0.307257	−	0.532185i	−0.0236352	−	0.0409373i
$170$	−2.26192			−0.173482
$171$		0			0
$172$	−9.99565			−0.762161
$173$	6.00303	+	10.3976i	0.456402	+	0.790512i	0.998768	−	0.0496308i	$-0.0158045\pi$
$173$	6.00303	+	10.3976i	0.456402	+	0.790512i	−0.542365	+	0.840143i	$0.682471\pi$
$174$		0			0
$175$	−2.31897	+	4.01657i	−0.175298	+	0.303624i
$176$	−2.35188			−0.177279
$177$		0			0
$178$	1.02264	−	1.77127i	0.0766504	−	0.132762i
$179$	−20.0123			−1.49579			−0.747897	−	0.663815i	$-0.768936\pi$
$179$	−20.0123			−1.49579			−0.747897	+	0.663815i	$0.768936\pi$
$180$		0			0
$181$	−6.04514	−	10.4705i	−0.449332	−	0.778265i	0.549011	−	0.835815i	$-0.315005\pi$
$181$	−6.04514	−	10.4705i	−0.449332	−	0.778265i	−0.998343	+	0.0575498i	$0.981671\pi$
$182$	1.21726	−	2.10836i	0.0902293	−	0.156282i
$183$		0			0
$184$	3.02727	−	5.24339i	0.223173	−	0.386548i
$185$	10.7458			0.790046
$186$		0			0
$187$	−1.89963	−	3.29026i	−0.138915	−	0.240608i
$188$	12.6278	−	21.8721i	0.920980	−	1.59518i
$189$		0			0
$190$	1.56374	−	0.412446i	0.113445	−	0.0299220i
$191$	−1.34685	+	2.33282i	−0.0974548	+	0.168797i	−0.910631	−	0.413222i	$-0.864403\pi$
$191$	−1.34685	+	2.33282i	−0.0974548	+	0.168797i	0.813176	+	0.582018i	$0.197737\pi$
$192$		0			0
$193$	12.5244			0.901523			0.450762	−	0.892644i	$-0.351152\pi$
$193$	12.5244			0.901523			0.450762	+	0.892644i	$0.351152\pi$
$194$	−1.42970	+	2.47631i	−0.102646	+	0.177789i
$195$		0			0
$196$	−8.79950			−0.628536
$197$	11.8545			0.844595			0.422297	−	0.906457i	$-0.361224\pi$
$197$	11.8545			0.844595			0.422297	+	0.906457i	$0.361224\pi$
$198$		0			0
$199$	3.01833	+	5.22790i	0.213964	+	0.370596i	0.952952	−	0.303123i	$-0.0980292\pi$
$199$	3.01833	+	5.22790i	0.213964	+	0.370596i	−0.738988	+	0.673719i	$0.764696\pi$
$200$	1.05570			0.0746492
$201$		0			0
$202$	0.831147	+	1.43959i	0.0584793	+	0.101289i
$203$	2.00723	−	3.47663i	0.140880	−	0.244012i
$204$		0			0
$205$	7.69188			0.537224
$206$	1.30378	−	2.25821i	0.0908385	−	0.157337i
$207$		0			0
$208$	13.9253			0.965543
$209$	1.91323	+	1.92827i	0.132341	+	0.133381i
$210$		0			0
$211$	−5.65425			−0.389255			−0.194627	−	0.980877i	$-0.562350\pi$
$211$	−5.65425			−0.389255			−0.194627	+	0.980877i	$0.562350\pi$
$212$	−7.57669			−0.520369
$213$		0			0
$214$	0.992386	+	1.71886i	0.0678381	+	0.117499i
$215$	−4.85401	−	8.40739i	−0.331040	−	0.573379i
$216$		0			0
$217$	−6.16867			−0.418757
$218$	0.368086			0.0249300
$219$		0			0
$220$	−1.16504	−	2.01791i	−0.0785471	−	0.136048i
$221$	11.2476	+	19.4813i	0.756593	+	1.31046i
$222$		0			0
$223$	−14.5197	−	25.1489i	−0.972312	−	1.68409i	−0.688535	−	0.725203i	$-0.741746\pi$
$223$	−14.5197	−	25.1489i	−0.972312	−	1.68409i	−0.283777	−	0.958890i	$-0.591587\pi$
$224$	3.85923	+	6.68439i	0.257856	+	0.446619i
$225$		0			0
$226$	0.961214	−	1.66487i	0.0639390	−	0.110746i
$227$	11.5488	−	20.0031i	0.766522	−	1.32765i	−0.172916	−	0.984937i	$-0.555319\pi$
$227$	11.5488	−	20.0031i	0.766522	−	1.32765i	0.939438	−	0.342718i	$-0.111348\pi$
$228$		0			0
$229$	−1.94136	−	3.36253i	−0.128289	−	0.222202i	0.794725	−	0.606970i	$-0.207615\pi$
$229$	−1.94136	−	3.36253i	−0.128289	−	0.222202i	−0.923014	+	0.384767i	$0.874282\pi$
$230$	2.91203			0.192014
$231$		0			0
$232$	−0.913783			−0.0599928
$233$	3.05545	−	5.29220i	0.200169	−	0.346703i	−0.748414	−	0.663232i	$-0.769184\pi$
$233$	3.05545	−	5.29220i	0.200169	−	0.346703i	0.948583	+	0.316529i	$0.102517\pi$
$234$		0			0
$235$	24.5289			1.60009
$236$	−8.34319	+	14.4508i	−0.543095	+	0.940669i
$237$		0			0
$238$	−2.01127	+	3.48361i	−0.130371	+	0.225809i
$239$	9.61029	+	16.6455i	0.621638	+	1.07671i	0.989181	+	0.146702i	$0.0468659\pi$
$239$	9.61029	+	16.6455i	0.621638	+	1.07671i	−0.367543	+	0.930007i	$0.619801\pi$
$240$		0			0
$241$	10.6740			0.687573			0.343786	−	0.939048i	$-0.388290\pi$
$241$	10.6740			0.687573			0.343786	+	0.939048i	$0.388290\pi$
$242$	1.03301	−	1.78922i	0.0664044	−	0.115016i
$243$		0			0
$244$	3.57779	−	6.19691i	0.229044	−	0.396717i
$245$	−4.27314	−	7.40130i	−0.273001	−	0.472852i
$246$		0			0
$247$	−11.3281	−	11.4171i	−0.720787	−	0.726454i
$248$	0.702064	+	1.21601i	0.0445811	+	0.0772168i
$249$		0			0
$250$	1.18141	+	2.04627i	0.0747192	+	0.129417i
$251$	−9.04512	−	15.6666i	−0.570923	−	0.988867i	−0.996471	−	0.0839318i	$-0.973252\pi$
$251$	−9.04512	−	15.6666i	−0.570923	−	0.988867i	0.425549	−	0.904936i	$-0.360081\pi$
$252$		0			0
$253$	2.44561	+	4.23592i	0.153754	+	0.266310i
$254$	−0.842579	+	1.45939i	−0.0528681	+	0.0915702i
$255$		0			0
$256$	−6.52650	+	11.3042i	−0.407906	+	0.706515i
$257$	11.6856	−	20.2401i	0.728930	−	1.26254i	−0.228406	−	0.973566i	$-0.573351\pi$
$257$	11.6856	−	20.2401i	0.728930	−	1.26254i	0.957336	−	0.288978i	$-0.0933154\pi$
$258$		0			0
$259$	9.55498	−	16.5497i	0.593718	−	1.02835i
$260$	6.89811	+	11.9479i	0.427803	+	0.740976i
$261$		0			0
$262$	0.202916	+	0.351461i	0.0125362	+	0.0217133i
$263$	−12.1983	−	21.1280i	−0.752177	−	1.30281i	−0.946766	−	0.321924i	$-0.895670\pi$
$263$	−12.1983	−	21.1280i	−0.752177	−	1.30281i	0.194589	−	0.980885i	$-0.437663\pi$
$264$		0			0
$265$	−3.67933	−	6.37279i	−0.226019	−	0.391477i
$266$	0.755235	−	2.77507i	0.0463064	−	0.170150i
$267$		0			0
$268$	1.02622	+	1.77746i	0.0626864	+	0.108576i
$269$	−12.5243	+	21.6927i	−0.763620	+	1.32263i	0.177354	+	0.984147i	$0.443246\pi$
$269$	−12.5243	+	21.6927i	−0.763620	+	1.32263i	−0.940973	+	0.338481i	$0.890087\pi$
$270$		0			0
$271$	−1.42509	+	2.46833i	−0.0865679	+	0.149940i	−0.906058	−	0.423153i	$-0.860923\pi$
$271$	−1.42509	+	2.46833i	−0.0865679	+	0.149940i	0.819490	+	0.573093i	$0.194257\pi$
$272$	−23.0086			−1.39510
$273$		0			0
$274$	−1.65830	−	2.87226i	−0.100182	−	0.173520i
$275$	−0.426429	+	0.738596i	−0.0257146	+	0.0445390i
$276$		0			0
$277$	−1.14916	+	1.99041i	−0.0690465	+	0.119592i	−0.898482	−	0.439011i	$-0.855329\pi$
$277$	−1.14916	+	1.99041i	−0.0690465	+	0.119592i	0.829435	+	0.558603i	$0.188662\pi$
$278$	0.440419			0.0264146
$279$		0			0
$280$	−2.49084	+	4.31427i	−0.148856	+	0.257827i
$281$	−14.1908			−0.846554			−0.423277	−	0.906000i	$-0.639120\pi$
$281$	−14.1908			−0.846554			−0.423277	+	0.906000i	$0.639120\pi$
$282$		0			0
$283$	−8.27764			−0.492055			−0.246027	−	0.969263i	$-0.579125\pi$
$283$	−8.27764			−0.492055			−0.246027	+	0.969263i	$0.579125\pi$
$284$	3.06654	+	5.31140i	0.181965	+	0.315173i
$285$		0			0
$286$	0.223838	−	0.387700i	0.0132358	−	0.0229252i
$287$	6.83949	−	11.8464i	0.403723	−	0.699268i
$288$		0			0
$289$	−10.0842	−	17.4664i	−0.593190	−	1.02744i
$290$	−0.219749	−	0.380617i	−0.0129041	−	0.0223506i
$291$		0			0
$292$	−4.05939	−	7.03106i	−0.237558	−	0.411462i
$293$	−9.90459	−	17.1553i	−0.578632	−	1.00222i	−0.995637	−	0.0933160i	$-0.970253\pi$
$293$	−9.90459	−	17.1553i	−0.578632	−	1.00222i	0.417004	−	0.908905i	$-0.363080\pi$
$294$		0			0
$295$	−16.2062			−0.943562
$296$	−4.34986			−0.252830
$297$		0			0
$298$	0.234147	+	0.405555i	0.0135638	+	0.0234932i
$299$	−14.4803	−	25.0805i	−0.837415	−	1.45044i
$300$		0			0
$301$	−17.2644			−0.995104
$302$	−1.50425			−0.0865600
$303$		0			0
$304$	15.9065	−	4.19545i	0.912301	−	0.240626i
$305$	6.94967			0.397937
$306$		0			0
$307$	−9.08098	+	15.7287i	−0.518279	+	0.897685i	0.481496	+	0.876448i	$0.340094\pi$
$307$	−9.08098	+	15.7287i	−0.518279	+	0.897685i	−0.999774	+	0.0212367i	$0.993240\pi$
$308$	−4.14374			−0.236112
$309$		0			0
$310$	−0.337669	+	0.584860i	−0.0191783	+	0.0332178i
$311$	1.15887	+	2.00723i	0.0657137	+	0.113820i	0.897010	−	0.442010i	$-0.145734\pi$
$311$	1.15887	+	2.00723i	0.0657137	+	0.113820i	−0.831297	+	0.555829i	$0.812401\pi$
$312$		0			0
$313$	18.7101			1.05756			0.528779	−	0.848759i	$-0.322650\pi$
$313$	18.7101			1.05756			0.528779	+	0.848759i	$0.322650\pi$
$314$	0.529443	+	0.917023i	0.0298782	+	0.0517506i
$315$		0			0
$316$	32.0500			1.80295
$317$	14.3891			0.808171			0.404086	−	0.914721i	$-0.367590\pi$
$317$	14.3891			0.808171			0.404086	+	0.914721i	$0.367590\pi$
$318$		0			0
$319$	0.369105	−	0.639308i	0.0206659	−	0.0357944i
$320$	−13.5387			−0.756838
$321$		0			0
$322$	2.58933	−	4.48485i	0.144298	−	0.249931i
$323$	18.7172	+	18.8644i	1.04146	+	1.04964i
$324$		0			0
$325$	2.52485	−	4.37316i	0.140053	−	0.242580i
$326$	0.708124	+	1.22651i	0.0392194	+	0.0679299i
$327$		0			0
$328$	−3.11365			−0.171922
$329$	21.8107	−	37.7773i	1.20246	−	2.08273i
$330$		0			0
$331$	−14.2961	+	24.7615i	−0.785784	+	1.36102i	0.142746	+	0.989759i	$0.454407\pi$
$331$	−14.2961	+	24.7615i	−0.785784	+	1.36102i	−0.928530	+	0.371258i	$0.878927\pi$
$332$	10.5076	+	18.1996i	0.576677	+	0.998834i
$333$		0			0
$334$	0.868977			0.0475483
$335$	−0.996689	+	1.72632i	−0.0544550	+	0.0943188i
$336$		0			0
$337$	20.3107			1.10640			0.553199	−	0.833049i	$-0.313407\pi$
$337$	20.3107			1.10640			0.553199	+	0.833049i	$0.313407\pi$
$338$	−0.0598209	+	0.103613i	−0.00325383	+	0.00563580i
$339$		0			0
$340$	−11.3977	−	19.7414i	−0.618126	−	1.07063i
$341$	−1.13434			−0.0614279
$342$		0			0
$343$	8.52398			0.460251
$344$	1.96488	+	3.40328i	0.105939	+	0.183493i
$345$		0			0
$346$	1.16875	−	2.02434i	0.0628325	−	0.108829i
$347$	35.7597			1.91968			0.959841	−	0.280544i	$-0.0905149\pi$
$347$	35.7597			1.91968			0.959841	+	0.280544i	$0.0905149\pi$
$348$		0			0
$349$	−1.94971	+	3.37700i	−0.104366	+	0.180767i	−0.913479	−	0.406886i	$-0.866615\pi$
$349$	−1.94971	+	3.37700i	−0.104366	+	0.180767i	0.809113	+	0.587653i	$0.199948\pi$
$350$	0.902976			0.0482661
$351$		0			0
$352$	0.709663	+	1.22917i	0.0378252	+	0.0655151i
$353$	−5.00251	+	8.66460i	−0.266257	+	0.461170i	−0.967892	−	0.251366i	$-0.919120\pi$
$353$	−5.00251	+	8.66460i	−0.266257	+	0.461170i	0.701635	+	0.712536i	$0.252454\pi$
$354$		0			0
$355$	−2.97829	+	5.15856i	−0.158071	+	0.273788i
$356$	20.6121			1.09244
$357$		0			0
$358$	1.94814	+	3.37427i	0.102962	+	0.178336i
$359$	−2.25793	+	3.91084i	−0.119169	+	0.206406i	−0.919439	−	0.393234i	$-0.871356\pi$
$359$	−2.25793	+	3.91084i	−0.119169	+	0.206406i	0.800270	+	0.599640i	$0.204690\pi$
$360$		0			0
$361$	−16.3796	−	9.62856i	−0.862083	−	0.506766i
$362$	−1.17695	+	2.03854i	−0.0618591	+	0.107143i
$363$		0			0
$364$	24.5348			1.28597
$365$	3.94257	−	6.82874i	0.206364	−	0.357432i
$366$		0			0
$367$	−23.4866			−1.22599			−0.612996	−	0.790086i	$-0.710036\pi$
$367$	−23.4866			−1.22599			−0.612996	+	0.790086i	$0.710036\pi$
$368$	29.6215			1.54413
$369$		0			0
$370$	−1.04607	−	1.81184i	−0.0543825	−	0.0941932i
$371$	−13.0864			−0.679412
$372$		0			0
$373$	−12.2017	−	21.1340i	−0.631782	−	1.09428i	−0.987187	−	0.159566i	$-0.948991\pi$
$373$	−12.2017	−	21.1340i	−0.631782	−	1.09428i	0.355406	−	0.934712i	$-0.384343\pi$
$374$	−0.369846	+	0.640592i	−0.0191243	+	0.0331242i
$375$		0			0
$376$	−9.92922			−0.512061
$377$	−2.18544	+	3.78529i	−0.112556	+	0.194952i
$378$		0			0
$379$	−17.7118			−0.909793			−0.454896	−	0.890544i	$-0.650324\pi$
$379$	−17.7118			−0.909793			−0.454896	+	0.890544i	$0.650324\pi$
$380$	11.4793	+	11.5695i	0.588874	+	0.593503i
$381$		0			0
$382$	0.524447			0.0268330
$383$	−4.07577			−0.208262			−0.104131	−	0.994564i	$-0.533206\pi$
$383$	−4.07577			−0.208262			−0.104131	+	0.994564i	$0.533206\pi$
$384$		0			0
$385$	−2.01225	−	3.48532i	−0.102554	−	0.177629i
$386$	−1.21921	−	2.11173i	−0.0620559	−	0.107484i
$387$		0			0
$388$	−28.8166			−1.46294
$389$	−5.31159			−0.269308			−0.134654	−	0.990893i	$-0.542992\pi$
$389$	−5.31159			−0.269308			−0.134654	+	0.990893i	$0.542992\pi$
$390$		0			0
$391$	23.9256	+	41.4403i	1.20997	+	2.09573i
$392$	1.72975	+	2.99602i	0.0873657	+	0.151322i
$393$		0			0
$394$	−1.15399	−	1.99877i	−0.0581373	−	0.100697i
$395$	15.5639	+	26.9574i	0.783103	+	1.35637i
$396$		0			0
$397$	9.38913	−	16.2624i	0.471227	−	0.816189i	−0.528232	−	0.849100i	$-0.677145\pi$
$397$	9.38913	−	16.2624i	0.471227	−	0.816189i	0.999458	+	0.0329117i	$0.0104780\pi$
$398$	0.587649	−	1.01784i	0.0294562	−	0.0510196i
$399$		0			0
$400$	2.58248	+	4.47298i	0.129124	+	0.223649i
$401$	−20.9083			−1.04411			−0.522055	−	0.852912i	$-0.674834\pi$
$401$	−20.9083			−1.04411			−0.522055	+	0.852912i	$0.674834\pi$
$402$		0			0
$403$	6.71633			0.334564
$404$	−8.37619	+	14.5080i	−0.416731	+	0.721799i
$405$		0			0
$406$	−0.781590			−0.0387897
$407$	1.75704	−	3.04328i	0.0870932	−	0.150850i
$408$		0			0
$409$	0.569856	−	0.987019i	0.0281776	−	0.0488050i	−0.851593	−	0.524204i	$-0.824363\pi$
$409$	0.569856	−	0.987019i	0.0281776	−	0.0488050i	0.879770	+	0.475399i	$0.157696\pi$
$410$	−0.748780	−	1.29692i	−0.0369796	−	0.0640505i
$411$		0			0
$412$	26.2786			1.29465
$413$	−14.4103	+	24.9594i	−0.709084	+	1.22817i
$414$		0			0
$415$	−10.2052	+	17.6759i	−0.500953	+	0.867676i
$416$	−4.20186	−	7.27783i	−0.206013	−	0.356825i
$417$		0			0
$418$	0.138878	−	0.510299i	0.00679275	−	0.0249596i
$419$	−3.86547	−	6.69519i	−0.188840	−	0.327081i	0.756023	−	0.654545i	$-0.227140\pi$
$419$	−3.86547	−	6.69519i	−0.188840	−	0.327081i	−0.944864	+	0.327463i	$0.893806\pi$
$420$		0			0
$421$	6.69993	+	11.6046i	0.326535	+	0.565575i	0.981822	−	0.189805i	$-0.0607856\pi$
$421$	6.69993	+	11.6046i	0.326535	+	0.565575i	−0.655287	+	0.755380i	$0.727452\pi$
$422$	0.550423	+	0.953361i	0.0267942	+	0.0464089i
$423$		0			0
$424$	1.48938	+	2.57968i	0.0723307	+	0.125280i
$425$	−4.17178	+	7.22574i	−0.202361	+	0.350500i
$426$		0			0
$427$	6.17953	−	10.7033i	0.299048	−	0.517967i
$428$	−10.0011	+	17.3225i	−0.483423	+	0.837313i
$429$		0			0
$430$	−0.945043	+	1.63686i	−0.0455740	+	0.0789365i
$431$	−17.1747	−	29.7474i	−0.827275	−	1.43288i	−0.900168	−	0.435542i	$-0.856557\pi$
$431$	−17.1747	−	29.7474i	−0.827275	−	1.43288i	0.0728934	−	0.997340i	$-0.476777\pi$
$432$		0			0
$433$	−0.930181	−	1.61112i	−0.0447016	−	0.0774255i	0.842809	−	0.538213i	$-0.180900\pi$
$433$	−0.930181	−	1.61112i	−0.0447016	−	0.0774255i	−0.887511	+	0.460787i	$0.847567\pi$
$434$	0.600500	+	1.04010i	0.0288249	+	0.0499262i
$435$		0			0
$436$	1.85476	+	3.21254i	0.0888270	+	0.153853i
$437$	−24.0968	−	24.2863i	−1.15271	−	1.16177i
$438$		0			0
$439$	7.53926	+	13.0584i	0.359829	+	0.623243i	0.987932	−	0.154888i	$-0.0495016\pi$
$439$	7.53926	+	13.0584i	0.359829	+	0.623243i	−0.628103	+	0.778130i	$0.716168\pi$
$440$	−0.458034	+	0.793338i	−0.0218359	+	0.0378209i
$441$		0			0
$442$	2.18983	−	3.79289i	0.104159	−	0.180409i
$443$	−5.10805			−0.242691			−0.121345	−	0.992610i	$-0.538721\pi$
$443$	−5.10805			−0.242691			−0.121345	+	0.992610i	$0.538721\pi$
$444$		0			0
$445$	10.0095	+	17.3370i	0.474496	+	0.821851i
$446$	−2.82689	+	4.89632i	−0.133857	+	0.231848i
$447$		0			0
$448$	−12.0384	+	20.8511i	−0.568762	+	0.985124i
$449$	13.4001			0.632392			0.316196	−	0.948694i	$-0.397594\pi$
$449$	13.4001			0.632392			0.316196	+	0.948694i	$0.397594\pi$
$450$		0			0
$451$	1.25770	−	2.17839i	0.0592226	−	0.102577i
$452$	19.3740			0.911275
$453$		0			0
$454$	−4.49696			−0.211053
$455$	11.9144	+	20.6363i	0.558554	+	0.967445i
$456$		0			0
$457$	−12.1509	+	21.0459i	−0.568394	+	0.984487i	0.428331	+	0.903622i	$0.359102\pi$
$457$	−12.1509	+	21.0459i	−0.568394	+	0.984487i	−0.996725	+	0.0808654i	$0.974232\pi$
$458$	−0.377970	+	0.654663i	−0.0176614	+	0.0305904i
$459$		0			0
$460$	14.6735	+	25.4153i	0.684156	+	1.18499i
$461$	2.28981	+	3.96607i	0.106647	+	0.184719i	0.914410	−	0.404789i	$-0.132655\pi$
$461$	2.28981	+	3.96607i	0.106647	+	0.184719i	−0.807763	+	0.589508i	$0.799322\pi$
$462$		0			0
$463$	−14.8382	−	25.7005i	−0.689589	−	1.19440i	−0.971971	−	0.235101i	$-0.924458\pi$
$463$	−14.8382	−	25.7005i	−0.689589	−	1.19440i	0.282382	−	0.959302i	$-0.408875\pi$
$464$	−2.23532	−	3.87168i	−0.103772	−	0.179738i
$465$		0			0
$466$	−1.18975			−0.0551142
$467$	−38.8322			−1.79694			−0.898469	−	0.439037i	$-0.855320\pi$
$467$	−38.8322			−1.79694			−0.898469	+	0.439037i	$0.855320\pi$
$468$		0			0
$469$	1.77248	+	3.07002i	0.0818455	+	0.141761i
$470$	−2.38781	−	4.13581i	−0.110141	−	0.190771i
$471$		0			0
$472$	6.56022			0.301959
$473$	−3.17470			−0.145973
$474$		0			0
$475$	1.56651	−	5.75606i	0.0718766	−	0.264106i
$476$	−40.5385			−1.85808
$477$		0			0
$478$	1.87106	−	3.24077i	0.0855803	−	0.148229i
$479$	−9.99299			−0.456591			−0.228296	−	0.973592i	$-0.573315\pi$
$479$	−9.99299			−0.456591			−0.228296	+	0.973592i	$0.573315\pi$
$480$		0			0
$481$	−10.4033	+	18.0190i	−0.474349	+	0.821596i
$482$	−1.03908	−	1.79974i	−0.0473287	−	0.0819758i
$483$		0			0
$484$	20.8211			0.946412
$485$	−13.9937	−	24.2378i	−0.635421	−	1.10058i
$486$		0			0
$487$	−17.8510			−0.808906			−0.404453	−	0.914559i	$-0.632538\pi$
$487$	−17.8510			−0.808906			−0.404453	+	0.914559i	$0.632538\pi$
$488$	−2.81320			−0.127348
$489$		0			0
$490$	−0.831953	+	1.44098i	−0.0375838	+	0.0650971i
$491$	13.4844			0.608544			0.304272	−	0.952585i	$-0.401587\pi$
$491$	13.4844			0.608544			0.304272	+	0.952585i	$0.401587\pi$
$492$		0			0
$493$	3.61097	−	6.25439i	0.162630	−	0.281684i
$494$	−0.822285	+	3.02144i	−0.0369964	+	0.135941i
$495$		0			0
$496$	−3.43481	+	5.94927i	−0.154228	+	0.267130i
$497$	5.29650	+	9.17380i	0.237580	+	0.411501i
$498$		0			0
$499$	15.2752			0.683811			0.341905	−	0.939734i	$-0.388928\pi$
$499$	15.2752			0.683811			0.341905	+	0.939734i	$0.388928\pi$
$500$	−11.9061	+	20.6220i	−0.532458	+	0.922245i
$501$		0			0
$502$	−1.76103	+	3.05019i	−0.0785984	+	0.136136i
$503$	−0.700770	−	1.21377i	−0.0312458	−	0.0541193i	0.849980	−	0.526816i	$-0.176614\pi$
$503$	−0.700770	−	1.21377i	−0.0312458	−	0.0541193i	−0.881225	+	0.472696i	$0.843281\pi$
$504$		0			0
$505$	−16.2703			−0.724019
$506$	0.476144	−	0.824706i	0.0211672	−	0.0366627i
$507$		0			0
$508$	−16.9828			−0.753490
$509$	7.65770	−	13.2635i	0.339421	−	0.587895i	−0.644903	−	0.764265i	$-0.723102\pi$
$509$	7.65770	−	13.2635i	0.339421	−	0.587895i	0.984324	+	0.176370i	$0.0564354\pi$
$510$		0			0
$511$	−7.01134	−	12.1440i	−0.310163	−	0.537219i
$512$	14.4180			0.637192
$513$		0			0
$514$	−4.55023			−0.200702
$515$	12.7612	+	22.1030i	0.562325	+	0.973976i
$516$		0			0
$517$	4.01071	−	6.94675i	0.176391	−	0.305518i
$518$	−3.72058			−0.163473
$519$		0			0
$520$	2.71198	−	4.69729i	0.118928	−	0.205990i
$521$	−23.8486			−1.04483			−0.522414	−	0.852692i	$-0.674968\pi$
$521$	−23.8486			−1.04483			−0.522414	+	0.852692i	$0.674968\pi$
$522$		0			0
$523$	7.28432	+	12.6168i	0.318521	+	0.551694i	0.980180	−	0.198111i	$-0.0634805\pi$
$523$	7.28432	+	12.6168i	0.318521	+	0.551694i	−0.661659	+	0.749805i	$0.730147\pi$
$524$	−2.04496	+	3.54198i	−0.0893345	+	0.154732i
$525$		0			0
$526$	−2.37492	+	4.11348i	−0.103552	+	0.179356i
$527$	−11.0973			−0.483407
$528$		0			0
$529$	−19.3021	−	33.4322i	−0.839221	−	1.45357i
$530$	−0.716341	+	1.24074i	−0.0311159	+	0.0538943i
$531$		0			0
$532$	28.0255	−	7.39192i	1.21506	−	0.320480i
$533$	−7.44671	+	12.8981i	−0.322553	+	0.558678i
$534$		0			0
$535$	−19.4267			−0.839889
$536$	0.403456	−	0.698807i	0.0174267	−	0.0301839i
$537$		0			0
$538$	4.87680			0.210254
$539$	−2.79480			−0.120380
$540$		0			0
$541$	20.7123	+	35.8747i	0.890490	+	1.54237i	0.839289	+	0.543686i	$0.182972\pi$
$541$	20.7123	+	35.8747i	0.890490	+	1.54237i	0.0512015	+	0.998688i	$0.483695\pi$
$542$	0.554911			0.0238355
$543$		0			0
$544$	6.94268	+	12.0251i	0.297665	+	0.515571i
$545$	−1.80139	+	3.12010i	−0.0771631	+	0.133650i
$546$		0			0
$547$	34.3461			1.46853			0.734266	−	0.678862i	$-0.237526\pi$
$547$	34.3461			1.46853			0.734266	+	0.678862i	$0.237526\pi$
$548$	16.7122	−	28.9463i	0.713908	−	1.23652i
$549$		0			0
$550$	0.166046			0.00708021
$551$	−1.35593	+	4.98228i	−0.0577645	+	0.212252i
$552$		0			0
$553$	55.3565			2.35400
$554$	0.447469			0.0190111
$555$		0			0
$556$	2.21924	+	3.84384i	0.0941168	+	0.163015i
$557$	−2.91894	−	5.05575i	−0.123679	−	0.214219i	0.797537	−	0.603271i	$-0.206136\pi$
$557$	−2.91894	−	5.05575i	−0.123679	−	0.214219i	−0.921216	+	0.389052i	$0.872803\pi$
$558$		0			0
$559$	18.7971			0.795035
$560$	−24.3726			−1.02993
$561$		0			0
$562$	1.38143	+	2.39271i	0.0582721	+	0.100930i
$563$	−17.0958	−	29.6108i	−0.720503	−	1.24795i	−0.960799	−	0.277247i	$-0.910578\pi$
$563$	−17.0958	−	29.6108i	−0.720503	−	1.24795i	0.240296	−	0.970700i	$-0.422756\pi$
$564$		0			0
$565$	9.40823	+	16.2955i	0.395807	+	0.685559i
$566$	0.805801	+	1.39569i	0.0338704	+	0.0586652i
$567$		0			0
$568$	1.20560	−	2.08817i	0.0505860	−	0.0876175i
$569$	20.3407	−	35.2311i	0.852727	−	1.47697i	−0.0260109	−	0.999662i	$-0.508280\pi$
$569$	20.3407	−	35.2311i	0.852727	−	1.47697i	0.878738	−	0.477305i	$-0.158386\pi$
$570$		0			0
$571$	2.75438	+	4.77073i	0.115267	+	0.199649i	0.917887	−	0.396843i	$-0.129894\pi$
$571$	2.75438	+	4.77073i	0.115267	+	0.199649i	−0.802619	+	0.596492i	$0.796561\pi$
$572$	4.51163			0.188641
$573$		0			0
$574$	−2.66321			−0.111160
$575$	5.37080	−	9.30250i	0.223978	−	0.387941i
$576$		0			0
$577$	−39.7898			−1.65647			−0.828235	−	0.560381i	$-0.810655\pi$
$577$	−39.7898			−1.65647			−0.828235	+	0.560381i	$0.810655\pi$
$578$	−1.96333	+	3.40059i	−0.0816639	+	0.141446i
$579$		0			0
$580$	2.21461	−	3.83581i	0.0919565	−	0.159273i
$581$	18.1486	+	31.4343i	0.752930	+	1.30411i
$582$		0			0
$583$	−2.40642			−0.0996638
$584$	−1.59594	+	2.76425i	−0.0660405	+	0.114385i
$585$		0			0
$586$	−1.92836	+	3.34002i	−0.0796598	+	0.137975i
$587$	2.86972	+	4.97050i	0.118446	+	0.205154i	0.919152	−	0.393903i	$-0.128875\pi$
$587$	2.86972	+	4.97050i	0.118446	+	0.205154i	−0.800706	+	0.599057i	$0.795542\pi$
$588$		0			0
$589$	7.67191	−	2.02352i	0.316115	−	0.0833776i
$590$	1.57762	+	2.73252i	0.0649497	+	0.112496i
$591$		0			0
$592$	−10.6407	−	18.4303i	−0.437331	−	0.757480i
$593$	13.0607	+	22.6219i	0.536340	+	0.928968i	0.999097	+	0.0424831i	$0.0135269\pi$
$593$	13.0607	+	22.6219i	0.536340	+	0.928968i	−0.462757	+	0.886485i	$0.653140\pi$
$594$		0			0
$595$	−19.6860	−	34.0971i	−0.807047	−	1.39785i
$596$	−2.35970	+	4.08713i	−0.0966573	+	0.167415i
$597$		0			0
$598$	−2.81921	+	4.88301i	−0.115286	+	0.199681i
$599$	−18.0733	+	31.3039i	−0.738456	+	1.27904i	0.214734	+	0.976673i	$0.431112\pi$
$599$	−18.0733	+	31.3039i	−0.738456	+	1.27904i	−0.953190	+	0.302371i	$0.902222\pi$
$600$		0			0
$601$	−20.5640	+	35.6178i	−0.838821	+	1.45288i	0.0520595	+	0.998644i	$0.483421\pi$
$601$	−20.5640	+	35.6178i	−0.838821	+	1.45288i	−0.890881	+	0.454237i	$0.849912\pi$
$602$	1.68063	+	2.91094i	0.0684975	+	0.118641i
$603$		0			0
$604$	−7.57983	−	13.1286i	−0.308419	−	0.534197i
$605$	10.1110	+	17.5127i	0.411069	+	0.711992i
$606$		0			0
$607$	−18.4789	−	32.0064i	−0.750035	−	1.29910i	−0.947805	−	0.318850i	$-0.896703\pi$
$607$	−18.4789	−	32.0064i	−0.750035	−	1.29910i	0.197770	−	0.980248i	$-0.436630\pi$
$608$	−6.99238	−	7.04735i	−0.283578	−	0.285808i
$609$		0			0
$610$	−0.676527	−	1.17178i	−0.0273918	−	0.0474440i
$611$	−23.7471	+	41.1311i	−0.960704	+	1.66399i
$612$		0			0
$613$	16.4713	−	28.5292i	0.665270	−	1.15228i	−0.313942	−	0.949442i	$-0.601650\pi$
$613$	16.4713	−	28.5292i	0.665270	−	1.15228i	0.979212	−	0.202839i	$-0.0650169\pi$
$614$	3.53601			0.142702
$615$		0			0
$616$	0.814553	+	1.41085i	0.0328193	+	0.0568446i
$617$	−6.58944	+	11.4132i	−0.265281	+	0.459480i	−0.967637	−	0.252346i	$-0.918798\pi$
$617$	−6.58944	+	11.4132i	−0.265281	+	0.459480i	0.702356	+	0.711826i	$0.252131\pi$
$618$		0			0
$619$	−15.4316	+	26.7283i	−0.620249	+	1.07430i	0.369190	+	0.929354i	$0.379635\pi$
$619$	−15.4316	+	26.7283i	−0.620249	+	1.07430i	−0.989439	+	0.144949i	$0.953698\pi$
$620$	−6.80597			−0.273334
$621$		0			0
$622$	0.225625	−	0.390794i	0.00904675	−	0.0156694i
$623$	35.6011			1.42633
$624$		0			0
$625$	−16.2842			−0.651369
$626$	−1.82137	−	3.15470i	−0.0727966	−	0.126087i
$627$		0			0
$628$	−5.33566	+	9.24163i	−0.212916	+	0.368781i
$629$	17.1892	−	29.7726i	0.685379	−	1.18711i
$630$		0			0
$631$	−9.33975	−	16.1769i	−0.371810	−	0.643993i	0.618034	−	0.786151i	$-0.287929\pi$
$631$	−9.33975	−	16.1769i	−0.371810	−	0.643993i	−0.989844	+	0.142158i	$0.954596\pi$
$632$	−6.30020	−	10.9123i	−0.250609	−	0.434067i
$633$		0			0
$634$	−1.40073	−	2.42613i	−0.0556301	−	0.0963541i
$635$	−8.24705	−	14.2843i	−0.327274	−	0.566856i
$636$		0			0
$637$	16.5478			0.655646
$638$	−0.143724			−0.00569011
$639$		0			0
$640$	5.65815	+	9.80020i	0.223658	+	0.387387i
$641$	−12.3252	−	21.3478i	−0.486815	−	0.843188i	0.513070	−	0.858347i	$-0.328508\pi$
$641$	−12.3252	−	21.3478i	−0.486815	−	0.843188i	−0.999885	+	0.0151588i	$0.995175\pi$
$642$		0			0
$643$	5.23393			0.206406			0.103203	−	0.994660i	$-0.467091\pi$
$643$	5.23393			0.206406			0.103203	+	0.994660i	$0.467091\pi$
$644$	52.1898			2.05657
$645$		0			0
$646$	1.35865	−	4.99229i	0.0534555	−	0.196419i
$647$	7.54367			0.296572			0.148286	−	0.988944i	$-0.452624\pi$
$647$	7.54367			0.296572			0.148286	+	0.988944i	$0.452624\pi$
$648$		0			0
$649$	−2.64987	+	4.58971i	−0.104016	+	0.180162i
$650$	−0.983143			−0.0385620
$651$		0			0
$652$	−7.13638	+	12.3606i	−0.279482	+	0.484077i
$653$	−9.82702	−	17.0209i	−0.384561	−	0.666079i	0.607147	−	0.794589i	$-0.292314\pi$
$653$	−9.82702	−	17.0209i	−0.384561	−	0.666079i	−0.991708	+	0.128510i	$0.958980\pi$
$654$		0			0
$655$	−3.97223			−0.155208
$656$	−7.61668	−	13.1925i	−0.297381	−	0.515080i
$657$		0			0
$658$	−8.49280			−0.331084
$659$	34.9152			1.36010			0.680051	−	0.733165i	$-0.261958\pi$
$659$	34.9152			1.36010			0.680051	+	0.733165i	$0.261958\pi$
$660$		0			0
$661$	12.1794	−	21.0954i	0.473725	−	0.820515i	−0.525823	−	0.850594i	$-0.676243\pi$
$661$	12.1794	−	21.0954i	0.473725	−	0.820515i	0.999548	+	0.0300790i	$0.00957589\pi$
$662$	5.56671			0.216356
$663$		0			0
$664$	4.13103	−	7.15515i	0.160315	−	0.277674i
$665$	19.8269	+	19.9828i	0.768854	+	0.774899i
$666$		0			0
$667$	−4.64881	+	8.05198i	−0.180003	+	0.311774i
$668$	4.37872	+	7.58416i	0.169418	+	0.293440i
$669$		0			0
$670$	0.388098			0.0149935
$671$	1.13634	−	1.96819i	0.0438678	−	0.0759812i
$672$		0			0
$673$	−7.88496	+	13.6572i	−0.303943	+	0.526445i	−0.977025	−	0.213123i	$-0.931637\pi$
$673$	−7.88496	+	13.6572i	−0.303943	+	0.526445i	0.673083	+	0.739567i	$0.264970\pi$
$674$	−1.97718	−	3.42458i	−0.0761583	−	0.131910i
$675$		0			0
$676$	−1.20573			−0.0463744
$677$	19.7783	−	34.2569i	0.760140	−	1.31660i	−0.182638	−	0.983180i	$-0.558464\pi$
$677$	19.7783	−	34.2569i	0.760140	−	1.31660i	0.942778	−	0.333421i	$-0.108203\pi$
$678$		0			0
$679$	−49.7718			−1.91007
$680$	−4.48098	+	7.76128i	−0.171838	+	0.297632i
$681$		0			0
$682$	0.110424	+	0.191260i	0.00422836	+	0.00732374i
$683$	−4.78389			−0.183051			−0.0915253	−	0.995803i	$-0.529174\pi$
$683$	−4.78389			−0.183051			−0.0915253	+	0.995803i	$0.529174\pi$
$684$		0			0
$685$	32.4625			1.24033
$686$	−0.829781	−	1.43722i	−0.0316812	−	0.0548734i
$687$		0			0
$688$	−9.61310	+	16.6504i	−0.366496	+	0.634789i
$689$	14.2482			0.542814
$690$		0			0
$691$	8.12539	−	14.0736i	0.309104	−	0.535384i	−0.669062	−	0.743206i	$-0.733304\pi$
$691$	8.12539	−	14.0736i	0.309104	−	0.535384i	0.978167	+	0.207822i	$0.0666375\pi$
$692$	23.5570			0.895504
$693$		0			0
$694$	−3.48109	−	6.02943i	−0.132140	−	0.228874i
$695$	−2.15538	+	3.73323i	−0.0817583	+	0.141610i
$696$		0			0
$697$	12.3041	−	21.3114i	0.466052	−	0.807225i
$698$	0.759192			0.0287358
$699$		0			0
$700$	4.55004	+	7.88089i	0.171975	+	0.297870i
$701$	11.1768	−	19.3588i	0.422142	−	0.731171i	−0.574007	−	0.818850i	$-0.694612\pi$
$701$	11.1768	−	19.3588i	0.422142	−	0.731171i	0.996149	+	0.0876795i	$0.0279451\pi$
$702$		0			0
$703$	−6.45460	+	23.7170i	−0.243440	+	0.894505i
$704$	−2.21371	+	3.83426i	−0.0834323	+	0.144509i
$705$		0			0
$706$	1.94791			0.0733106
$707$	−14.4673	+	25.0581i	−0.544098	+	0.942406i
$708$		0			0
$709$	−16.7749			−0.629993			−0.314996	−	0.949093i	$-0.602003\pi$
$709$	−16.7749			−0.629993			−0.314996	+	0.949093i	$0.602003\pi$
$710$	1.15971			0.0435231
$711$		0			0
$712$	−4.05181	−	7.01795i	−0.151848	−	0.263009i
$713$	14.2868			0.535046
$714$		0			0
$715$	2.19090	+	3.79475i	0.0819350	+	0.141916i
$716$	−19.6331	+	34.0055i	−0.733722	+	1.27084i
$717$		0			0
$718$	0.879207			0.0328117
$719$	24.2869	−	42.0661i	0.905747	−	1.56880i	0.0858361	−	0.996309i	$-0.472644\pi$
$719$	24.2869	−	42.0661i	0.905747	−	1.56880i	0.819911	−	0.572491i	$-0.194023\pi$
$720$		0			0
$721$	45.3882			1.69034
$722$	−0.0289680	+	3.69906i	−0.00107808	+	0.137665i
$723$		0			0
$724$	−23.7223			−0.881631
$725$	−1.62118			−0.0602091
$726$		0			0
$727$	−15.7902	−	27.3495i	−0.585627	−	1.01434i	−0.994797	−	0.101877i	$-0.967515\pi$
$727$	−15.7902	−	27.3495i	−0.585627	−	1.01434i	0.409170	−	0.912458i	$-0.365818\pi$
$728$	−4.82290	−	8.35350i	−0.178748	−	0.309601i
$729$		0			0
$730$	−1.53519			−0.0568198
$731$	−31.0583			−1.14873
$732$		0			0
$733$	−17.0488	−	29.5294i	−0.629712	−	1.09069i	−0.987609	−	0.156932i	$-0.949840\pi$
$733$	−17.0488	−	29.5294i	−0.629712	−	1.09069i	0.357898	−	0.933761i	$-0.383494\pi$
$734$	2.28634	+	3.96007i	0.0843905	+	0.146169i
$735$		0			0
$736$	−8.93810	−	15.4812i	−0.329463	−	0.570646i
$737$	0.325936	+	0.564538i	0.0120060	+	0.0207950i
$738$		0			0
$739$	16.0360	−	27.7752i	0.589894	−	1.02173i	−0.404352	−	0.914603i	$-0.632503\pi$
$739$	16.0360	−	27.7752i	0.589894	−	1.02173i	0.994246	−	0.107123i	$-0.0341637\pi$
$740$	10.5421	−	18.2595i	0.387536	−	0.671233i
$741$		0			0
$742$	1.27392	+	2.20649i	0.0467670	+	0.0810028i
$743$	19.2215			0.705170			0.352585	−	0.935780i	$-0.385303\pi$
$743$	19.2215			0.705170			0.352585	+	0.935780i	$0.385303\pi$
$744$		0			0
$745$	−4.58360			−0.167930
$746$	−2.37560	+	4.11465i	−0.0869768	+	0.150648i
$747$		0			0
$748$	−7.45452			−0.272564
$749$	−17.2739	+	29.9192i	−0.631174	+	1.09323i
$750$		0			0
$751$	−11.1484	+	19.3096i	−0.406811	+	0.704618i	−0.994530	−	0.104447i	$-0.966693\pi$
$751$	−11.1484	+	19.3096i	−0.406811	+	0.704618i	0.587719	+	0.809065i	$0.300026\pi$
$752$	−24.2891	−	42.0700i	−0.885732	−	1.53413i
$753$		0			0
$754$	0.850980			0.0309909
$755$	7.36171	−	12.7509i	0.267920	−	0.464051i
$756$		0			0
$757$	12.7479	−	22.0801i	0.463331	−	0.802513i	−0.535793	−	0.844349i	$-0.679987\pi$
$757$	12.7479	−	22.0801i	0.463331	−	0.802513i	0.999124	+	0.0418359i	$0.0133207\pi$
$758$	1.72418	+	2.98637i	0.0626252	+	0.108470i
$759$		0			0
$760$	1.68262	−	6.18268i	0.0610350	−	0.224269i
$761$	−6.39108	−	11.0697i	−0.231676	−	0.401275i	0.726625	−	0.687034i	$-0.241088\pi$
$761$	−6.39108	−	11.0697i	−0.231676	−	0.401275i	−0.958302	+	0.285759i	$0.907754\pi$
$762$		0			0
$763$	3.20353	+	5.54868i	0.115976	+	0.200876i
$764$	2.64265	+	4.57721i	0.0956078	+	0.165598i
$765$		0			0
$766$	0.396763	+	0.687214i	0.0143356	+	0.0248301i
$767$	15.6896	−	27.1753i	0.566520	−	0.981242i
$768$		0			0
$769$	−0.952422	+	1.64964i	−0.0343452	+	0.0594877i	−0.882687	−	0.469961i	$-0.844268\pi$
$769$	−0.952422	+	1.64964i	−0.0343452	+	0.0594877i	0.848342	+	0.529449i	$0.177601\pi$
$770$	−0.391772	+	0.678570i	−0.0141185	+	0.0244539i
$771$		0			0
$772$	12.2870	−	21.2817i	0.442218	−	0.765945i
$773$	−16.8937	−	29.2607i	−0.607623	−	1.05243i	−0.991631	−	0.129104i	$-0.958790\pi$
$773$	−16.8937	−	29.2607i	−0.607623	−	1.05243i	0.384008	−	0.923330i	$-0.374544\pi$
$774$		0			0
$775$	1.24556	+	2.15737i	0.0447419	+	0.0774952i
$776$	5.66460	+	9.81137i	0.203347	+	0.352208i
$777$		0			0
$778$	0.517066	+	0.895584i	0.0185377	+	0.0321082i
$779$	−4.62023	+	16.9768i	−0.165537	+	0.608255i
$780$		0			0
$781$	0.973958	+	1.68695i	0.0348510	+	0.0603636i
$782$	4.65815	−	8.06816i	0.166575	−	0.288517i
$783$		0			0
$784$	−8.46273	+	14.6579i	−0.302240	+	0.523496i
$785$	−10.3642			−0.369916
$786$		0			0
$787$	−0.571053	−	0.989094i	−0.0203559	−	0.0352574i	0.855668	−	0.517525i	$-0.173147\pi$
$787$	−0.571053	−	0.989094i	−0.0203559	−	0.0352574i	−0.876024	+	0.482268i	$0.839813\pi$
$788$	11.6298	−	20.1434i	0.414294	−	0.717578i
$789$		0			0
$790$	3.03018	−	5.24843i	0.107809	−	0.186731i
$791$	33.4626			1.18979
$792$		0			0
$793$	−6.72815	+	11.6535i	−0.238924	+	0.413828i
$794$	−3.65600			−0.129747
$795$		0			0
$796$	11.8445			0.419817
$797$	14.0447	+	24.3261i	0.497488	+	0.861674i	0.999996	−	0.00289827i	$-0.000922550\pi$
$797$	14.0447	+	24.3261i	0.497488	+	0.861674i	−0.502508	+	0.864573i	$0.667589\pi$
$798$		0			0
$799$	39.2371	−	67.9606i	1.38811	−	2.40427i
$800$	1.55849	−	2.69939i	0.0551010	−	0.0954377i
$801$		0			0
$802$	2.03535	+	3.52533i	0.0718708	+	0.124484i
$803$	−1.28930	−	2.23313i	−0.0454983	−	0.0788053i
$804$		0			0
$805$	25.3440	+	43.8971i	0.893259	+	1.54717i
$806$	−0.653812	−	1.13244i	−0.0230296	−	0.0398884i
$807$		0			0
$808$	6.58616			0.231700
$809$	19.5465			0.687217			0.343609	−	0.939113i	$-0.388351\pi$
$809$	19.5465			0.687217			0.343609	+	0.939113i	$0.388351\pi$
$810$		0			0
$811$	11.5944	+	20.0821i	0.407134	+	0.705176i	0.994567	−	0.104096i	$-0.0331950\pi$
$811$	11.5944	+	20.0821i	0.407134	+	0.705176i	−0.587433	+	0.809272i	$0.699862\pi$
$812$	−3.93838	−	6.82148i	−0.138210	−	0.239387i
$813$		0			0
$814$	−0.684168			−0.0239801
$815$	−13.8620			−0.485566
$816$		0			0
$817$	21.4716	−	5.66327i	0.751195	−	0.198133i
$818$	−0.221894			−0.00775835
$819$		0			0
$820$	7.54610	−	13.0702i	0.263521	−	0.456432i
$821$	1.73188			0.0604429			0.0302214	−	0.999543i	$-0.490379\pi$
$821$	1.73188			0.0604429			0.0302214	+	0.999543i	$0.490379\pi$
$822$		0			0
$823$	5.42401	−	9.39465i	0.189069	−	0.327477i	−0.755871	−	0.654720i	$-0.772786\pi$
$823$	5.42401	−	9.39465i	0.189069	−	0.327477i	0.944940	+	0.327243i	$0.106120\pi$
$824$	−5.16569	−	8.94723i	−0.179955	−	0.311692i
$825$		0			0
$826$	5.61118			0.195238
$827$	−23.9980	−	41.5658i	−0.834493	−	1.44538i	−0.894442	−	0.447183i	$-0.852427\pi$
$827$	−23.9980	−	41.5658i	−0.834493	−	1.44538i	0.0599489	−	0.998201i	$-0.480906\pi$
$828$		0			0
$829$	−36.8202			−1.27882			−0.639409	−	0.768867i	$-0.720821\pi$
$829$	−36.8202			−1.27882			−0.639409	+	0.768867i	$0.720821\pi$
$830$	3.97377			0.137932
$831$		0			0
$832$	13.1072	−	22.7023i	0.454410	−	0.787061i
$833$	−27.3417			−0.947333
$834$		0			0
$835$	−4.25271	+	7.36592i	−0.147171	+	0.254908i
$836$	5.15353	−	1.35928i	0.178239	−	0.0470117i
$837$		0			0
$838$	−0.752581	+	1.30351i	−0.0259975	+	0.0450290i
$839$	12.9609	+	22.4490i	0.447461	+	0.775025i	0.998220	−	0.0596394i	$-0.0189951\pi$
$839$	12.9609	+	22.4490i	0.447461	+	0.775025i	−0.550759	+	0.834664i	$0.685662\pi$
$840$		0			0
$841$	−27.5968			−0.951612
$842$	1.30443	−	2.25934i	0.0449537	−	0.0778621i
$843$		0			0
$844$	−5.54709	+	9.60784i	−0.190939	+	0.330716i
$845$	−0.585519	−	1.01415i	−0.0201425	−	0.0348878i
$846$		0			0
$847$	35.9620			1.23567
$848$	−7.28671	+	12.6210i	−0.250227	+	0.433405i
$849$		0			0
$850$	1.62444			0.0557177
$851$	−22.1296	+	38.3296i	−0.758594	+	1.31392i
$852$		0			0
$853$	−21.3868	−	37.0430i	−0.732270	−	1.26833i	−0.955911	−	0.293658i	$-0.905127\pi$
$853$	−21.3868	−	37.0430i	−0.732270	−	1.26833i	0.223640	−	0.974672i	$-0.428206\pi$
$854$	−2.40623			−0.0823394
$855$		0			0
$856$	7.86385			0.268781
$857$	−16.8665	−	29.2136i	−0.576149	−	0.997919i	−0.995916	−	0.0902869i	$-0.971222\pi$
$857$	−16.8665	−	29.2136i	−0.576149	−	0.997919i	0.419767	−	0.907632i	$-0.362112\pi$
$858$		0			0
$859$	−4.24540	+	7.35325i	−0.144851	+	0.250890i	−0.929317	−	0.369282i	$-0.879604\pi$
$859$	−4.24540	+	7.35325i	−0.144851	+	0.250890i	0.784466	+	0.620172i	$0.212937\pi$
$860$	−19.0480			−0.649533
$861$		0			0
$862$	−3.34380	+	5.79162i	−0.113890	+	0.197264i
$863$	1.25544			0.0427358			0.0213679	−	0.999772i	$-0.493198\pi$
$863$	1.25544			0.0427358			0.0213679	+	0.999772i	$0.493198\pi$
$864$		0			0
$865$	11.4396	+	19.8139i	0.388958	+	0.673694i
$866$	−0.181100	+	0.313675i	−0.00615403	+	0.0106591i
$867$		0			0
$868$	−6.05176	+	10.4819i	−0.205410	+	0.355780i
$869$	10.1794			0.345311
$870$		0			0
$871$	−1.92984	−	3.34258i	−0.0653902	−	0.113259i
$872$	0.729197	−	1.26301i	0.0246937	−	0.0427708i
$873$		0			0
$874$	−1.74915	+	6.42714i	−0.0591658	+	0.217401i
$875$	−20.5642	+	35.6182i	−0.695196	+	1.20412i
$876$		0			0
$877$	−3.81281			−0.128750			−0.0643748	−	0.997926i	$-0.520505\pi$
$877$	−3.81281			−0.128750			−0.0643748	+	0.997926i	$0.520505\pi$
$878$	1.46785	−	2.54238i	0.0495374	−	0.0858012i
$879$		0			0
$880$	−4.48182			−0.151082
$881$	17.1658			0.578331			0.289165	−	0.957279i	$-0.406622\pi$
$881$	17.1658			0.578331			0.289165	+	0.957279i	$0.406622\pi$
$882$		0			0
$883$	−1.40205	−	2.42843i	−0.0471829	−	0.0817231i	0.841469	−	0.540305i	$-0.181691\pi$
$883$	−1.40205	−	2.42843i	−0.0471829	−	0.0817231i	−0.888652	+	0.458582i	$0.848358\pi$
$884$	44.1376			1.48451
$885$		0			0
$886$	0.497252	+	0.861265i	0.0167055	+	0.0289348i
$887$	−19.9965	+	34.6349i	−0.671416	+	1.16293i	0.306087	+	0.952004i	$0.400980\pi$
$887$	−19.9965	+	34.6349i	−0.671416	+	1.16293i	−0.977503	+	0.210923i	$0.932353\pi$
$888$		0			0
$889$	−29.3326			−0.983783
$890$	1.94878	−	3.37539i	0.0653234	−	0.113143i
$891$		0			0
$892$	−56.9781			−1.90777
$893$	−14.7336	+	54.1378i	−0.493041	+	1.81165i
$894$		0			0
$895$	−38.1362			−1.27475
$896$	20.1245			0.672313
$897$		0			0
$898$	−1.30446	−	2.25939i	−0.0435304	−	0.0753968i
$899$	−1.07812	−	1.86736i	−0.0359574	−	0.0622800i
$900$		0			0
$901$	−23.5422			−0.784304
$902$	−0.489730			−0.0163062
$903$		0			0
$904$	−3.80842	−	6.59638i	−0.126666	−	0.219392i
$905$	−11.5198	−	19.9529i	−0.382932	−	0.663257i
$906$		0			0
$907$	27.7430	+	48.0523i	0.921192	+	1.59555i	0.797574	+	0.603221i	$0.206116\pi$
$907$	27.7430	+	48.0523i	0.921192	+	1.59555i	0.123618	+	0.992330i	$0.460550\pi$
$908$	−22.6599	−	39.2480i	−0.751994	−	1.30249i
$909$		0			0
$910$	2.31965	−	4.01775i	0.0768957	−	0.133187i
$911$	−1.10191	+	1.90856i	−0.0365078	+	0.0632334i	−0.883702	−	0.468050i	$-0.844957\pi$
$911$	−1.10191	+	1.90856i	−0.0365078	+	0.0632334i	0.847194	+	0.531283i	$0.178290\pi$
$912$		0			0
$913$	3.33729	+	5.78036i	0.110448	+	0.191302i
$914$	4.73139			0.156501
$915$		0			0
$916$	−7.61826			−0.251714
$917$	−3.53204	+	6.11767i	−0.116638	+	0.202023i
$918$		0			0
$919$	23.5600			0.777173			0.388587	−	0.921412i	$-0.372963\pi$
$919$	23.5600			0.777173			0.388587	+	0.921412i	$0.372963\pi$
$920$	5.76887	−	9.99197i	0.190194	−	0.329426i
$921$		0			0
$922$	0.445812	−	0.772169i	0.0146820	−	0.0254300i
$923$	−5.76672	−	9.98826i	−0.189814	−	0.328768i
$924$		0			0
$925$	−7.71726			−0.253742
$926$	−2.88890	+	5.00372i	−0.0949351	+	0.164432i
$927$		0			0
$928$	−1.34899	+	2.33651i	−0.0442826	+	0.0766997i
$929$	−4.86468	−	8.42587i	−0.159605	−	0.276444i	0.775121	−	0.631812i	$-0.217689\pi$
$929$	−4.86468	−	8.42587i	−0.159605	−	0.276444i	−0.934726	+	0.355369i	$0.884355\pi$
$930$		0			0
$931$	18.9021	−	4.98557i	0.619492	−	0.163395i
$932$	−5.99508	−	10.3838i	−0.196376	−	0.340132i
$933$		0			0
$934$	3.78018	+	6.54747i	0.123691	+	0.214240i
$935$	−3.62000	−	6.27003i	−0.118387	−	0.205052i
$936$		0			0
$937$	0.131215	+	0.227271i	0.00428661	+	0.00742463i	0.868161	−	0.496283i	$-0.165302\pi$
$937$	0.131215	+	0.227271i	0.00428661	+	0.00742463i	−0.863874	+	0.503708i	$0.831969\pi$
$938$	0.345090	−	0.597714i	0.0112676	−	0.0195160i
$939$		0			0
$940$	24.0640	−	41.6801i	0.784882	−	1.35946i
$941$	1.75150	−	3.03369i	0.0570974	−	0.0988956i	−0.836064	−	0.548632i	$-0.815149\pi$
$941$	1.75150	−	3.03369i	0.0570974	−	0.0988956i	0.893161	+	0.449737i	$0.148482\pi$
$942$		0			0
$943$	−15.8405	+	27.4365i	−0.515837	+	0.893456i
$944$	16.0478	+	27.7955i	0.522310	+	0.904668i
$945$		0			0
$946$	0.309047	+	0.535285i	0.0100480	+	0.0174036i
$947$	4.20377	+	7.28114i	0.136604	+	0.236605i	0.926209	−	0.377010i	$-0.123048\pi$
$947$	4.20377	+	7.28114i	0.136604	+	0.236605i	−0.789605	+	0.613616i	$0.789714\pi$
$948$		0			0
$949$	7.63381	+	13.2221i	0.247804	+	0.429209i
$950$	−1.12302	+	0.296205i	−0.0364356	+	0.00961015i
$951$		0			0
$952$	7.96882	+	13.8024i	0.258271	+	0.447339i
$953$	−1.92560	+	3.33524i	−0.0623764	+	0.108039i	−0.895527	−	0.445007i	$-0.853201\pi$
$953$	−1.92560	+	3.33524i	−0.0623764	+	0.108039i	0.833151	+	0.553046i	$0.186535\pi$
$954$		0			0
$955$	−2.56661	+	4.44550i	−0.0830535	+	0.143853i
$956$	37.7126			1.21971
$957$		0			0
$958$	0.972785	+	1.68491i	0.0314293	+	0.0544371i
$959$	28.8651	−	49.9958i	0.932103	−	1.61445i
$960$		0			0
$961$	13.8433	−	23.9774i	0.446560	−	0.773464i
$962$	4.05090			0.130606
$963$		0			0
$964$	10.4717	−	18.1375i	0.337271	−	0.584170i
$965$	23.8668			0.768301
$966$		0			0
$967$	42.6171			1.37047			0.685236	−	0.728321i	$-0.259699\pi$
$967$	42.6171			1.37047			0.685236	+	0.728321i	$0.259699\pi$
$968$	−4.09288	−	7.08908i	−0.131550	−	0.227852i
$969$		0			0
$970$	−2.72448	+	4.71894i	−0.0874777	+	0.151516i
$971$	−28.5146	+	49.3887i	−0.915076	+	1.58496i	−0.108286	+	0.994120i	$0.534536\pi$
$971$	−28.5146	+	49.3887i	−0.915076	+	1.58496i	−0.806790	+	0.590838i	$0.798797\pi$
$972$		0			0
$973$	3.83306	+	6.63905i	0.122882	+	0.212838i
$974$	1.73774	+	3.00985i	0.0556807	+	0.0964417i
$975$		0			0
$976$	−6.88172	−	11.9195i	−0.220278	−	0.381534i
$977$	12.6223	+	21.8624i	0.403822	+	0.699441i	0.994184	−	0.107698i	$-0.0343481\pi$
$977$	12.6223	+	21.8624i	0.403822	+	0.699441i	−0.590361	+	0.807139i	$0.701015\pi$
$978$		0			0
$979$	6.54659			0.209230
$980$	−16.7686			−0.535654
$981$		0			0
$982$	−1.31266	−	2.27360i	−0.0418888	−	0.0725536i
$983$	1.33119	+	2.30569i	0.0424584	+	0.0735400i	0.886474	−	0.462779i	$-0.153148\pi$
$983$	1.33119	+	2.30569i	0.0424584	+	0.0735400i	−0.844015	+	0.536319i	$0.819814\pi$
$984$		0			0
$985$	22.5902			0.719785
$986$	−1.40607			−0.0447783
$987$		0			0
$988$	−30.5136	+	8.04818i	−0.970767	+	0.256047i
$989$	39.9849			1.27145
$990$		0			0
$991$	10.1431	−	17.5684i	0.322207	−	0.558079i	−0.658736	−	0.752374i	$-0.728909\pi$
$991$	10.1431	−	17.5684i	0.322207	−	0.558079i	0.980943	+	0.194295i	$0.0622418\pi$
$992$	4.14573			0.131627
$993$		0			0
$994$	1.03119	−	1.78608i	0.0327075	−	0.0566510i
$995$	5.75183	+	9.96246i	0.182345	+	0.315831i
$996$		0			0
$997$	28.4073			0.899668			0.449834	−	0.893112i	$-0.351483\pi$
$997$	28.4073			0.899668			0.449834	+	0.893112i	$0.351483\pi$
$998$	−1.48699	−	2.57554i	−0.0470698	−	0.0815273i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	513.2.g.c.505.7		32
3.2	odd	2		171.2.g.c.106.10	✓	32
9.4	even	3		513.2.h.c.334.10		32
9.5	odd	6		171.2.h.c.49.7	yes	32
19.7	even	3		513.2.h.c.235.10		32
57.26	odd	6		171.2.h.c.7.7	yes	32
171.121	even	3	inner	513.2.g.c.64.7		32
171.140	odd	6		171.2.g.c.121.10	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
171.2.g.c.106.10	✓	32	3.2	odd	2
171.2.g.c.121.10	yes	32	171.140	odd	6
171.2.h.c.7.7	yes	32	57.26	odd	6
171.2.h.c.49.7	yes	32	9.5	odd	6
513.2.g.c.64.7		32	171.121	even	3	inner
513.2.g.c.505.7		32	1.1	even	1	trivial
513.2.h.c.235.10		32	19.7	even	3
513.2.h.c.334.10		32	9.4	even	3

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 513 = 3^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	513.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.0973467 - 0.168609i) q^{2} +(0.981047 - 1.69922i) q^{4} +1.90563 q^{5} +(1.69446 - 2.93489i) q^{7} -0.771394 q^{8} +(-0.185507 - 0.321308i) q^{10} +(0.311589 - 0.539688i) q^{11} +(-1.84489 + 3.19545i) q^{13} -0.659800 q^{14} +(-1.88700 - 3.26838i) q^{16} +(3.04830 - 5.27981i) q^{17} +(-1.14464 + 4.20592i) q^{19} +(1.86952 - 3.23810i) q^{20} -0.121329 q^{22} +(-3.92442 + 6.79729i) q^{23} -1.36856 q^{25} +0.718377 q^{26} +(-3.32469 - 5.75853i) q^{28} +1.18459 q^{29} +(-0.910124 - 1.57638i) q^{31} +(-1.13878 + 1.97243i) q^{32} -1.18697 q^{34} +(3.22902 - 5.59282i) q^{35} +5.63896 q^{37} +(0.820586 - 0.216435i) q^{38} -1.46999 q^{40} +4.03639 q^{41} +(-2.54719 - 4.41186i) q^{43} +(-0.611367 - 1.05892i) q^{44} +1.52812 q^{46} +12.8718 q^{47} +(-2.24237 - 3.88391i) q^{49} +(0.133225 + 0.230752i) q^{50} +(3.61985 + 6.26977i) q^{52} +(-1.93076 - 3.34418i) q^{53} +(0.593775 - 1.02845i) q^{55} +(-1.30709 + 2.26395i) q^{56} +(-0.115316 - 0.199733i) q^{58} -8.50437 q^{59} +3.64691 q^{61} +(-0.177195 + 0.306911i) q^{62} -7.10458 q^{64} +(-3.51569 + 6.08935i) q^{65} +(-0.523023 + 0.905902i) q^{67} +(-5.98105 - 10.3595i) q^{68} -1.25734 q^{70} +(-1.56289 + 2.70700i) q^{71} +(2.06890 - 3.58345i) q^{73} +(-0.548934 - 0.950782i) q^{74} +(6.02386 + 6.07121i) q^{76} +(-1.05595 - 1.82896i) q^{77} +(8.16729 + 14.1462i) q^{79} +(-3.59593 - 6.22834i) q^{80} +(-0.392929 - 0.680574i) q^{82} +(-5.35528 + 9.27561i) q^{83} +(5.80894 - 10.0614i) q^{85} +(-0.495921 + 0.858960i) q^{86} +(-0.240358 + 0.416312i) q^{88} +(5.25259 + 9.09775i) q^{89} +(6.25218 + 10.8291i) q^{91} +(7.70007 + 13.3369i) q^{92} +(-1.25303 - 2.17031i) q^{94} +(-2.18127 + 8.01495i) q^{95} +(-7.34332 - 12.7190i) q^{97} +(-0.436576 + 0.756171i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - q^{2} - 17 q^{4} + 6 q^{5} + q^{7} + 36 q^{8} - 8 q^{10} - 7 q^{11} - 4 q^{13} + 2 q^{14} - 11 q^{16} + 7 q^{17} + 7 q^{19} + 3 q^{20} + 16 q^{22} - 5 q^{23} + 18 q^{25} + 4 q^{26} - 10 q^{28}+ \cdots - 18 q^{98}+O(q^{100}) \) 32 * q - q^2 - 17 * q^4 + 6 * q^5 + q^7 + 36 * q^8 - 8 * q^10 - 7 * q^11 - 4 * q^13 + 2 * q^14 - 11 * q^16 + 7 * q^17 + 7 * q^19 + 3 * q^20 + 16 * q^22 - 5 * q^23 + 18 * q^25 + 4 * q^26 - 10 * q^28 + 20 * q^29 - 10 * q^31 - 17 * q^32 + 26 * q^34 + 3 * q^35 + 2 * q^37 - 38 * q^38 - 24 * q^40 + 12 * q^41 + 7 * q^43 - 20 * q^44 - 18 * q^47 - 13 * q^49 - q^50 + 19 * q^52 - 16 * q^53 + 15 * q^55 + 6 * q^56 + 74 * q^59 + 24 * q^61 - 54 * q^62 - 64 * q^64 - 54 * q^65 - 11 * q^67 + 2 * q^68 - 48 * q^70 - 9 * q^71 - 10 * q^73 - 6 * q^74 + 29 * q^76 - 46 * q^77 - 8 * q^79 + 24 * q^80 + 7 * q^82 - 3 * q^83 - 27 * q^85 - 17 * q^86 + 9 * q^88 - 30 * q^89 - q^91 + 17 * q^92 - 18 * q^94 + 6 * q^95 - 18 * q^98

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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