LMFDB - Embedded newform 108.5.f.a.19.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,5,Mod(19,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("108.19");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	108.f (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.1639560131$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.20
Character	$\chi$	$=$	108.19
Dual form			108.5.f.a.91.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.86509 - 1.03009i) q^{2} +(13.8778 - 7.96277i) q^{4} +(5.89438 + 10.2094i) q^{5} +(50.5548 + 29.1878i) q^{7} +(45.4367 - 45.0722i) q^{8} +O(q^{10})$	\(q+(3.86509 - 1.03009i) q^{2} +(13.8778 - 7.96277i) q^{4} +(5.89438 + 10.2094i) q^{5} +(50.5548 + 29.1878i) q^{7} +(45.4367 - 45.0722i) q^{8} +(33.2988 + 33.3884i) q^{10} +(-86.9742 - 50.2146i) q^{11} +(85.3178 + 147.775i) q^{13} +(225.465 + 60.7377i) q^{14} +(129.189 - 221.012i) q^{16} +398.571 q^{17} -404.608i q^{19} +(163.096 + 94.7483i) q^{20} +(-387.889 - 104.493i) q^{22} +(-291.091 + 168.062i) q^{23} +(243.013 - 420.910i) q^{25} +(481.982 + 483.278i) q^{26} +(934.007 + 2.50777i) q^{28} +(-327.671 + 567.543i) q^{29} +(-550.166 + 317.638i) q^{31} +(271.664 - 987.307i) q^{32} +(1540.51 - 410.563i) q^{34} +688.176i q^{35} -1599.91 q^{37} +(-416.782 - 1563.85i) q^{38} +(727.980 + 198.207i) q^{40} +(1231.63 + 2133.25i) q^{41} +(-1933.38 - 1116.24i) q^{43} +(-1606.86 - 4.31435i) q^{44} +(-951.976 + 949.423i) q^{46} +(-2514.55 - 1451.78i) q^{47} +(503.358 + 871.842i) q^{49} +(505.691 - 1877.18i) q^{50} +(2360.72 + 1371.43i) q^{52} -1291.73 q^{53} -1183.94i q^{55} +(3612.60 - 952.417i) q^{56} +(-681.858 + 2531.13i) q^{58} +(1002.24 - 578.642i) q^{59} +(-2960.81 + 5128.28i) q^{61} +(-1799.24 + 1794.42i) q^{62} +(32.9923 - 4095.87i) q^{64} +(-1005.79 + 1742.08i) q^{65} +(3085.87 - 1781.63i) q^{67} +(5531.30 - 3173.73i) q^{68} +(708.882 + 2659.86i) q^{70} +5639.73i q^{71} -5496.39 q^{73} +(-6183.80 + 1648.05i) q^{74} +(-3221.80 - 5615.09i) q^{76} +(-2931.31 - 5077.18i) q^{77} +(-2788.94 - 1610.20i) q^{79} +(3017.88 + 16.2058i) q^{80} +(6957.81 + 6976.52i) q^{82} +(-7063.92 - 4078.36i) q^{83} +(2349.33 + 4069.15i) q^{85} +(-8622.53 - 2322.81i) q^{86} +(-6215.11 + 1638.53i) q^{88} -910.873 q^{89} +9960.97i q^{91} +(-2701.48 + 4650.22i) q^{92} +(-11214.4 - 3021.04i) q^{94} +(4130.79 - 2384.91i) q^{95} +(8804.44 - 15249.7i) q^{97} +(2843.60 + 2851.24i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + q^{2} - q^{4} + 2 q^{5} - 122 q^{8}+O(q^{10}) $ 44 * q + q^2 - q^4 + 2 * q^5 - 122 * q^8	$ 44 q + q^{2} - q^{4} + 2 q^{5} - 122 q^{8} + 28 q^{10} - 2 q^{13} - 252 q^{14} - q^{16} + 56 q^{17} + 140 q^{20} - 33 q^{22} - 1752 q^{25} - 1096 q^{26} - 516 q^{28} - 526 q^{29} + 121 q^{32} + 385 q^{34} - 8 q^{37} - 1395 q^{38} - 2276 q^{40} + 2762 q^{41} - 6714 q^{44} + 3576 q^{46} + 3428 q^{49} - 6375 q^{50} + 1438 q^{52} + 10088 q^{53} + 7506 q^{56} - 4064 q^{58} - 2 q^{61} + 18324 q^{62} + 9026 q^{64} + 2014 q^{65} + 11405 q^{68} + 3666 q^{70} - 3416 q^{73} - 14620 q^{74} + 1581 q^{76} + 3942 q^{77} - 45520 q^{80} - 8486 q^{82} - 1252 q^{85} - 22113 q^{86} + 1995 q^{88} - 13048 q^{89} + 30294 q^{92} + 7524 q^{94} + 5638 q^{97} + 92938 q^{98}+O(q^{100}) $ 44 * q + q^2 - q^4 + 2 * q^5 - 122 * q^8 + 28 * q^10 - 2 * q^13 - 252 * q^14 - q^16 + 56 * q^17 + 140 * q^20 - 33 * q^22 - 1752 * q^25 - 1096 * q^26 - 516 * q^28 - 526 * q^29 + 121 * q^32 + 385 * q^34 - 8 * q^37 - 1395 * q^38 - 2276 * q^40 + 2762 * q^41 - 6714 * q^44 + 3576 * q^46 + 3428 * q^49 - 6375 * q^50 + 1438 * q^52 + 10088 * q^53 + 7506 * q^56 - 4064 * q^58 - 2 * q^61 + 18324 * q^62 + 9026 * q^64 + 2014 * q^65 + 11405 * q^68 + 3666 * q^70 - 3416 * q^73 - 14620 * q^74 + 1581 * q^76 + 3942 * q^77 - 45520 * q^80 - 8486 * q^82 - 1252 * q^85 - 22113 * q^86 + 1995 * q^88 - 13048 * q^89 + 30294 * q^92 + 7524 * q^94 + 5638 * q^97 + 92938 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	3.86509	−	1.03009i	0.966272	−	0.257522i
$2$	3.86509	−	1.03009i	0.966272	−	0.257522i
$3$		0			0
$3$		0			0
$4$	13.8778	−	7.96277i	0.867365	−	0.497673i
$5$	5.89438	+	10.2094i	0.235775	+	0.408374i	0.959498	−	0.281717i	$-0.0909038\pi$
$5$	5.89438	+	10.2094i	0.235775	+	0.408374i	−0.723723	+	0.690091i	$0.757570\pi$
$6$		0			0
$7$	50.5548	+	29.1878i	1.03173	+	0.595670i	0.917480	−	0.397782i	$-0.130220\pi$
$7$	50.5548	+	29.1878i	1.03173	+	0.595670i	0.114251	+	0.993452i	$0.463553\pi$
$8$	45.4367	−	45.0722i	0.709949	−	0.704253i
$9$		0			0
$10$	33.2988	+	33.3884i	0.332988	+	0.333884i
$11$	−86.9742	−	50.2146i	−0.718795	−	0.414997i	0.0955138	−	0.995428i	$-0.469551\pi$
$11$	−86.9742	−	50.2146i	−0.718795	−	0.414997i	−0.814309	+	0.580431i	$0.802884\pi$
$12$		0			0
$13$	85.3178	+	147.775i	0.504839	+	0.874407i	0.999984	+	0.00559684i	$0.00178154\pi$
$13$	85.3178	+	147.775i	0.504839	+	0.874407i	−0.495145	+	0.868810i	$0.664885\pi$
$14$	225.465	+	60.7377i	1.15033	+	0.309886i
$15$		0			0
$16$	129.189	−	221.012i	0.504643	−	0.863328i
$17$	398.571			1.37914			0.689569	−	0.724220i	$-0.257800\pi$
$17$	398.571			1.37914			0.689569	+	0.724220i	$0.257800\pi$
$18$		0			0
$19$		−	404.608i		−	1.12080i	−0.828223	−	0.560399i	$-0.810648\pi$
$19$		−	404.608i		−	1.12080i	0.828223	−	0.560399i	$-0.189352\pi$
$20$	163.096	+	94.7483i	0.407740	+	0.236871i
$21$		0			0
$22$	−387.889	−	104.493i	−0.801423	−	0.215894i
$23$	−291.091	+	168.062i	−0.550267	+	0.317697i	−0.749230	−	0.662310i	$-0.769576\pi$
$23$	−291.091	+	168.062i	−0.550267	+	0.317697i	0.198963	+	0.980007i	$0.436243\pi$
$24$		0			0
$25$	243.013	−	420.910i	0.388820	−	0.673456i
$26$	481.982	+	483.278i	0.712991	+	0.714908i
$27$		0			0
$28$	934.007	+	2.50777i	1.19134	+	0.00319868i
$29$	−327.671	+	567.543i	−0.389621	+	0.674843i	−0.992398	−	0.123066i	$-0.960727\pi$
$29$	−327.671	+	567.543i	−0.389621	+	0.674843i	0.602778	+	0.797909i	$0.294061\pi$
$30$		0			0
$31$	−550.166	+	317.638i	−0.572493	+	0.330529i	−0.758144	−	0.652087i	$-0.773894\pi$
$31$	−550.166	+	317.638i	−0.572493	+	0.330529i	0.185651	+	0.982616i	$0.440560\pi$
$32$	271.664	−	987.307i	0.265297	−	0.964167i
$33$		0			0
$34$	1540.51	−	410.563i	1.33262	−	0.355158i
$35$			688.176i			0.561776i
$36$		0			0
$37$	−1599.91			−1.16867			−0.584336	−	0.811512i	$-0.698645\pi$
$37$	−1599.91			−1.16867			−0.584336	+	0.811512i	$0.698645\pi$
$38$	−416.782	−	1563.85i	−0.288630	−	1.08300i
$39$		0			0
$40$	727.980	+	198.207i	0.454987	+	0.123880i
$41$	1231.63	+	2133.25i	0.732679	+	1.26904i	0.955734	+	0.294232i	$0.0950637\pi$
$41$	1231.63	+	2133.25i	0.732679	+	1.26904i	−0.223055	+	0.974806i	$0.571603\pi$
$42$		0			0
$43$	−1933.38	−	1116.24i	−1.04564	−	0.603699i	−0.124212	−	0.992256i	$-0.539640\pi$
$43$	−1933.38	−	1116.24i	−1.04564	−	0.603699i	−0.921425	+	0.388557i	$0.872974\pi$
$44$	−1606.86	−	4.31435i	−0.829990	−	0.00222849i
$45$		0			0
$46$	−951.976	+	949.423i	−0.449894	+	0.448688i
$47$	−2514.55	−	1451.78i	−1.13832	−	0.657211i	−0.192308	−	0.981335i	$-0.561597\pi$
$47$	−2514.55	−	1451.78i	−1.13832	−	0.657211i	−0.946015	+	0.324124i	$0.894931\pi$
$48$		0			0
$49$	503.358	+	871.842i	0.209645	+	0.363116i
$50$	505.691	−	1877.18i	0.202276	−	0.750872i
$51$		0			0
$52$	2360.72	+	1371.43i	0.873048	+	0.507185i
$53$	−1291.73			−0.459852			−0.229926	−	0.973208i	$-0.573848\pi$
$53$	−1291.73			−0.459852			−0.229926	+	0.973208i	$0.573848\pi$
$54$		0			0
$55$		−	1183.94i		−	0.391384i
$56$	3612.60	−	952.417i	1.15198	−	0.303704i
$57$		0			0
$58$	−681.858	+	2531.13i	−0.202693	+	0.752418i
$59$	1002.24	−	578.642i	0.287917	−	0.166229i	−0.349085	−	0.937091i	$-0.613508\pi$
$59$	1002.24	−	578.642i	0.287917	−	0.166229i	0.637002	+	0.770862i	$0.280174\pi$
$60$		0			0
$61$	−2960.81	+	5128.28i	−0.795703	+	1.37820i	0.126688	+	0.991943i	$0.459565\pi$
$61$	−2960.81	+	5128.28i	−0.795703	+	1.37820i	−0.922392	+	0.386256i	$0.873768\pi$
$62$	−1799.24	+	1794.42i	−0.468066	+	0.466811i
$63$		0			0
$64$	32.9923	−	4095.87i	0.00805476	−	0.999968i
$65$	−1005.79	+	1742.08i	−0.238057	+	0.412327i
$66$		0			0
$67$	3085.87	−	1781.63i	0.687430	−	0.396888i	−0.115219	−	0.993340i	$-0.536757\pi$
$67$	3085.87	−	1781.63i	0.687430	−	0.396888i	0.802648	+	0.596452i	$0.203424\pi$
$68$	5531.30	−	3173.73i	1.19622	−	0.686360i
$69$		0			0
$70$	708.882	+	2659.86i	0.144670	+	0.542829i
$71$			5639.73i			1.11877i	0.828907	+	0.559386i	$0.188963\pi$
$71$			5639.73i			1.11877i	−0.828907	+	0.559386i	$0.811037\pi$
$72$		0			0
$73$	−5496.39			−1.03141			−0.515705	−	0.856766i	$-0.672470\pi$
$73$	−5496.39			−1.03141			−0.515705	+	0.856766i	$0.672470\pi$
$74$	−6183.80	+	1648.05i	−1.12926	+	0.300959i
$75$		0			0
$76$	−3221.80	−	5615.09i	−0.557791	−	0.972141i
$77$	−2931.31	−	5077.18i	−0.494402	−	0.856329i
$78$		0			0
$79$	−2788.94	−	1610.20i	−0.446874	−	0.258003i	0.259635	−	0.965707i	$-0.416398\pi$
$79$	−2788.94	−	1610.20i	−0.446874	−	0.258003i	−0.706509	+	0.707704i	$0.749731\pi$
$80$	3017.88	+	16.2058i	0.471543	+	0.00253216i
$81$		0			0
$82$	6957.81	+	6976.52i	1.03477	+	1.03755i
$83$	−7063.92	−	4078.36i	−1.02539	−	0.592010i	−0.109730	−	0.993961i	$-0.534999\pi$
$83$	−7063.92	−	4078.36i	−1.02539	−	0.592010i	−0.915661	+	0.401951i	$0.868332\pi$
$84$		0			0
$85$	2349.33	+	4069.15i	0.325166	+	0.563205i
$86$	−8622.53	−	2322.81i	−1.16584	−	0.314063i
$87$		0			0
$88$	−6215.11	+	1638.53i	−0.802571	+	0.211588i
$89$	−910.873			−0.114995			−0.0574974	−	0.998346i	$-0.518312\pi$
$89$	−910.873			−0.114995			−0.0574974	+	0.998346i	$0.518312\pi$
$90$		0			0
$91$			9960.97i			1.20287i
$92$	−2701.48	+	4650.22i	−0.319173	+	0.549412i
$93$		0			0
$94$	−11214.4	−	3021.04i	−1.26918	−	0.341902i
$95$	4130.79	−	2384.91i	0.457705	−	0.264256i
$96$		0			0
$97$	8804.44	−	15249.7i	0.935747	−	1.62076i	0.162450	−	0.986717i	$-0.448060\pi$
$97$	8804.44	−	15249.7i	0.935747	−	1.62076i	0.773297	−	0.634044i	$-0.218606\pi$
$98$	2843.60	+	2851.24i	0.296085	+	0.296881i
$99$		0			0
$100$	20.8792	−	7776.38i	0.00208792	−	0.777638i
$101$	3330.41	−	5768.44i	0.326479	−	0.565478i	−0.655332	−	0.755341i	$-0.727471\pi$
$101$	3330.41	−	5768.44i	0.326479	−	0.565478i	0.981810	+	0.189863i	$0.0608045\pi$
$102$		0			0
$103$	5848.70	−	3376.75i	0.551296	−	0.318291i	−0.198348	−	0.980132i	$-0.563558\pi$
$103$	5848.70	−	3376.75i	0.551296	−	0.318291i	0.749645	+	0.661841i	$0.230224\pi$
$104$	10537.1	+	2868.94i	0.974214	+	0.265250i
$105$		0			0
$106$	−4992.64	+	1330.59i	−0.444343	+	0.118422i
$107$			30.7569i			0.00268643i	0.999999	+	0.00134321i	$0.000427558\pi$
$107$			30.7569i			0.00268643i	−0.999999	+	0.00134321i	$0.999572\pi$
$108$		0			0
$109$	10691.4			0.899872			0.449936	−	0.893061i	$-0.351447\pi$
$109$	10691.4			0.899872			0.449936	+	0.893061i	$0.351447\pi$
$110$	−1219.56	−	4576.02i	−0.100790	−	0.378183i
$111$		0			0
$112$	12982.0	−	7402.48i	1.03491	−	0.590121i
$113$	5008.09	+	8674.27i	0.392207	+	0.679322i	0.992740	−	0.120277i	$-0.0383784\pi$
$113$	5008.09	+	8674.27i	0.392207	+	0.679322i	−0.600533	+	0.799600i	$0.705045\pi$
$114$		0			0
$115$	−3431.60	−	1981.24i	−0.259479	−	0.149810i
$116$	−28.1529	+	10485.4i	−0.00209222	+	0.779238i
$117$		0			0
$118$	3277.69	−	3268.90i	0.235398	−	0.234767i
$119$	20149.7	+	11633.4i	1.42290	+	0.821511i
$120$		0			0
$121$	−2277.49	−	3944.73i	−0.155556	−	0.269430i
$122$	−6161.23	+	22871.1i	−0.413950	+	1.53663i
$123$		0			0
$124$	−5105.83	+	8788.97i	−0.332065	+	0.571603i
$125$	13097.6			0.838247
$126$		0			0
$127$			16087.8i			0.997444i	0.866762	+	0.498722i	$0.166197\pi$
$127$			16087.8i			0.997444i	−0.866762	+	0.498722i	$0.833803\pi$
$128$	−4091.59	−	15864.9i	−0.249731	−	0.968315i
$129$		0			0
$130$	−2092.97	+	7769.35i	−0.123845	+	0.459725i
$131$	18105.5	−	10453.2i	1.05504	−	0.609127i	0.130983	−	0.991385i	$-0.458187\pi$
$131$	18105.5	−	10453.2i	1.05504	−	0.609127i	0.924056	+	0.382257i	$0.124853\pi$
$132$		0			0
$133$	11809.6	−	20454.9i	0.667626	−	1.15636i
$134$	10091.9	−	10064.9i	0.562037	−	0.560530i
$135$		0			0
$136$	18109.8	−	17964.5i	0.979117	−	0.971262i
$137$	2338.02	−	4049.57i	0.124568	−	0.215759i	−0.796996	−	0.603985i	$-0.793579\pi$
$137$	2338.02	−	4049.57i	0.124568	−	0.215759i	0.921564	+	0.388226i	$0.126912\pi$
$138$		0			0
$139$	8058.42	−	4652.53i	0.417081	−	0.240802i	−0.276747	−	0.960943i	$-0.589256\pi$
$139$	8058.42	−	4652.53i	0.417081	−	0.240802i	0.693828	+	0.720141i	$0.255923\pi$
$140$	5479.79	+	9550.40i	0.279581	+	0.487265i
$141$		0			0
$142$	5809.42	+	21798.0i	0.288108	+	1.08104i
$143$		−	17136.8i		−	0.838026i
$144$		0			0
$145$	−7725.67			−0.367451
$146$	−21244.0	+	5661.77i	−0.996624	+	0.265611i
$147$		0			0
$148$	−22203.3	+	12739.7i	−1.01367	+	0.581617i
$149$	−12385.8	−	21452.8i	−0.557893	−	0.966299i	−0.997672	−	0.0681928i	$-0.978277\pi$
$149$	−12385.8	−	21452.8i	−0.557893	−	0.966299i	0.439779	−	0.898106i	$-0.355057\pi$
$150$		0			0
$151$	8841.72	+	5104.77i	0.387778	+	0.223884i	0.681197	−	0.732100i	$-0.261460\pi$
$151$	8841.72	+	5104.77i	0.387778	+	0.223884i	−0.293419	+	0.955984i	$0.594793\pi$
$152$	−18236.6	−	18384.1i	−0.789326	−	0.795709i
$153$		0			0
$154$	−16559.7	−	16604.2i	−0.698251	−	0.700128i
$155$	−6485.77	−	3744.56i	−0.269959	−	0.155861i
$156$		0			0
$157$	14486.5	+	25091.4i	0.587712	+	1.01795i	0.994531	+	0.104439i	$0.0333046\pi$
$157$	14486.5	+	25091.4i	0.587712	+	1.01795i	−0.406819	+	0.913509i	$0.633362\pi$
$158$	−12438.2	−	3350.70i	−0.498244	−	0.134221i
$159$		0			0
$160$	11681.1	−	3046.04i	0.456291	−	0.118986i
$161$	−19621.4			−0.756970
$162$		0			0
$163$			17736.4i			0.667560i	0.942651	+	0.333780i	$0.108324\pi$
$163$			17736.4i			0.667560i	−0.942651	+	0.333780i	$0.891676\pi$
$164$	34079.0	+	19797.7i	1.26707	+	0.736084i
$165$		0			0
$166$	−31503.8	−	8486.75i	−1.14326	−	0.307982i
$167$	−35562.1	+	20531.8i	−1.27513	+	0.736197i	−0.975949	−	0.217999i	$-0.930047\pi$
$167$	−35562.1	+	20531.8i	−1.27513	+	0.736197i	−0.299182	+	0.954196i	$0.596714\pi$
$168$		0			0
$169$	−277.761	+	481.096i	−0.00972518	+	0.0168445i
$170$	13271.9	+	13307.6i	0.459237	+	0.460472i
$171$		0			0
$172$	−35719.5	−	95.9053i	−1.20739	−	0.00324180i
$173$	3477.87	−	6023.84i	0.116204	−	0.201271i	−0.802056	−	0.597248i	$-0.796261\pi$
$173$	3477.87	−	6023.84i	0.116204	−	0.201271i	0.918260	+	0.395977i	$0.129594\pi$
$174$		0			0
$175$	24570.9	−	14186.0i	0.802315	−	0.463217i
$176$	−22334.1	+	12735.2i	−0.721013	+	0.411131i
$177$		0			0
$178$	−3520.61	+	938.280i	−0.111116	+	0.0296137i
$179$			1754.50i			0.0547580i	0.999625	+	0.0273790i	$0.00871609\pi$
$179$			1754.50i			0.0547580i	−0.999625	+	0.0273790i	$0.991284\pi$
$180$		0			0
$181$	−43787.9			−1.33659			−0.668293	−	0.743898i	$-0.732975\pi$
$181$	−43787.9			−1.33659			−0.668293	+	0.743898i	$0.732975\pi$
$182$	10260.7	+	38500.0i	0.309766	+	1.16230i
$183$		0			0
$184$	−5651.33	+	20756.3i	−0.166922	+	0.613076i
$185$	−9430.49	−	16334.1i	−0.275544	−	0.477256i
$186$		0			0
$187$	−34665.4	−	20014.1i	−0.991318	−	0.572338i
$188$	−46456.8	−	124.734i	−1.31442	−	0.00352915i
$189$		0			0
$190$	13509.2	−	13473.0i	0.374216	−	0.373213i
$191$	34403.1	+	19862.7i	0.943042	+	0.544466i	0.890913	−	0.454174i	$-0.150066\pi$
$191$	34403.1	+	19862.7i	0.943042	+	0.544466i	0.0521297	+	0.998640i	$0.483399\pi$
$192$		0			0
$193$	10547.2	+	18268.3i	0.283154	+	0.490437i	0.972160	−	0.234319i	$-0.0752859\pi$
$193$	10547.2	+	18268.3i	0.283154	+	0.490437i	−0.689006	+	0.724756i	$0.741953\pi$
$194$	18321.4	−	68011.0i	0.486805	−	1.80707i
$195$		0			0
$196$	13927.8	+	8091.15i	0.362552	+	0.210619i
$197$	−28256.1			−0.728080			−0.364040	−	0.931383i	$-0.618603\pi$
$197$	−28256.1			−0.728080			−0.364040	+	0.931383i	$0.618603\pi$
$198$		0			0
$199$		−	24063.5i		−	0.607650i	−0.952728	−	0.303825i	$-0.901736\pi$
$199$		−	24063.5i		−	0.607650i	0.952728	−	0.303825i	$-0.0982638\pi$
$200$	−7929.65	−	30077.9i	−0.198241	−	0.751947i
$201$		0			0
$202$	6930.33	−	25726.1i	0.169844	−	0.630481i
$203$	−33130.7	+	19128.0i	−0.803967	+	0.464171i
$204$		0			0
$205$	−14519.4	+	25148.4i	−0.345495	+	0.598415i
$206$	19127.4	−	19076.1i	0.450735	−	0.449527i
$207$		0			0
$208$	43682.1	+	234.571i	1.00966	+	0.00542184i
$209$	−20317.2	+	35190.5i	−0.465127	+	0.805624i
$210$		0			0
$211$	−50298.6	+	29039.9i	−1.12977	+	0.652274i	−0.943878	−	0.330295i	$-0.892852\pi$
$211$	−50298.6	+	29039.9i	−1.12977	+	0.652274i	−0.185895	+	0.982570i	$0.559518\pi$
$212$	−17926.4	+	10285.7i	−0.398860	+	0.228856i
$213$		0			0
$214$	31.6823	+	118.878i	0.000691814	+	0.00259582i
$215$		−	26318.1i		−	0.569349i
$216$		0			0
$217$	−37084.7			−0.787545
$218$	41323.1	−	11013.1i	0.869522	−	0.231737i
$219$		0			0
$220$	−9427.40	−	16430.5i	−0.194781	−	0.339472i
$221$	34005.2	+	58898.7i	0.696243	+	1.20593i
$222$		0			0
$223$	14429.6	+	8330.91i	0.290164	+	0.167526i	0.638016	−	0.770023i	$-0.279755\pi$
$223$	14429.6	+	8330.91i	0.290164	+	0.167526i	−0.347852	+	0.937550i	$0.613089\pi$
$224$	42551.3	−	41983.8i	0.848040	−	0.836731i
$225$		0			0
$226$	28292.0	+	28368.0i	0.553919	+	0.555409i
$227$	−48721.5	−	28129.4i	−0.945515	−	0.545894i	−0.0538304	−	0.998550i	$-0.517143\pi$
$227$	−48721.5	−	28129.4i	−0.945515	−	0.545894i	−0.891685	+	0.452657i	$0.850476\pi$
$228$		0			0
$229$	−1223.91	−	2119.87i	−0.0233388	−	0.0404239i	0.854120	−	0.520076i	$-0.174096\pi$
$229$	−1223.91	−	2119.87i	−0.0233388	−	0.0404239i	−0.877459	+	0.479652i	$0.840763\pi$
$230$	−15304.3	−	4122.81i	−0.289306	−	0.0779358i
$231$		0			0
$232$	10692.1	+	40556.1i	0.198649	+	0.753495i
$233$	76971.2			1.41781			0.708903	−	0.705306i	$-0.249191\pi$
$233$	76971.2			1.41781			0.708903	+	0.705306i	$0.249191\pi$
$234$		0			0
$235$		−	34229.3i		−	0.619816i
$236$	9301.30	−	16010.9i	0.167001	−	0.287469i
$237$		0			0
$238$	89863.7	+	24208.3i	1.58646	+	0.427375i
$239$	22567.5	−	13029.4i	0.395083	−	0.228101i	−0.289277	−	0.957245i	$-0.593415\pi$
$239$	22567.5	−	13029.4i	0.395083	−	0.228101i	0.684360	+	0.729144i	$0.260082\pi$
$240$		0			0
$241$	13999.8	−	24248.4i	0.241039	−	0.417492i	−0.719971	−	0.694004i	$-0.755845\pi$
$241$	13999.8	−	24248.4i	0.241039	−	0.417492i	0.961011	+	0.276512i	$0.0891784\pi$
$242$	−12866.1	−	12900.7i	−0.219693	−	0.220284i
$243$		0			0
$244$	−254.388	+	94745.6i	−0.00427284	+	1.59140i
$245$	−5933.96	+	10277.9i	−0.0988582	+	0.171227i
$246$		0			0
$247$	59790.9	−	34520.3i	0.980034	−	0.565823i
$248$	−10681.1	+	39229.6i	−0.173665	+	0.637839i
$249$		0			0
$250$	50623.4	−	13491.7i	0.809975	−	0.215867i
$251$		−	19782.5i		−	0.314003i	−0.987598	−	0.157001i	$-0.949817\pi$
$251$		−	19782.5i		−	0.314003i	0.987598	−	0.157001i	$-0.0501827\pi$
$252$		0			0
$253$	33756.6			0.527373
$254$	16571.8	+	62180.7i	0.256864	+	0.963803i
$255$		0			0
$256$	−32156.6	−	57104.5i	−0.490670	−	0.871345i
$257$	38636.9	+	66921.1i	0.584974	+	1.01320i	0.994879	+	0.101076i	$0.0322285\pi$
$257$	38636.9	+	66921.1i	0.584974	+	1.01320i	−0.409905	+	0.912128i	$0.634438\pi$
$258$		0			0
$259$	−80883.2	−	46698.0i	−1.20575	−	0.696143i
$260$	−86.4158	+	32185.2i	−0.00127834	+	0.476112i
$261$		0			0
$262$	59211.7	−	59053.0i	0.862592	−	0.860279i
$263$	18370.5	+	10606.2i	0.265588	+	0.153337i	0.626881	−	0.779115i	$-0.284331\pi$
$263$	18370.5	+	10606.2i	0.265588	+	0.153337i	−0.361293	+	0.932452i	$0.617665\pi$
$264$		0			0
$265$	−7613.92	−	13187.7i	−0.108422	−	0.187792i
$266$	24574.9	−	91224.9i	0.347320	−	1.28929i
$267$		0			0
$268$	28638.5	−	49297.2i	0.398732	−	0.686361i
$269$	−1106.24			−0.0152878			−0.00764389	−	0.999971i	$-0.502433\pi$
$269$	−1106.24			−0.0152878			−0.00764389	+	0.999971i	$0.502433\pi$
$270$		0			0
$271$			33038.3i			0.449861i	0.974375	+	0.224931i	$0.0722155\pi$
$271$			33038.3i			0.449861i	−0.974375	+	0.224931i	$0.927784\pi$
$272$	51490.8	−	88088.9i	0.695972	−	1.19065i
$273$		0			0
$274$	4865.25	−	18060.3i	0.0648043	−	0.240561i
$275$	−42271.7	+	24405.6i	−0.558964	+	0.322718i
$276$		0			0
$277$	−14421.3	+	24978.4i	−0.187951	+	0.325540i	−0.944567	−	0.328319i	$-0.893518\pi$
$277$	−14421.3	+	24978.4i	−0.187951	+	0.325540i	0.756616	+	0.653859i	$0.226851\pi$
$278$	26354.0	−	26283.3i	0.341002	−	0.340088i
$279$		0			0
$280$	31017.6	+	31268.5i	0.395633	+	0.398833i
$281$	16062.9	−	27821.8i	0.203428	−	0.352348i	−0.746203	−	0.665719i	$-0.768125\pi$
$281$	16062.9	−	27821.8i	0.203428	−	0.352348i	0.949631	+	0.313371i	$0.101458\pi$
$282$		0			0
$283$	−61782.5	+	35670.2i	−0.771424	+	0.445382i	−0.833382	−	0.552697i	$-0.813599\pi$
$283$	−61782.5	+	35670.2i	−0.771424	+	0.445382i	0.0619586	+	0.998079i	$0.480265\pi$
$284$	44907.8	+	78267.2i	0.556782	+	0.970383i
$285$		0			0
$286$	−17652.4	−	66235.3i	−0.215810	−	0.809762i
$287$			143795.i			1.74574i
$288$		0			0
$289$	75337.7			0.902021
$290$	−29860.4	+	7958.12i	−0.355058	+	0.0946268i
$291$		0			0
$292$	−76278.0	+	43766.5i	−0.894609	+	0.513305i
$293$	−18320.8	−	31732.5i	−0.213407	−	0.369631i	0.739372	−	0.673297i	$-0.235123\pi$
$293$	−18320.8	−	31732.5i	−0.213407	−	0.369631i	−0.952779	+	0.303666i	$0.901789\pi$
$294$		0			0
$295$	11815.1	+	6821.47i	0.135767	+	0.0783852i
$296$	−72694.8	+	72111.6i	−0.829698	+	0.823041i
$297$		0			0
$298$	−69970.4	−	70158.5i	−0.787920	−	0.790038i
$299$	−49670.5	−	28677.3i	−0.555593	−	0.320772i
$300$		0			0
$301$	−65161.2	−	112863.i	−0.719211	−	1.24571i
$302$	39432.4	+	10622.6i	0.432354	+	0.116471i
$303$		0			0
$304$	−89423.2	−	52270.8i	−0.967616	−	0.565603i
$305$	−69808.6			−0.750428
$306$		0			0
$307$			11668.1i			0.123801i	0.998082	+	0.0619005i	$0.0197161\pi$
$307$			11668.1i			0.123801i	−0.998082	+	0.0619005i	$0.980284\pi$
$308$	−81108.6	−	47118.9i	−0.854999	−	0.496699i
$309$		0			0
$310$	−28925.3	−	7792.15i	−0.300992	−	0.0810837i
$311$	3755.11	−	2168.01i	0.0388242	−	0.0224151i	−0.480462	−	0.877015i	$-0.659531\pi$
$311$	3755.11	−	2168.01i	0.0388242	−	0.0224151i	0.519286	+	0.854600i	$0.326198\pi$
$312$		0			0
$313$	−43249.3	+	74909.9i	−0.441459	+	0.764629i	−0.997798	−	0.0663262i	$-0.978872\pi$
$313$	−43249.3	+	74909.9i	−0.441459	+	0.764629i	0.556339	+	0.830955i	$0.312206\pi$
$314$	81838.0	+	82058.1i	0.830034	+	0.832266i
$315$		0			0
$316$	−51526.1	−	138.345i	−0.516004	−	0.00138545i
$317$	−12316.1	+	21332.1i	−0.122562	+	0.212283i	−0.920777	−	0.390089i	$-0.872444\pi$
$317$	−12316.1	+	21332.1i	−0.122562	+	0.212283i	0.798215	+	0.602372i	$0.205778\pi$
$318$		0			0
$319$	56997.9	−	32907.7i	0.560115	−	0.323383i
$320$	42010.7	−	23805.8i	0.410260	−	0.232478i
$321$		0			0
$322$	−75838.5	+	20211.8i	−0.731439	+	0.194936i
$323$		−	161265.i		−	1.54573i
$324$		0			0
$325$	82933.2			0.785167
$326$	18270.0	+	68552.7i	0.171911	+	0.645044i
$327$		0			0
$328$	152112.	+	41415.5i	1.41389	+	0.384960i
$329$	−84748.5	−	146789.i	−0.782961	−	1.35613i
$330$		0			0
$331$	162176.	+	93632.3i	1.48023	+	0.854614i	0.999749	−	0.0223896i	$-0.00712742\pi$
$331$	162176.	+	93632.3i	1.48023	+	0.854614i	0.480485	+	0.877003i	$0.340461\pi$
$332$	−130507.	−	350.405i	−1.18402	−	0.00317903i
$333$		0			0
$334$	−116301.	+	115989.i	−1.04254	+	1.03974i
$335$	36378.6	+	21003.2i	0.324158	+	0.187152i
$336$		0			0
$337$	50479.6	+	87433.2i	0.444484	+	0.769868i	0.998016	−	0.0629592i	$-0.0200538\pi$
$337$	50479.6	+	87433.2i	0.444484	+	0.769868i	−0.553532	+	0.832828i	$0.686720\pi$
$338$	−577.999	+	2145.60i	−0.00505934	+	0.0187808i
$339$		0			0
$340$	65005.3	+	37763.9i	0.562330	+	0.326677i
$341$	63800.3			0.548674
$342$		0			0
$343$		−	81392.2i		−	0.691823i
$344$	−138158.	+	36423.6i	−1.16751	+	0.307798i
$345$		0			0
$346$	7237.18	−	26865.2i	0.0604529	−	0.224408i
$347$	151470.	−	87451.5i	1.25797	−	0.726287i	0.285287	−	0.958442i	$-0.407911\pi$
$347$	151470.	−	87451.5i	1.25797	−	0.726287i	0.972679	+	0.232155i	$0.0745777\pi$
$348$		0			0
$349$	−21948.5	+	38015.9i	−0.180199	+	0.312114i	−0.941948	−	0.335758i	$-0.891008\pi$
$349$	−21948.5	+	38015.9i	−0.180199	+	0.312114i	0.761749	+	0.647872i	$0.224341\pi$
$350$	80355.9	−	80140.4i	0.655967	−	0.654208i
$351$		0			0
$352$	−73205.0	+	72228.8i	−0.590820	+	0.582941i
$353$	77789.6	−	134736.i	0.624270	−	1.08127i	−0.364412	−	0.931238i	$-0.618730\pi$
$353$	77789.6	−	134736.i	0.624270	−	1.08127i	0.988682	−	0.150029i	$-0.0479367\pi$
$354$		0			0
$355$	−57578.0	+	33242.7i	−0.456878	+	0.263778i
$356$	−12641.0	+	7253.07i	−0.0997424	+	0.0572298i
$357$		0			0
$358$	1807.29	+	6781.30i	0.0141014	+	0.0529111i
$359$			184004.i			1.42771i	0.700295	+	0.713853i	$0.253052\pi$
$359$			184004.i			1.42771i	−0.700295	+	0.713853i	$0.746948\pi$
$360$		0			0
$361$	−33386.7			−0.256188
$362$	−169244.	+	45105.4i	−1.29151	+	0.344200i
$363$		0			0
$364$	79316.9	+	138237.i	0.598636	+	1.04333i
$365$	−32397.8	−	56114.6i	−0.243181	−	0.421202i
$366$		0			0
$367$	143674.	+	82950.4i	1.06671	+	0.615866i	0.927281	−	0.374366i	$-0.122140\pi$
$367$	143674.	+	82950.4i	1.06671	+	0.615866i	0.139430	+	0.990232i	$0.455473\pi$
$368$	−462.064	+	86046.3i	−0.00341198	+	0.635385i
$369$		0			0
$370$	−53275.2	−	53418.5i	−0.389154	−	0.390201i
$371$	−65302.9	−	37702.7i	−0.474444	−	0.273920i
$372$		0			0
$373$	−65160.0	−	112861.i	−0.468343	−	0.811193i	0.531003	−	0.847370i	$-0.321815\pi$
$373$	−65160.0	−	112861.i	−0.468343	−	0.811193i	−0.999345	+	0.0361768i	$0.988482\pi$
$374$	−154601.	−	41647.8i	−1.10527	−	0.297748i
$375$		0			0
$376$	−179688.	+	47372.4i	−1.27099	+	0.335081i
$377$	−111825.			−0.786783
$378$		0			0
$379$			43645.6i			0.303852i	0.988392	+	0.151926i	$0.0485475\pi$
$379$			43645.6i			0.303852i	−0.988392	+	0.151926i	$0.951453\pi$
$380$	38335.9	−	65990.0i	0.265484	−	0.456994i
$381$		0			0
$382$	153431.	+	41332.7i	1.05145	+	0.283248i
$383$	237186.	−	136939.i	1.61693	−	0.933535i	0.629223	−	0.777225i	$-0.283373\pi$
$383$	237186.	−	136939.i	1.61693	−	0.933535i	0.987708	−	0.156310i	$-0.0499599\pi$
$384$		0			0
$385$	34556.5	−	59853.6i	0.233135	−	0.403802i
$386$	59583.9	+	59744.1i	0.399902	+	0.400978i
$387$		0			0
$388$	756.462	−	281741.i	0.00502486	−	1.87149i
$389$	−122594.	+	212339.i	−0.810159	+	1.40324i	0.102594	+	0.994723i	$0.467286\pi$
$389$	−122594.	+	212339.i	−0.810159	+	1.40324i	−0.912753	+	0.408513i	$0.866048\pi$
$390$		0			0
$391$	−116020.	+	66984.5i	−0.758894	+	0.438148i
$392$	62166.8	+	16926.2i	0.404563	+	0.110151i
$393$		0			0
$394$	−109212.	+	29106.2i	−0.703524	+	0.187497i
$395$		−	37964.4i		−	0.243323i
$396$		0			0
$397$	−4252.39			−0.0269806			−0.0134903	−	0.999909i	$-0.504294\pi$
$397$	−4252.39			−0.0269806			−0.0134903	+	0.999909i	$0.504294\pi$
$398$	−24787.6	−	93007.8i	−0.156483	−	0.587155i
$399$		0			0
$400$	−61631.7	−	108086.i	−0.385198	−	0.675535i
$401$	3665.61	+	6349.02i	0.0227959	+	0.0394837i	0.877198	−	0.480128i	$-0.159410\pi$
$401$	3665.61	+	6349.02i	0.0227959	+	0.0394837i	−0.854402	+	0.519612i	$0.826077\pi$
$402$		0			0
$403$	−93877.9	−	54200.4i	−0.578034	−	0.333728i
$404$	286.143	−	106573.i	0.00175315	−	0.652955i
$405$		0			0
$406$	−108349.	+	108059.i	−0.657317	+	0.655554i
$407$	139151.	+	80339.0i	0.840036	+	0.484995i
$408$		0			0
$409$	14207.0	+	24607.2i	0.0849289	+	0.147101i	0.905361	−	0.424643i	$-0.139600\pi$
$409$	14207.0	+	24607.2i	0.0849289	+	0.147101i	−0.820432	+	0.571744i	$0.806267\pi$
$410$	−30213.8	+	112157.i	−0.179737	+	0.667204i
$411$		0			0
$412$	54279.1	−	93433.8i	0.319770	−	0.550440i
$413$	67557.2			0.396070
$414$		0			0
$415$		−	96157.5i		−	0.558325i
$416$	169077.	−	44089.8i	0.977007	−	0.254772i
$417$		0			0
$418$	−42278.6	+	156943.i	−0.241974	+	0.898233i
$419$	−137256.	+	79245.0i	−0.781816	+	0.451382i	−0.837073	−	0.547091i	$-0.815735\pi$
$419$	−137256.	+	79245.0i	−0.781816	+	0.451382i	0.0552577	+	0.998472i	$0.482402\pi$
$420$		0			0
$421$	142796.	−	247330.i	0.805659	−	1.39544i	−0.110186	−	0.993911i	$-0.535145\pi$
$421$	142796.	−	247330.i	0.805659	−	1.39544i	0.915845	−	0.401532i	$-0.131522\pi$
$422$	−164495.	+	164054.i	−0.923693	+	0.921216i
$423$		0			0
$424$	−58691.8	+	58220.9i	−0.326472	+	0.323853i
$425$	96857.7	−	167763.i	0.536237	−	0.928789i
$426$		0			0
$427$	−299366.	+	172839.i	−1.64190	+	0.947953i
$428$	244.910	+	426.839i	0.00133696	+	0.00233011i
$429$		0			0
$430$	−27110.0	−	101722.i	−0.146620	−	0.550146i
$431$			115124.i			0.619741i	0.950779	+	0.309870i	$0.100286\pi$
$431$			115124.i			0.619741i	−0.950779	+	0.309870i	$0.899714\pi$
$432$		0			0
$433$	95600.5			0.509899			0.254950	−	0.966954i	$-0.417941\pi$
$433$	95600.5			0.509899			0.254950	+	0.966954i	$0.417941\pi$
$434$	−143336.	+	38200.5i	−0.760983	+	0.202810i
$435$		0			0
$436$	148373.	−	85133.0i	0.780517	−	0.447842i
$437$	67999.1	+	117778.i	0.356074	+	0.616738i
$438$		0			0
$439$	321749.	+	185762.i	1.66951	+	0.963890i	0.967903	+	0.251322i	$0.0808654\pi$
$439$	321749.	+	185762.i	1.66951	+	0.963890i	0.701603	+	0.712568i	$0.252468\pi$
$440$	−53362.6	−	53794.1i	−0.275633	−	0.277862i
$441$		0			0
$442$	192104.	+	192620.i	0.983313	+	0.985957i
$443$	−119741.	−	69132.2i	−0.610146	−	0.352268i	0.162877	−	0.986646i	$-0.447923\pi$
$443$	−119741.	−	69132.2i	−0.610146	−	0.352268i	−0.773023	+	0.634379i	$0.781256\pi$
$444$		0			0
$445$	−5369.03	−	9299.44i	−0.0271129	−	0.0469609i
$446$	64353.2	+	17336.0i	0.323519	+	0.0871524i
$447$		0			0
$448$	121217.	−	206103.i	0.603961	−	1.02690i
$449$	−128427.			−0.637035			−0.318518	−	0.947917i	$-0.603185\pi$
$449$	−128427.			−0.637035			−0.318518	+	0.947917i	$0.603185\pi$
$450$		0			0
$451$		−	247384.i		−	1.21624i
$452$	138573.	+	80501.8i	0.678267	+	0.394030i
$453$		0			0
$454$	−217289.	−	58535.0i	−1.05421	−	0.283991i
$455$	−101695.	+	58713.7i	−0.491221	+	0.283607i
$456$		0			0
$457$	−146543.	+	253819.i	−0.701668	+	1.21532i	0.266213	+	0.963914i	$0.414227\pi$
$457$	−146543.	+	253819.i	−0.701668	+	1.21532i	−0.967881	+	0.251410i	$0.919106\pi$
$458$	−6914.17	−	6932.76i	−0.0329617	−	0.0330503i
$459$		0			0
$460$	−63399.4	−	170.224i	−0.299619	−	0.000804463i
$461$	148067.	−	256460.i	0.696717	−	1.20675i	−0.272881	−	0.962048i	$-0.587977\pi$
$461$	148067.	−	256460.i	0.696717	−	1.20675i	0.969598	−	0.244702i	$-0.0786900\pi$
$462$		0			0
$463$	307165.	−	177342.i	1.43288	−	0.827273i	0.435539	−	0.900170i	$-0.356558\pi$
$463$	307165.	−	177342.i	1.43288	−	0.827273i	0.997339	+	0.0728974i	$0.0232246\pi$
$464$	83102.4	+	145739.i	0.385991	+	0.676925i
$465$		0			0
$466$	297501.	−	79287.2i	1.36999	−	0.365116i
$467$		−	116644.i		−	0.534848i	−0.963579	−	0.267424i	$-0.913828\pi$
$467$		−	116644.i		−	0.534848i	0.963579	−	0.267424i	$-0.0861724\pi$
$468$		0			0
$469$	208007.			0.945656
$470$	−35259.2	−	132299.i	−0.159616	−	0.598911i
$471$		0			0
$472$	19457.7	−	71464.7i	0.0873389	−	0.320780i
$473$	112103.	+	194168.i	0.501066	+	0.867872i
$474$		0			0
$475$	−170304.	−	98324.9i	−0.754809	−	0.435789i
$476$	372268.	+	999.522i	1.64302	+	0.00441142i
$477$		0			0
$478$	73804.1	−	73606.2i	0.323017	−	0.322151i
$479$	−90134.6	−	52039.3i	−0.392845	−	0.226809i	0.290547	−	0.956861i	$-0.406163\pi$
$479$	−90134.6	−	52039.3i	−0.392845	−	0.226809i	−0.683392	+	0.730052i	$0.739496\pi$
$480$		0			0
$481$	−136501.	−	236427.i	−0.589992	−	1.02190i
$482$	29132.5	−	108143.i	0.125396	−	0.465484i
$483$		0			0
$484$	−63017.5	−	36609.1i	−0.269011	−	0.156278i
$485$	207587.			0.882503
$486$		0			0
$487$			101284.i			0.427055i	0.976937	+	0.213527i	$0.0684953\pi$
$487$			101284.i			0.427055i	−0.976937	+	0.213527i	$0.931505\pi$
$488$	96613.2	+	366462.i	0.405692	+	1.53883i
$489$		0			0
$490$	−12348.1	+	45837.6i	−0.0514291	+	0.190911i
$491$	−151749.	+	87612.6i	−0.629454	+	0.363416i	−0.780541	−	0.625105i	$-0.785056\pi$
$491$	−151749.	+	87612.6i	−0.629454	+	0.363416i	0.151086	+	0.988521i	$0.451723\pi$
$492$		0			0
$493$	−130600.	+	226206.i	−0.537341	+	0.930701i
$494$	195538.	−	195014.i	0.801268	−	0.799119i
$495$		0			0
$496$	−873.306	+	162628.i	−0.00354979	+	0.661048i
$497$	−164611.	+	285115.i	−0.666418	+	1.15427i
$498$		0			0
$499$	83227.2	−	48051.2i	0.334244	−	0.192976i	−0.323480	−	0.946235i	$-0.604853\pi$
$499$	83227.2	−	48051.2i	0.334244	−	0.192976i	0.657724	+	0.753259i	$0.271519\pi$
$500$	181766.	−	104293.i	0.727066	−	0.417173i
$501$		0			0
$502$	−20377.7	−	76461.1i	−0.0808627	−	0.303412i
$503$		−	164729.i		−	0.651080i	−0.945528	−	0.325540i	$-0.894454\pi$
$503$		−	164729.i		−	0.651080i	0.945528	−	0.325540i	$-0.105546\pi$
$504$		0			0
$505$	78522.7			0.307902
$506$	130472.	−	34772.3i	0.509586	−	0.135810i
$507$		0			0
$508$	128103.	+	223264.i	0.496401	+	0.865148i
$509$	−42970.1	−	74426.4i	−0.165856	−	0.287271i	0.771103	−	0.636710i	$-0.219705\pi$
$509$	−42970.1	−	74426.4i	−0.165856	−	0.287271i	−0.936959	+	0.349440i	$0.886372\pi$
$510$		0			0
$511$	−277869.	−	160428.i	−1.06414	−	0.614380i
$512$	−183111.	−	187590.i	−0.698512	−	0.715598i
$513$		0			0
$514$	218270.	+	218857.i	0.826166	+	0.828388i
$515$	68948.9	+	39807.7i	0.259964	+	0.150090i
$516$		0			0
$517$	145801.	+	252535.i	0.545481	+	0.944800i
$518$	−360724.	−	97174.9i	−1.34436	−	0.362155i
$519$		0			0
$520$	32819.6	+	124488.i	0.121374	+	0.460383i
$521$	173047.			0.637514			0.318757	−	0.947836i	$-0.396735\pi$
$521$	173047.			0.637514			0.318757	+	0.947836i	$0.396735\pi$
$522$		0			0
$523$			252188.i			0.921978i	0.887406	+	0.460989i	$0.152505\pi$
$523$			252188.i			0.921978i	−0.887406	+	0.460989i	$0.847495\pi$
$524$	168029.	−	289238.i	0.611958	−	1.05340i
$525$		0			0
$526$	81928.8	+	22070.7i	0.296118	+	0.0797709i
$527$	−219280.	+	126601.i	−0.789547	+	0.455845i
$528$		0			0
$529$	−83431.1	+	144507.i	−0.298137	+	0.516389i
$530$	−43013.0	−	43128.6i	−0.153126	−	0.153537i
$531$		0			0
$532$	1014.66	−	377907.i	0.00358508	−	1.33525i
$533$	−210161.	+	364009.i	−0.739770	+	1.28132i
$534$		0			0
$535$	−314.008	+	181.293i	−0.00109707	+	0.000633393i
$536$	59910.0	−	220038.i	0.208530	−	0.765894i
$537$		0			0
$538$	−4275.71	+	1139.52i	−0.0147722	+	0.00393694i
$539$		−	101104.i		−	0.348008i
$540$		0			0
$541$	−472358.			−1.61390			−0.806950	−	0.590620i	$-0.798883\pi$
$541$	−472358.			−1.61390			−0.806950	+	0.590620i	$0.798883\pi$
$542$	34032.3	+	127696.i	0.115849	+	0.434688i
$543$		0			0
$544$	108277.	−	393512.i	0.365881	−	1.32972i
$545$	63019.0	+	109152.i	0.212167	+	0.367485i
$546$		0			0
$547$	−332881.	−	192189.i	−1.11254	−	0.642323i	−0.173051	−	0.984913i	$-0.555362\pi$
$547$	−332881.	−	192189.i	−1.11254	−	0.642323i	−0.939485	+	0.342590i	$0.888696\pi$
$548$	200.879	−	74816.5i	0.000668918	−	0.249136i
$549$		0			0
$550$	−138244.	+	137873.i	−0.457005	+	0.455779i
$551$	229632.	+	132578.i	0.756362	+	0.436686i
$552$		0			0
$553$	−93996.3	−	162806.i	−0.307369	−	0.532379i
$554$	−30009.5	+	111399.i	−0.0977777	+	0.362962i
$555$		0			0
$556$	74786.4	−	128734.i	0.241921	−	0.416433i
$557$	19803.1			0.0638297			0.0319148	−	0.999491i	$-0.489839\pi$
$557$	19803.1			0.0638297			0.0319148	+	0.999491i	$0.489839\pi$
$558$		0			0
$559$		−	380940.i		−	1.21908i
$560$	152095.	+	88904.6i	0.484997	+	0.283497i
$561$		0			0
$562$	33425.7	−	124080.i	0.105830	−	0.392851i
$563$	−132566.	+	76536.8i	−0.418229	+	0.241465i	−0.694319	−	0.719667i	$-0.744294\pi$
$563$	−132566.	+	76536.8i	−0.418229	+	0.241465i	0.276090	+	0.961132i	$0.410961\pi$
$564$		0			0
$565$	−59039.2	+	102259.i	−0.184945	+	0.320335i
$566$	−202052.	+	201510.i	−0.630710	+	0.629019i
$567$		0			0
$568$	254195.	+	256251.i	0.787898	+	0.794271i
$569$	−25955.5	+	44956.2i	−0.0801687	+	0.138856i	−0.903322	−	0.428963i	$-0.858879\pi$
$569$	−25955.5	+	44956.2i	−0.0801687	+	0.138856i	0.823154	+	0.567819i	$0.192213\pi$
$570$		0			0
$571$	92961.9	−	53671.6i	0.285123	−	0.164616i	−0.350617	−	0.936519i	$-0.614028\pi$
$571$	92961.9	−	53671.6i	0.285123	−	0.164616i	0.635741	+	0.771903i	$0.280695\pi$
$572$	−136456.	−	237822.i	−0.417063	−	0.726874i
$573$		0			0
$574$	148121.	+	555780.i	0.449566	+	1.68686i
$575$			163364.i			0.494108i
$576$		0			0
$577$	−114098.			−0.342710			−0.171355	−	0.985209i	$-0.554814\pi$
$577$	−114098.			−0.342710			−0.171355	+	0.985209i	$0.554814\pi$
$578$	291187.	−	77604.5i	0.871598	−	0.232290i
$579$		0			0
$580$	−107216.	+	61517.7i	−0.318714	+	0.182871i
$581$	−238077.	−	412361.i	−0.705285	−	1.22159i
$582$		0			0
$583$	112347.	+	64863.5i	0.330540	+	0.190837i
$584$	−249738.	+	247734.i	−0.732249	+	0.726374i
$585$		0			0
$586$	−103499.	−	103777.i	−0.301397	−	0.302208i
$587$	−45237.1	−	26117.7i	−0.131286	−	0.0757980i	0.432919	−	0.901433i	$-0.357484\pi$
$587$	−45237.1	−	26117.7i	−0.131286	−	0.0757980i	−0.564205	+	0.825635i	$0.690817\pi$
$588$		0			0
$589$	128519.	+	222602.i	0.370456	+	0.641649i
$590$	52693.3	+	14195.0i	0.151374	+	0.0407784i
$591$		0			0
$592$	−206691.	+	353600.i	−0.589763	+	1.00895i
$593$	−277354.			−0.788724			−0.394362	−	0.918955i	$-0.629034\pi$
$593$	−277354.			−0.788724			−0.394362	+	0.918955i	$0.629034\pi$
$594$		0			0
$595$			274287.i			0.774767i
$596$	−342711.	−	199093.i	−0.964797	−	0.560485i
$597$		0			0
$598$	−221521.	−	59675.3i	−0.619460	−	0.166875i
$599$	16547.3	−	9553.58i	0.0461183	−	0.0266264i	−0.476764	−	0.879032i	$-0.658190\pi$
$599$	16547.3	−	9553.58i	0.0461183	−	0.0266264i	0.522882	+	0.852405i	$0.324857\pi$
$600$		0			0
$601$	209446.	−	362771.i	0.579861	−	1.00435i	−0.415634	−	0.909532i	$-0.636440\pi$
$601$	209446.	−	362771.i	0.579861	−	1.00435i	0.995495	−	0.0948161i	$-0.0302263\pi$
$602$	−368112.	−	369102.i	−1.01575	−	1.01848i
$603$		0			0
$604$	163352.	+	438.593i	0.447765	+	0.00120223i
$605$	26848.8	−	46503.4i	0.0733522	−	0.127050i
$606$		0			0
$607$	−331153.	+	191191.i	−0.898776	+	0.518909i	−0.876803	−	0.480850i	$-0.840328\pi$
$607$	−331153.	+	191191.i	−0.898776	+	0.518909i	−0.0219735	+	0.999759i	$0.506995\pi$
$608$	−399472.	−	109917.i	−1.08064	−	0.297344i
$609$		0			0
$610$	−269816.	+	71909.0i	−0.725118	+	0.193252i
$611$		−	495450.i		−	1.32714i
$612$		0			0
$613$	−210852.			−0.561121			−0.280560	−	0.959836i	$-0.590520\pi$
$613$	−210852.			−0.561121			−0.280560	+	0.959836i	$0.590520\pi$
$614$	12019.2	+	45098.3i	0.0318815	+	0.119625i
$615$		0			0
$616$	−362029.	−	98569.7i	−0.954073	−	0.259766i
$617$	313290.	+	542634.i	0.822955	+	1.42540i	0.903472	+	0.428647i	$0.141010\pi$
$617$	313290.	+	542634.i	0.822955	+	1.42540i	−0.0805170	+	0.996753i	$0.525657\pi$
$618$		0			0
$619$	−35684.5	−	20602.5i	−0.0931319	−	0.0537697i	0.452711	−	0.891657i	$-0.350457\pi$
$619$	−35684.5	−	20602.5i	−0.0931319	−	0.0537697i	−0.545843	+	0.837888i	$0.683790\pi$
$620$	−119825.	−	321.726i	−0.311721	−	0.000836956i
$621$		0			0
$622$	12280.6	−	12247.7i	0.0317423	−	0.0316572i
$623$	−46049.0	−	26586.4i	−0.118644	−	0.0684989i
$624$		0			0
$625$	−74680.7	−	129351.i	−0.191183	−	0.331138i
$626$	−89998.5	+	334084.i	−0.229661	+	0.852525i
$627$		0			0
$628$	400838.	+	232861.i	1.01637	+	0.590443i
$629$	−637678.			−1.61176
$630$		0			0
$631$			150814.i			0.378777i	0.981902	+	0.189389i	$0.0606506\pi$
$631$			150814.i			0.378777i	−0.981902	+	0.189389i	$0.939349\pi$
$632$	−199296.	+	52541.7i	−0.498958	+	0.131544i
$633$		0			0
$634$	−25628.9	+	95137.3i	−0.0637605	+	0.236686i
$635$	−164246.	+	94827.4i	−0.407331	+	0.235172i
$636$		0			0
$637$	−85890.8	+	148767.i	−0.211674	+	0.366630i
$638$	186404.	−	185904.i	0.457946	−	0.456718i
$639$		0			0
$640$	137853.	−	135286.i	0.336555	−	0.330288i
$641$	214189.	−	370987.i	0.521293	−	0.902906i	−0.478400	−	0.878142i	$-0.658783\pi$
$641$	214189.	−	370987.i	0.521293	−	0.902906i	0.999693	−	0.0247640i	$-0.00788343\pi$
$642$		0			0
$643$	−74279.9	+	42885.5i	−0.179659	+	0.103726i	−0.587133	−	0.809491i	$-0.699743\pi$
$643$	−74279.9	+	42885.5i	−0.179659	+	0.103726i	0.407473	+	0.913217i	$0.366410\pi$
$644$	−272303.	+	156241.i	−0.656569	+	0.376723i
$645$		0			0
$646$	−166117.	−	623304.i	−0.398061	−	1.49360i
$647$			128368.i			0.306653i	0.988176	+	0.153327i	$0.0489986\pi$
$647$			128368.i			0.306653i	−0.988176	+	0.153327i	$0.951001\pi$
$648$		0			0
$649$	−116225.			−0.275937
$650$	320544.	−	85428.6i	0.758685	−	0.202198i
$651$		0			0
$652$	141231.	+	246143.i	0.332226	+	0.579018i
$653$	−232940.	−	403463.i	−0.546282	−	0.946189i	−0.998525	−	0.0542939i	$-0.982709\pi$
$653$	−232940.	−	403463.i	−0.546282	−	0.946189i	0.452243	−	0.891895i	$-0.350624\pi$
$654$		0			0
$655$	213442.	+	123231.i	0.497504	+	0.287234i
$656$	630587.	+	3386.22i	1.46534	+	0.00786878i
$657$		0			0
$658$	−478766.	−	480053.i	−1.10579	−	1.10876i
$659$	303989.	+	175508.i	0.699983	+	0.404135i	0.807341	−	0.590085i	$-0.200906\pi$
$659$	303989.	+	175508.i	0.699983	+	0.404135i	−0.107358	+	0.994220i	$0.534239\pi$
$660$		0			0
$661$	141131.	+	244446.i	0.323013	+	0.559475i	0.981108	−	0.193460i	$-0.0619709\pi$
$661$	141131.	+	244446.i	0.323013	+	0.559475i	−0.658095	+	0.752935i	$0.728638\pi$
$662$	723274.	+	194842.i	1.65039	+	0.444597i
$663$		0			0
$664$	−504782.	+	133079.i	−1.14490	+	0.301838i
$665$	278442.			0.629638
$666$		0			0
$667$		−	220276.i		−	0.495125i
$668$	−330035.	+	568110.i	−0.739618	+	1.27315i
$669$		0			0
$670$	162242.	+	43706.0i	0.361420	+	0.0973625i
$671$	515029.	−	297352.i	1.14390	−	0.660428i
$672$		0			0
$673$	398590.	−	690378.i	0.880028	−	1.52425i	0.0287190	−	0.999588i	$-0.490857\pi$
$673$	398590.	−	690378.i	0.880028	−	1.52425i	0.851309	−	0.524665i	$-0.175809\pi$
$674$	285172.	+	285939.i	0.627751	+	0.629438i
$675$		0			0
$676$	−23.8647	+	8888.32i	−5.22231e−5	+	0.0194503i
$677$	140673.	−	243653.i	0.306926	−	0.531612i	−0.670762	−	0.741673i	$-0.734033\pi$
$677$	140673.	−	243653.i	0.306926	−	0.531612i	0.977688	+	0.210061i	$0.0673662\pi$
$678$		0			0
$679$	890213.	−	513965.i	1.93088	−	1.11479i
$680$	290151.	+	78999.7i	0.627490	+	0.170847i
$681$		0			0
$682$	246594.	−	65720.0i	0.530168	−	0.141296i
$683$			687094.i			1.47291i	0.676489	+	0.736453i	$0.263501\pi$
$683$			687094.i			1.47291i	−0.676489	+	0.736453i	$0.736499\pi$
$684$		0			0
$685$	55124.8			0.117480
$686$	−83841.2	−	314588.i	−0.178160	−	0.668489i
$687$		0			0
$688$	−496473.	+	283095.i	−1.04886	+	0.598075i
$689$	−110207.	−	190884.i	−0.232152	−	0.402098i
$690$		0			0
$691$	284957.	+	164520.i	0.596792	+	0.344558i	0.767779	−	0.640715i	$-0.221362\pi$
$691$	284957.	+	164520.i	0.596792	+	0.344558i	−0.170986	+	0.985273i	$0.554695\pi$
$692$	298.812	−	111291.i	0.000624002	−	0.232407i
$693$		0			0
$694$	495364.	−	494036.i	1.02850	−	1.02574i
$695$	94998.8	+	54847.6i	0.196675	+	0.113550i
$696$		0			0
$697$	490893.	+	850252.i	1.01047	+	1.75018i
$698$	−45673.1	+	169544.i	−0.0937453	+	0.347993i
$699$		0			0
$700$	228031.	−	392524.i	0.465369	−	0.801069i
$701$	961471.			1.95659			0.978296	−	0.207214i	$-0.0664395\pi$
$701$	961471.			1.95659			0.978296	+	0.207214i	$0.0664395\pi$
$702$		0			0
$703$			647338.i			1.30985i
$704$	−208542.	+	354578.i	−0.420773	+	0.715429i
$705$		0			0
$706$	161874.	−	600895.i	0.324764	−	1.20556i
$707$	336736.	−	194415.i	0.673676	−	0.388947i
$708$		0			0
$709$	299138.	−	518122.i	0.595085	−	1.03072i	−0.398450	−	0.917190i	$-0.630452\pi$
$709$	299138.	−	518122.i	0.595085	−	1.03072i	0.993535	−	0.113528i	$-0.0362151\pi$
$710$	−188301.	+	187796.i	−0.373540	+	0.372538i
$711$		0			0
$712$	−41387.1	+	41055.1i	−0.0816404	+	0.0809854i
$713$	106766.	−	184923.i	0.210016	−	0.363758i
$714$		0			0
$715$	174956.	−	101011.i	0.342229	−	0.197586i
$716$	13970.7	+	24348.7i	0.0272516	+	0.0474951i
$717$		0			0
$718$	189541.	+	711193.i	0.367666	+	1.37955i
$719$		−	608601.i		−	1.17727i	−0.808400	−	0.588633i	$-0.799666\pi$
$719$		−	608601.i		−	1.17727i	0.808400	−	0.588633i	$-0.200334\pi$
$720$		0			0
$721$	394240.			0.758385
$722$	−129043.	+	34391.3i	−0.247548	+	0.0659742i
$723$		0			0
$724$	−607681.	+	348673.i	−1.15931	+	0.665183i
$725$	159256.	+	275840.i	0.302985	+	0.524785i
$726$		0			0
$727$	−396978.	−	229195.i	−0.751100	−	0.433648i	0.0749911	−	0.997184i	$-0.476107\pi$
$727$	−396978.	−	229195.i	−0.751100	−	0.433648i	−0.826091	+	0.563536i	$0.809440\pi$
$728$	448963.	+	452594.i	0.847125	+	0.853976i
$729$		0			0
$730$	−183023.	−	183515.i	−0.343448	−	0.344371i
$731$	−770590.	−	444900.i	−1.44208	−	0.832584i
$732$		0			0
$733$	−35347.8	−	61224.2i	−0.0657892	−	0.113950i	0.831255	−	0.555892i	$-0.187623\pi$
$733$	−35347.8	−	61224.2i	−0.0657892	−	0.113950i	−0.897044	+	0.441942i	$0.854290\pi$
$734$	640760.	+	172614.i	1.18933	+	0.320393i
$735$		0			0
$736$	86849.4	+	333053.i	0.160329	+	0.614833i
$737$	−357855.			−0.658828
$738$		0			0
$739$			476430.i			0.872390i	0.899852	+	0.436195i	$0.143674\pi$
$739$			476430.i			0.872390i	−0.899852	+	0.436195i	$0.856326\pi$
$740$	−260939.	−	151589.i	−0.476514	−	0.276824i
$741$		0			0
$742$	−291239.	−	78456.4i	−0.528982	−	0.142502i
$743$	−109137.	+	63010.2i	−0.197694	+	0.114139i	−0.595579	−	0.803296i	$-0.703078\pi$
$743$	−109137.	+	63010.2i	−0.197694	+	0.114139i	0.397885	+	0.917435i	$0.369744\pi$
$744$		0			0
$745$	146013.	−	252902.i	0.263074	−	0.455658i
$746$	−368106.	−	369095.i	−0.661447	−	0.663225i
$747$		0			0
$748$	−640448.	−	1719.57i	−1.14467	−	0.00307339i
$749$	−897.727	+	1554.91i	−0.00160022	+	0.00277167i
$750$		0			0
$751$	−176908.	+	102138.i	−0.313667	+	0.181096i	−0.648566	−	0.761158i	$-0.724631\pi$
$751$	−176908.	+	102138.i	−0.313667	+	0.181096i	0.334899	+	0.942254i	$0.391298\pi$
$752$	−645712.	+	368193.i	−1.14184	+	0.651089i
$753$		0			0
$754$	−432212.	+	115189.i	−0.760247	+	0.202614i
$755$			120358.i			0.211145i
$756$		0			0
$757$	588244.			1.02652			0.513258	−	0.858235i	$-0.328438\pi$
$757$	588244.			1.02652			0.513258	+	0.858235i	$0.328438\pi$
$758$	44958.8	+	168694.i	0.0782485	+	0.293603i
$759$		0			0
$760$	80196.3	−	294546.i	0.138844	−	0.509949i
$761$	−25368.8	−	43940.0i	−0.0438056	−	0.0758736i	0.843291	−	0.537457i	$-0.180615\pi$
$761$	−25368.8	−	43940.0i	−0.0438056	−	0.0758736i	−0.887097	+	0.461583i	$0.847282\pi$
$762$		0			0
$763$	540501.	+	312058.i	0.928426	+	0.536027i
$764$	635603.	+	1706.56i	1.08893	+	0.00292372i
$765$		0			0
$766$	775685.	−	773605.i	1.32199	−	1.31844i
$767$	171017.	+	98737.0i	0.290703	+	0.167838i
$768$		0			0
$769$	−441340.	−	764423.i	−0.746312	−	1.29265i	−0.949579	−	0.313526i	$-0.898490\pi$
$769$	−441340.	−	764423.i	−0.746312	−	1.29265i	0.203268	−	0.979123i	$-0.434844\pi$
$770$	71909.4	−	266936.i	0.121284	−	0.450221i
$771$		0			0
$772$	291839.	+	169540.i	0.489675	+	0.284470i
$773$	100820.			0.168728			0.0843642	−	0.996435i	$-0.473114\pi$
$773$	100820.			0.168728			0.0843642	+	0.996435i	$0.473114\pi$
$774$		0			0
$775$			308760.i			0.514065i
$776$	−287294.	−	1.08973e6i	−0.477094	−	1.80966i
$777$		0			0
$778$	−255109.	+	946992.i	−0.421470	+	1.56454i
$779$	863131.	−	498329.i	1.42233	−	0.821185i
$780$		0			0
$781$	283197.	−	490511.i	0.464286	−	0.804168i
$782$	−379430.	+	378412.i	−0.620466	+	0.618802i
$783$		0			0
$784$	257716.	+	1383.92i	0.419284	+	0.00225153i
$785$	−170778.	+	295796.i	−0.277136	+	0.480013i
$786$		0			0
$787$	98569.7	−	56909.2i	0.159145	−	0.0918826i	−0.418312	−	0.908303i	$-0.637378\pi$
$787$	98569.7	−	56909.2i	0.159145	−	0.0918826i	0.577458	+	0.816421i	$0.304045\pi$
$788$	−392133.	+	224996.i	−0.631511	+	0.362346i
$789$		0			0
$790$	−39106.7	−	146736.i	−0.0626610	−	0.235116i
$791$			584701.i			0.934504i
$792$		0			0
$793$	−1.01044e6			−1.60681
$794$	−16435.9	+	4380.34i	−0.0260707	+	0.00694811i
$795$		0			0
$796$	−191612.	−	333950.i	−0.302411	−	0.527054i
$797$	−350591.	−	607241.i	−0.551930	−	0.955971i	−0.998135	−	0.0610403i	$-0.980558\pi$
$797$	−350591.	−	607241.i	−0.551930	−	0.955971i	0.446205	−	0.894931i	$-0.352775\pi$
$798$		0			0
$799$	−1.00223e6	−	578637.i	−1.56990	−	0.906384i
$800$	−349550.	−	354274.i	−0.546171	−	0.553553i
$801$		0			0
$802$	20708.0	+	20763.6i	0.0321950	+	0.0322816i
$803$	478044.	+	275999.i	0.741373	+	0.428032i
$804$		0			0
$805$	−115656.	−	200322.i	−0.178475	−	0.309127i
$806$	−418678.	−	112787.i	−0.644480	−	0.173616i
$807$		0			0
$808$	−108673.	−	412208.i	−0.166456	−	0.631384i
$809$	−514560.			−0.786211			−0.393105	−	0.919493i	$-0.628599\pi$
$809$	−514560.			−0.786211			−0.393105	+	0.919493i	$0.628599\pi$
$810$		0			0
$811$		−	36669.2i		−	0.0557519i	−0.999611	−	0.0278759i	$-0.991126\pi$
$811$		−	36669.2i		−	0.0557519i	0.999611	−	0.0278759i	$-0.00887434\pi$
$812$	−307470.	+	529267.i	−0.466327	+	0.802718i
$813$		0			0
$814$	620588.	+	167179.i	0.936601	+	0.252310i
$815$	−181077.	+	104545.i	−0.272614	+	0.157394i
$816$		0			0
$817$	−451640.	+	782263.i	−0.676625	+	1.17195i
$818$	80258.9	+	80474.7i	0.119946	+	0.120269i
$819$		0			0
$820$	−1247.48	+	464620.i	−0.00185527	+	0.690987i
$821$	−239492.	+	414812.i	−0.355307	+	0.615410i	−0.987170	−	0.159670i	$-0.948957\pi$
$821$	−239492.	+	414812.i	−0.355307	+	0.615410i	0.631863	+	0.775080i	$0.282290\pi$
$822$		0			0
$823$	−679126.	+	392093.i	−1.00265	+	0.578882i	−0.909032	−	0.416726i	$-0.863177\pi$
$823$	−679126.	+	392093.i	−1.00265	+	0.578882i	−0.0936206	+	0.995608i	$0.529844\pi$
$824$	113548.	−	417042.i	0.167235	−	0.614222i
$825$		0			0
$826$	261115.	−	69589.9i	0.382711	−	0.101997i
$827$			1.21724e6i			1.77978i	0.456175	+	0.889890i	$0.349219\pi$
$827$			1.21724e6i			1.77978i	−0.456175	+	0.889890i	$0.650781\pi$
$828$		0			0
$829$	−335235.			−0.487799			−0.243900	−	0.969801i	$-0.578427\pi$
$829$	−335235.			−0.487799			−0.243900	+	0.969801i	$0.578427\pi$
$830$	−99050.7	−	371657.i	−0.143781	−	0.539494i
$831$		0			0
$832$	608081.	−	344575.i	0.878445	−	0.497780i
$833$	200624.	+	347491.i	0.289130	+	0.500787i
$834$		0			0
$835$	−419233.	−	242044.i	−0.601288	−	0.347154i
$836$	−1745.62	+	650149.i	−0.00249768	+	0.930252i
$837$		0			0
$838$	−448879.	+	447675.i	−0.639206	+	0.637492i
$839$	−808477.	−	466775.i	−1.14853	−	0.663107i	−0.200005	−	0.979795i	$-0.564096\pi$
$839$	−808477.	−	466775.i	−1.14853	−	0.663107i	−0.948530	+	0.316688i	$0.897429\pi$
$840$		0			0
$841$	138904.	+	240589.i	0.196391	+	0.340160i
$842$	297147.	−	1.10304e6i	0.419129	−	1.55585i
$843$		0			0
$844$	−466798.	+	803527.i	−0.655305	+	1.12802i
$845$	−6548.91			−0.00917182
$846$		0			0
$847$		−	265900.i		−	0.370639i
$848$	−166876.	+	285487.i	−0.232061	+	0.397004i
$849$		0			0
$850$	201554.	−	748189.i	0.278967	−	1.03556i
$851$	465721.	−	268884.i	0.643082	−	0.371284i
$852$		0			0
$853$	−124910.	+	216350.i	−0.171672	+	0.297344i	−0.939004	−	0.343905i	$-0.888250\pi$
$853$	−124910.	+	216350.i	−0.171672	+	0.297344i	0.767333	+	0.641249i	$0.221583\pi$
$854$	−979039.	+	976413.i	−1.34241	+	1.33881i
$855$		0			0
$856$	1386.28	+	1397.49i	0.00189193	+	0.00190723i
$857$	330493.	−	572431.i	0.449988	−	0.779402i	−0.548397	−	0.836218i	$-0.684762\pi$
$857$	330493.	−	572431.i	0.449988	−	0.779402i	0.998385	+	0.0568162i	$0.0180949\pi$
$858$		0			0
$859$	716685.	−	413779.i	0.971275	−	0.560766i	0.0716503	−	0.997430i	$-0.477173\pi$
$859$	716685.	−	413779.i	0.971275	−	0.560766i	0.899625	+	0.436664i	$0.143840\pi$
$860$	−209565.	−	365239.i	−0.283349	−	0.493833i
$861$		0			0
$862$	118588.	+	444963.i	0.159597	+	0.598838i
$863$		−	1.22724e6i		−	1.64781i	−0.566728	−	0.823905i	$-0.691791\pi$
$863$		−	1.22724e6i		−	1.64781i	0.566728	−	0.823905i	$-0.308209\pi$
$864$		0			0
$865$	81999.4			0.109592
$866$	369505.	−	98477.0i	0.492702	−	0.131310i
$867$		0			0
$868$	−514655.	+	295297.i	−0.683088	+	0.391940i
$869$	161711.	+	280091.i	0.214141	+	0.370903i
$870$		0			0
$871$	526560.	+	304009.i	0.694083	+	0.400729i
$872$	485781.	−	481884.i	0.638863	−	0.633738i
$873$		0			0
$874$	384144.	+	385177.i	0.502888	+	0.504240i
$875$	662147.	+	382291.i	0.864845	+	0.499318i
$876$		0			0
$877$	313105.	+	542314.i	0.407091	+	0.705102i	0.994562	−	0.104143i	$-0.0332099\pi$
$877$	313105.	+	542314.i	0.407091	+	0.705102i	−0.587472	+	0.809245i	$0.699877\pi$
$878$	1.43494e6	+	386556.i	1.86142	+	0.501446i
$879$		0			0
$880$	−261664.	−	152951.i	−0.337892	−	0.197509i
$881$	−447853.			−0.577011			−0.288505	−	0.957478i	$-0.593158\pi$
$881$	−447853.			−0.577011			−0.288505	+	0.957478i	$0.593158\pi$
$882$		0			0
$883$		−	1.38655e6i		−	1.77833i	−0.457582	−	0.889167i	$-0.651285\pi$
$883$		−	1.38655e6i		−	1.77833i	0.457582	−	0.889167i	$-0.348715\pi$
$884$	940915.	+	546611.i	1.20405	+	0.699478i
$885$		0			0
$886$	−534020.	−	143859.i	−0.680284	−	0.183261i
$887$	−1.32667e6	+	765956.i	−1.68623	+	0.973546i	−0.728870	+	0.684652i	$0.759954\pi$
$887$	−1.32667e6	+	765956.i	−1.68623	+	0.973546i	−0.957361	+	0.288895i	$0.906712\pi$
$888$		0			0
$889$	−469567.	+	813314.i	−0.594147	+	1.02909i
$890$	−30331.0	−	30412.6i	−0.0382919	−	0.0383949i
$891$		0			0
$892$	266588.	+	715.777i	0.335051	+	0.000899598i
$893$	−587401.	+	1.01741e6i	−0.736601	+	1.27583i
$894$		0			0
$895$	−17912.3	+	10341.7i	−0.0223618	+	0.0129106i
$896$	256212.	−	921470.i	0.319142	−	1.14780i
$897$		0			0
$898$	−496382.	+	132291.i	−0.615550	+	0.164051i
$899$		−	416323.i		−	0.515124i
$900$		0			0
$901$	−514844.			−0.634200
$902$	−254827.	−	956161.i	−0.313208	−	1.17522i
$903$		0			0
$904$	618520.	+	168405.i	0.756862	+	0.206071i
$905$	−258102.	−	447047.i	−0.315134	−	0.545828i
$906$		0			0
$907$	282696.	+	163214.i	0.343641	+	0.198401i	0.661881	−	0.749609i	$-0.269758\pi$
$907$	282696.	+	163214.i	0.343641	+	0.198401i	−0.318240	+	0.948010i	$0.603092\pi$
$908$	−900136.	−	2416.82i	−1.09178	−	0.00293139i
$909$		0			0
$910$	−332580.	+	331689.i	−0.401619	+	0.400542i
$911$	−1.11746e6	−	645168.i	−1.34647	−	0.777384i	−0.358722	−	0.933445i	$-0.616787\pi$
$911$	−1.11746e6	−	645168.i	−1.34647	−	0.777384i	−0.987748	+	0.156060i	$0.950121\pi$
$912$		0			0
$913$	409586.	+	709424.i	0.491364	+	0.851068i
$914$	−304944.	+	1.13199e6i	−0.365029	+	1.35503i
$915$		0			0
$916$	−33865.2	−	19673.5i	−0.0403611	−	0.0234472i
$917$	1.22043e6			1.45135
$918$		0			0
$919$			844321.i			0.999715i	0.866108	+	0.499858i	$0.166614\pi$
$919$			844321.i			0.999715i	−0.866108	+	0.499858i	$0.833386\pi$
$920$	−245220.	+	64649.0i	−0.289721	+	0.0763812i
$921$		0			0
$922$	308116.	−	1.14376e6i	0.362454	−	1.34547i
$923$	−833409.	+	481169.i	−0.978262	+	0.564800i
$924$		0			0
$925$	−388799.	+	673419.i	−0.454403	+	0.787050i
$926$	1.00454e6	−	1.00185e6i	1.17151	−	1.16837i
$927$		0			0
$928$	471322.	+	477693.i	0.547296	+	0.554693i
$929$	301633.	−	522445.i	0.349501	−	0.605353i	−0.636660	−	0.771145i	$-0.719685\pi$
$929$	301633.	−	522445.i	0.349501	−	0.605353i	0.986161	+	0.165792i	$0.0530179\pi$
$930$		0			0
$931$	352754.	−	203663.i	0.406980	−	0.234970i
$932$	1.06819e6	−	612904.i	1.22975	−	0.705603i
$933$		0			0
$934$	−120154.	−	450841.i	−0.137735	−	0.516809i
$935$		−	471882.i		−	0.539772i
$936$		0			0
$937$	−109044.			−0.124200			−0.0621002	−	0.998070i	$-0.519780\pi$
$937$	−109044.			−0.124200			−0.0621002	+	0.998070i	$0.519780\pi$
$938$	803967.	−	214266.i	0.913761	−	0.243527i
$939$		0			0
$940$	−272560.	−	475029.i	−0.308466	−	0.537606i
$941$	345476.	+	598382.i	0.390156	+	0.675770i	0.992470	−	0.122489i	$-0.0390877\pi$
$941$	345476.	+	598382.i	0.390156	+	0.675770i	−0.602314	+	0.798259i	$0.705754\pi$
$942$		0			0
$943$	−717036.	−	413981.i	−0.806338	−	0.465540i
$944$	1590.90	−	296261.i	0.00178525	−	0.332453i
$945$		0			0
$946$	633299.	+	635001.i	0.707663	+	0.709565i
$947$	−1.04225e6	−	601745.i	−1.16218	−	0.670984i	−0.210354	−	0.977625i	$-0.567462\pi$
$947$	−1.04225e6	−	601745.i	−1.16218	−	0.670984i	−0.951825	+	0.306641i	$0.900795\pi$
$948$		0			0
$949$	−468940.	−	812228.i	−0.520697	−	0.901873i
$950$	−759522.	−	204607.i	−0.841576	−	0.226711i
$951$		0			0
$952$	1.43988e6	−	379606.i	1.58874	−	0.418850i
$953$	−1.58732e6			−1.74775			−0.873873	−	0.486154i	$-0.838400\pi$
$953$	−1.58732e6			−1.74775			−0.873873	+	0.486154i	$0.838400\pi$
$954$		0			0
$955$			468312.i			0.513486i
$956$	209439.	−	360519.i	0.229161	−	0.394469i
$957$		0			0
$958$	−401984.	−	108290.i	−0.438003	−	0.117993i
$959$	236397.	−	136484.i	0.257042	−	0.148403i
$960$		0			0
$961$	−259972.	+	450285.i	−0.281501	+	0.487574i
$962$	−771129.	−	773202.i	−0.833253	−	0.835493i
$963$		0			0
$964$	1202.84	−	447992.i	0.00129435	−	0.482077i
$965$	−124338.	+	215361.i	−0.133521	+	0.231266i
$966$		0			0
$967$	−854421.	+	493300.i	−0.913732	+	0.527544i	−0.881630	−	0.471941i	$-0.843554\pi$
$967$	−854421.	+	493300.i	−0.913732	+	0.527544i	−0.0321023	+	0.999485i	$0.510220\pi$
$968$	−281279.	−	76584.0i	−0.300183	−	0.0817311i
$969$		0			0
$970$	802342.	−	213833.i	0.852738	−	0.227264i
$971$			1.42706e6i			1.51358i	0.653658	+	0.756790i	$0.273233\pi$
$971$			1.42706e6i			1.51358i	−0.653658	+	0.756790i	$0.726767\pi$
$972$		0			0
$973$	543189.			0.573754
$974$	104332.	+	391472.i	0.109976	+	0.412651i
$975$		0			0
$976$	750907.	+	1.31689e6i	0.788291	+	1.38245i
$977$	801658.	+	1.38851e6i	0.839847	+	1.45466i	0.890022	+	0.455917i	$0.150689\pi$
$977$	801658.	+	1.38851e6i	0.839847	+	1.45466i	−0.0501755	+	0.998740i	$0.515978\pi$
$978$		0			0
$979$	79222.5	+	45739.1i	0.0826577	+	0.0477224i
$980$	−509.836	+	189886.i	−0.000530858	+	0.197716i
$981$		0			0
$982$	−496277.	+	494946.i	−0.514637	+	0.513257i
$983$	1.27188e6	+	734318.i	1.31625	+	0.759936i	0.983123	−	0.182946i	$-0.0585634\pi$
$983$	1.27188e6	+	734318.i	1.31625	+	0.759936i	0.333126	+	0.942882i	$0.391897\pi$
$984$		0			0
$985$	−166552.	−	288476.i	−0.171663	−	0.297329i
$986$	−271769.	+	1.00884e6i	−0.279541	+	1.03769i
$987$		0			0
$988$	554891.	−	955168.i	0.568452	−	0.978511i
$989$	750388.			0.767173
$990$		0			0
$991$		−	1.48147e6i		−	1.50850i	−0.656585	−	0.754252i	$-0.728000\pi$
$991$		−	1.48147e6i		−	1.50850i	0.656585	−	0.754252i	$-0.272000\pi$
$992$	164146.	+	629473.i	0.166804	+	0.639667i
$993$		0			0
$994$	−342544.	+	1.27156e6i	−0.346692	+	1.28696i
$995$	245673.	−	141840.i	0.248149	−	0.143269i
$996$		0			0
$997$	23467.9	−	40647.6i	0.0236093	−	0.0408926i	−0.853979	−	0.520307i	$-0.825818\pi$
$997$	23467.9	−	40647.6i	0.0236093	−	0.0408926i	0.877589	+	0.479414i	$0.159151\pi$
$998$	272184.	−	271454.i	0.273276	−	0.272543i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.5.f.a.19.20		44
3.2	odd	2		36.5.f.a.7.3	✓	44
4.3	odd	2	inner	108.5.f.a.19.10		44
9.2	odd	6		324.5.d.f.163.18		22
9.4	even	3	inner	108.5.f.a.91.10		44
9.5	odd	6		36.5.f.a.31.13	yes	44
9.7	even	3		324.5.d.e.163.5		22
12.11	even	2		36.5.f.a.7.13	yes	44
36.7	odd	6		324.5.d.e.163.6		22
36.11	even	6		324.5.d.f.163.17		22
36.23	even	6		36.5.f.a.31.3	yes	44
36.31	odd	6	inner	108.5.f.a.91.20		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.5.f.a.7.3	✓	44	3.2	odd	2
36.5.f.a.7.13	yes	44	12.11	even	2
36.5.f.a.31.3	yes	44	36.23	even	6
36.5.f.a.31.13	yes	44	9.5	odd	6
108.5.f.a.19.10		44	4.3	odd	2	inner
108.5.f.a.19.20		44	1.1	even	1	trivial
108.5.f.a.91.10		44	9.4	even	3	inner
108.5.f.a.91.20		44	36.31	odd	6	inner
324.5.d.e.163.5		22	9.7	even	3
324.5.d.e.163.6		22	36.7	odd	6
324.5.d.f.163.17		22	36.11	even	6
324.5.d.f.163.18		22	9.2	odd	6

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:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	108.f (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(3.86509 - 1.03009i) q^{2} +(13.8778 - 7.96277i) q^{4} +(5.89438 + 10.2094i) q^{5} +(50.5548 + 29.1878i) q^{7} +(45.4367 - 45.0722i) q^{8} +O(q^{10})\)	\(q+(3.86509 - 1.03009i) q^{2} +(13.8778 - 7.96277i) q^{4} +(5.89438 + 10.2094i) q^{5} +(50.5548 + 29.1878i) q^{7} +(45.4367 - 45.0722i) q^{8} +(33.2988 + 33.3884i) q^{10} +(-86.9742 - 50.2146i) q^{11} +(85.3178 + 147.775i) q^{13} +(225.465 + 60.7377i) q^{14} +(129.189 - 221.012i) q^{16} +398.571 q^{17} -404.608i q^{19} +(163.096 + 94.7483i) q^{20} +(-387.889 - 104.493i) q^{22} +(-291.091 + 168.062i) q^{23} +(243.013 - 420.910i) q^{25} +(481.982 + 483.278i) q^{26} +(934.007 + 2.50777i) q^{28} +(-327.671 + 567.543i) q^{29} +(-550.166 + 317.638i) q^{31} +(271.664 - 987.307i) q^{32} +(1540.51 - 410.563i) q^{34} +688.176i q^{35} -1599.91 q^{37} +(-416.782 - 1563.85i) q^{38} +(727.980 + 198.207i) q^{40} +(1231.63 + 2133.25i) q^{41} +(-1933.38 - 1116.24i) q^{43} +(-1606.86 - 4.31435i) q^{44} +(-951.976 + 949.423i) q^{46} +(-2514.55 - 1451.78i) q^{47} +(503.358 + 871.842i) q^{49} +(505.691 - 1877.18i) q^{50} +(2360.72 + 1371.43i) q^{52} -1291.73 q^{53} -1183.94i q^{55} +(3612.60 - 952.417i) q^{56} +(-681.858 + 2531.13i) q^{58} +(1002.24 - 578.642i) q^{59} +(-2960.81 + 5128.28i) q^{61} +(-1799.24 + 1794.42i) q^{62} +(32.9923 - 4095.87i) q^{64} +(-1005.79 + 1742.08i) q^{65} +(3085.87 - 1781.63i) q^{67} +(5531.30 - 3173.73i) q^{68} +(708.882 + 2659.86i) q^{70} +5639.73i q^{71} -5496.39 q^{73} +(-6183.80 + 1648.05i) q^{74} +(-3221.80 - 5615.09i) q^{76} +(-2931.31 - 5077.18i) q^{77} +(-2788.94 - 1610.20i) q^{79} +(3017.88 + 16.2058i) q^{80} +(6957.81 + 6976.52i) q^{82} +(-7063.92 - 4078.36i) q^{83} +(2349.33 + 4069.15i) q^{85} +(-8622.53 - 2322.81i) q^{86} +(-6215.11 + 1638.53i) q^{88} -910.873 q^{89} +9960.97i q^{91} +(-2701.48 + 4650.22i) q^{92} +(-11214.4 - 3021.04i) q^{94} +(4130.79 - 2384.91i) q^{95} +(8804.44 - 15249.7i) q^{97} +(2843.60 + 2851.24i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + q^{2} - q^{4} + 2 q^{5} - 122 q^{8}+O(q^{10}) \) 44 * q + q^2 - q^4 + 2 * q^5 - 122 * q^8	\( 44 q + q^{2} - q^{4} + 2 q^{5} - 122 q^{8} + 28 q^{10} - 2 q^{13} - 252 q^{14} - q^{16} + 56 q^{17} + 140 q^{20} - 33 q^{22} - 1752 q^{25} - 1096 q^{26} - 516 q^{28} - 526 q^{29} + 121 q^{32} + 385 q^{34} - 8 q^{37} - 1395 q^{38} - 2276 q^{40} + 2762 q^{41} - 6714 q^{44} + 3576 q^{46} + 3428 q^{49} - 6375 q^{50} + 1438 q^{52} + 10088 q^{53} + 7506 q^{56} - 4064 q^{58} - 2 q^{61} + 18324 q^{62} + 9026 q^{64} + 2014 q^{65} + 11405 q^{68} + 3666 q^{70} - 3416 q^{73} - 14620 q^{74} + 1581 q^{76} + 3942 q^{77} - 45520 q^{80} - 8486 q^{82} - 1252 q^{85} - 22113 q^{86} + 1995 q^{88} - 13048 q^{89} + 30294 q^{92} + 7524 q^{94} + 5638 q^{97} + 92938 q^{98}+O(q^{100}) \) 44 * q + q^2 - q^4 + 2 * q^5 - 122 * q^8 + 28 * q^10 - 2 * q^13 - 252 * q^14 - q^16 + 56 * q^17 + 140 * q^20 - 33 * q^22 - 1752 * q^25 - 1096 * q^26 - 516 * q^28 - 526 * q^29 + 121 * q^32 + 385 * q^34 - 8 * q^37 - 1395 * q^38 - 2276 * q^40 + 2762 * q^41 - 6714 * q^44 + 3576 * q^46 + 3428 * q^49 - 6375 * q^50 + 1438 * q^52 + 10088 * q^53 + 7506 * q^56 - 4064 * q^58 - 2 * q^61 + 18324 * q^62 + 9026 * q^64 + 2014 * q^65 + 11405 * q^68 + 3666 * q^70 - 3416 * q^73 - 14620 * q^74 + 1581 * q^76 + 3942 * q^77 - 45520 * q^80 - 8486 * q^82 - 1252 * q^85 - 22113 * q^86 + 1995 * q^88 - 13048 * q^89 + 30294 * q^92 + 7524 * q^94 + 5638 * q^97 + 92938 * q^98

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