LMFDB - Embedded newform 108.5.f.a.91.20

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			91.20
Character	$\chi$	$=$	108.91
Dual form			108.5.f.a.19.20

$q$-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 $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

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

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	−0.723723	−	0.690091i	$-0.757570\pi$
$5$	5.89438	−	10.2094i	0.235775	−	0.408374i	0.959498	+	0.281717i	$0.0909038\pi$
$6$		0			0
$7$	50.5548	−	29.1878i	1.03173	−	0.595670i	0.114251	−	0.993452i	$-0.463553\pi$
$7$	50.5548	−	29.1878i	1.03173	−	0.595670i	0.917480	+	0.397782i	$0.130220\pi$
$8$	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	−0.814309	−	0.580431i	$-0.802884\pi$
$11$	−86.9742	+	50.2146i	−0.718795	+	0.414997i	0.0955138	+	0.995428i	$0.469551\pi$
$12$		0			0
$13$	85.3178	−	147.775i	0.504839	−	0.874407i	−0.495145	−	0.868810i	$-0.664885\pi$
$13$	85.3178	−	147.775i	0.504839	−	0.874407i	0.999984	−	0.00559684i	$-0.00178154\pi$
$14$	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	$0.189352\pi$
$19$			404.608i			1.12080i	−0.828223	+	0.560399i	$0.810648\pi$
$20$	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	0.198963	−	0.980007i	$-0.436243\pi$
$23$	−291.091	−	168.062i	−0.550267	−	0.317697i	−0.749230	+	0.662310i	$0.769576\pi$
$24$		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	0.602778	−	0.797909i	$-0.294061\pi$
$29$	−327.671	−	567.543i	−0.389621	−	0.674843i	−0.992398	+	0.123066i	$0.960727\pi$
$30$		0			0
$31$	−550.166	−	317.638i	−0.572493	−	0.330529i	0.185651	−	0.982616i	$-0.440560\pi$
$31$	−550.166	−	317.638i	−0.572493	−	0.330529i	−0.758144	+	0.652087i	$0.773894\pi$
$32$	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	−0.223055	−	0.974806i	$-0.571603\pi$
$41$	1231.63	−	2133.25i	0.732679	−	1.26904i	0.955734	−	0.294232i	$-0.0950637\pi$
$42$		0			0
$43$	−1933.38	+	1116.24i	−1.04564	+	0.603699i	−0.921425	−	0.388557i	$-0.872974\pi$
$43$	−1933.38	+	1116.24i	−1.04564	+	0.603699i	−0.124212	+	0.992256i	$0.539640\pi$
$44$	−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	−0.946015	−	0.324124i	$-0.894931\pi$
$47$	−2514.55	+	1451.78i	−1.13832	+	0.657211i	−0.192308	+	0.981335i	$0.561597\pi$
$48$		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	0.637002	−	0.770862i	$-0.280174\pi$
$59$	1002.24	+	578.642i	0.287917	+	0.166229i	−0.349085	+	0.937091i	$0.613508\pi$
$60$		0			0
$61$	−2960.81	−	5128.28i	−0.795703	−	1.37820i	−0.922392	−	0.386256i	$-0.873768\pi$
$61$	−2960.81	−	5128.28i	−0.795703	−	1.37820i	0.126688	−	0.991943i	$-0.459565\pi$
$62$	−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	0.802648	−	0.596452i	$-0.203424\pi$
$67$	3085.87	+	1781.63i	0.687430	+	0.396888i	−0.115219	+	0.993340i	$0.536757\pi$
$68$	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	$-0.811037\pi$
$71$		−	5639.73i		−	1.11877i	0.828907	−	0.559386i	$-0.188963\pi$
$72$		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	−0.706509	−	0.707704i	$-0.749731\pi$
$79$	−2788.94	+	1610.20i	−0.446874	+	0.258003i	0.259635	+	0.965707i	$0.416398\pi$
$80$	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	−0.915661	−	0.401951i	$-0.868332\pi$
$83$	−7063.92	+	4078.36i	−1.02539	+	0.592010i	−0.109730	+	0.993961i	$0.534999\pi$
$84$		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	0.773297	+	0.634044i	$0.218606\pi$
$97$	8804.44	+	15249.7i	0.935747	+	1.62076i	0.162450	+	0.986717i	$0.448060\pi$
$98$	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	0.981810	−	0.189863i	$-0.0608045\pi$
$101$	3330.41	+	5768.44i	0.326479	+	0.565478i	−0.655332	+	0.755341i	$0.727471\pi$
$102$		0			0
$103$	5848.70	+	3376.75i	0.551296	+	0.318291i	0.749645	−	0.661841i	$-0.230224\pi$
$103$	5848.70	+	3376.75i	0.551296	+	0.318291i	−0.198348	+	0.980132i	$0.563558\pi$
$104$	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	$-0.999572\pi$
$107$		−	30.7569i		−	0.00268643i	0.999999	−	0.00134321i	$-0.000427558\pi$
$108$		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	−0.600533	−	0.799600i	$-0.705045\pi$
$113$	5008.09	−	8674.27i	0.392207	−	0.679322i	0.992740	+	0.120277i	$0.0383784\pi$
$114$		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	$-0.833803\pi$
$127$		−	16087.8i		−	0.997444i	0.866762	−	0.498722i	$-0.166197\pi$
$128$	−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	0.924056	−	0.382257i	$-0.124853\pi$
$131$	18105.5	+	10453.2i	1.05504	+	0.609127i	0.130983	+	0.991385i	$0.458187\pi$
$132$		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	0.921564	−	0.388226i	$-0.126912\pi$
$137$	2338.02	+	4049.57i	0.124568	+	0.215759i	−0.796996	+	0.603985i	$0.793579\pi$
$138$		0			0
$139$	8058.42	+	4652.53i	0.417081	+	0.240802i	0.693828	−	0.720141i	$-0.255923\pi$
$139$	8058.42	+	4652.53i	0.417081	+	0.240802i	−0.276747	+	0.960943i	$0.589256\pi$
$140$	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	0.439779	+	0.898106i	$0.355057\pi$
$149$	−12385.8	+	21452.8i	−0.557893	+	0.966299i	−0.997672	+	0.0681928i	$0.978277\pi$
$150$		0			0
$151$	8841.72	−	5104.77i	0.387778	−	0.223884i	−0.293419	−	0.955984i	$-0.594793\pi$
$151$	8841.72	−	5104.77i	0.387778	−	0.223884i	0.681197	+	0.732100i	$0.261460\pi$
$152$	−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	−0.406819	−	0.913509i	$-0.633362\pi$
$157$	14486.5	−	25091.4i	0.587712	−	1.01795i	0.994531	−	0.104439i	$-0.0333046\pi$
$158$	−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	$-0.891676\pi$
$163$		−	17736.4i		−	0.667560i	0.942651	−	0.333780i	$-0.108324\pi$
$164$	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	−0.299182	−	0.954196i	$-0.596714\pi$
$167$	−35562.1	−	20531.8i	−1.27513	−	0.736197i	−0.975949	+	0.217999i	$0.930047\pi$
$168$		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	0.918260	−	0.395977i	$-0.129594\pi$
$173$	3477.87	+	6023.84i	0.116204	+	0.201271i	−0.802056	+	0.597248i	$0.796261\pi$
$174$		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	$-0.991284\pi$
$179$		−	1754.50i		−	0.0547580i	0.999625	−	0.0273790i	$-0.00871609\pi$
$180$		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	0.0521297	−	0.998640i	$-0.483399\pi$
$191$	34403.1	−	19862.7i	0.943042	−	0.544466i	0.890913	+	0.454174i	$0.150066\pi$
$192$		0			0
$193$	10547.2	−	18268.3i	0.283154	−	0.490437i	−0.689006	−	0.724756i	$-0.741953\pi$
$193$	10547.2	−	18268.3i	0.283154	−	0.490437i	0.972160	+	0.234319i	$0.0752859\pi$
$194$	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	$0.0982638\pi$
$199$			24063.5i			0.607650i	−0.952728	+	0.303825i	$0.901736\pi$
$200$	−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	−0.185895	−	0.982570i	$-0.559518\pi$
$211$	−50298.6	−	29039.9i	−1.12977	−	0.652274i	−0.943878	+	0.330295i	$0.892852\pi$
$212$	−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	−0.347852	−	0.937550i	$-0.613089\pi$
$223$	14429.6	−	8330.91i	0.290164	−	0.167526i	0.638016	+	0.770023i	$0.279755\pi$
$224$	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	−0.891685	−	0.452657i	$-0.850476\pi$
$227$	−48721.5	+	28129.4i	−0.945515	+	0.545894i	−0.0538304	+	0.998550i	$0.517143\pi$
$228$		0			0
$229$	−1223.91	+	2119.87i	−0.0233388	+	0.0404239i	−0.877459	−	0.479652i	$-0.840763\pi$
$229$	−1223.91	+	2119.87i	−0.0233388	+	0.0404239i	0.854120	+	0.520076i	$0.174096\pi$
$230$	−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	0.684360	−	0.729144i	$-0.260082\pi$
$239$	22567.5	+	13029.4i	0.395083	+	0.228101i	−0.289277	+	0.957245i	$0.593415\pi$
$240$		0			0
$241$	13999.8	+	24248.4i	0.241039	+	0.417492i	0.961011	−	0.276512i	$-0.0891784\pi$
$241$	13999.8	+	24248.4i	0.241039	+	0.417492i	−0.719971	+	0.694004i	$0.755845\pi$
$242$	−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	$0.0501827\pi$
$251$			19782.5i			0.314003i	−0.987598	+	0.157001i	$0.949817\pi$
$252$		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	−0.409905	−	0.912128i	$-0.634438\pi$
$257$	38636.9	−	66921.1i	0.584974	−	1.01320i	0.994879	−	0.101076i	$-0.0322285\pi$
$258$		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	−0.361293	−	0.932452i	$-0.617665\pi$
$263$	18370.5	−	10606.2i	0.265588	−	0.153337i	0.626881	+	0.779115i	$0.284331\pi$
$264$		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	$-0.927784\pi$
$271$		−	33038.3i		−	0.449861i	0.974375	−	0.224931i	$-0.0722155\pi$
$272$	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	0.756616	−	0.653859i	$-0.226851\pi$
$277$	−14421.3	−	24978.4i	−0.187951	−	0.325540i	−0.944567	+	0.328319i	$0.893518\pi$
$278$	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	0.949631	−	0.313371i	$-0.101458\pi$
$281$	16062.9	+	27821.8i	0.203428	+	0.352348i	−0.746203	+	0.665719i	$0.768125\pi$
$282$		0			0
$283$	−61782.5	−	35670.2i	−0.771424	−	0.445382i	0.0619586	−	0.998079i	$-0.480265\pi$
$283$	−61782.5	−	35670.2i	−0.771424	−	0.445382i	−0.833382	+	0.552697i	$0.813599\pi$
$284$	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	−0.952779	−	0.303666i	$-0.901789\pi$
$293$	−18320.8	+	31732.5i	−0.213407	+	0.369631i	0.739372	+	0.673297i	$0.235123\pi$
$294$		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	$-0.980284\pi$
$307$		−	11668.1i		−	0.123801i	0.998082	−	0.0619005i	$-0.0197161\pi$
$308$	−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	0.519286	−	0.854600i	$-0.326198\pi$
$311$	3755.11	+	2168.01i	0.0388242	+	0.0224151i	−0.480462	+	0.877015i	$0.659531\pi$
$312$		0			0
$313$	−43249.3	−	74909.9i	−0.441459	−	0.764629i	0.556339	−	0.830955i	$-0.312206\pi$
$313$	−43249.3	−	74909.9i	−0.441459	−	0.764629i	−0.997798	+	0.0663262i	$0.978872\pi$
$314$	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	0.798215	−	0.602372i	$-0.205778\pi$
$317$	−12316.1	−	21332.1i	−0.122562	−	0.212283i	−0.920777	+	0.390089i	$0.872444\pi$
$318$		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	0.480485	−	0.877003i	$-0.340461\pi$
$331$	162176.	−	93632.3i	1.48023	−	0.854614i	0.999749	+	0.0223896i	$0.00712742\pi$
$332$	−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	−0.553532	−	0.832828i	$-0.686720\pi$
$337$	50479.6	−	87433.2i	0.444484	−	0.769868i	0.998016	+	0.0629592i	$0.0200538\pi$
$338$	−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	0.972679	−	0.232155i	$-0.0745777\pi$
$347$	151470.	+	87451.5i	1.25797	+	0.726287i	0.285287	+	0.958442i	$0.407911\pi$
$348$		0			0
$349$	−21948.5	−	38015.9i	−0.180199	−	0.312114i	0.761749	−	0.647872i	$-0.224341\pi$
$349$	−21948.5	−	38015.9i	−0.180199	−	0.312114i	−0.941948	+	0.335758i	$0.891008\pi$
$350$	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	0.988682	+	0.150029i	$0.0479367\pi$
$353$	77789.6	+	134736.i	0.624270	+	1.08127i	−0.364412	+	0.931238i	$0.618730\pi$
$354$		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	$-0.746948\pi$
$359$		−	184004.i		−	1.42771i	0.700295	−	0.713853i	$-0.253052\pi$
$360$		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	0.139430	−	0.990232i	$-0.455473\pi$
$367$	143674.	−	82950.4i	1.06671	−	0.615866i	0.927281	+	0.374366i	$0.122140\pi$
$368$	−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	−0.999345	−	0.0361768i	$-0.988482\pi$
$373$	−65160.0	+	112861.i	−0.468343	+	0.811193i	0.531003	+	0.847370i	$0.321815\pi$
$374$	−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	$-0.951453\pi$
$379$		−	43645.6i		−	0.303852i	0.988392	−	0.151926i	$-0.0485475\pi$
$380$	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	0.987708	+	0.156310i	$0.0499599\pi$
$383$	237186.	+	136939.i	1.61693	+	0.933535i	0.629223	+	0.777225i	$0.283373\pi$
$384$		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	−0.912753	−	0.408513i	$-0.866048\pi$
$389$	−122594.	−	212339.i	−0.810159	−	1.40324i	0.102594	−	0.994723i	$-0.467286\pi$
$390$		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	−0.854402	−	0.519612i	$-0.826077\pi$
$401$	3665.61	−	6349.02i	0.0227959	−	0.0394837i	0.877198	+	0.480128i	$0.159410\pi$
$402$		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	−0.820432	−	0.571744i	$-0.806267\pi$
$409$	14207.0	−	24607.2i	0.0849289	−	0.147101i	0.905361	+	0.424643i	$0.139600\pi$
$410$	−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	0.0552577	−	0.998472i	$-0.482402\pi$
$419$	−137256.	−	79245.0i	−0.781816	−	0.451382i	−0.837073	+	0.547091i	$0.815735\pi$
$420$		0			0
$421$	142796.	+	247330.i	0.805659	+	1.39544i	0.915845	+	0.401532i	$0.131522\pi$
$421$	142796.	+	247330.i	0.805659	+	1.39544i	−0.110186	+	0.993911i	$0.535145\pi$
$422$	−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	$-0.899714\pi$
$431$		−	115124.i		−	0.619741i	0.950779	−	0.309870i	$-0.100286\pi$
$432$		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	0.701603	−	0.712568i	$-0.252468\pi$
$439$	321749.	−	185762.i	1.66951	−	0.963890i	0.967903	−	0.251322i	$-0.0808654\pi$
$440$	−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	−0.773023	−	0.634379i	$-0.781256\pi$
$443$	−119741.	+	69132.2i	−0.610146	+	0.352268i	0.162877	+	0.986646i	$0.447923\pi$
$444$		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	−0.967881	−	0.251410i	$-0.919106\pi$
$457$	−146543.	−	253819.i	−0.701668	−	1.21532i	0.266213	−	0.963914i	$-0.414227\pi$
$458$	−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	0.969598	+	0.244702i	$0.0786900\pi$
$461$	148067.	+	256460.i	0.696717	+	1.20675i	−0.272881	+	0.962048i	$0.587977\pi$
$462$		0			0
$463$	307165.	+	177342.i	1.43288	+	0.827273i	0.997339	−	0.0728974i	$-0.0232246\pi$
$463$	307165.	+	177342.i	1.43288	+	0.827273i	0.435539	+	0.900170i	$0.356558\pi$
$464$	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	$0.0861724\pi$
$467$			116644.i			0.534848i	−0.963579	+	0.267424i	$0.913828\pi$
$468$		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	−0.683392	−	0.730052i	$-0.739496\pi$
$479$	−90134.6	+	52039.3i	−0.392845	+	0.226809i	0.290547	+	0.956861i	$0.406163\pi$
$480$		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	$-0.931505\pi$
$487$		−	101284.i		−	0.427055i	0.976937	−	0.213527i	$-0.0684953\pi$
$488$	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	0.151086	−	0.988521i	$-0.451723\pi$
$491$	−151749.	−	87612.6i	−0.629454	−	0.363416i	−0.780541	+	0.625105i	$0.785056\pi$
$492$		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	0.657724	−	0.753259i	$-0.271519\pi$
$499$	83227.2	+	48051.2i	0.334244	+	0.192976i	−0.323480	+	0.946235i	$0.604853\pi$
$500$	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	$0.105546\pi$
$503$			164729.i			0.651080i	−0.945528	+	0.325540i	$0.894454\pi$
$504$		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	−0.936959	−	0.349440i	$-0.886372\pi$
$509$	−42970.1	+	74426.4i	−0.165856	+	0.287271i	0.771103	+	0.636710i	$0.219705\pi$
$510$		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	$-0.847495\pi$
$523$		−	252188.i		−	0.921978i	0.887406	−	0.460989i	$-0.152505\pi$
$524$	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	−0.939485	−	0.342590i	$-0.888696\pi$
$547$	−332881.	+	192189.i	−1.11254	+	0.642323i	−0.173051	+	0.984913i	$0.555362\pi$
$548$	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	0.276090	−	0.961132i	$-0.410961\pi$
$563$	−132566.	−	76536.8i	−0.418229	−	0.241465i	−0.694319	+	0.719667i	$0.744294\pi$
$564$		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	0.823154	−	0.567819i	$-0.192213\pi$
$569$	−25955.5	−	44956.2i	−0.0801687	−	0.138856i	−0.903322	+	0.428963i	$0.858879\pi$
$570$		0			0
$571$	92961.9	+	53671.6i	0.285123	+	0.164616i	0.635741	−	0.771903i	$-0.280695\pi$
$571$	92961.9	+	53671.6i	0.285123	+	0.164616i	−0.350617	+	0.936519i	$0.614028\pi$
$572$	−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	−0.564205	−	0.825635i	$-0.690817\pi$
$587$	−45237.1	+	26117.7i	−0.131286	+	0.0757980i	0.432919	+	0.901433i	$0.357484\pi$
$588$		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	0.522882	−	0.852405i	$-0.324857\pi$
$599$	16547.3	+	9553.58i	0.0461183	+	0.0266264i	−0.476764	+	0.879032i	$0.658190\pi$
$600$		0			0
$601$	209446.	+	362771.i	0.579861	+	1.00435i	0.995495	+	0.0948161i	$0.0302263\pi$
$601$	209446.	+	362771.i	0.579861	+	1.00435i	−0.415634	+	0.909532i	$0.636440\pi$
$602$	−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	−0.0219735	−	0.999759i	$-0.506995\pi$
$607$	−331153.	−	191191.i	−0.898776	−	0.518909i	−0.876803	+	0.480850i	$0.840328\pi$
$608$	−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	−0.0805170	−	0.996753i	$-0.525657\pi$
$617$	313290.	−	542634.i	0.822955	−	1.42540i	0.903472	−	0.428647i	$-0.141010\pi$
$618$		0			0
$619$	−35684.5	+	20602.5i	−0.0931319	+	0.0537697i	−0.545843	−	0.837888i	$-0.683790\pi$
$619$	−35684.5	+	20602.5i	−0.0931319	+	0.0537697i	0.452711	+	0.891657i	$0.350457\pi$
$620$	−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	$-0.939349\pi$
$631$		−	150814.i		−	0.378777i	0.981902	−	0.189389i	$-0.0606506\pi$
$632$	−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	0.999693	+	0.0247640i	$0.00788343\pi$
$641$	214189.	+	370987.i	0.521293	+	0.902906i	−0.478400	+	0.878142i	$0.658783\pi$
$642$		0			0
$643$	−74279.9	−	42885.5i	−0.179659	−	0.103726i	0.407473	−	0.913217i	$-0.366410\pi$
$643$	−74279.9	−	42885.5i	−0.179659	−	0.103726i	−0.587133	+	0.809491i	$0.699743\pi$
$644$	−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	$-0.951001\pi$
$647$		−	128368.i		−	0.306653i	0.988176	−	0.153327i	$-0.0489986\pi$
$648$		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	0.452243	+	0.891895i	$0.350624\pi$
$653$	−232940.	+	403463.i	−0.546282	+	0.946189i	−0.998525	+	0.0542939i	$0.982709\pi$
$654$		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	−0.107358	−	0.994220i	$-0.534239\pi$
$659$	303989.	−	175508.i	0.699983	−	0.404135i	0.807341	+	0.590085i	$0.200906\pi$
$660$		0			0
$661$	141131.	−	244446.i	0.323013	−	0.559475i	−0.658095	−	0.752935i	$-0.728638\pi$
$661$	141131.	−	244446.i	0.323013	−	0.559475i	0.981108	+	0.193460i	$0.0619709\pi$
$662$	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	0.851309	+	0.524665i	$0.175809\pi$
$673$	398590.	+	690378.i	0.880028	+	1.52425i	0.0287190	+	0.999588i	$0.490857\pi$
$674$	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	0.977688	−	0.210061i	$-0.0673662\pi$
$677$	140673.	+	243653.i	0.306926	+	0.531612i	−0.670762	+	0.741673i	$0.734033\pi$
$678$		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	$-0.736499\pi$
$683$		−	687094.i		−	1.47291i	0.676489	−	0.736453i	$-0.263501\pi$
$684$		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	−0.170986	−	0.985273i	$-0.554695\pi$
$691$	284957.	−	164520.i	0.596792	−	0.344558i	0.767779	+	0.640715i	$0.221362\pi$
$692$	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	0.993535	+	0.113528i	$0.0362151\pi$
$709$	299138.	+	518122.i	0.595085	+	1.03072i	−0.398450	+	0.917190i	$0.630452\pi$
$710$	−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	$0.200334\pi$
$719$			608601.i			1.17727i	−0.808400	+	0.588633i	$0.799666\pi$
$720$		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	−0.826091	−	0.563536i	$-0.809440\pi$
$727$	−396978.	+	229195.i	−0.751100	+	0.433648i	0.0749911	+	0.997184i	$0.476107\pi$
$728$	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	−0.897044	−	0.441942i	$-0.854290\pi$
$733$	−35347.8	+	61224.2i	−0.0657892	+	0.113950i	0.831255	+	0.555892i	$0.187623\pi$
$734$	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	$-0.856326\pi$
$739$		−	476430.i		−	0.872390i	0.899852	−	0.436195i	$-0.143674\pi$
$740$	−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	0.397885	−	0.917435i	$-0.369744\pi$
$743$	−109137.	−	63010.2i	−0.197694	−	0.114139i	−0.595579	+	0.803296i	$0.703078\pi$
$744$		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	0.334899	−	0.942254i	$-0.391298\pi$
$751$	−176908.	−	102138.i	−0.313667	−	0.181096i	−0.648566	+	0.761158i	$0.724631\pi$
$752$	−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	−0.887097	−	0.461583i	$-0.847282\pi$
$761$	−25368.8	+	43940.0i	−0.0438056	+	0.0758736i	0.843291	+	0.537457i	$0.180615\pi$
$762$		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	0.203268	+	0.979123i	$0.434844\pi$
$769$	−441340.	+	764423.i	−0.746312	+	1.29265i	−0.949579	+	0.313526i	$0.898490\pi$
$770$	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	0.577458	−	0.816421i	$-0.304045\pi$
$787$	98569.7	+	56909.2i	0.159145	+	0.0918826i	−0.418312	+	0.908303i	$0.637378\pi$
$788$	−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	0.446205	+	0.894931i	$0.352775\pi$
$797$	−350591.	+	607241.i	−0.551930	+	0.955971i	−0.998135	+	0.0610403i	$0.980558\pi$
$798$		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	$0.00887434\pi$
$811$			36669.2i			0.0557519i	−0.999611	+	0.0278759i	$0.991126\pi$
$812$	−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	0.631863	−	0.775080i	$-0.282290\pi$
$821$	−239492.	−	414812.i	−0.355307	−	0.615410i	−0.987170	+	0.159670i	$0.948957\pi$
$822$		0			0
$823$	−679126.	−	392093.i	−1.00265	−	0.578882i	−0.0936206	−	0.995608i	$-0.529844\pi$
$823$	−679126.	−	392093.i	−1.00265	−	0.578882i	−0.909032	+	0.416726i	$0.863177\pi$
$824$	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	$-0.650781\pi$
$827$		−	1.21724e6i		−	1.77978i	0.456175	−	0.889890i	$-0.349219\pi$
$828$		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	−0.948530	−	0.316688i	$-0.897429\pi$
$839$	−808477.	+	466775.i	−1.14853	+	0.663107i	−0.200005	+	0.979795i	$0.564096\pi$
$840$		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	0.767333	−	0.641249i	$-0.221583\pi$
$853$	−124910.	−	216350.i	−0.171672	−	0.297344i	−0.939004	+	0.343905i	$0.888250\pi$
$854$	−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	0.998385	−	0.0568162i	$-0.0180949\pi$
$857$	330493.	+	572431.i	0.449988	+	0.779402i	−0.548397	+	0.836218i	$0.684762\pi$
$858$		0			0
$859$	716685.	+	413779.i	0.971275	+	0.560766i	0.899625	−	0.436664i	$-0.143840\pi$
$859$	716685.	+	413779.i	0.971275	+	0.560766i	0.0716503	+	0.997430i	$0.477173\pi$
$860$	−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	$0.308209\pi$
$863$			1.22724e6i			1.64781i	−0.566728	+	0.823905i	$0.691791\pi$
$864$		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	−0.587472	−	0.809245i	$-0.699877\pi$
$877$	313105.	−	542314.i	0.407091	−	0.705102i	0.994562	+	0.104143i	$0.0332099\pi$
$878$	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	$0.348715\pi$
$883$			1.38655e6i			1.77833i	−0.457582	+	0.889167i	$0.651285\pi$
$884$	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	−0.957361	−	0.288895i	$-0.906712\pi$
$887$	−1.32667e6	−	765956.i	−1.68623	−	0.973546i	−0.728870	−	0.684652i	$-0.759954\pi$
$888$		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	−0.318240	−	0.948010i	$-0.603092\pi$
$907$	282696.	−	163214.i	0.343641	−	0.198401i	0.661881	+	0.749609i	$0.269758\pi$
$908$	−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	−0.987748	−	0.156060i	$-0.950121\pi$
$911$	−1.11746e6	+	645168.i	−1.34647	+	0.777384i	−0.358722	+	0.933445i	$0.616787\pi$
$912$		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	$-0.833386\pi$
$919$		−	844321.i		−	0.999715i	0.866108	−	0.499858i	$-0.166614\pi$
$920$	−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	0.986161	−	0.165792i	$-0.0530179\pi$
$929$	301633.	+	522445.i	0.349501	+	0.605353i	−0.636660	+	0.771145i	$0.719685\pi$
$930$		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	−0.602314	−	0.798259i	$-0.705754\pi$
$941$	345476.	−	598382.i	0.390156	−	0.675770i	0.992470	+	0.122489i	$0.0390877\pi$
$942$		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	−0.951825	−	0.306641i	$-0.900795\pi$
$947$	−1.04225e6	+	601745.i	−1.16218	+	0.670984i	−0.210354	+	0.977625i	$0.567462\pi$
$948$		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	−0.0321023	−	0.999485i	$-0.510220\pi$
$967$	−854421.	−	493300.i	−0.913732	−	0.527544i	−0.881630	+	0.471941i	$0.843554\pi$
$968$	−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	$-0.726767\pi$
$971$		−	1.42706e6i		−	1.51358i	0.653658	−	0.756790i	$-0.273233\pi$
$972$		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	−0.0501755	−	0.998740i	$-0.515978\pi$
$977$	801658.	−	1.38851e6i	0.839847	−	1.45466i	0.890022	−	0.455917i	$-0.150689\pi$
$978$		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	0.333126	−	0.942882i	$-0.391897\pi$
$983$	1.27188e6	−	734318.i	1.31625	−	0.759936i	0.983123	+	0.182946i	$0.0585634\pi$
$984$		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	$0.272000\pi$
$991$			1.48147e6i			1.50850i	−0.656585	+	0.754252i	$0.728000\pi$
$992$	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	0.877589	−	0.479414i	$-0.159151\pi$
$997$	23467.9	+	40647.6i	0.0236093	+	0.0408926i	−0.853979	+	0.520307i	$0.825818\pi$
$998$	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.91.20		44
3.2	odd	2		36.5.f.a.31.3	yes	44
4.3	odd	2	inner	108.5.f.a.91.10		44
9.2	odd	6		36.5.f.a.7.13	yes	44
9.4	even	3		324.5.d.e.163.6		22
9.5	odd	6		324.5.d.f.163.17		22
9.7	even	3	inner	108.5.f.a.19.10		44
12.11	even	2		36.5.f.a.31.13	yes	44
36.7	odd	6	inner	108.5.f.a.19.20		44
36.11	even	6		36.5.f.a.7.3	✓	44
36.23	even	6		324.5.d.f.163.18		22
36.31	odd	6		324.5.d.e.163.5		22

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