LMFDB - Embedded newform 108.5.f.a.91.10

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			91.10
Character	$\chi$	$=$	108.91
Dual form			108.5.f.a.19.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.04046 + 3.86231i) q^{2} +(-13.8349 - 8.03717i) q^{4} +(5.89438 - 10.2094i) q^{5} +(-50.5548 + 29.1878i) q^{7} +(45.4367 - 45.0722i) q^{8} +O(q^{10})$	\(q+(-1.04046 + 3.86231i) q^{2} +(-13.8349 - 8.03717i) q^{4} +(5.89438 - 10.2094i) q^{5} +(-50.5548 + 29.1878i) q^{7} +(45.4367 - 45.0722i) q^{8} +(33.2988 + 33.3884i) q^{10} +(86.9742 - 50.2146i) q^{11} +(85.3178 - 147.775i) q^{13} +(-60.1321 - 225.627i) q^{14} +(126.808 + 222.387i) q^{16} +398.571 q^{17} -404.608i q^{19} +(-163.602 + 93.8711i) q^{20} +(103.451 + 388.168i) q^{22} +(291.091 + 168.062i) q^{23} +(243.013 + 420.910i) q^{25} +(481.982 + 483.278i) q^{26} +(934.007 + 2.50777i) q^{28} +(-327.671 - 567.543i) q^{29} +(550.166 + 317.638i) q^{31} +(-990.865 + 258.386i) q^{32} +(-414.698 + 1539.40i) q^{34} +688.176i q^{35} -1599.91 q^{37} +(1562.72 + 420.979i) q^{38} +(-192.337 - 729.553i) q^{40} +(1231.63 - 2133.25i) q^{41} +(1933.38 - 1116.24i) q^{43} +(-1606.86 - 4.31435i) q^{44} +(-951.976 + 949.423i) q^{46} +(2514.55 - 1451.78i) q^{47} +(503.358 - 871.842i) q^{49} +(-1878.53 + 500.649i) q^{50} +(-2368.05 + 1358.73i) q^{52} -1291.73 q^{53} -1183.94i q^{55} +(-981.485 + 3604.82i) q^{56} +(2532.96 - 675.060i) q^{58} +(-1002.24 - 578.642i) q^{59} +(-2960.81 - 5128.28i) q^{61} +(-1799.24 + 1794.42i) q^{62} +(32.9923 - 4095.87i) q^{64} +(-1005.79 - 1742.08i) q^{65} +(-3085.87 - 1781.63i) q^{67} +(-5514.18 - 3203.38i) q^{68} +(-2657.95 - 716.021i) q^{70} +5639.73i q^{71} -5496.39 q^{73} +(1664.65 - 6179.36i) q^{74} +(-3251.91 + 5597.70i) q^{76} +(-2931.31 + 5077.18i) q^{77} +(2788.94 - 1610.20i) q^{79} +(3017.88 + 16.2058i) q^{80} +(6957.81 + 6976.52i) q^{82} +(7063.92 - 4078.36i) q^{83} +(2349.33 - 4069.15i) q^{85} +(2299.65 + 8628.73i) q^{86} +(1688.54 - 6201.71i) q^{88} -910.873 q^{89} +9960.97i q^{91} +(-2676.47 - 4664.66i) q^{92} +(2990.92 + 11222.5i) q^{94} +(-4130.79 - 2384.91i) q^{95} +(8804.44 + 15249.7i) q^{97} +(2843.60 + 2851.24i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.04046	+	3.86231i	−0.260116	+	0.965577i
$2$	−1.04046	+	3.86231i	−0.260116	+	0.965577i
$3$		0			0
$3$		0			0
$4$	−13.8349	−	8.03717i	−0.864680	−	0.502323i
$5$	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	−0.917480	−	0.397782i	$-0.869780\pi$
$7$	−50.5548	+	29.1878i	−1.03173	+	0.595670i	−0.114251	+	0.993452i	$0.536447\pi$
$8$	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	$-0.530449\pi$
$11$	86.9742	−	50.2146i	0.718795	−	0.414997i	0.814309	+	0.580431i	$0.197116\pi$
$12$		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	$-0.00178154\pi$
$14$	−60.1321	−	225.627i	−0.306796	−	1.15116i
$15$		0			0
$16$	126.808	+	222.387i	0.495342	+	0.868698i
$17$	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	$-0.189352\pi$
$20$	−163.602	+	93.8711i	−0.409006	+	0.234678i
$21$		0			0
$22$	103.451	+	388.168i	0.213742	+	0.802000i
$23$	291.091	+	168.062i	0.550267	+	0.317697i	0.749230	−	0.662310i	$-0.230424\pi$
$23$	291.091	+	168.062i	0.550267	+	0.317697i	−0.198963	+	0.980007i	$0.563757\pi$
$24$		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	0.758144	−	0.652087i	$-0.226106\pi$
$31$	550.166	+	317.638i	0.572493	+	0.330529i	−0.185651	+	0.982616i	$0.559440\pi$
$32$	−990.865	+	258.386i	−0.967641	+	0.252330i
$33$		0			0
$34$	−414.698	+	1539.40i	−0.358735	+	1.33166i
$35$			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	$0.698645\pi$
$38$	1562.72	+	420.979i	1.08222	+	0.291537i
$39$		0			0
$40$	−192.337	−	729.553i	−0.120211	−	0.455970i
$41$	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	0.124212	−	0.992256i	$-0.460360\pi$
$43$	1933.38	−	1116.24i	1.04564	−	0.603699i	0.921425	+	0.388557i	$0.127026\pi$
$44$	−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	$-0.438403\pi$
$47$	2514.55	−	1451.78i	1.13832	−	0.657211i	0.946015	+	0.324124i	$0.105069\pi$
$48$		0			0
$49$	503.358	−	871.842i	0.209645	−	0.363116i
$50$	−1878.53	+	500.649i	−0.751412	+	0.200260i
$51$		0			0
$52$	−2368.05	+	1358.73i	−0.875759	+	0.502490i
$53$	−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
$56$	−981.485	+	3604.82i	−0.312973	+	1.14949i
$57$		0			0
$58$	2532.96	−	675.060i	0.752959	−	0.200672i
$59$	−1002.24	−	578.642i	−0.287917	−	0.166229i	0.349085	−	0.937091i	$-0.386492\pi$
$59$	−1002.24	−	578.642i	−0.287917	−	0.166229i	−0.637002	+	0.770862i	$0.719826\pi$
$60$		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	0.115219	−	0.993340i	$-0.463243\pi$
$67$	−3085.87	−	1781.63i	−0.687430	−	0.396888i	−0.802648	+	0.596452i	$0.796576\pi$
$68$	−5514.18	−	3203.38i	−1.19251	−	0.692773i
$69$		0			0
$70$	−2657.95	−	716.021i	−0.542439	−	0.146127i
$71$			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	$0.672470\pi$
$74$	1664.65	−	6179.36i	0.303990	−	1.12844i
$75$		0			0
$76$	−3251.91	+	5597.70i	−0.563003	+	0.969132i
$77$	−2931.31	+	5077.18i	−0.494402	+	0.856329i
$78$		0			0
$79$	2788.94	−	1610.20i	0.446874	−	0.258003i	−0.259635	−	0.965707i	$-0.583602\pi$
$79$	2788.94	−	1610.20i	0.446874	−	0.258003i	0.706509	+	0.707704i	$0.250269\pi$
$80$	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	$-0.465001\pi$
$83$	7063.92	−	4078.36i	1.02539	−	0.592010i	0.915661	+	0.401951i	$0.131668\pi$
$84$		0			0
$85$	2349.33	−	4069.15i	0.325166	−	0.563205i
$86$	2299.65	+	8628.73i	0.310932	+	1.16668i
$87$		0			0
$88$	1688.54	−	6201.71i	0.218045	−	0.800840i
$89$	−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
$92$	−2676.47	−	4664.66i	−0.316218	−	0.551118i
$93$		0			0
$94$	2990.92	+	11222.5i	0.338493	+	1.27009i
$95$	−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	0.198348	−	0.980132i	$-0.436442\pi$
$103$	−5848.70	−	3376.75i	−0.551296	−	0.318291i	−0.749645	+	0.661841i	$0.769776\pi$
$104$	−2783.97	−	10559.9i	−0.257394	−	0.976319i
$105$		0			0
$106$	1343.99	−	4989.04i	0.119615	−	0.444023i
$107$			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	$0.351447\pi$
$110$	4572.72	+	1231.84i	0.377911	+	0.101805i
$111$		0			0
$112$	−12901.7	−	7541.47i	−1.02852	−	0.601202i
$113$	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
$122$	22887.6	−	6099.80i	1.53773	−	0.409822i
$123$		0			0
$124$	−5058.56	−	8816.26i	−0.328991	−	0.573378i
$125$	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	$0.833803\pi$
$128$	15785.2	+	4389.02i	0.963451	+	0.267885i
$129$		0			0
$130$	7774.94	−	2072.11i	0.460056	−	0.122610i
$131$	−18105.5	−	10453.2i	−1.05504	−	0.609127i	−0.130983	−	0.991385i	$-0.541813\pi$
$131$	−18105.5	−	10453.2i	−1.05504	−	0.609127i	−0.924056	+	0.382257i	$0.875147\pi$
$132$		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	0.276747	−	0.960943i	$-0.410744\pi$
$139$	−8058.42	−	4652.53i	−0.417081	−	0.240802i	−0.693828	+	0.720141i	$0.744077\pi$
$140$	5530.99	−	9520.83i	0.282193	−	0.485757i
$141$		0			0
$142$	−21782.4	−	5867.92i	−1.08026	−	0.291010i
$143$		−	17136.8i		−	0.838026i
$144$		0			0
$145$	−7725.67			−0.367451
$146$	5718.78	−	21228.8i	0.268286	−	0.995907i
$147$		0			0
$148$	22134.6	+	12858.8i	1.01053	+	0.587051i
$149$	−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	−0.681197	−	0.732100i	$-0.738540\pi$
$151$	−8841.72	+	5104.77i	−0.387778	+	0.223884i	0.293419	+	0.955984i	$0.405207\pi$
$152$	−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	$-0.0333046\pi$
$158$	3317.29	+	12447.1i	0.132883	+	0.498603i
$159$		0			0
$160$	−3202.58	+	11639.1i	−0.125101	+	0.454653i
$161$	−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	$0.891676\pi$
$164$	−34184.8	+	19614.4i	−1.27100	+	0.729269i
$165$		0			0
$166$	8402.14	+	31526.4i	0.304911	+	1.14409i
$167$	35562.1	+	20531.8i	1.27513	+	0.736197i	0.975949	−	0.217999i	$-0.0699530\pi$
$167$	35562.1	+	20531.8i	1.27513	+	0.736197i	0.299182	+	0.954196i	$0.403286\pi$
$168$		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
$176$	22196.1	+	12974.3i	0.716556	+	0.418851i
$177$		0			0
$178$	947.729	−	3518.08i	0.0299119	−	0.111036i
$179$			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	$0.732975\pi$
$182$	−38472.3	−	10364.0i	−1.16146	−	0.312885i
$183$		0			0
$184$	20801.1	−	5483.96i	0.614401	−	0.161979i
$185$	−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	$-0.849934\pi$
$191$	−34403.1	+	19862.7i	−0.943042	+	0.544466i	−0.0521297	+	0.998640i	$0.516601\pi$
$192$		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	$0.0752859\pi$
$194$	−68059.9	+	18138.7i	−1.80837	+	0.481951i
$195$		0			0
$196$	−13971.0	+	8016.25i	−0.363678	+	0.208669i
$197$	−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	$-0.0982638\pi$
$200$	30013.1	+	8171.67i	0.750326	+	0.204292i
$201$		0			0
$202$	−25744.7	+	6861.23i	−0.630935	+	0.168151i
$203$	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	$-0.107148\pi$
$211$	50298.6	+	29039.9i	1.12977	+	0.652274i	0.185895	+	0.982570i	$0.440482\pi$
$212$	17870.9	+	10381.8i	0.397625	+	0.230995i
$213$		0			0
$214$	−118.793	−	32.0014i	−0.00259395	−	0.000698781i
$215$		−	26318.1i		−	0.569349i
$216$		0			0
$217$	−37084.7			−0.787545
$218$	−11124.0	+	41293.4i	−0.234071	+	0.868896i
$219$		0			0
$220$	−9515.49	+	16379.6i	−0.196601	+	0.338421i
$221$	34005.2	−	58898.7i	0.696243	−	1.20593i
$222$		0			0
$223$	−14429.6	+	8330.91i	−0.290164	+	0.167526i	−0.638016	−	0.770023i	$-0.720245\pi$
$223$	−14429.6	+	8330.91i	−0.290164	+	0.167526i	0.347852	+	0.937550i	$0.386911\pi$
$224$	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	$-0.482857\pi$
$227$	48721.5	−	28129.4i	0.945515	−	0.545894i	0.891685	+	0.452657i	$0.149524\pi$
$228$		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	$0.174096\pi$
$230$	4081.70	+	15315.3i	0.0771588	+	0.289515i
$231$		0			0
$232$	−40468.7	−	11018.4i	−0.751871	−	0.204712i
$233$	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
$236$	9215.19	+	16060.6i	0.165455	+	0.288362i
$237$		0			0
$238$	−23966.9	−	89928.4i	−0.423114	−	1.58761i
$239$	−22567.5	−	13029.4i	−0.395083	−	0.228101i	0.289277	−	0.957245i	$-0.406585\pi$
$239$	−22567.5	−	13029.4i	−0.395083	−	0.228101i	−0.684360	+	0.729144i	$0.739918\pi$
$240$		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
$248$	39314.4	−	10364.7i	0.639217	−	0.168521i
$249$		0			0
$250$	−13627.6	+	50587.0i	−0.218041	+	0.809392i
$251$		−	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
$254$	−62136.0	−	16738.7i	−0.963110	−	0.259451i
$255$		0			0
$256$	−33375.6	+	56400.7i	−0.509272	+	0.860606i
$257$	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	−0.626881	−	0.779115i	$-0.715669\pi$
$263$	−18370.5	+	10606.2i	−0.265588	+	0.153337i	0.361293	+	0.932452i	$0.382335\pi$
$264$		0			0
$265$	−7613.92	+	13187.7i	−0.108422	+	0.187792i
$266$	−91290.6	+	24329.9i	−1.29022	+	0.343857i
$267$		0			0
$268$	28373.4	+	49450.3i	0.395041	+	0.688493i
$269$	−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	$0.927784\pi$
$272$	50541.8	+	88636.8i	0.683145	+	1.19805i
$273$		0			0
$274$	−18073.3	+	4816.74i	−0.240734	+	0.0641582i
$275$	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	0.833382	−	0.552697i	$-0.186401\pi$
$283$	61782.5	+	35670.2i	0.771424	+	0.445382i	−0.0619586	+	0.998079i	$0.519735\pi$
$284$	45327.5	−	78024.9i	0.561985	−	0.967379i
$285$		0			0
$286$	66187.6	+	17830.2i	0.809179	+	0.217984i
$287$			143795.i			1.74574i
$288$		0			0
$289$	75337.7			0.902021
$290$	8038.26	−	29838.9i	0.0955798	−	0.354803i
$291$		0			0
$292$	76041.9	+	44175.4i	0.891840	+	0.518102i
$293$	−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
$302$	−10516.7	−	39460.8i	−0.115310	−	0.432665i
$303$		0			0
$304$	89979.4	−	51307.4i	0.973635	−	0.555179i
$305$	−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	$0.980284\pi$
$308$	81360.5	−	46682.7i	0.857654	−	0.492101i
$309$		0			0
$310$	7714.46	+	28946.1i	0.0802753	+	0.301208i
$311$	−3755.11	−	2168.01i	−0.0388242	−	0.0224151i	0.480462	−	0.877015i	$-0.340469\pi$
$311$	−3755.11	−	2168.01i	−0.0388242	−	0.0224151i	−0.519286	+	0.854600i	$0.673802\pi$
$312$		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
$320$	−41621.7	−	24479.4i	−0.406462	−	0.239057i
$321$		0			0
$322$	20415.3	−	75784.0i	0.196900	−	0.730913i
$323$		−	161265.i		−	1.54573i
$324$		0			0
$325$	82933.2			0.785167
$326$	−68503.4	−	18454.0i	−0.644580	−	0.173643i
$327$		0			0
$328$	−40189.0	−	152440.i	−0.373559	−	1.41694i
$329$	−84748.5	+	146789.i	−0.782961	+	1.35613i
$330$		0			0
$331$	−162176.	+	93632.3i	−1.48023	+	0.854614i	−0.999749	−	0.0223896i	$-0.992873\pi$
$331$	−162176.	+	93632.3i	−1.48023	+	0.854614i	−0.480485	+	0.877003i	$0.659539\pi$
$332$	−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	$0.0200538\pi$
$338$	2147.14	−	572.236i	0.0187943	−	0.00500890i
$339$		0			0
$340$	−65207.1	+	37414.3i	−0.564076	+	0.323653i
$341$	63800.3			0.548674
$342$		0			0
$343$		−	81392.2i		−	0.691823i
$344$	37535.2	−	137860.i	0.317192	−	1.16499i
$345$		0			0
$346$	−26884.5	+	7165.02i	−0.224569	+	0.0598501i
$347$	−151470.	−	87451.5i	−1.25797	−	0.726287i	−0.285287	−	0.958442i	$-0.592089\pi$
$347$	−151470.	−	87451.5i	−1.25797	−	0.726287i	−0.972679	+	0.232155i	$0.925422\pi$
$348$		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
$356$	12601.8	+	7320.85i	0.0994336	+	0.0577646i
$357$		0			0
$358$	−6776.42	−	1825.49i	−0.0528731	−	0.0142434i
$359$			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
$362$	45559.7	−	169122.i	0.347667	−	1.29058i
$363$		0			0
$364$	80058.0	−	137809.i	0.604230	−	1.04010i
$365$	−32397.8	+	56114.6i	−0.243181	+	0.421202i
$366$		0			0
$367$	−143674.	+	82950.4i	−1.06671	+	0.615866i	−0.927281	−	0.374366i	$-0.877860\pi$
$367$	−143674.	+	82950.4i	−1.06671	+	0.615866i	−0.139430	+	0.990232i	$0.544527\pi$
$368$	−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	$0.321815\pi$
$374$	41232.5	+	154712.i	0.294779	+	1.10607i
$375$		0			0
$376$	48818.3	−	179301.i	0.345308	−	1.26825i
$377$	−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	$0.951453\pi$
$380$	37981.0	+	66194.9i	0.263026	+	0.458413i
$381$		0			0
$382$	−40920.6	−	153542.i	−0.280424	−	1.05220i
$383$	−237186.	−	136939.i	−1.61693	−	0.933535i	−0.987708	−	0.156310i	$-0.950040\pi$
$383$	−237186.	−	136939.i	−1.61693	−	0.933535i	−0.629223	−	0.777225i	$-0.716627\pi$
$384$		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
$392$	−16424.9	−	62301.1i	−0.106888	−	0.405437i
$393$		0			0
$394$	29399.4	−	109134.i	0.189385	−	0.703018i
$395$		−	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	$0.504294\pi$
$398$	92940.9	+	25037.2i	0.586733	+	0.158059i
$399$		0			0
$400$	−62789.0	+	107417.i	−0.392431	+	0.671359i
$401$	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	$0.139600\pi$
$410$	112238.	−	29912.6i	0.667685	−	0.177945i
$411$		0			0
$412$	53776.5	+	93723.9i	0.316810	+	0.552149i
$413$	67557.2			0.396070
$414$		0			0
$415$		−	96157.5i		−	0.558325i
$416$	−46355.6	+	168470.i	−0.267864	+	0.973498i
$417$		0			0
$418$	157056.	−	41857.1i	0.898880	−	0.239561i
$419$	137256.	+	79245.0i	0.781816	+	0.451382i	0.837073	−	0.547091i	$-0.184265\pi$
$419$	137256.	+	79245.0i	0.781816	+	0.451382i	−0.0552577	+	0.998472i	$0.517598\pi$
$420$		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
$428$	247.199	−	425.518i	0.00134946	−	0.00232290i
$429$		0			0
$430$	101649.	+	27383.0i	0.549750	+	0.148096i
$431$			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	$0.417941\pi$
$434$	38585.2	−	143233.i	0.204853	−	0.760435i
$435$		0			0
$436$	−147914.	−	85928.5i	−0.778101	−	0.452027i
$437$	67999.1	−	117778.i	0.356074	−	0.616738i
$438$		0			0
$439$	−321749.	+	185762.i	−1.66951	+	0.963890i	−0.701603	+	0.712568i	$0.747532\pi$
$439$	−321749.	+	185762.i	−1.66951	+	0.963890i	−0.967903	+	0.251322i	$0.919135\pi$
$440$	−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	$-0.552077\pi$
$443$	119741.	−	69132.2i	0.610146	−	0.352268i	0.773023	+	0.634379i	$0.218744\pi$
$444$		0			0
$445$	−5369.03	+	9299.44i	−0.0271129	+	0.0469609i
$446$	−17163.2	−	64399.5i	−0.0862834	−	0.323752i
$447$		0			0
$448$	117882.	+	208029.i	0.587340	+	1.03649i
$449$	−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
$452$	−139003.	+	79756.5i	−0.680373	+	0.390382i
$453$		0			0
$454$	57951.4	+	217445.i	0.281159	+	1.05496i
$455$	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	−0.435539	−	0.900170i	$-0.643442\pi$
$463$	−307165.	−	177342.i	−1.43288	−	0.827273i	−0.997339	+	0.0728974i	$0.976775\pi$
$464$	84662.8	−	144838.i	0.393239	−	0.672741i
$465$		0			0
$466$	−80085.7	+	297287.i	−0.368793	+	1.36900i
$467$		−	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
$470$	132204.	+	35614.3i	0.598480	+	0.161224i
$471$		0			0
$472$	−71619.1	+	18881.5i	−0.321473	+	0.0847523i
$473$	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	$-0.593837\pi$
$479$	90134.6	−	52039.3i	0.392845	−	0.226809i	0.683392	+	0.730052i	$0.260504\pi$
$480$		0			0
$481$	−136501.	+	236427.i	−0.589992	+	1.02190i
$482$	−108221.	+	28842.1i	−0.465819	+	0.124146i
$483$		0			0
$484$	63213.2	−	36270.2i	0.269847	−	0.154832i
$485$	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	$0.931505\pi$
$488$	−365672.	−	99561.8i	−1.53551	−	0.418074i
$489$		0			0
$490$	45870.6	−	12225.0i	0.191048	−	0.0509163i
$491$	151749.	+	87612.6i	0.629454	+	0.363416i	0.780541	−	0.625105i	$-0.214944\pi$
$491$	151749.	+	87612.6i	0.629454	+	0.363416i	−0.151086	+	0.988521i	$0.548277\pi$
$492$		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	$-0.395147\pi$
$499$	−83227.2	−	48051.2i	−0.334244	−	0.192976i	−0.657724	+	0.753259i	$0.728481\pi$
$500$	−181204.	−	105268.i	−0.724815	−	0.421071i
$501$		0			0
$502$	76406.1	+	20582.9i	0.303194	+	0.0816770i
$503$		−	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
$506$	−35122.5	+	130378.i	−0.137178	+	0.509219i
$507$		0			0
$508$	129300.	−	222572.i	0.501040	−	0.862470i
$509$	−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
$518$	96206.0	+	360984.i	0.358544	+	1.34533i
$519$		0			0
$520$	−124219.	−	33821.2i	−0.459391	−	0.125079i
$521$	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	$0.847495\pi$
$524$	166473.	+	290136.i	0.606292	+	1.05667i
$525$		0			0
$526$	−21850.6	−	81987.8i	−0.0789755	−	0.296331i
$527$	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
$536$	−220514.	+	58135.7i	−0.767549	+	0.202355i
$537$		0			0
$538$	1151.00	−	4272.64i	0.00397659	−	0.0147615i
$539$		−	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	$0.798883\pi$
$542$	−127604.	−	34375.1i	−0.434376	−	0.117016i
$543$		0			0
$544$	−394930.	+	102985.i	−1.33451	+	0.347997i
$545$	63019.0	−	109152.i	0.212167	−	0.367485i
$546$		0			0
$547$	332881.	−	192189.i	1.11254	−	0.642323i	0.173051	−	0.984913i	$-0.444638\pi$
$547$	332881.	−	192189.i	1.11254	−	0.642323i	0.939485	+	0.342590i	$0.111304\pi$
$548$	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
$554$	111479.	−	29710.3i	0.363223	−	0.0968028i
$555$		0			0
$556$	74094.1	+	129134.i	0.239681	+	0.417726i
$557$	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
$560$	−153041.	+	87266.0i	−0.488014	+	0.278272i
$561$		0			0
$562$	−124169.	+	33092.4i	−0.393134	+	0.104775i
$563$	132566.	+	76536.8i	0.418229	+	0.241465i	0.694319	−	0.719667i	$-0.255706\pi$
$563$	132566.	+	76536.8i	0.418229	+	0.241465i	−0.276090	+	0.961132i	$0.589039\pi$
$564$		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	0.350617	−	0.936519i	$-0.385972\pi$
$571$	−92961.9	−	53671.6i	−0.285123	−	0.164616i	−0.635741	+	0.771903i	$0.719305\pi$
$572$	−137731.	+	237086.i	−0.420960	+	0.724624i
$573$		0			0
$574$	−555380.	−	149613.i	−1.68565	−	0.454094i
$575$			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	$0.554814\pi$
$578$	−78386.0	+	290977.i	−0.234630	+	0.870971i
$579$		0			0
$580$	106884.	+	62092.5i	0.317728	+	0.184579i
$581$	−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	$-0.642516\pi$
$587$	45237.1	−	26117.7i	0.131286	−	0.0757980i	0.564205	+	0.825635i	$0.309183\pi$
$588$		0			0
$589$	128519.	−	222602.i	0.370456	−	0.641649i
$590$	−14053.4	−	52731.2i	−0.0403718	−	0.151483i
$591$		0			0
$592$	−202881.	−	355799.i	−0.578893	−	1.01522i
$593$	−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
$596$	343776.	−	197250.i	0.967793	−	0.555296i
$597$		0			0
$598$	59080.3	+	221681.i	0.165212	+	0.619906i
$599$	−16547.3	−	9553.58i	−0.0461183	−	0.0266264i	0.476764	−	0.879032i	$-0.341810\pi$
$599$	−16547.3	−	9553.58i	−0.0461183	−	0.0266264i	−0.522882	+	0.852405i	$0.675143\pi$
$600$		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	0.876803	−	0.480850i	$-0.159672\pi$
$607$	331153.	+	191191.i	0.898776	+	0.518909i	0.0219735	+	0.999759i	$0.493005\pi$
$608$	104545.	+	400912.i	0.282811	+	1.08453i
$609$		0			0
$610$	72633.2	−	269622.i	0.195198	−	0.724597i
$611$		−	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	$0.590520\pi$
$614$	−45065.9	−	12140.2i	−0.119539	−	0.0322026i
$615$		0			0
$616$	95650.5	+	362811.i	0.252073	+	0.956134i
$617$	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	−0.452711	−	0.891657i	$-0.649543\pi$
$619$	35684.5	−	20602.5i	0.0931319	−	0.0537697i	0.545843	+	0.837888i	$0.316210\pi$
$620$	−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
$626$	334325.	−	89101.2i	0.853139	−	0.227371i
$627$		0			0
$628$	−402083.	+	230706.i	−1.01952	+	0.584977i
$629$	−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	$0.939349\pi$
$632$	54145.3	−	198866.i	0.135558	−	0.497882i
$633$		0			0
$634$	95205.8	−	25373.4i	0.236856	−	0.0631248i
$635$	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	0.587133	−	0.809491i	$-0.300257\pi$
$643$	74279.9	+	42885.5i	0.179659	+	0.103726i	−0.407473	+	0.913217i	$0.633590\pi$
$644$	271460.	+	157701.i	0.654536	+	0.380244i
$645$		0			0
$646$	622855.	+	167790.i	1.49253	+	0.402070i
$647$			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
$650$	−86288.9	+	320314.i	−0.204234	+	0.758139i
$651$		0			0
$652$	142550.	−	245381.i	0.335331	−	0.577225i
$653$	−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	−0.807341	−	0.590085i	$-0.799094\pi$
$659$	−303989.	+	175508.i	−0.699983	+	0.404135i	0.107358	+	0.994220i	$0.465761\pi$
$660$		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	$0.0619709\pi$
$662$	−192899.	−	723795.i	−0.440164	−	1.65158i
$663$		0			0
$664$	137141.	−	503694.i	0.311051	−	1.14243i
$665$	278442.			0.629638
$666$		0			0
$667$		−	220276.i		−	0.495125i
$668$	−326980.	−	569874.i	−0.732771	−	1.27710i
$669$		0			0
$670$	−43270.3	−	162358.i	−0.0963918	−	0.361680i
$671$	−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
$680$	−76660.0	−	290778.i	−0.165787	−	0.628846i
$681$		0			0
$682$	−66381.8	+	246417.i	−0.142719	+	0.529787i
$683$			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
$686$	314362.	+	84685.5i	0.668008	+	0.179954i
$687$		0			0
$688$	493405.	+	288411.i	1.04238	+	0.609305i
$689$	−110207.	+	190884.i	−0.232152	+	0.402098i
$690$		0			0
$691$	−284957.	+	164520.i	−0.596792	+	0.344558i	−0.767779	−	0.640715i	$-0.778638\pi$
$691$	−284957.	+	164520.i	−0.596792	+	0.344558i	0.170986	+	0.985273i	$0.445305\pi$
$692$	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
$698$	169666.	−	45217.7i	0.348243	−	0.0928106i
$699$		0			0
$700$	225920.	+	393742.i	0.461061	+	0.803556i
$701$	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
$704$	−202803.	−	357892.i	−0.409193	−	0.722115i
$705$		0			0
$706$	−601328.	+	160260.i	−1.20643	+	0.321526i
$707$	−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
$716$	14101.2	−	24273.3i	0.0275062	−	0.0473481i
$717$		0			0
$718$	−710682.	−	191450.i	−1.37856	−	0.371369i
$719$		−	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
$722$	34737.6	−	128950.i	0.0666386	−	0.247370i
$723$		0			0
$724$	605800.	+	351931.i	1.15572	+	0.671399i
$725$	159256.	−	275840.i	0.302985	−	0.524785i
$726$		0			0
$727$	396978.	−	229195.i	0.751100	−	0.433648i	−0.0749911	−	0.997184i	$-0.523893\pi$
$727$	396978.	−	229195.i	0.751100	−	0.433648i	0.826091	+	0.563536i	$0.190560\pi$
$728$	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	$0.187623\pi$
$734$	−170892.	−	641221.i	−0.317198	−	1.19019i
$735$		0			0
$736$	−331857.	−	91312.6i	−0.612626	−	0.168568i
$737$	−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	$0.856326\pi$
$740$	261750.	−	150186.i	0.477994	−	0.274261i
$741$		0			0
$742$	77674.1	+	291448.i	0.141081	+	0.529363i
$743$	109137.	+	63010.2i	0.197694	+	0.114139i	0.595579	−	0.803296i	$-0.296922\pi$
$743$	109137.	+	63010.2i	0.197694	+	0.114139i	−0.397885	+	0.917435i	$0.630256\pi$
$744$		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	$-0.275369\pi$
$751$	176908.	+	102138.i	0.313667	+	0.181096i	−0.334899	+	0.942254i	$0.608702\pi$
$752$	641721.	+	375107.i	1.13478	+	0.663314i
$753$		0			0
$754$	116349.	−	431902.i	0.204655	−	0.759700i
$755$			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	$0.328438\pi$
$758$	−168573.	−	45411.5i	−0.293392	−	0.0790365i
$759$		0			0
$760$	−295183.	+	77821.2i	−0.511051	+	0.134732i
$761$	−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	$0.898490\pi$
$770$	−267128.	+	71192.5i	−0.450545	+	0.120075i
$771$		0			0
$772$	−292745.	+	167970.i	−0.491196	+	0.281836i
$773$	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
$776$	1.08738e6	+	296063.i	1.80576	+	0.491655i
$777$		0			0
$778$	947674.	−	252565.i	1.56567	−	0.417268i
$779$	−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	$-0.362622\pi$
$787$	−98569.7	−	56909.2i	−0.159145	−	0.0918826i	−0.577458	+	0.816421i	$0.695955\pi$
$788$	390919.	+	227099.i	0.629556	+	0.365732i
$789$		0			0
$790$	146630.	+	39500.6i	0.234947	+	0.0632920i
$791$			584701.i			0.934504i
$792$		0			0
$793$	−1.01044e6			−1.60681
$794$	4424.45	−	16424.1i	0.00701809	−	0.0260519i
$795$		0			0
$796$	−193403.	+	332916.i	−0.305237	+	0.525423i
$797$	−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
$806$	111662.	+	418979.i	0.171885	+	0.644944i
$807$		0			0
$808$	411319.	+	111990.i	0.630023	+	0.171537i
$809$	−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	$-0.00887434\pi$
$812$	−304624.	−	530911.i	−0.462010	−	0.805210i
$813$		0			0
$814$	−165512.	−	621035.i	−0.249794	−	0.937275i
$815$	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	0.909032	−	0.416726i	$-0.136823\pi$
$823$	679126.	+	392093.i	1.00265	+	0.578882i	0.0936206	+	0.995608i	$0.470156\pi$
$824$	−417943.	+	110185.i	−0.615550	+	0.162282i
$825$		0			0
$826$	−70290.7	+	260927.i	−0.103024	+	0.382436i
$827$			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	$0.578427\pi$
$830$	371390.	+	100048.i	0.539106	+	0.145229i
$831$		0			0
$832$	−602451.	−	354326.i	−0.870312	−	0.511866i
$833$	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	$-0.435904\pi$
$839$	808477.	−	466775.i	1.14853	−	0.663107i	0.948530	+	0.316688i	$0.102571\pi$
$840$		0			0
$841$	138904.	−	240589.i	0.196391	−	0.340160i
$842$	−1.10384e6	+	294185.i	−1.55697	+	0.414950i
$843$		0			0
$844$	−462476.	−	806022.i	−0.649239	−	1.13152i
$845$	−6548.91			−0.00917182
$846$		0			0
$847$		−	265900.i		−	0.370639i
$848$	−163801.	−	287263.i	−0.227784	−	0.399473i
$849$		0			0
$850$	−748728.	+	199544.i	−1.03630	+	0.276186i
$851$	−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	−0.0716503	−	0.997430i	$-0.522827\pi$
$859$	−716685.	−	413779.i	−0.971275	−	0.560766i	−0.899625	+	0.436664i	$0.856160\pi$
$860$	−211524.	+	364108.i	−0.285997	+	0.492304i
$861$		0			0
$862$	−444643.	−	119782.i	−0.598408	−	0.161204i
$863$		−	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
$866$	−99468.7	+	369239.i	−0.132633	+	0.492347i
$867$		0			0
$868$	513062.	+	298056.i	0.680974	+	0.395602i
$869$	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	$0.0332099\pi$
$878$	−382702.	−	1.43597e6i	−0.496446	−	1.86276i
$879$		0			0
$880$	263291.	−	150132.i	0.339994	−	0.193869i
$881$	−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	$-0.348715\pi$
$884$	−943837.	+	541551.i	−1.20779	+	0.693002i
$885$		0			0
$886$	142425.	+	534404.i	0.181433	+	0.680773i
$887$	1.32667e6	+	765956.i	1.68623	+	0.973546i	0.957361	+	0.288895i	$0.0932877\pi$
$887$	1.32667e6	+	765956.i	1.68623	+	0.973546i	0.728870	+	0.684652i	$0.240046\pi$
$888$		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
$896$	−926123.	+	238849.i	−1.15359	+	0.297514i
$897$		0			0
$898$	133623.	−	496025.i	0.165703	−	0.615107i
$899$		−	416323.i		−	0.515124i
$900$		0			0
$901$	−514844.			−0.634200
$902$	955473.	+	257394.i	1.17437	+	0.316362i
$903$		0			0
$904$	−163417.	−	619856.i	−0.199968	−	0.758497i
$905$	−258102.	+	447047.i	−0.315134	+	0.545828i
$906$		0			0
$907$	−282696.	+	163214.i	−0.343641	+	0.198401i	−0.661881	−	0.749609i	$-0.730242\pi$
$907$	−282696.	+	163214.i	−0.343641	+	0.198401i	0.318240	+	0.948010i	$0.396908\pi$
$908$	−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	$-0.383213\pi$
$911$	1.11746e6	−	645168.i	1.34647	−	0.777384i	0.987748	+	0.156060i	$0.0498793\pi$
$912$		0			0
$913$	409586.	−	709424.i	0.491364	−	0.851068i
$914$	1.13280e6	−	301904.i	1.35600	−	0.361390i
$915$		0			0
$916$	33970.4	−	19491.4i	0.0404864	−	0.0232301i
$917$	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	$0.833386\pi$
$920$	66622.1	−	244691.i	0.0787123	−	0.289096i
$921$		0			0
$922$	−1.14458e6	+	305044.i	−1.34644	+	0.358840i
$923$	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
$932$	−1.06489e6	−	618631.i	−1.22595	−	0.712197i
$933$		0			0
$934$	450517.	+	121364.i	0.516437	+	0.139122i
$935$		−	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	$0.519780\pi$
$938$	−216424.	+	803389.i	−0.245980	+	0.913104i
$939$		0			0
$940$	−275107.	+	473559.i	−0.311348	+	0.535942i
$941$	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	0.210354	−	0.977625i	$-0.432538\pi$
$947$	1.04225e6	−	601745.i	1.16218	−	0.670984i	0.951825	+	0.306641i	$0.0992051\pi$
$948$		0			0
$949$	−468940.	+	812228.i	−0.520697	+	0.901873i
$950$	202567.	+	760069.i	0.224451	+	0.842182i
$951$		0			0
$952$	−391191.	+	1.43677e6i	−0.431633	+	1.58531i
$953$	−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
$956$	207500.	+	361639.i	0.227040	+	0.395694i
$957$		0			0
$958$	107210.	+	402273.i	0.116817	+	0.438318i
$959$	−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	$-0.156446\pi$
$967$	854421.	+	493300.i	0.913732	+	0.527544i	0.0321023	+	0.999485i	$0.489780\pi$
$968$	74315.9	+	281887.i	0.0793105	+	0.300832i
$969$		0			0
$970$	−215986.	+	801765.i	−0.229553	+	0.852125i
$971$			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
$974$	−391191.	−	105382.i	−0.412354	−	0.111084i
$975$		0			0
$976$	765007.	−	1.30875e6i	0.803093	−	1.37391i
$977$	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	−0.983123	−	0.182946i	$-0.941437\pi$
$983$	−1.27188e6	+	734318.i	−1.31625	+	0.759936i	−0.333126	+	0.942882i	$0.608103\pi$
$984$		0			0
$985$	−166552.	+	288476.i	−0.171663	+	0.297329i
$986$	1.00956e6	−	269059.i	1.03843	−	0.276754i
$987$		0			0
$988$	549754.	+	958134.i	0.563189	+	0.981549i
$989$	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	$-0.272000\pi$
$992$	−627213.	−	172582.i	−0.637370	−	0.175377i
$993$		0			0
$994$	1.27248e6	−	339128.i	1.28788	−	0.343235i
$995$	−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.91.10		44
3.2	odd	2		36.5.f.a.31.13	yes	44
4.3	odd	2	inner	108.5.f.a.91.20		44
9.2	odd	6		36.5.f.a.7.3	✓	44
9.4	even	3		324.5.d.e.163.5		22
9.5	odd	6		324.5.d.f.163.18		22
9.7	even	3	inner	108.5.f.a.19.20		44
12.11	even	2		36.5.f.a.31.3	yes	44
36.7	odd	6	inner	108.5.f.a.19.10		44
36.11	even	6		36.5.f.a.7.13	yes	44
36.23	even	6		324.5.d.f.163.17		22
36.31	odd	6		324.5.d.e.163.6		22

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

\(f(q)\)	\(=\)	\(q+(-1.04046 + 3.86231i) q^{2} +(-13.8349 - 8.03717i) q^{4} +(5.89438 - 10.2094i) q^{5} +(-50.5548 + 29.1878i) q^{7} +(45.4367 - 45.0722i) q^{8} +O(q^{10})\)	\(q+(-1.04046 + 3.86231i) q^{2} +(-13.8349 - 8.03717i) q^{4} +(5.89438 - 10.2094i) q^{5} +(-50.5548 + 29.1878i) q^{7} +(45.4367 - 45.0722i) q^{8} +(33.2988 + 33.3884i) q^{10} +(86.9742 - 50.2146i) q^{11} +(85.3178 - 147.775i) q^{13} +(-60.1321 - 225.627i) q^{14} +(126.808 + 222.387i) q^{16} +398.571 q^{17} -404.608i q^{19} +(-163.602 + 93.8711i) q^{20} +(103.451 + 388.168i) q^{22} +(291.091 + 168.062i) q^{23} +(243.013 + 420.910i) q^{25} +(481.982 + 483.278i) q^{26} +(934.007 + 2.50777i) q^{28} +(-327.671 - 567.543i) q^{29} +(550.166 + 317.638i) q^{31} +(-990.865 + 258.386i) q^{32} +(-414.698 + 1539.40i) q^{34} +688.176i q^{35} -1599.91 q^{37} +(1562.72 + 420.979i) q^{38} +(-192.337 - 729.553i) q^{40} +(1231.63 - 2133.25i) q^{41} +(1933.38 - 1116.24i) q^{43} +(-1606.86 - 4.31435i) q^{44} +(-951.976 + 949.423i) q^{46} +(2514.55 - 1451.78i) q^{47} +(503.358 - 871.842i) q^{49} +(-1878.53 + 500.649i) q^{50} +(-2368.05 + 1358.73i) q^{52} -1291.73 q^{53} -1183.94i q^{55} +(-981.485 + 3604.82i) q^{56} +(2532.96 - 675.060i) q^{58} +(-1002.24 - 578.642i) q^{59} +(-2960.81 - 5128.28i) q^{61} +(-1799.24 + 1794.42i) q^{62} +(32.9923 - 4095.87i) q^{64} +(-1005.79 - 1742.08i) q^{65} +(-3085.87 - 1781.63i) q^{67} +(-5514.18 - 3203.38i) q^{68} +(-2657.95 - 716.021i) q^{70} +5639.73i q^{71} -5496.39 q^{73} +(1664.65 - 6179.36i) q^{74} +(-3251.91 + 5597.70i) q^{76} +(-2931.31 + 5077.18i) q^{77} +(2788.94 - 1610.20i) q^{79} +(3017.88 + 16.2058i) q^{80} +(6957.81 + 6976.52i) q^{82} +(7063.92 - 4078.36i) q^{83} +(2349.33 - 4069.15i) q^{85} +(2299.65 + 8628.73i) q^{86} +(1688.54 - 6201.71i) q^{88} -910.873 q^{89} +9960.97i q^{91} +(-2676.47 - 4664.66i) q^{92} +(2990.92 + 11222.5i) q^{94} +(-4130.79 - 2384.91i) q^{95} +(8804.44 + 15249.7i) q^{97} +(2843.60 + 2851.24i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + q^{2} - q^{4} + 2 q^{5} - 122 q^{8}+O(q^{10}) \) 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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