LMFDB - Embedded newform 81.5.f.a.17.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [81,5,Mod(8,81)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(81, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("81.8");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	81.f (of order $18$, degree $6$, 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:	$8.37296700979$
Analytic rank:	$0$
Dimension:	$66$
Relative dimension:	$11$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			17.7
Character	$\chi$	$=$	81.17
Dual form			81.5.f.a.62.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.410788 - 1.12863i) q^{2} +(11.1517 + 9.35735i) q^{4} +(-35.6423 - 6.28469i) q^{5} +(50.7952 - 42.6222i) q^{7} +(31.7844 - 18.3507i) q^{8} +(-21.7345 + 37.6453i) q^{10} +(144.976 - 25.5631i) q^{11} +(154.041 - 56.0663i) q^{13} +(-27.2387 - 74.8377i) q^{14} +(32.7914 + 185.970i) q^{16} +(117.897 + 68.0677i) q^{17} +(-137.905 - 238.858i) q^{19} +(-338.662 - 403.602i) q^{20} +(30.7029 - 174.125i) q^{22} +(321.030 - 382.589i) q^{23} +(643.566 + 234.239i) q^{25} -196.887i q^{26} +965.281 q^{28} +(22.1851 - 60.9530i) q^{29} +(-892.294 - 748.724i) q^{31} +(801.663 + 141.355i) q^{32} +(125.254 - 105.100i) q^{34} +(-2078.32 + 1199.92i) q^{35} +(-1249.62 + 2164.41i) q^{37} +(-326.232 + 57.5236i) q^{38} +(-1248.20 + 454.306i) q^{40} +(431.354 + 1185.14i) q^{41} +(-129.173 - 732.574i) q^{43} +(1855.92 + 1071.52i) q^{44} +(-299.926 - 519.487i) q^{46} +(-1032.91 - 1230.97i) q^{47} +(346.568 - 1965.48i) q^{49} +(528.738 - 630.126i) q^{50} +(2242.44 + 816.182i) q^{52} +3827.30i q^{53} -5327.92 q^{55} +(832.345 - 2286.85i) q^{56} +(-59.6801 - 50.0775i) q^{58} +(26.5512 + 4.68169i) q^{59} +(-33.7723 + 28.3383i) q^{61} +(-1211.58 + 699.504i) q^{62} +(-1021.86 + 1769.91i) q^{64} +(-5842.73 + 1030.23i) q^{65} +(3124.90 - 1137.37i) q^{67} +(677.810 + 1862.27i) q^{68} +(500.517 + 2838.57i) q^{70} +(-2541.62 - 1467.40i) q^{71} +(2224.61 + 3853.13i) q^{73} +(1929.49 + 2299.47i) q^{74} +(697.212 - 3954.09i) q^{76} +(6274.51 - 7477.67i) q^{77} +(1896.27 + 690.187i) q^{79} -6834.46i q^{80} +1514.78 q^{82} +(409.909 - 1126.22i) q^{83} +(-3774.32 - 3167.03i) q^{85} +(-879.868 - 155.144i) q^{86} +(4138.86 - 3472.92i) q^{88} +(4841.49 - 2795.24i) q^{89} +(5434.87 - 9413.46i) q^{91} +(7160.03 - 1262.51i) q^{92} +(-1813.62 + 660.103i) q^{94} +(3414.09 + 9380.14i) q^{95} +(-980.336 - 5559.76i) q^{97} +(-2075.94 - 1198.54i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q + 6 q^{2} - 6 q^{4} - 3 q^{5} - 6 q^{7} + 9 q^{8} - 3 q^{10} + 492 q^{11} - 6 q^{13} - 1137 q^{14} - 54 q^{16} + 9 q^{17} - 3 q^{19} + 2487 q^{20} + 1002 q^{22} + 2724 q^{23} + 435 q^{25} - 12 q^{28}+ \cdots + 259938 q^{98}+O(q^{100}) $ 66 * q + 6 * q^2 - 6 * q^4 - 3 * q^5 - 6 * q^7 + 9 * q^8 - 3 * q^10 + 492 * q^11 - 6 * q^13 - 1137 * q^14 - 54 * q^16 + 9 * q^17 - 3 * q^19 + 2487 * q^20 + 1002 * q^22 + 2724 * q^23 + 435 * q^25 - 12 * q^28 - 5016 * q^29 - 1671 * q^31 - 10224 * q^32 - 342 * q^34 + 2682 * q^35 - 3 * q^37 + 6564 * q^38 - 1113 * q^40 - 5754 * q^41 - 1266 * q^43 + 4545 * q^44 - 3 * q^46 + 9159 * q^47 + 5898 * q^49 + 34977 * q^50 + 2871 * q^52 - 12 * q^55 - 39243 * q^56 - 12291 * q^58 - 24762 * q^59 - 8358 * q^61 - 38304 * q^62 + 6141 * q^64 - 23727 * q^65 + 15996 * q^67 + 43533 * q^68 - 7251 * q^70 + 19773 * q^71 + 6108 * q^73 + 74847 * q^74 - 28614 * q^76 + 33909 * q^77 - 5658 * q^79 - 12 * q^82 - 18813 * q^83 + 24219 * q^85 - 96474 * q^86 + 36042 * q^88 - 110232 * q^89 - 6042 * q^91 - 73545 * q^92 + 2631 * q^94 + 65163 * q^95 - 3696 * q^97 + 259938 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{11}{18}\right)$

Coefficient data

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

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

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

$2$	0.410788	−	1.12863i	0.102697	−	0.282158i	−0.877693	−	0.479222i	$-0.840919\pi$
$2$	0.410788	−	1.12863i	0.102697	−	0.282158i	0.980390	+	0.197065i	$0.0631409\pi$
$3$		0			0
$3$		0			0
$4$	11.1517	+	9.35735i	0.696978	+	0.584834i
$5$	−35.6423	−	6.28469i	−1.42569	−	0.251388i	−0.593034	−	0.805177i	$-0.702070\pi$
$5$	−35.6423	−	6.28469i	−1.42569	−	0.251388i	−0.832657	+	0.553790i	$0.813181\pi$
$6$		0			0
$7$	50.7952	−	42.6222i	1.03664	−	0.869841i	0.0450107	−	0.998987i	$-0.485668\pi$
$7$	50.7952	−	42.6222i	1.03664	−	0.869841i	0.991626	+	0.129145i	$0.0412234\pi$
$8$	31.7844	−	18.3507i	0.496631	−	0.286730i
$9$		0			0
$10$	−21.7345	+	37.6453i	−0.217345	+	0.376453i
$11$	144.976	−	25.5631i	1.19815	−	0.211266i	0.461249	−	0.887271i	$-0.347401\pi$
$11$	144.976	−	25.5631i	1.19815	−	0.211266i	0.736897	+	0.676005i	$0.236290\pi$
$12$		0			0
$13$	154.041	−	56.0663i	0.911485	−	0.331753i	0.156639	−	0.987656i	$-0.449934\pi$
$13$	154.041	−	56.0663i	0.911485	−	0.331753i	0.754845	+	0.655903i	$0.227712\pi$
$14$	−27.2387	−	74.8377i	−0.138973	−	0.381825i
$15$		0			0
$16$	32.7914	+	185.970i	0.128092	+	0.726443i
$17$	117.897	+	68.0677i	0.407947	+	0.235528i	0.689907	−	0.723898i	$-0.257651\pi$
$17$	117.897	+	68.0677i	0.407947	+	0.235528i	−0.281960	+	0.959426i	$0.590985\pi$
$18$		0			0
$19$	−137.905	−	238.858i	−0.382008	−	0.661657i	0.609341	−	0.792908i	$-0.291434\pi$
$19$	−137.905	−	238.858i	−0.382008	−	0.661657i	−0.991349	+	0.131251i	$0.958101\pi$
$20$	−338.662	−	403.602i	−0.846655	−	1.00900i
$21$		0			0
$22$	30.7029	−	174.125i	0.0634358	−	0.359762i
$23$	321.030	−	382.589i	0.606862	−	0.723230i	−0.371890	−	0.928277i	$-0.621290\pi$
$23$	321.030	−	382.589i	0.606862	−	0.723230i	0.978752	+	0.205047i	$0.0657347\pi$
$24$		0			0
$25$	643.566	+	234.239i	1.02971	+	0.374782i
$26$		−	196.887i		−	0.291252i
$27$		0			0
$28$	965.281			1.23123
$29$	22.1851	−	60.9530i	0.0263794	−	0.0724768i	−0.925804	−	0.378004i	$-0.876611\pi$
$29$	22.1851	−	60.9530i	0.0263794	−	0.0724768i	0.952183	+	0.305527i	$0.0988327\pi$
$30$		0			0
$31$	−892.294	−	748.724i	−0.928506	−	0.779109i	0.0470428	−	0.998893i	$-0.485020\pi$
$31$	−892.294	−	748.724i	−0.928506	−	0.779109i	−0.975549	+	0.219784i	$0.929465\pi$
$32$	801.663	+	141.355i	0.782874	+	0.138042i
$33$		0			0
$34$	125.254	−	105.100i	0.108351	−	0.0909174i
$35$	−2078.32	+	1199.92i	−1.69659	+	0.979527i
$36$		0			0
$37$	−1249.62	+	2164.41i	−0.912798	+	1.58101i	−0.102704	+	0.994712i	$0.532750\pi$
$37$	−1249.62	+	2164.41i	−0.912798	+	1.58101i	−0.810094	+	0.586301i	$0.800584\pi$
$38$	−326.232	+	57.5236i	−0.225923	+	0.0398363i
$39$		0			0
$40$	−1248.20	+	454.306i	−0.780122	+	0.283941i
$41$	431.354	+	1185.14i	0.256606	+	0.705018i	0.999371	+	0.0354662i	$0.0112916\pi$
$41$	431.354	+	1185.14i	0.256606	+	0.705018i	−0.742765	+	0.669552i	$0.766486\pi$
$42$		0			0
$43$	−129.173	−	732.574i	−0.0698608	−	0.396200i	−0.999608	−	0.0280014i	$-0.991086\pi$
$43$	−129.173	−	732.574i	−0.0698608	−	0.396200i	0.929747	−	0.368199i	$-0.120025\pi$
$44$	1855.92	+	1071.52i	0.958637	+	0.553469i
$45$		0			0
$46$	−299.926	−	519.487i	−0.141742	−	0.245504i
$47$	−1032.91	−	1230.97i	−0.467590	−	0.557252i	0.479781	−	0.877388i	$-0.340716\pi$
$47$	−1032.91	−	1230.97i	−0.467590	−	0.557252i	−0.947372	+	0.320136i	$0.896272\pi$
$48$		0			0
$49$	346.568	−	1965.48i	0.144343	−	0.818610i
$50$	528.738	−	630.126i	0.211495	−	0.252050i
$51$		0			0
$52$	2242.44	+	816.182i	0.829305	+	0.301843i
$53$			3827.30i			1.36251i	0.732044	+	0.681257i	$0.238566\pi$
$53$			3827.30i			1.36251i	−0.732044	+	0.681257i	$0.761434\pi$
$54$		0			0
$55$	−5327.92			−1.76130
$56$	832.345	−	2286.85i	0.265416	−	0.729225i
$57$		0			0
$58$	−59.6801	−	50.0775i	−0.0177408	−	0.0148863i
$59$	26.5512	+	4.68169i	0.00762745	+	0.00134493i	0.177461	−	0.984128i	$-0.443212\pi$
$59$	26.5512	+	4.68169i	0.00762745	+	0.00134493i	−0.169833	+	0.985473i	$0.554323\pi$
$60$		0			0
$61$	−33.7723	+	28.3383i	−0.00907613	+	0.00761578i	−0.647314	−	0.762223i	$-0.724108\pi$
$61$	−33.7723	+	28.3383i	−0.00907613	+	0.00761578i	0.638238	+	0.769839i	$0.279663\pi$
$62$	−1211.58	+	699.504i	−0.315186	+	0.181973i
$63$		0			0
$64$	−1021.86	+	1769.91i	−0.249477	+	0.432106i
$65$	−5842.73	+	1030.23i	−1.38289	+	0.243841i
$66$		0			0
$67$	3124.90	−	1137.37i	0.696123	−	0.253368i	0.0303685	−	0.999539i	$-0.490332\pi$
$67$	3124.90	−	1137.37i	0.696123	−	0.253368i	0.665755	+	0.746171i	$0.268110\pi$
$68$	677.810	+	1862.27i	0.146585	+	0.402740i
$69$		0			0
$70$	500.517	+	2838.57i	0.102146	+	0.579300i
$71$	−2541.62	−	1467.40i	−0.504189	−	0.291094i	0.226253	−	0.974069i	$-0.427352\pi$
$71$	−2541.62	−	1467.40i	−0.504189	−	0.291094i	−0.730442	+	0.682975i	$0.760686\pi$
$72$		0			0
$73$	2224.61	+	3853.13i	0.417453	+	0.723050i	0.995683	−	0.0928241i	$-0.0295894\pi$
$73$	2224.61	+	3853.13i	0.417453	+	0.723050i	−0.578229	+	0.815874i	$0.696256\pi$
$74$	1929.49	+	2299.47i	0.352353	+	0.419918i
$75$		0			0
$76$	697.212	−	3954.09i	0.120709	−	0.684572i
$77$	6274.51	−	7477.67i	1.05827	−	1.26120i
$78$		0			0
$79$	1896.27	+	690.187i	0.303841	+	0.110589i	0.489441	−	0.872036i	$-0.337201\pi$
$79$	1896.27	+	690.187i	0.303841	+	0.110589i	−0.185600	+	0.982625i	$0.559423\pi$
$80$		−	6834.46i		−	1.06788i
$81$		0			0
$82$	1514.78			0.225279
$83$	409.909	−	1126.22i	0.0595020	−	0.163480i	−0.906380	−	0.422464i	$-0.861165\pi$
$83$	409.909	−	1126.22i	0.0595020	−	0.163480i	0.965882	+	0.258983i	$0.0833875\pi$
$84$		0			0
$85$	−3774.32	−	3167.03i	−0.522398	−	0.438344i
$86$	−879.868	−	155.144i	−0.118965	−	0.0209768i
$87$		0			0
$88$	4138.86	−	3472.92i	0.534460	−	0.448465i
$89$	4841.49	−	2795.24i	0.611222	−	0.352889i	−0.162221	−	0.986754i	$-0.551866\pi$
$89$	4841.49	−	2795.24i	0.611222	−	0.352889i	0.773444	+	0.633865i	$0.218533\pi$
$90$		0			0
$91$	5434.87	−	9413.46i	0.656305	−	1.13675i
$92$	7160.03	−	1262.51i	0.845939	−	0.149162i
$93$		0			0
$94$	−1813.62	+	660.103i	−0.205253	+	0.0747060i
$95$	3414.09	+	9380.14i	0.378293	+	1.03935i
$96$		0			0
$97$	−980.336	−	5559.76i	−0.104191	−	0.590898i	−0.991540	−	0.129800i	$-0.958567\pi$
$97$	−980.336	−	5559.76i	−0.104191	−	0.590898i	0.887349	−	0.461099i	$-0.152545\pi$
$98$	−2075.94	−	1198.54i	−0.216154	−	0.124796i
$99$		0			0
$100$	4984.97	+	8634.22i	0.498497	+	0.863422i
$101$	−8777.57	−	10460.7i	−0.860462	−	1.02546i	−0.999382	−	0.0351551i	$-0.988807\pi$
$101$	−8777.57	−	10460.7i	−0.860462	−	1.02546i	0.138920	−	0.990304i	$-0.455637\pi$
$102$		0			0
$103$	−1631.18	+	9250.89i	−0.153754	+	0.871985i	0.806161	+	0.591696i	$0.201541\pi$
$103$	−1631.18	+	9250.89i	−0.153754	+	0.871985i	−0.959916	+	0.280289i	$0.909570\pi$
$104$	3867.24	−	4608.79i	0.357548	−	0.426109i
$105$		0			0
$106$	4319.61	+	1572.21i	0.384444	+	0.139926i
$107$			14316.5i			1.25046i	0.780442	+	0.625228i	$0.214994\pi$
$107$			14316.5i			1.25046i	−0.780442	+	0.625228i	$0.785006\pi$
$108$		0			0
$109$	−2023.48			−0.170312			−0.0851562	−	0.996368i	$-0.527139\pi$
$109$	−2023.48			−0.170312			−0.0851562	+	0.996368i	$0.527139\pi$
$110$	−2188.64	+	6013.25i	−0.180880	+	0.496963i
$111$		0			0
$112$	9592.08	+	8048.71i	0.764675	+	0.641638i
$113$	−18947.1	−	3340.89i	−1.48384	−	0.261641i	−0.627728	−	0.778432i	$-0.716015\pi$
$113$	−18947.1	−	3340.89i	−1.48384	−	0.261641i	−0.856111	+	0.516791i	$0.827126\pi$
$114$		0			0
$115$	−13846.7	+	11618.7i	−1.04701	+	0.878544i
$116$	817.759	−	472.133i	0.0607728	−	0.0350872i
$117$		0			0
$118$	16.1908	−	28.0433i	0.00116280	−	0.00201402i
$119$	8889.79	−	1567.51i	0.627765	−	0.110692i
$120$		0			0
$121$	6606.44	−	2404.55i	0.451229	−	0.164234i
$122$	18.1102	+	49.7575i	0.00121676	+	0.00334302i
$123$		0			0
$124$	−2944.49	−	16699.0i	−0.191499	−	1.08604i
$125$	−1876.47	−	1083.38i	−0.120094	−	0.0693365i
$126$		0			0
$127$	−12084.8	−	20931.6i	−0.749262	−	1.29776i	−0.948177	−	0.317742i	$-0.897075\pi$
$127$	−12084.8	−	20931.6i	−0.749262	−	1.29776i	0.198915	−	0.980017i	$-0.436258\pi$
$128$	9949.78	+	11857.7i	0.607286	+	0.723736i
$129$		0			0
$130$	−1237.37	+	7017.48i	−0.0732173	+	0.415236i
$131$	−4739.53	+	5648.35i	−0.276180	+	0.329139i	−0.886249	−	0.463210i	$-0.846698\pi$
$131$	−4739.53	+	5648.35i	−0.276180	+	0.329139i	0.610068	+	0.792349i	$0.291142\pi$
$132$		0			0
$133$	−17185.6	−	6255.04i	−0.971540	−	0.353612i
$134$		−	3994.07i		−	0.222437i
$135$		0			0
$136$	4996.37			0.270132
$137$	−3334.13	+	9160.43i	−0.177640	+	0.488062i	−0.996273	−	0.0862549i	$-0.972510\pi$
$137$	−3334.13	+	9160.43i	−0.177640	+	0.488062i	0.818633	+	0.574317i	$0.194732\pi$
$138$		0			0
$139$	−243.736	−	204.519i	−0.0126151	−	0.0105853i	0.636458	−	0.771311i	$-0.280399\pi$
$139$	−243.736	−	204.519i	−0.0126151	−	0.0105853i	−0.649073	+	0.760726i	$0.724843\pi$
$140$	−34404.8	−	6066.49i	−1.75535	−	0.309515i
$141$		0			0
$142$	−2700.22	+	2265.75i	−0.133913	+	0.112366i
$143$	20899.0	−	12066.0i	1.02200	−	0.590054i
$144$		0			0
$145$	−1173.80	+	2033.08i	−0.0558287	+	0.0966981i
$146$	5262.61	−	927.940i	0.246885	−	0.0435325i
$147$		0			0
$148$	−34188.4	+	12443.6i	−1.56083	+	0.568096i
$149$	9232.26	+	25365.4i	0.415849	+	1.14254i	0.954031	+	0.299707i	$0.0968889\pi$
$149$	9232.26	+	25365.4i	0.415849	+	1.14254i	−0.538183	+	0.842828i	$0.680889\pi$
$150$		0			0
$151$	6274.17	+	35582.6i	0.275171	+	1.56057i	0.738419	+	0.674342i	$0.235573\pi$
$151$	6274.17	+	35582.6i	0.275171	+	1.56057i	−0.463248	+	0.886229i	$0.653316\pi$
$152$	−8766.44	−	5061.31i	−0.379434	−	0.219066i
$153$		0			0
$154$	−5862.03	−	10153.3i	−0.247176	−	0.428122i
$155$	27097.9	+	32294.0i	1.12790	+	1.34418i
$156$		0			0
$157$	−1346.51	+	7636.45i	−0.0546275	+	0.309808i	−0.999862	−	0.0165827i	$-0.994721\pi$
$157$	−1346.51	+	7636.45i	−0.0546275	+	0.309808i	0.945235	+	0.326390i	$0.105832\pi$
$158$	1557.93	−	1856.67i	0.0624072	−	0.0743739i
$159$		0			0
$160$	−27684.7	−	10076.4i	−1.08143	−	0.393610i
$161$		−	33116.7i		−	1.27760i
$162$		0			0
$163$	42526.9			1.60062			0.800311	−	0.599585i	$-0.204668\pi$
$163$	42526.9			1.60062			0.800311	+	0.599585i	$0.204668\pi$
$164$	−6279.41	+	17252.5i	−0.233470	+	0.641454i
$165$		0			0
$166$	−1102.70	−	925.273i	−0.0400166	−	0.0335779i
$167$	−27972.6	−	4932.32i	−1.00300	−	0.176855i	−0.352052	−	0.935981i	$-0.614516\pi$
$167$	−27972.6	−	4932.32i	−1.00300	−	0.176855i	−0.650945	+	0.759125i	$0.725627\pi$
$168$		0			0
$169$	−1293.83	+	1085.65i	−0.0453006	+	0.0380117i
$170$	−5124.86	+	2958.84i	−0.177331	+	0.102382i
$171$		0			0
$172$	5414.46	−	9378.12i	0.183020	−	0.317000i
$173$	−34016.6	+	5998.04i	−1.13658	+	0.200409i	−0.710107	−	0.704093i	$-0.751354\pi$
$173$	−34016.6	+	5998.04i	−1.13658	+	0.200409i	−0.426469	+	0.904502i	$0.640243\pi$
$174$		0			0
$175$	42673.8	−	15532.0i	1.39343	−	0.507167i
$176$	9507.92	+	26122.8i	0.306945	+	0.843324i
$177$		0			0
$178$	−1165.96	−	6612.50i	−0.0367997	−	0.208702i
$179$	23626.9	+	13641.0i	0.737396	+	0.425736i	0.821122	−	0.570753i	$-0.193349\pi$
$179$	23626.9	+	13641.0i	0.737396	+	0.425736i	−0.0837257	+	0.996489i	$0.526682\pi$
$180$		0			0
$181$	−5479.39	−	9490.59i	−0.167253	−	0.289692i	0.770200	−	0.637803i	$-0.220156\pi$
$181$	−5479.39	−	9490.59i	−0.167253	−	0.289692i	−0.937453	+	0.348111i	$0.886823\pi$
$182$	−8391.74	−	10000.9i	−0.253343	−	0.301923i
$183$		0			0
$184$	3182.96	−	18051.5i	0.0940147	−	0.533184i
$185$	58141.9	−	69290.9i	1.69881	−	2.02457i
$186$		0			0
$187$	18832.2	+	6854.36i	0.538540	+	0.196012i
$188$		−	23392.6i		−	0.661856i
$189$		0			0
$190$	11989.2			0.332110
$191$	23195.6	−	63729.3i	0.635826	−	1.74692i	−0.0286315	−	0.999590i	$-0.509115\pi$
$191$	23195.6	−	63729.3i	0.635826	−	1.74692i	0.664457	−	0.747326i	$-0.268663\pi$
$192$		0			0
$193$	46751.1	+	39228.8i	1.25510	+	1.05315i	0.996186	+	0.0872505i	$0.0278081\pi$
$193$	46751.1	+	39228.8i	1.25510	+	1.05315i	0.258911	+	0.965901i	$0.416636\pi$
$194$	−6677.63	−	1177.45i	−0.177427	−	0.0312851i
$195$		0			0
$196$	22256.5	−	18675.4i	0.579355	−	0.486137i
$197$	−48769.1	+	28156.8i	−1.25664	+	0.725523i	−0.972420	−	0.233235i	$-0.925069\pi$
$197$	−48769.1	+	28156.8i	−1.25664	+	0.725523i	−0.284223	+	0.958758i	$0.591736\pi$
$198$		0			0
$199$	−7056.96	+	12223.0i	−0.178202	+	0.308654i	−0.941265	−	0.337670i	$-0.890361\pi$
$199$	−7056.96	+	12223.0i	−0.178202	+	0.308654i	0.763063	+	0.646324i	$0.223695\pi$
$200$	24753.8	−	4364.76i	0.618845	−	0.109119i
$201$		0			0
$202$	−15412.0	+	5609.51i	−0.377708	+	0.137474i
$203$	−1471.06	−	4041.70i	−0.0356975	−	0.0980780i
$204$		0			0
$205$	−7926.22	−	44951.8i	−0.188607	−	1.06965i
$206$	9770.76	+	5641.15i	0.230247	+	0.132933i
$207$		0			0
$208$	15477.8	+	26808.4i	0.357753	+	0.619647i
$209$	−26098.8	−	31103.4i	−0.597487	−	0.712057i
$210$		0			0
$211$	−5587.31	+	31687.2i	−0.125498	+	0.711736i	0.855513	+	0.517782i	$0.173242\pi$
$211$	−5587.31	+	31687.2i	−0.125498	+	0.711736i	−0.981011	+	0.193954i	$0.937869\pi$
$212$	−35813.4	+	42680.7i	−0.796845	+	0.949642i
$213$		0			0
$214$	16158.0	+	5881.03i	0.352826	+	0.128418i
$215$			26922.4i			0.582421i
$216$		0			0
$217$	−77236.5			−1.64022
$218$	−831.222	+	2283.76i	−0.0174906	+	0.0480549i
$219$		0			0
$220$	−59415.1	−	49855.2i	−1.22758	−	1.03007i
$221$	21977.2	+	3875.18i	0.449975	+	0.0793427i
$222$		0			0
$223$	15458.5	−	12971.3i	0.310856	−	0.260839i	−0.473990	−	0.880530i	$-0.657187\pi$
$223$	15458.5	−	12971.3i	0.310856	−	0.260839i	0.784846	+	0.619691i	$0.212742\pi$
$224$	46745.5	−	26988.5i	0.931630	−	0.537877i
$225$		0			0
$226$	−11553.9	+	20011.9i	−0.226210	+	0.391807i
$227$	10532.6	−	1857.18i	0.204401	−	0.0360415i	−0.0705099	−	0.997511i	$-0.522463\pi$
$227$	10532.6	−	1857.18i	0.204401	−	0.0360415i	0.274911	+	0.961470i	$0.411352\pi$
$228$		0			0
$229$	27864.4	−	10141.8i	0.531348	−	0.193395i	−0.0623921	−	0.998052i	$-0.519873\pi$
$229$	27864.4	−	10141.8i	0.531348	−	0.193395i	0.593740	+	0.804657i	$0.297651\pi$
$230$	7425.22	+	20400.6i	0.140363	+	0.385645i
$231$		0			0
$232$	−413.393	−	2344.47i	−0.00768045	−	0.0435580i
$233$	12853.1	+	7420.75i	0.236754	+	0.136690i	0.613684	−	0.789552i	$-0.289687\pi$
$233$	12853.1	+	7420.75i	0.236754	+	0.136690i	−0.376930	+	0.926242i	$0.623020\pi$
$234$		0			0
$235$	29078.9	+	50366.1i	0.526553	+	0.912016i
$236$	252.281	+	300.657i	0.00452961	+	0.00539818i
$237$		0			0
$238$	1882.68	−	10677.2i	0.0332370	−	0.188497i
$239$	63446.2	−	75612.3i	1.11073	−	1.32372i	0.169667	−	0.985501i	$-0.445731\pi$
$239$	63446.2	−	75612.3i	1.11073	−	1.32372i	0.941067	−	0.338220i	$-0.109825\pi$
$240$		0			0
$241$	−8491.34	−	3090.60i	−0.146198	−	0.0532118i	0.267885	−	0.963451i	$-0.413675\pi$
$241$	−8491.34	−	3090.60i	−0.146198	−	0.0532118i	−0.414083	+	0.910239i	$0.635898\pi$
$242$		−	8443.99i		−	0.144184i
$243$		0			0
$244$	−641.788			−0.0107798
$245$	−24704.9	+	67876.2i	−0.411577	+	1.13080i
$246$		0			0
$247$	−34634.9	−	29062.1i	−0.567701	−	0.476358i
$248$	−42100.6	−	7423.48i	−0.684518	−	0.120699i
$249$		0			0
$250$	−1993.57	+	1672.80i	−0.0318971	+	0.0267649i
$251$	−63946.3	+	36919.4i	−1.01501	+	0.586013i	−0.912653	−	0.408735i	$-0.865970\pi$
$251$	−63946.3	+	36919.4i	−1.01501	+	0.586013i	−0.102352	+	0.994748i	$0.532637\pi$
$252$		0			0
$253$	36761.4	−	63672.6i	0.574316	−	0.994744i
$254$	−28588.3	+	5040.89i	−0.443120	+	0.0781339i
$255$		0			0
$256$	−13257.2	+	4825.23i	−0.202289	+	0.0736271i
$257$	22515.5	+	61860.9i	0.340891	+	0.936590i	0.985137	+	0.171772i	$0.0549492\pi$
$257$	22515.5	+	61860.9i	0.340891	+	0.936590i	−0.644246	+	0.764819i	$0.722829\pi$
$258$		0			0
$259$	28777.1	+	163203.i	0.428990	+	2.43292i
$260$	−74796.3	−	43183.6i	−1.10645	−	0.638811i
$261$		0			0
$262$	4427.96	+	7669.46i	0.0645062	+	0.111728i
$263$	−43622.8	−	51987.7i	−0.630670	−	0.751604i	0.352195	−	0.935927i	$-0.385435\pi$
$263$	−43622.8	−	51987.7i	−0.630670	−	0.751604i	−0.982866	+	0.184323i	$0.940991\pi$
$264$		0			0
$265$	24053.4	−	136414.i	0.342519	−	1.94252i
$266$	−14119.3	+	16826.7i	−0.199548	+	0.237813i
$267$		0			0
$268$	45490.5	+	16557.2i	0.633361	+	0.230525i
$269$			99903.1i			1.38062i	0.723513	+	0.690310i	$0.242526\pi$
$269$			99903.1i			1.38062i	−0.723513	+	0.690310i	$0.757474\pi$
$270$		0			0
$271$	−126957.			−1.72869			−0.864346	−	0.502897i	$-0.832267\pi$
$271$	−126957.			−1.72869			−0.864346	+	0.502897i	$0.832267\pi$
$272$	−8792.52	+	24157.2i	−0.118843	+	0.326520i
$273$		0			0
$274$	8969.13	+	7525.99i	0.119467	+	0.100245i
$275$	99289.3	+	17507.4i	1.31292	+	0.231503i
$276$		0			0
$277$	−16027.4	+	13448.6i	−0.208883	+	0.175274i	−0.741227	−	0.671254i	$-0.765756\pi$
$277$	−16027.4	+	13448.6i	−0.208883	+	0.175274i	0.532344	+	0.846528i	$0.321311\pi$
$278$	−330.950	+	191.074i	−0.00428226	+	0.00247236i
$279$		0			0
$280$	−44038.8	+	76277.4i	−0.561719	+	0.972926i
$281$	−56865.4	+	10026.9i	−0.720171	+	0.126986i	−0.521710	−	0.853123i	$-0.674706\pi$
$281$	−56865.4	+	10026.9i	−0.720171	+	0.126986i	−0.198462	+	0.980109i	$0.563594\pi$
$282$		0			0
$283$	−64785.9	+	23580.1i	−0.808924	+	0.294424i	−0.713179	−	0.700982i	$-0.752745\pi$
$283$	−64785.9	+	23580.1i	−0.808924	+	0.294424i	−0.0957447	+	0.995406i	$0.530523\pi$
$284$	−14612.2	−	40146.8i	−0.181167	−	0.497753i
$285$		0			0
$286$	−5033.04	−	28543.8i	−0.0615316	−	0.348963i
$287$	72423.8	+	41813.9i	0.879261	+	0.507641i
$288$		0			0
$289$	−32494.1	−	56281.4i	−0.389053	−	0.673859i
$290$	1812.41	+	2159.95i	0.0215507	+	0.0256831i
$291$		0			0
$292$	−11247.1	+	63785.2i	−0.131909	+	0.748091i
$293$	−23649.5	+	28184.4i	−0.275478	+	0.328302i	−0.885989	−	0.463706i	$-0.846519\pi$
$293$	−23649.5	+	28184.4i	−0.275478	+	0.328302i	0.610511	+	0.792007i	$0.290964\pi$
$294$		0			0
$295$	−916.920	−	333.732i	−0.0105363	−	0.00383490i
$296$			91725.7i			1.04691i
$297$		0			0
$298$	32420.7			0.365081
$299$	28001.4	−	76933.2i	0.313211	−	0.860541i
$300$		0			0
$301$	−37785.3	−	31705.6i	−0.417051	−	0.349948i
$302$	42736.9	+	7535.67i	0.468586	+	0.0826244i
$303$		0			0
$304$	39898.3	−	33478.6i	0.431725	−	0.362260i
$305$	1381.82	−	797.793i	0.0148543	−	0.00857611i
$306$		0			0
$307$	−16983.2	+	29415.7i	−0.180195	+	0.312107i	−0.941947	−	0.335762i	$-0.891006\pi$
$307$	−16983.2	+	29415.7i	−0.180195	+	0.312107i	0.761752	+	0.647869i	$0.224339\pi$
$308$	139942.	−	24675.6i	1.47519	−	0.260116i
$309$		0			0
$310$	47579.5	−	17317.5i	0.495104	−	0.180203i
$311$	−19832.8	−	54490.3i	−0.205052	−	0.563376i	0.793953	−	0.607980i	$-0.208020\pi$
$311$	−19832.8	−	54490.3i	−0.205052	−	0.563376i	−0.999005	+	0.0446036i	$0.985798\pi$
$312$		0			0
$313$	−12985.0	−	73641.4i	−0.132542	−	0.751681i	−0.976540	−	0.215335i	$-0.930916\pi$
$313$	−12985.0	−	73641.4i	−0.132542	−	0.751681i	0.843999	−	0.536345i	$-0.180196\pi$
$314$	8065.60	+	4656.68i	0.0818046	+	0.0472299i
$315$		0			0
$316$	14688.3	+	25440.8i	0.147094	+	0.254775i
$317$	−7859.12	−	9366.13i	−0.0782088	−	0.0932056i	0.725521	−	0.688200i	$-0.241599\pi$
$317$	−7859.12	−	9366.13i	−0.0782088	−	0.0932056i	−0.803730	+	0.594994i	$0.797154\pi$
$318$		0			0
$319$	1658.15	−	9403.83i	0.0162945	−	0.0924109i
$320$	47544.6	−	56661.4i	0.464303	−	0.553334i
$321$		0			0
$322$	−37376.5	−	13603.9i	−0.360485	−	0.131206i
$323$		−	37547.5i		−	0.359895i
$324$		0			0
$325$	112268.			1.06290
$326$	17469.5	−	47997.2i	0.164379	−	0.451628i
$327$		0			0
$328$	35458.4	+	29753.1i	0.329588	+	0.276557i
$329$	−104933.	−	18502.6i	−0.969442	−	0.170939i
$330$		0			0
$331$	41511.0	−	34831.9i	0.378885	−	0.317922i	−0.433380	−	0.901212i	$-0.642679\pi$
$331$	41511.0	−	34831.9i	0.378885	−	0.317922i	0.812265	+	0.583289i	$0.198235\pi$
$332$	15109.6	−	8723.51i	0.137081	−	0.0791435i
$333$		0			0
$334$	−17057.6	+	29544.6i	−0.152906	+	0.264841i
$335$	−118526.	+	20899.4i	−1.05615	+	0.186228i
$336$		0			0
$337$	−83937.6	+	30550.8i	−0.739089	+	0.269006i	−0.684007	−	0.729475i	$-0.739764\pi$
$337$	−83937.6	+	30550.8i	−0.739089	+	0.269006i	−0.0550821	+	0.998482i	$0.517542\pi$
$338$	693.810	+	1906.23i	0.00607306	+	0.0166856i
$339$		0			0
$340$	−12454.9	−	70635.3i	−0.107741	−	0.611032i
$341$	−148501.	−	85736.9i	−1.27708	−	0.737325i
$342$		0			0
$343$	13433.9	+	23268.3i	0.114187	+	0.197777i
$344$	−17548.9	−	20914.0i	−0.148297	−	0.176734i
$345$		0			0
$346$	−7204.03	+	40856.1i	−0.0601760	+	0.341275i
$347$	−117336.	+	139835.i	−0.974476	+	1.16134i	0.0124111	+	0.999923i	$0.496049\pi$
$347$	−117336.	+	139835.i	−0.974476	+	1.16134i	−0.986887	+	0.161412i	$0.948395\pi$
$348$		0			0
$349$	149797.	+	54521.6i	1.22985	+	0.447628i	0.873546	−	0.486742i	$-0.161815\pi$
$349$	149797.	+	54521.6i	1.22985	+	0.447628i	0.356303	+	0.934370i	$0.384037\pi$
$350$		−	54543.3i		−	0.445252i
$351$		0			0
$352$	119835.			0.967161
$353$	66345.1	−	182282.i	0.532426	−	1.46283i	−0.323748	−	0.946143i	$-0.604943\pi$
$353$	66345.1	−	182282.i	0.532426	−	1.46283i	0.856175	−	0.516686i	$-0.172835\pi$
$354$		0			0
$355$	81366.8	+	68274.9i	0.645640	+	0.541756i
$356$	80146.6	+	14132.0i	0.632390	+	0.111507i
$357$		0			0
$358$	25101.3	−	21062.5i	0.195853	−	0.164340i
$359$	111366.	−	64297.3i	0.864101	−	0.498889i	−0.00128245	−	0.999999i	$-0.500408\pi$
$359$	111366.	−	64297.3i	0.864101	−	0.498889i	0.865383	+	0.501110i	$0.167075\pi$
$360$		0			0
$361$	27125.0	−	46981.8i	0.208140	−	0.360509i
$362$	−12962.2	+	2285.59i	−0.0989151	+	0.0174414i
$363$		0			0
$364$	148693.	−	54119.7i	1.12224	−	0.408463i
$365$	−55074.3	−	151315.i	−0.413393	−	1.13579i
$366$		0			0
$367$	−863.036	−	4894.52i	−0.00640762	−	0.0363394i	0.981436	−	0.191788i	$-0.0614287\pi$
$367$	−863.036	−	4894.52i	−0.00640762	−	0.0363394i	−0.987844	+	0.155449i	$0.950318\pi$
$368$	81676.8	+	47156.2i	0.603119	+	0.348211i
$369$		0			0
$370$	−54319.8	−	94084.6i	−0.396784	−	0.687251i
$371$	163128.	+	194408.i	1.18517	+	1.41243i
$372$		0			0
$373$	137.489	−	779.736i	0.000988209	−	0.00560441i	−0.984310	−	0.176450i	$-0.943539\pi$
$373$	137.489	−	779.736i	0.000988209	−	0.00560441i	0.985298	+	0.170845i	$0.0546498\pi$
$374$	15472.1	−	18438.9i	0.110613	−	0.131823i
$375$		0			0
$376$	−55419.5	−	20171.0i	−0.392001	−	0.142677i
$377$		−	10633.1i		−	0.0748130i
$378$		0			0
$379$	53057.5			0.369376			0.184688	−	0.982797i	$-0.440873\pi$
$379$	53057.5			0.369376			0.184688	+	0.982797i	$0.440873\pi$
$380$	−49700.5	+	136551.i	−0.344186	+	0.945643i
$381$		0			0
$382$	−62398.3	−	52358.4i	−0.427608	−	0.358806i
$383$	233753.	+	41216.9i	1.59352	+	0.280981i	0.898822	−	0.438315i	$-0.144424\pi$
$383$	233753.	+	41216.9i	1.59352	+	0.280981i	0.694703	+	0.719296i	$0.255536\pi$
$384$		0			0
$385$	−270633.	+	227088.i	−1.82582	+	1.53205i
$386$	63479.7	−	36650.0i	0.426049	−	0.245980i
$387$		0			0
$388$	41092.2	−	71173.9i	0.272958	−	0.472778i
$389$	−51131.7	+	9015.90i	−0.337902	+	0.0595813i	−0.340025	−	0.940416i	$-0.610435\pi$
$389$	−51131.7	+	9015.90i	−0.337902	+	0.0595813i	0.00212264	+	0.999998i	$0.499324\pi$
$390$		0			0
$391$	63890.3	−	23254.2i	0.417909	−	0.152106i
$392$	−25052.6	−	68831.4i	−0.163035	−	0.447935i
$393$		0			0
$394$	11744.9	+	66608.8i	0.0756585	+	0.429081i
$395$	−63249.9	−	36517.3i	−0.405383	−	0.234048i
$396$		0			0
$397$	−111904.	−	193824.i	−0.710011	−	1.22977i	−0.964852	−	0.262792i	$-0.915357\pi$
$397$	−111904.	−	193824.i	−0.710011	−	1.22977i	0.254842	−	0.966983i	$-0.417977\pi$
$398$	10896.4	+	12985.8i	0.0687884	+	0.0819788i
$399$		0			0
$400$	−22457.8	+	127365.i	−0.140361	+	0.796029i
$401$	−133605.	+	159224.i	−0.830871	+	0.990194i	0.169118	+	0.985596i	$0.445908\pi$
$401$	−133605.	+	159224.i	−0.830871	+	0.990194i	−0.999989	+	0.00459801i	$0.998536\pi$
$402$		0			0
$403$	−179428.	−	65306.4i	−1.10479	−	0.402111i
$404$		−	198789.i		−	1.21795i
$405$		0			0
$406$	−5165.88			−0.0313395
$407$	−125836.	+	345731.i	−0.759652	+	2.08713i
$408$		0			0
$409$	108001.	+	90623.7i	0.645627	+	0.541746i	0.905741	−	0.423832i	$-0.139315\pi$
$409$	108001.	+	90623.7i	0.645627	+	0.541746i	−0.260113	+	0.965578i	$0.583760\pi$
$410$	−53990.0	−	9519.90i	−0.321178	−	0.0566323i
$411$		0			0
$412$	−104754.	+	87899.1i	−0.617130	+	0.517834i
$413$	1548.21	−	893.862i	0.00907677	−	0.00524047i
$414$		0			0
$415$	−21688.0	+	37564.8i	−0.125928	+	0.218114i
$416$	131414.	−	23171.9i	0.759373	−	0.133898i
$417$		0			0
$418$	−45825.3	+	16679.0i	−0.262272	+	0.0954594i
$419$	−40012.8	−	109934.i	−0.227914	−	0.626189i	0.772042	−	0.635572i	$-0.219236\pi$
$419$	−40012.8	−	109934.i	−0.227914	−	0.626189i	−0.999956	+	0.00938263i	$0.997013\pi$
$420$		0			0
$421$	−32654.4	−	185192.i	−0.184237	−	1.04486i	−0.926932	−	0.375230i	$-0.877564\pi$
$421$	−32654.4	−	185192.i	−0.184237	−	1.04486i	0.742695	−	0.669630i	$-0.233547\pi$
$422$	33467.9	+	19322.7i	0.187933	+	0.108503i
$423$		0			0
$424$	70233.7	+	121648.i	0.390673	+	0.676666i
$425$	59930.2	+	71422.1i	0.331794	+	0.395416i
$426$		0			0
$427$	−507.628	+	2878.90i	−0.00278413	+	0.0157896i
$428$	−133964.	+	159652.i	−0.731309	+	0.871541i
$429$		0			0
$430$	30385.4	+	11059.4i	0.164334	+	0.0598129i
$431$		−	195978.i		−	1.05500i	−0.849555	−	0.527500i	$-0.823129\pi$
$431$		−	195978.i		−	1.05500i	0.849555	−	0.527500i	$-0.176871\pi$
$432$		0			0
$433$	14688.2			0.0783414			0.0391707	−	0.999233i	$-0.487528\pi$
$433$	14688.2			0.0783414			0.0391707	+	0.999233i	$0.487528\pi$
$434$	−31727.8	+	87171.5i	−0.168446	+	0.462802i
$435$		0			0
$436$	−22565.2	−	18934.4i	−0.118704	−	0.0996045i
$437$	−135656.	−	23919.8i	−0.710356	−	0.125255i
$438$		0			0
$439$	205802.	−	172688.i	1.06788	−	0.896054i	0.0730172	−	0.997331i	$-0.476737\pi$
$439$	205802.	−	172688.i	1.06788	−	0.896054i	0.994858	+	0.101277i	$0.0322927\pi$
$440$	−169345.	+	97771.1i	−0.874714	+	0.505016i
$441$		0			0
$442$	13401.6	−	23212.3i	0.0685982	−	0.118816i
$443$	197082.	−	34750.8i	1.00424	−	0.177075i	0.352740	−	0.935721i	$-0.385250\pi$
$443$	197082.	−	34750.8i	1.00424	−	0.177075i	0.651503	+	0.758646i	$0.274139\pi$
$444$		0			0
$445$	−190129.	+	69201.3i	−0.960126	+	0.349457i
$446$	−8289.58	−	22775.4i	−0.0416738	−	0.114498i
$447$		0			0
$448$	23532.0	+	133457.i	0.117247	+	0.664942i
$449$	203083.	+	117250.i	1.00735	+	0.581595i	0.910415	−	0.413695i	$-0.135762\pi$
$449$	203083.	+	117250.i	1.00735	+	0.581595i	0.0969372	+	0.995290i	$0.469095\pi$
$450$		0			0
$451$	92831.6	+	160789.i	0.456397	+	0.790503i
$452$	−180030.	−	214552.i	−0.881187	−	1.05016i
$453$		0			0
$454$	2230.59	−	12650.3i	0.0108220	−	0.0613748i
$455$	−252872.	+	301361.i	−1.22145	+	1.45567i
$456$		0			0
$457$	−323870.	−	117879.i	−1.55074	−	0.564423i	−0.582148	−	0.813083i	$-0.697788\pi$
$457$	−323870.	−	117879.i	−1.55074	−	0.564423i	−0.968591	+	0.248660i	$0.920010\pi$
$458$		−	35614.8i		−	0.169785i
$459$		0			0
$460$	−263134.			−1.24354
$461$	49596.9	−	136266.i	0.233374	−	0.641190i	−0.766626	−	0.642094i	$-0.778066\pi$
$461$	49596.9	−	136266.i	0.233374	−	0.641190i	1.00000		0.000904688i	$0.000287971\pi$
$462$		0			0
$463$	61984.1	+	52010.8i	0.289147	+	0.242623i	0.775810	−	0.630967i	$-0.217342\pi$
$463$	61984.1	+	52010.8i	0.289147	+	0.242623i	−0.486663	+	0.873590i	$0.661786\pi$
$464$	12062.9	+	2127.01i	0.0560293	+	0.00987948i
$465$		0			0
$466$	13655.2	−	11458.1i	0.0628819	−	0.0527642i
$467$	−47739.7	+	27562.5i	−0.218900	+	0.126382i	−0.605441	−	0.795890i	$-0.707003\pi$
$467$	−47739.7	+	27562.5i	−0.218900	+	0.126382i	0.386541	+	0.922272i	$0.373670\pi$
$468$		0			0
$469$	110253.	−	190963.i	0.501237	−	0.868167i
$470$	68790.0	−	12129.5i	0.311408	−	0.0549096i
$471$		0			0
$472$	929.824	−	338.428i	0.00417366	−	0.00151909i
$473$	−37453.8	−	102903.i	−0.167407	−	0.459946i
$474$		0			0
$475$	−32801.0	−	186024.i	−0.145378	−	0.824482i
$476$	113804.	+	65704.5i	0.502275	+	0.289989i
$477$		0			0
$478$	−59275.4	−	102668.i	−0.259429	−	0.449344i
$479$	78857.1	+	93978.2i	0.343692	+	0.409597i	0.910007	−	0.414592i	$-0.136076\pi$
$479$	78857.1	+	93978.2i	0.343692	+	0.409597i	−0.566315	+	0.824189i	$0.691631\pi$
$480$		0			0
$481$	−71142.4	+	403469.i	−0.307495	+	1.74389i
$482$	−6976.28	+	8314.01i	−0.0300282	+	0.0357863i
$483$		0			0
$484$	96172.9	+	35004.1i	0.410546	+	0.149427i
$485$			204324.i			0.868630i
$486$		0			0
$487$	−159807.			−0.673810			−0.336905	−	0.941539i	$-0.609380\pi$
$487$	−159807.			−0.673810			−0.336905	+	0.941539i	$0.609380\pi$
$488$	−553.402	+	1520.46i	−0.00232381	+	0.00638463i
$489$		0			0
$490$	66458.7	+	55765.5i	0.276796	+	0.232259i
$491$	270288.	+	47659.0i	1.12115	+	0.197689i	0.703345	−	0.710848i	$-0.251689\pi$
$491$	270288.	+	47659.0i	1.12115	+	0.197689i	0.417804	+	0.908537i	$0.362800\pi$
$492$		0			0
$493$	6764.48	−	5676.07i	0.0278318	−	0.0233536i
$494$	−47028.0	+	27151.6i	−0.192709	+	0.111261i
$495$		0			0
$496$	109980.	−	190491.i	0.447045	−	0.774304i
$497$	−191646.	+	33792.3i	−0.775866	+	0.136806i
$498$		0			0
$499$	91652.9	−	33358.9i	0.368082	−	0.133971i	−0.151355	−	0.988479i	$-0.548364\pi$
$499$	91652.9	−	33358.9i	0.368082	−	0.133971i	0.519438	+	0.854508i	$0.326141\pi$
$500$	−10788.2	−	29640.3i	−0.0431528	−	0.118561i
$501$		0			0
$502$	15400.0	+	87337.8i	0.0611102	+	0.346573i
$503$	−165783.	−	95715.0i	−0.655247	−	0.378307i	0.135217	−	0.990816i	$-0.456827\pi$
$503$	−165783.	−	95715.0i	−0.655247	−	0.378307i	−0.790463	+	0.612509i	$0.790160\pi$
$504$		0			0
$505$	247110.	+	428008.i	0.968965	+	1.67830i
$506$	−56761.7	−	67645.9i	−0.221694	−	0.264205i
$507$		0			0
$508$	61097.9	−	346503.i	0.236755	−	1.34270i
$509$	321632.	−	383306.i	1.24143	−	1.47948i	0.421705	−	0.906733i	$-0.361432\pi$
$509$	321632.	−	383306.i	1.24143	−	1.47948i	0.819729	−	0.572751i	$-0.194124\pi$
$510$		0			0
$511$	277229.	+	100903.i	1.06169	+	0.386422i
$512$			264610.i			1.00941i
$513$		0			0
$514$	79067.1			0.299275
$515$	116278.	−	319471.i	0.438413	−	1.20453i
$516$		0			0
$517$	−181214.	−	152057.i	−0.677970	−	0.568884i
$518$	196017.	+	34563.1i	0.730524	+	0.128811i
$519$		0			0
$520$	−166802.	+	139963.i	−0.616871	+	0.517616i
$521$	154680.	−	89304.6i	0.569848	−	0.329002i	−0.187241	−	0.982314i	$-0.559954\pi$
$521$	154680.	−	89304.6i	0.569848	−	0.329002i	0.757089	+	0.653312i	$0.226621\pi$
$522$		0			0
$523$	−99520.1	+	172374.i	−0.363837	+	0.630185i	−0.988589	−	0.150639i	$-0.951867\pi$
$523$	−99520.1	+	172374.i	−0.363837	+	0.630185i	0.624752	+	0.780824i	$0.285200\pi$
$524$	−105707.	+	18639.0i	−0.384983	+	0.0678830i
$525$		0			0
$526$	−76594.6	+	27878.2i	−0.276839	+	0.100761i
$527$	−54234.7	−	149009.i	−0.195279	−	0.536525i
$528$		0			0
$529$	5280.08	+	29944.8i	0.0188681	+	0.107006i
$530$	−144080.	−	83184.5i	−0.512922	−	0.296136i
$531$		0			0
$532$	−133117.	−	230565.i	−0.470338	−	0.814650i
$533$	132892.	+	158375.i	0.467784	+	0.557483i
$534$		0			0
$535$	89974.6	−	510271.i	0.314349	−	1.78276i
$536$	78451.4	−	93494.7i	0.273068	−	0.325430i
$537$		0			0
$538$	112754.	+	41039.0i	0.389553	+	0.141786i
$539$		−	293807.i		−	1.01131i
$540$		0			0
$541$	405776.			1.38641			0.693204	−	0.720741i	$-0.256198\pi$
$541$	405776.			1.38641			0.693204	+	0.720741i	$0.256198\pi$
$542$	−52152.4	+	143287.i	−0.177531	+	0.487764i
$543$		0			0
$544$	84891.8	+	71232.6i	0.286859	+	0.240703i
$545$	72121.5	+	12717.0i	0.242813	+	0.0428144i
$546$		0			0
$547$	105202.	−	88274.6i	0.351599	−	0.295026i	−0.449833	−	0.893113i	$-0.648516\pi$
$547$	105202.	−	88274.6i	0.351599	−	0.295026i	0.801432	+	0.598086i	$0.204072\pi$
$548$	−122898.	+	70955.4i	−0.409246	+	0.236279i
$549$		0			0
$550$	60546.2	−	104869.i	0.200153	−	0.346675i
$551$	−17618.6	+	3106.63i	−0.0580320	+	0.0102326i
$552$		0			0
$553$	125739.	−	45765.2i	0.411168	−	0.149653i
$554$	8594.63	+	23613.5i	0.0280032	+	0.0769381i
$555$		0			0
$556$	−804.305	−	4561.44i	−0.00260178	−	0.0147555i
$557$	−61387.4	−	35442.0i	−0.197865	−	0.114237i	0.397794	−	0.917475i	$-0.369776\pi$
$557$	−61387.4	−	35442.0i	−0.197865	−	0.114237i	−0.595659	+	0.803237i	$0.703109\pi$
$558$		0			0
$559$	−60970.6	−	105604.i	−0.195118	−	0.337954i
$560$	−291300.	−	347158.i	−0.928890	−	1.10701i
$561$		0			0
$562$	−12043.0	+	68299.0i	−0.0381295	+	0.216243i
$563$	−269692.	+	321407.i	−0.850847	+	1.01400i	0.148837	+	0.988862i	$0.452447\pi$
$563$	−269692.	+	321407.i	−0.850847	+	1.01400i	−0.999684	+	0.0251387i	$0.991997\pi$
$564$		0			0
$565$	654323.	+	238154.i	2.04972	+	0.746038i
$566$			82805.8i			0.258481i
$567$		0			0
$568$	−107712.			−0.333861
$569$	164403.	−	451694.i	0.507791	−	1.39515i	−0.375719	−	0.926734i	$-0.622604\pi$
$569$	164403.	−	451694.i	0.507791	−	1.39515i	0.883510	−	0.468412i	$-0.155174\pi$
$570$		0			0
$571$	−236655.	−	198577.i	−0.725844	−	0.609055i	0.203151	−	0.979147i	$-0.434882\pi$
$571$	−236655.	−	198577.i	−0.725844	−	0.609055i	−0.928995	+	0.370092i	$0.879326\pi$
$572$	345964.	+	61002.7i	1.05740	+	0.186448i
$573$		0			0
$574$	76943.3	−	64563.1i	0.233532	−	0.195957i
$575$	296221.	−	171023.i	0.895942	−	0.517273i
$576$		0			0
$577$	−122389.	+	211984.i	−0.367612	+	0.636723i	−0.989192	−	0.146628i	$-0.953158\pi$
$577$	−122389.	+	211984.i	−0.367612	+	0.636723i	0.621579	+	0.783351i	$0.286491\pi$
$578$	−76869.1	+	13554.1i	−0.230089	+	0.0405709i
$579$		0			0
$580$	−32114.0	+	11688.5i	−0.0954637	+	0.0347459i
$581$	−27180.4	−	74677.6i	−0.0805201	−	0.221227i
$582$		0			0
$583$	97837.8	+	554866.i	0.287852	+	1.63249i
$584$	141416.	+	81646.3i	0.414640	+	0.239393i
$585$		0			0
$586$	22094.8	+	38269.3i	0.0643421	+	0.111444i
$587$	169517.	+	202023.i	0.491969	+	0.586306i	0.953717	−	0.300705i	$-0.0972221\pi$
$587$	169517.	+	202023.i	0.491969	+	0.586306i	−0.461748	+	0.887011i	$0.652778\pi$
$588$		0			0
$589$	−55787.1	+	316384.i	−0.160806	+	0.911978i
$590$	−753.320	+	897.771i	−0.00216409	+	0.00257906i
$591$		0			0
$592$	−443490.	−	161417.i	−1.26544	−	0.460582i
$593$			241174.i			0.685837i	0.939365	+	0.342919i	$0.111416\pi$
$593$			241174.i			0.685837i	−0.939365	+	0.342919i	$0.888584\pi$
$594$		0			0
$595$	−326703.			−0.922826
$596$	−134398.	+	369256.i	−0.378356	+	1.03952i
$597$		0			0
$598$	−75326.6	−	63206.5i	−0.210642	−	0.176750i
$599$	−448712.	−	79120.0i	−1.25059	−	0.220512i	−0.491139	−	0.871081i	$-0.663419\pi$
$599$	−448712.	−	79120.0i	−1.25059	−	0.220512i	−0.759447	+	0.650569i	$0.774531\pi$
$600$		0			0
$601$	426431.	−	357818.i	1.18059	−	0.990634i	0.180617	−	0.983554i	$-0.442191\pi$
$601$	426431.	−	357818.i	1.18059	−	0.990634i	0.999975	−	0.00708070i	$-0.00225387\pi$
$602$	−51305.6	+	29621.3i	−0.141570	+	0.0817357i
$603$		0			0
$604$	−262991.	+	455514.i	−0.720887	+	1.24861i
$605$	−250580.	+	44184.1i	−0.684599	+	0.120713i
$606$		0			0
$607$	196829.	−	71639.9i	0.534210	−	0.194437i	−0.0608072	−	0.998150i	$-0.519367\pi$
$607$	196829.	−	71639.9i	0.534210	−	0.194437i	0.595017	+	0.803713i	$0.297145\pi$
$608$	−76789.5	−	210977.i	−0.207728	−	0.570727i
$609$		0			0
$610$	−332.779	−	1887.29i	−0.000894328	−	0.00507198i
$611$	−228126.	−	131709.i	−0.611072	−	0.352802i
$612$		0			0
$613$	13308.1	+	23050.4i	0.0354157	+	0.0613419i	0.883190	−	0.469015i	$-0.155391\pi$
$613$	13308.1	+	23050.4i	0.0354157	+	0.0613419i	−0.847774	+	0.530357i	$0.822058\pi$
$614$	26223.0	+	31251.4i	0.0695578	+	0.0828957i
$615$		0			0
$616$	62210.8	−	352815.i	0.163947	−	0.929791i
$617$	172424.	−	205487.i	0.452927	−	0.539777i	−0.490463	−	0.871462i	$-0.663172\pi$
$617$	172424.	−	205487.i	0.452927	−	0.539777i	0.943390	+	0.331684i	$0.107617\pi$
$618$		0			0
$619$	−417414.	−	151926.i	−1.08940	−	0.396508i	−0.265999	−	0.963973i	$-0.585702\pi$
$619$	−417414.	−	151926.i	−1.08940	−	0.396508i	−0.823397	+	0.567466i	$0.807924\pi$
$620$			613696.i			1.59650i
$621$		0			0
$622$	−69646.5			−0.180019
$623$	126785.	−	348340.i	0.326658	−	0.897484i
$624$		0			0
$625$	−267827.	−	224733.i	−0.685637	−	0.575317i
$626$	−88448.0	−	15595.8i	−0.225704	−	0.0397977i
$627$		0			0
$628$	−86472.8	+	72559.3i	−0.219260	+	0.183981i
$629$	−294652.	+	170118.i	−0.744747	+	0.429980i
$630$		0			0
$631$	−330922.	+	573174.i	−0.831127	+	1.43955i	0.0660179	+	0.997818i	$0.478971\pi$
$631$	−330922.	+	573174.i	−0.831127	+	1.43955i	−0.897145	+	0.441736i	$0.854363\pi$
$632$	72937.3	−	12860.8i	0.182606	−	0.0321984i
$633$		0			0
$634$	−13799.3	+	5022.55i	−0.0343305	+	0.0124953i
$635$	299183.	+	821998.i	0.741974	+	2.03856i
$636$		0			0
$637$	−56811.8	−	322196.i	−0.140010	−	0.794037i
$638$	−9932.30	−	5734.41i	−0.0244010	−	0.0140879i
$639$		0			0
$640$	−280111.	−	485166.i	−0.683864	−	1.18449i
$641$	−217131.	−	258767.i	−0.528452	−	0.629785i	0.434105	−	0.900862i	$-0.357065\pi$
$641$	−217131.	−	258767.i	−0.528452	−	0.629785i	−0.962558	+	0.271077i	$0.912620\pi$
$642$		0			0
$643$	−2876.13	+	16311.3i	−0.00695642	+	0.0394518i	−0.988088	−	0.153887i	$-0.950821\pi$
$643$	−2876.13	+	16311.3i	−0.00695642	+	0.0394518i	0.981132	+	0.193339i	$0.0619318\pi$
$644$	309884.	−	369306.i	0.747184	−	0.890459i
$645$		0			0
$646$	−42377.2	−	15424.1i	−0.101547	−	0.0369601i
$647$			71969.5i			0.171925i	0.996298	+	0.0859627i	$0.0273966\pi$
$647$			71969.5i			0.171925i	−0.996298	+	0.0859627i	$0.972603\pi$
$648$		0			0
$649$	3968.95			0.00942294
$650$	46118.5	−	126709.i	0.109156	−	0.299904i
$651$		0			0
$652$	474246.	+	397939.i	1.11560	+	0.936099i
$653$	552513.	+	97422.9i	1.29573	+	0.228473i	0.778648	−	0.627461i	$-0.215906\pi$
$653$	552513.	+	97422.9i	1.29573	+	0.228473i	0.517086	+	0.855934i	$0.327017\pi$
$654$		0			0
$655$	204426.	−	171534.i	0.476489	−	0.399822i
$656$	−206254.	+	119081.i	−0.479287	+	0.276716i
$657$		0			0
$658$	−63988.0	+	110830.i	−0.147790	+	0.255981i
$659$	131239.	−	23140.9i	0.302197	−	0.0532855i	−0.0204935	−	0.999790i	$-0.506524\pi$
$659$	131239.	−	23140.9i	0.302197	−	0.0532855i	0.322691	+	0.946504i	$0.395413\pi$
$660$		0			0
$661$	−150281.	+	54697.6i	−0.343954	+	0.125189i	−0.508220	−	0.861227i	$-0.669696\pi$
$661$	−150281.	+	54697.6i	−0.343954	+	0.125189i	0.164267	+	0.986416i	$0.447474\pi$
$662$	−22260.1	−	61159.1i	−0.0507938	−	0.139555i
$663$		0			0
$664$	−7638.17	−	43318.2i	−0.0173242	−	0.0982505i
$665$	573222.	+	330950.i	1.29622	+	0.748374i
$666$		0			0
$667$	−16197.9	−	28055.5i	−0.0364087	−	0.0630618i
$668$	−265787.	−	316753.i	−0.595636	−	0.709851i
$669$		0			0
$670$	−25101.5	+	142358.i	−0.0559178	+	0.317126i
$671$	−4171.74	+	4971.69i	−0.00926558	+	0.0110423i
$672$		0			0
$673$	−126102.	−	45897.4i	−0.278415	−	0.101335i	0.199039	−	0.979992i	$-0.436218\pi$
$673$	−126102.	−	45897.4i	−0.278415	−	0.101335i	−0.477454	+	0.878657i	$0.658440\pi$
$674$			107284.i			0.236166i
$675$		0			0
$676$	−24587.1			−0.0538040
$677$	−271246.	+	745241.i	−0.591814	+	1.62600i	0.175322	+	0.984511i	$0.443903\pi$
$677$	−271246.	+	745241.i	−0.591814	+	1.62600i	−0.767136	+	0.641485i	$0.778319\pi$
$678$		0			0
$679$	−286766.	−	240625.i	−0.621996	−	0.521917i
$680$	−178082.	−	31400.6i	−0.385125	−	0.0679079i
$681$		0			0
$682$	−157768.	+	132383.i	−0.339195	+	0.284618i
$683$	−91618.7	+	52896.1i	−0.196401	+	0.113392i	−0.594975	−	0.803744i	$-0.702838\pi$
$683$	−91618.7	+	52896.1i	−0.196401	+	0.113392i	0.398575	+	0.917136i	$0.369505\pi$
$684$		0			0
$685$	176406.	−	305545.i	0.375952	−	0.651169i
$686$	31779.8	−	5603.63i	0.0675309	−	0.0119075i
$687$		0			0
$688$	132001.	−	48044.3i	0.278868	−	0.101500i
$689$	214583.	+	589561.i	0.452018	+	1.24191i
$690$		0			0
$691$	72008.8	+	408382.i	0.150810	+	0.855285i	0.962517	+	0.271221i	$0.0874273\pi$
$691$	72008.8	+	408382.i	0.150810	+	0.855285i	−0.811707	+	0.584064i	$0.801462\pi$
$692$	−435467.	−	251417.i	−0.909375	−	0.525028i
$693$		0			0
$694$	109622.	+	189871.i	0.227604	+	0.394221i
$695$	7401.96	+	8821.31i	0.0153242	+	0.0182626i
$696$		0			0
$697$	−29814.2	+	169085.i	−0.0613703	+	0.348048i
$698$	123069.	−	146668.i	0.252604	−	0.301041i
$699$		0			0
$700$	621222.	+	226106.i	1.26780	+	0.461441i
$701$		−	209011.i		−	0.425336i	−0.977124	−	0.212668i	$-0.931785\pi$
$701$		−	209011.i		−	0.425336i	0.977124	−	0.212668i	$-0.0682153\pi$
$702$		0			0
$703$	689315.			1.39478
$704$	−102900.	+	282715.i	−0.207620	+	0.570432i
$705$		0			0
$706$	−178475.	−	149758.i	−0.358070	−	0.300456i
$707$	−891717.	−	157234.i	−1.78397	−	0.314562i
$708$		0			0
$709$	−537635.	+	451129.i	−1.06954	+	0.897447i	−0.995010	−	0.0997723i	$-0.968189\pi$
$709$	−537635.	+	451129.i	−1.06954	+	0.897447i	−0.0745252	+	0.997219i	$0.523744\pi$
$710$	110482.	−	63786.6i	0.219166	−	0.126536i
$711$		0			0
$712$	102589.	−	177690.i	0.202368	−	0.350511i
$713$	−572906.	+	101019.i	−1.12695	+	0.198712i
$714$		0			0
$715$	−820717.	+	298717.i	−1.60539	+	0.584316i
$716$	135835.	+	373205.i	0.264964	+	0.727983i
$717$		0			0
$718$	−26820.0	−	152104.i	−0.0520248	−	0.295047i
$719$	−454446.	−	262374.i	−0.879072	−	0.507532i	−0.00871937	−	0.999962i	$-0.502775\pi$
$719$	−454446.	−	262374.i	−0.879072	−	0.507532i	−0.870352	+	0.492430i	$0.836109\pi$
$720$		0			0
$721$	311437.	+	539425.i	0.599101	+	1.03767i
$722$	−41882.5	−	49913.7i	−0.0803449	−	0.0957514i
$723$		0			0
$724$	27702.4	−	157108.i	0.0528495	−	0.299724i
$725$	28555.1	−	34030.7i	0.0543260	−	0.0647432i
$726$		0			0
$727$	−231474.	−	84249.7i	−0.437959	−	0.159404i	0.113624	−	0.993524i	$-0.463754\pi$
$727$	−231474.	−	84249.7i	−0.437959	−	0.159404i	−0.551583	+	0.834120i	$0.685976\pi$
$728$		−	398935.i		−	0.752730i
$729$		0			0
$730$	−193403.			−0.362926
$731$	34635.6	−	95160.6i	0.0648169	−	0.178083i
$732$		0			0
$733$	365504.	+	306694.i	0.680274	+	0.570817i	0.916086	−	0.400981i	$-0.131331\pi$
$733$	365504.	+	306694.i	0.680274	+	0.570817i	−0.235813	+	0.971799i	$0.575775\pi$
$734$	−5878.63	−	1036.56i	−0.0109115	−	0.00192399i
$735$		0			0
$736$	311439.	−	261328.i	0.574932	−	0.482425i
$737$	423959.	−	244773.i	0.780530	−	0.450639i
$738$		0			0
$739$	470387.	−	814735.i	0.861324	−	1.49186i	−0.00932662	−	0.999957i	$-0.502969\pi$
$739$	470387.	−	814735.i	0.861324	−	1.49186i	0.870651	−	0.491901i	$-0.163698\pi$
$740$	1.29676e6	−	228653.i	2.36807	−	0.417555i
$741$		0			0
$742$	286426.	−	104251.i	0.520242	−	0.189352i
$743$	−229947.	−	631774.i	−0.416533	−	1.14442i	−0.953653	−	0.300910i	$-0.902710\pi$
$743$	−229947.	−	631774.i	−0.416533	−	1.14442i	0.537119	−	0.843506i	$-0.319513\pi$
$744$		0			0
$745$	−169645.	−	962103.i	−0.305652	−	1.73344i
$746$	−823.556	−	475.480i	−0.00147984	−	0.000854387i
$747$		0			0
$748$	145871.	+	252657.i	0.260716	+	0.451573i
$749$	610200.	+	727208.i	1.08770	+	1.29627i
$750$		0			0
$751$	68724.3	−	389755.i	0.121851	−	0.691053i	−0.861277	−	0.508136i	$-0.830335\pi$
$751$	68724.3	−	389755.i	0.121851	−	0.691053i	0.983128	−	0.182917i	$-0.0585541\pi$
$752$	195053.	−	232455.i	0.344918	−	0.411057i
$753$		0			0
$754$	−12000.8	−	4367.95i	−0.0211090	−	0.00768307i
$755$		−	1.30767e6i		−	2.29407i
$756$		0			0
$757$	−110211.			−0.192325			−0.0961623	−	0.995366i	$-0.530657\pi$
$757$	−110211.			−0.192325			−0.0961623	+	0.995366i	$0.530657\pi$
$758$	21795.4	−	59882.3i	0.0379337	−	0.104222i
$759$		0			0
$760$	280647.	+	235491.i	0.485885	+	0.407706i
$761$	−246547.	−	43472.8i	−0.425726	−	0.0750669i	−0.0433195	−	0.999061i	$-0.513793\pi$
$761$	−246547.	−	43472.8i	−0.425726	−	0.0750669i	−0.382406	+	0.923994i	$0.624904\pi$
$762$		0			0
$763$	−102783.	+	86245.3i	−0.176552	+	0.148145i
$764$	855005.	−	493638.i	1.46481	−	0.845710i
$765$		0			0
$766$	142541.	−	246889.i	0.242931	−	0.420769i
$767$	4352.45	−	767.454i	0.00739849	−	0.00130455i
$768$		0			0
$769$	576169.	−	209708.i	0.974310	−	0.354620i	0.194685	−	0.980866i	$-0.437632\pi$
$769$	576169.	−	209708.i	0.974310	−	0.354620i	0.779625	+	0.626246i	$0.215409\pi$
$770$	145126.	+	398729.i	0.244772	+	0.672507i
$771$		0			0
$772$	154274.	+	874933.i	0.258856	+	1.46805i
$773$	553450.	+	319535.i	0.926231	+	0.534760i	0.885618	−	0.464415i	$-0.153735\pi$
$773$	553450.	+	319535.i	0.926231	+	0.534760i	0.0406138	+	0.999175i	$0.487069\pi$
$774$		0			0
$775$	−398870.	−	690863.i	−0.664091	−	1.15024i
$776$	−133185.	−	158724.i	−0.221173	−	0.263584i
$777$		0			0
$778$	−10828.7	+	61412.4i	−0.0178902	+	0.101460i
$779$	223594.	−	266468.i	0.368455	−	0.439108i
$780$		0			0
$781$	−405984.	−	147766.i	−0.665590	−	0.242255i
$782$		−	81661.1i		−	0.133537i
$783$		0			0
$784$	376884.			0.613163
$785$	95985.5	−	263718.i	0.155764	−	0.427957i
$786$		0			0
$787$	191502.	+	160689.i	0.309188	+	0.259440i	0.784156	−	0.620563i	$-0.213096\pi$
$787$	191502.	+	160689.i	0.309188	+	0.259440i	−0.474968	+	0.880003i	$0.657540\pi$
$788$	−807329.	−	142354.i	−1.30016	−	0.229254i
$789$		0			0
$790$	−67196.8	+	56384.8i	−0.107670	+	0.0903458i
$791$	−1.10482e6	+	637868.i	−1.76579	+	1.01948i
$792$		0			0
$793$	−3613.49	+	6258.74i	−0.00574619	+	0.00995270i
$794$	−264724.	+	46678.0i	−0.419906	+	0.0740408i
$795$		0			0
$796$	−193072.	+	70272.4i	−0.304714	+	0.110907i
$797$	−177034.	−	486397.i	−0.278702	−	0.765728i	−0.997510	−	0.0705195i	$-0.977534\pi$
$797$	−177034.	−	486397.i	−0.278702	−	0.765728i	0.718808	−	0.695208i	$-0.244688\pi$
$798$		0			0
$799$	−37987.0	−	215435.i	−0.0595034	−	0.337460i
$800$	482812.	+	278752.i	0.754394	+	0.435549i
$801$		0			0
$802$	124822.	+	216198.i	0.194063	+	0.336127i
$803$	421012.	+	501743.i	0.652926	+	0.778126i
$804$		0			0
$805$	−208128.	+	1.18035e6i	−0.321173	+	1.82146i
$806$	−147414.	+	175681.i	−0.226917	+	0.270429i
$807$		0			0
$808$	−470951.	−	171412.i	−0.721362	−	0.262554i
$809$			521331.i			0.796556i	0.917265	+	0.398278i	$0.130392\pi$
$809$			521331.i			0.796556i	−0.917265	+	0.398278i	$0.869608\pi$
$810$		0			0
$811$	−1.18228e6			−1.79755			−0.898773	−	0.438414i	$-0.855540\pi$
$811$	−1.18228e6			−1.79755			−0.898773	+	0.438414i	$0.855540\pi$
$812$	21414.8	−	58836.8i	0.0324790	−	0.0892353i
$813$		0			0
$814$	338510.	+	284044.i	0.510885	+	0.428683i
$815$	−1.51576e6	−	267269.i	−2.28199	−	0.402377i
$816$		0			0
$817$	−157168.	+	131879.i	−0.235461	+	0.197575i
$818$	146646.	−	84666.3i	0.219162	−	0.126533i
$819$		0			0
$820$	332239.	−	575456.i	0.494110	−	0.855823i
$821$	332691.	−	58662.5i	0.493578	−	0.0870310i	0.0786814	−	0.996900i	$-0.474929\pi$
$821$	332691.	−	58662.5i	0.493578	−	0.0870310i	0.414896	+	0.909869i	$0.363818\pi$
$822$		0			0
$823$	750058.	−	272999.i	1.10738	−	0.403052i	0.277346	−	0.960770i	$-0.410545\pi$
$823$	750058.	−	272999.i	1.10738	−	0.403052i	0.830030	+	0.557718i	$0.188323\pi$
$824$	117914.	+	323967.i	0.173665	+	0.477141i
$825$		0			0
$826$	−372.852	−	2114.55i	−0.000546483	−	0.00309926i
$827$	574656.	+	331778.i	0.840227	+	0.485105i	0.857341	−	0.514748i	$-0.172115\pi$
$827$	574656.	+	331778.i	0.840227	+	0.485105i	−0.0171143	+	0.999854i	$0.505448\pi$
$828$		0			0
$829$	−208452.	−	361050.i	−0.303317	−	0.525361i	0.673568	−	0.739125i	$-0.264761\pi$
$829$	−208452.	−	361050.i	−0.303317	−	0.525361i	−0.976885	+	0.213764i	$0.931428\pi$
$830$	33487.6	+	39908.9i	0.0486102	+	0.0579314i
$831$		0			0
$832$	−58175.5	+	329930.i	−0.0840415	+	0.476623i
$833$	174645.	−	208134.i	0.251690	−	0.299953i
$834$		0			0
$835$	966008.	+	351598.i	1.38550	+	0.504282i
$836$		−	591070.i		−	0.845719i
$837$		0			0
$838$	−140512.			−0.200090
$839$	198240.	−	544660.i	0.281623	−	0.773752i	−0.715547	−	0.698565i	$-0.753822\pi$
$839$	198240.	−	544660.i	0.281623	−	0.773752i	0.997169	−	0.0751870i	$-0.0239554\pi$
$840$		0			0
$841$	538586.	+	451927.i	0.761487	+	0.638964i
$842$	−222427.	−	39220.0i	−0.313736	−	0.0553201i
$843$		0			0
$844$	−358816.	+	301082.i	−0.503717	+	0.422669i
$845$	52938.0	−	30563.8i	0.0741402	−	0.0428049i
$846$		0			0
$847$	233088.	−	403721.i	0.324903	−	0.562748i
$848$	−711761.	+	125503.i	−0.989789	+	0.174527i
$849$		0			0
$850$	105228.	−	38299.8i	0.145644	−	0.0530100i
$851$	426912.	+	1.17293e6i	0.589493	+	1.61962i
$852$		0			0
$853$	20343.6	+	115374.i	0.0279596	+	0.158567i	0.995591	−	0.0938012i	$-0.0299018\pi$
$853$	20343.6	+	115374.i	0.0279596	+	0.158567i	−0.967631	+	0.252368i	$0.918791\pi$
$854$	3040.69	+	1755.54i	0.00416923	+	0.00240711i
$855$		0			0
$856$	262718.	+	455040.i	0.358543	+	0.621015i
$857$	114785.	+	136795.i	0.156287	+	0.186255i	0.838506	−	0.544892i	$-0.183429\pi$
$857$	114785.	+	136795.i	0.156287	+	0.186255i	−0.682219	+	0.731148i	$0.738985\pi$
$858$		0			0
$859$	18082.8	−	102553.i	0.0245064	−	0.138983i	−0.970100	−	0.242707i	$-0.921965\pi$
$859$	18082.8	−	102553.i	0.0245064	−	0.138983i	0.994606	+	0.103724i	$0.0330758\pi$
$860$	−251922.	+	300229.i	−0.340620	+	0.405935i
$861$		0			0
$862$	−221187.	−	80505.4i	−0.297677	−	0.108345i
$863$		−	39746.7i		−	0.0533678i	−0.999644	−	0.0266839i	$-0.991505\pi$
$863$		−	39746.7i		−	0.0533678i	0.999644	−	0.0266839i	$-0.00849476\pi$
$864$		0			0
$865$	1.25012e6			1.67079
$866$	6033.72	−	16577.5i	0.00804543	−	0.0221046i
$867$		0			0
$868$	−861314.	−	722729.i	−1.14320	−	0.959259i
$869$	292557.	+	51585.7i	0.387410	+	0.0683108i
$870$		0			0
$871$	417594.	−	350403.i	0.550450	−	0.461882i
$872$	−64315.1	+	37132.3i	−0.0845824	+	0.0488337i
$873$		0			0
$874$	−82722.5	+	143280.i	−0.108293	+	0.187569i
$875$	−141492.	+	24948.8i	−0.184806	+	0.0325862i
$876$		0			0
$877$	−1.05563e6	+	384217.i	−1.37250	+	0.499548i	−0.919895	−	0.392165i	$-0.871726\pi$
$877$	−1.05563e6	+	384217.i	−1.37250	+	0.499548i	−0.452602	+	0.891713i	$0.649504\pi$
$878$	−110360.	−	303213.i	−0.143161	−	0.393331i
$879$		0			0
$880$	−174710.	−	990830.i	−0.225607	−	1.27948i
$881$	−1.28549e6	−	742178.i	−1.65621	−	0.956216i	−0.974438	−	0.224655i	$-0.927874\pi$
$881$	−1.28549e6	−	742178.i	−1.65621	−	0.956216i	−0.681776	−	0.731561i	$-0.738792\pi$
$882$		0			0
$883$	167184.	+	289570.i	0.214423	+	0.371392i	0.953094	−	0.302674i	$-0.0978794\pi$
$883$	167184.	+	289570.i	0.214423	+	0.371392i	−0.738671	+	0.674067i	$0.764546\pi$
$884$	208821.	+	248863.i	0.267220	+	0.318461i
$885$		0			0
$886$	41737.9	−	236708.i	0.0531696	−	0.301540i
$887$	208976.	−	249048.i	0.265613	−	0.316545i	−0.616709	−	0.787191i	$-0.711535\pi$
$887$	208976.	−	249048.i	0.265613	−	0.316545i	0.882322	+	0.470646i	$0.155979\pi$
$888$		0			0
$889$	−1.50600e6	−	548140.i	−1.90556	−	0.693566i
$890$			243012.i			0.306795i
$891$		0			0
$892$	293765.			0.369207
$893$	−151585.	+	416475.i	−0.190087	+	0.522259i
$894$		0			0
$895$	−756387.	−	634684.i	−0.944274	−	0.792340i
$896$	1.01080e6	+	178232.i	1.25907	+	0.222008i
$897$		0			0
$898$	215756.	−	181041.i	0.267554	−	0.224504i
$899$	−65432.6	+	37777.5i	−0.0809608	+	0.0467427i
$900$		0			0
$901$	−260516.	+	451226.i	−0.320911	+	0.555834i
$902$	219606.	−	38722.4i	0.269917	−	0.0475937i
$903$		0			0
$904$	−663531.	+	241506.i	−0.811941	+	0.295522i
$905$	135653.	+	372702.i	0.165627	+	0.455056i
$906$		0			0
$907$	50689.7	+	287476.i	0.0616177	+	0.349451i	0.999993	+	0.00383228i	$0.00121986\pi$
$907$	50689.7	+	287476.i	0.0616177	+	0.349451i	−0.938375	+	0.345619i	$0.887669\pi$
$908$	134834.	+	77846.5i	0.163542	+	0.0944208i
$909$		0			0
$910$	236248.	+	409194.i	0.285290	+	0.494136i
$911$	484509.	+	577416.i	0.583802	+	0.695748i	0.974402	−	0.224813i	$-0.0721770\pi$
$911$	484509.	+	577416.i	0.583802	+	0.695748i	−0.390600	+	0.920560i	$0.627733\pi$
$912$		0			0
$913$	30637.3	−	173753.i	0.0367543	−	0.208444i
$914$	−266084.	+	317107.i	−0.318512	+	0.379588i
$915$		0			0
$916$	405635.	+	147639.i	0.483442	+	0.175958i
$917$			488919.i			0.581431i
$918$		0			0
$919$	−167370.			−0.198174			−0.0990872	−	0.995079i	$-0.531592\pi$
$919$	−167370.			−0.198174			−0.0990872	+	0.995079i	$0.531592\pi$
$920$	−226896.	+	623391.i	−0.268072	+	0.736521i
$921$		0			0
$922$	−133420.	−	111953.i	−0.156950	−	0.131696i
$923$	−473785.	−	83541.0i	−0.556132	−	0.0980610i
$924$		0			0
$925$	−1.31120e6	+	1.10023e6i	−1.53245	+	1.28588i
$926$	84163.3	−	48591.7i	0.0981524	−	0.0566683i
$927$		0			0
$928$	26401.0	−	45727.8i	0.0306566	−	0.0530988i
$929$	−1.06509e6	+	187804.i	−1.23411	+	0.217608i	−0.752392	−	0.658716i	$-0.771100\pi$
$929$	−1.06509e6	+	187804.i	−1.23411	+	0.217608i	−0.481723	+	0.876324i	$0.659989\pi$
$930$		0			0
$931$	−517265.	+	188269.i	−0.596780	+	0.217210i
$932$	73894.9	+	203025.i	0.0850713	+	0.233731i
$933$		0			0
$934$	11497.0	+	65202.9i	0.0131793	+	0.0747434i
$935$	−628144.	−	362659.i	−0.718516	−	0.414835i
$936$		0			0
$937$	−739056.	−	1.28008e6i	−0.841779	−	1.45800i	−0.888389	−	0.459091i	$-0.848175\pi$
$937$	−739056.	−	1.28008e6i	−0.841779	−	1.45800i	0.0466097	−	0.998913i	$-0.485158\pi$
$938$	−170236.	−	202880.i	−0.193485	−	0.230586i
$939$		0			0
$940$	−147015.	+	833766.i	−0.166382	+	0.943601i
$941$	698940.	−	832964.i	0.789334	−	0.940691i	−0.209981	−	0.977705i	$-0.567340\pi$
$941$	698940.	−	832964.i	0.789334	−	0.940691i	0.999315	+	0.0370142i	$0.0117847\pi$
$942$		0			0
$943$	591897.	+	215433.i	0.665614	+	0.242264i
$944$			5091.23i			0.00571319i
$945$		0			0
$946$	−131525.			−0.146970
$947$	−241625.	+	663858.i	−0.269427	+	0.740245i	0.729018	+	0.684495i	$0.239977\pi$
$947$	−241625.	+	663858.i	−0.269427	+	0.740245i	−0.998445	+	0.0557500i	$0.982245\pi$
$948$		0			0
$949$	558712.	+	468815.i	0.620376	+	0.520558i
$950$	−223426.	−	39396.1i	−0.247564	−	0.0436522i
$951$		0			0
$952$	253791.	−	212956.i	0.280029	−	0.234972i
$953$	765950.	−	442221.i	0.843363	−	0.486916i	−0.0150432	−	0.999887i	$-0.504789\pi$
$953$	765950.	−	442221.i	0.843363	−	0.486916i	0.858406	+	0.512971i	$0.171455\pi$
$954$		0			0
$955$	−1.22726e6	+	2.12568e6i	−1.34564	+	2.33072i
$956$	1.41506e6	−	249513.i	1.54832	−	0.273010i
$957$		0			0
$958$	138460.	−	50395.4i	0.150867	−	0.0549111i
$959$	221081.	+	607414.i	0.240388	+	0.660461i
$960$		0			0
$961$	75233.9	+	426672.i	0.0814642	+	0.462006i
$962$	426143.	+	246034.i	0.460474	+	0.265855i
$963$		0			0
$964$	−65772.7	−	113922.i	−0.0707769	−	0.122589i
$965$	−1.41977e6	−	1.69202e6i	−1.52463	−	1.81698i
$966$		0			0
$967$	224682.	−	1.27423e6i	0.240279	−	1.36269i	−0.590928	−	0.806724i	$-0.701238\pi$
$967$	224682.	−	1.27423e6i	0.240279	−	1.36269i	0.831207	−	0.555964i	$-0.187651\pi$
$968$	165856.	−	197660.i	0.177003	−	0.210944i
$969$		0			0
$970$	230606.	+	83933.7i	0.245091	+	0.0892057i
$971$			1.42519e6i			1.51159i	0.654806	+	0.755797i	$0.272751\pi$
$971$			1.42519e6i			1.51159i	−0.654806	+	0.755797i	$0.727249\pi$
$972$		0			0
$973$	−21097.7			−0.0222848
$974$	−65646.7	+	180363.i	−0.0691982	+	0.190121i
$975$		0			0
$976$	−6377.50	−	5351.36i	−0.00669501	−	0.00561778i
$977$	1.06606e6	+	187975.i	1.11684	+	0.196930i	0.701455	−	0.712714i	$-0.252534\pi$
$977$	1.06606e6	+	187975.i	1.11684	+	0.196930i	0.415389	+	0.909644i	$0.363645\pi$
$978$		0			0
$979$	630444.	−	529005.i	0.657780	−	0.551943i
$980$	−910642.	+	525759.i	−0.948190	+	0.547438i
$981$		0			0
$982$	164820.	−	285477.i	0.170918	−	0.296039i
$983$	−286129.	+	50452.2i	−0.296111	+	0.0522123i	−0.319730	−	0.947509i	$-0.603592\pi$
$983$	−286129.	+	50452.2i	−0.296111	+	0.0522123i	0.0236192	+	0.999721i	$0.492481\pi$
$984$		0			0
$985$	1.91520e6	−	697075.i	1.97397	−	0.718467i
$986$	−3627.42	−	9966.26i	−0.00373116	−	0.0102513i
$987$		0			0
$988$	−114292.	−	648181.i	−0.117085	−	0.664022i
$989$	−321743.	−	185758.i	−0.328940	−	0.189913i
$990$		0			0
$991$	−402322.	−	696842.i	−0.409662	−	0.709556i	0.585189	−	0.810897i	$-0.301020\pi$
$991$	−402322.	−	696842.i	−0.409662	−	0.709556i	−0.994852	+	0.101340i	$0.967687\pi$
$992$	−609483.	−	726354.i	−0.619353	−	0.738117i
$993$		0			0
$994$	−40586.7	+	230179.i	−0.0410782	+	0.232966i
$995$	328344.	−	391305.i	0.331652	−	0.395248i
$996$		0			0
$997$	1.40822e6	+	512550.i	1.41671	+	0.515640i	0.933091	−	0.359640i	$-0.117100\pi$
$997$	1.40822e6	+	512550.i	1.41671	+	0.515640i	0.483617	+	0.875280i	$0.339323\pi$
$998$		−	117146.i		−	0.117616i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.5.f.a.17.7		66
3.2	odd	2		27.5.f.a.23.5	yes	66
27.7	even	9		27.5.f.a.20.5	✓	66
27.20	odd	18	inner	81.5.f.a.62.7		66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.5.f.a.20.5	✓	66	27.7	even	9
27.5.f.a.23.5	yes	66	3.2	odd	2
81.5.f.a.17.7		66	1.1	even	1	trivial
81.5.f.a.62.7		66	27.20	odd	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	81.f (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.410788 - 1.12863i) q^{2} +(11.1517 + 9.35735i) q^{4} +(-35.6423 - 6.28469i) q^{5} +(50.7952 - 42.6222i) q^{7} +(31.7844 - 18.3507i) q^{8} +(-21.7345 + 37.6453i) q^{10} +(144.976 - 25.5631i) q^{11} +(154.041 - 56.0663i) q^{13} +(-27.2387 - 74.8377i) q^{14} +(32.7914 + 185.970i) q^{16} +(117.897 + 68.0677i) q^{17} +(-137.905 - 238.858i) q^{19} +(-338.662 - 403.602i) q^{20} +(30.7029 - 174.125i) q^{22} +(321.030 - 382.589i) q^{23} +(643.566 + 234.239i) q^{25} -196.887i q^{26} +965.281 q^{28} +(22.1851 - 60.9530i) q^{29} +(-892.294 - 748.724i) q^{31} +(801.663 + 141.355i) q^{32} +(125.254 - 105.100i) q^{34} +(-2078.32 + 1199.92i) q^{35} +(-1249.62 + 2164.41i) q^{37} +(-326.232 + 57.5236i) q^{38} +(-1248.20 + 454.306i) q^{40} +(431.354 + 1185.14i) q^{41} +(-129.173 - 732.574i) q^{43} +(1855.92 + 1071.52i) q^{44} +(-299.926 - 519.487i) q^{46} +(-1032.91 - 1230.97i) q^{47} +(346.568 - 1965.48i) q^{49} +(528.738 - 630.126i) q^{50} +(2242.44 + 816.182i) q^{52} +3827.30i q^{53} -5327.92 q^{55} +(832.345 - 2286.85i) q^{56} +(-59.6801 - 50.0775i) q^{58} +(26.5512 + 4.68169i) q^{59} +(-33.7723 + 28.3383i) q^{61} +(-1211.58 + 699.504i) q^{62} +(-1021.86 + 1769.91i) q^{64} +(-5842.73 + 1030.23i) q^{65} +(3124.90 - 1137.37i) q^{67} +(677.810 + 1862.27i) q^{68} +(500.517 + 2838.57i) q^{70} +(-2541.62 - 1467.40i) q^{71} +(2224.61 + 3853.13i) q^{73} +(1929.49 + 2299.47i) q^{74} +(697.212 - 3954.09i) q^{76} +(6274.51 - 7477.67i) q^{77} +(1896.27 + 690.187i) q^{79} -6834.46i q^{80} +1514.78 q^{82} +(409.909 - 1126.22i) q^{83} +(-3774.32 - 3167.03i) q^{85} +(-879.868 - 155.144i) q^{86} +(4138.86 - 3472.92i) q^{88} +(4841.49 - 2795.24i) q^{89} +(5434.87 - 9413.46i) q^{91} +(7160.03 - 1262.51i) q^{92} +(-1813.62 + 660.103i) q^{94} +(3414.09 + 9380.14i) q^{95} +(-980.336 - 5559.76i) q^{97} +(-2075.94 - 1198.54i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q + 6 q^{2} - 6 q^{4} - 3 q^{5} - 6 q^{7} + 9 q^{8} - 3 q^{10} + 492 q^{11} - 6 q^{13} - 1137 q^{14} - 54 q^{16} + 9 q^{17} - 3 q^{19} + 2487 q^{20} + 1002 q^{22} + 2724 q^{23} + 435 q^{25} - 12 q^{28}+ \cdots + 259938 q^{98}+O(q^{100}) \) 66 * q + 6 * q^2 - 6 * q^4 - 3 * q^5 - 6 * q^7 + 9 * q^8 - 3 * q^10 + 492 * q^11 - 6 * q^13 - 1137 * q^14 - 54 * q^16 + 9 * q^17 - 3 * q^19 + 2487 * q^20 + 1002 * q^22 + 2724 * q^23 + 435 * q^25 - 12 * q^28 - 5016 * q^29 - 1671 * q^31 - 10224 * q^32 - 342 * q^34 + 2682 * q^35 - 3 * q^37 + 6564 * q^38 - 1113 * q^40 - 5754 * q^41 - 1266 * q^43 + 4545 * q^44 - 3 * q^46 + 9159 * q^47 + 5898 * q^49 + 34977 * q^50 + 2871 * q^52 - 12 * q^55 - 39243 * q^56 - 12291 * q^58 - 24762 * q^59 - 8358 * q^61 - 38304 * q^62 + 6141 * q^64 - 23727 * q^65 + 15996 * q^67 + 43533 * q^68 - 7251 * q^70 + 19773 * q^71 + 6108 * q^73 + 74847 * q^74 - 28614 * q^76 + 33909 * q^77 - 5658 * q^79 - 12 * q^82 - 18813 * q^83 + 24219 * q^85 - 96474 * q^86 + 36042 * q^88 - 110232 * q^89 - 6042 * q^91 - 73545 * q^92 + 2631 * q^94 + 65163 * q^95 - 3696 * q^97 + 259938 * q^98

Introduction

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