LMFDB - Embedded newform 81.5.f.a.8.11

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			8.11
Character	$\chi$	$=$	81.8
Dual form			81.5.f.a.71.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(7.11993 + 1.25544i) q^{2} +(34.0822 + 12.4049i) q^{4} +(16.3502 + 19.4854i) q^{5} +(-60.7132 + 22.0978i) q^{7} +(126.911 + 73.2722i) q^{8} +(91.9496 + 159.261i) q^{10} +(86.4395 - 103.015i) q^{11} +(-27.2976 - 154.812i) q^{13} +(-460.017 + 81.1133i) q^{14} +(367.064 + 308.004i) q^{16} +(124.536 - 71.9009i) q^{17} +(79.9738 - 138.519i) q^{19} +(315.536 + 866.929i) q^{20} +(744.772 - 624.938i) q^{22} +(-193.010 + 530.290i) q^{23} +(-3.82186 + 21.6748i) q^{25} -1136.52i q^{26} -2343.37 q^{28} +(-929.364 - 163.872i) q^{29} +(298.389 + 108.605i) q^{31} +(719.645 + 857.639i) q^{32} +(976.955 - 355.583i) q^{34} +(-1423.26 - 821.718i) q^{35} +(-1074.59 - 1861.25i) q^{37} +(743.309 - 885.841i) q^{38} +(647.283 + 3670.93i) q^{40} +(162.159 - 28.5930i) q^{41} +(795.721 + 667.689i) q^{43} +(4223.94 - 2438.69i) q^{44} +(-2039.96 + 3533.31i) q^{46} +(879.993 + 2417.76i) q^{47} +(1358.51 - 1139.93i) q^{49} +(-54.4228 + 149.525i) q^{50} +(990.071 - 5614.97i) q^{52} +422.118i q^{53} +3420.58 q^{55} +(-9324.34 - 1644.13i) q^{56} +(-6411.28 - 2333.52i) q^{58} +(-677.524 - 807.441i) q^{59} +(-3638.45 + 1324.29i) q^{61} +(1988.16 + 1147.87i) q^{62} +(213.764 + 370.251i) q^{64} +(2570.26 - 3063.11i) q^{65} +(1308.73 + 7422.17i) q^{67} +(5136.39 - 905.685i) q^{68} +(-9101.88 - 7637.39i) q^{70} +(-4732.58 + 2732.36i) q^{71} +(2690.68 - 4660.39i) q^{73} +(-5314.34 - 14601.0i) q^{74} +(4444.00 - 3728.96i) q^{76} +(-2971.62 + 8164.47i) q^{77} +(-714.746 + 4053.52i) q^{79} +12188.3i q^{80} +1190.46 q^{82} +(6700.74 + 1181.52i) q^{83} +(3437.20 + 1251.04i) q^{85} +(4827.24 + 5752.88i) q^{86} +(18518.2 - 6740.08i) q^{88} +(-145.184 - 83.8223i) q^{89} +(5078.33 + 8795.93i) q^{91} +(-13156.4 + 15679.2i) q^{92} +(3230.15 + 18319.1i) q^{94} +(4006.68 - 706.485i) q^{95} +(6516.98 + 5468.39i) q^{97} +(11103.6 - 6410.67i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{18}\right)$

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 $

$2$	7.11993	+	1.25544i	1.77998	+	0.313859i	0.964334	−	0.264688i	$-0.0852689\pi$
$2$	7.11993	+	1.25544i	1.77998	+	0.313859i	0.815649	+	0.578547i	$0.196380\pi$
$3$		0			0
$3$		0			0
$4$	34.0822	+	12.4049i	2.13014	+	0.775308i
$5$	16.3502	+	19.4854i	0.654007	+	0.779416i	0.986513	−	0.163686i	$-0.0523383\pi$
$5$	16.3502	+	19.4854i	0.654007	+	0.779416i	−0.332505	+	0.943101i	$0.607894\pi$
$6$		0			0
$7$	−60.7132	+	22.0978i	−1.23905	+	0.450976i	−0.876686	−	0.481063i	$-0.840251\pi$
$7$	−60.7132	+	22.0978i	−1.23905	+	0.450976i	−0.362359	+	0.932038i	$0.618029\pi$
$8$	126.911	+	73.2722i	1.98299	+	1.14488i
$9$		0			0
$10$	91.9496	+	159.261i	0.919496	+	1.59261i
$11$	86.4395	−	103.015i	0.714376	−	0.851360i	−0.279695	−	0.960089i	$-0.590234\pi$
$11$	86.4395	−	103.015i	0.714376	−	0.851360i	0.994071	+	0.108729i	$0.0346779\pi$
$12$		0			0
$13$	−27.2976	−	154.812i	−0.161524	−	0.916048i	−0.952576	−	0.304300i	$-0.901578\pi$
$13$	−27.2976	−	154.812i	−0.161524	−	0.916048i	0.791052	−	0.611748i	$-0.209534\pi$
$14$	−460.017	+	81.1133i	−2.34702	+	0.413844i
$15$		0			0
$16$	367.064	+	308.004i	1.43385	+	1.20314i
$17$	124.536	−	71.9009i	0.430920	−	0.248792i	−0.268818	−	0.963191i	$-0.586633\pi$
$17$	124.536	−	71.9009i	0.430920	−	0.248792i	0.699739	+	0.714399i	$0.253300\pi$
$18$		0			0
$19$	79.9738	−	138.519i	0.221534	−	0.383708i	−0.733740	−	0.679430i	$-0.762227\pi$
$19$	79.9738	−	138.519i	0.221534	−	0.383708i	0.955274	+	0.295722i	$0.0955603\pi$
$20$	315.536	+	866.929i	0.788841	+	2.16732i
$21$		0			0
$22$	744.772	−	624.938i	1.53878	−	1.29119i
$23$	−193.010	+	530.290i	−0.364857	+	1.00244i	0.612431	+	0.790524i	$0.290192\pi$
$23$	−193.010	+	530.290i	−0.364857	+	1.00244i	−0.977288	+	0.211914i	$0.932030\pi$
$24$		0			0
$25$	−3.82186	+	21.6748i	−0.00611498	+	0.0346798i
$26$		−	1136.52i		−	1.68125i
$27$		0			0
$28$	−2343.37			−2.98899
$29$	−929.364	−	163.872i	−1.10507	−	0.194854i	−0.408793	−	0.912627i	$-0.634050\pi$
$29$	−929.364	−	163.872i	−1.10507	−	0.194854i	−0.696277	+	0.717773i	$0.745161\pi$
$30$		0			0
$31$	298.389	+	108.605i	0.310498	+	0.113012i	0.492569	−	0.870273i	$-0.336058\pi$
$31$	298.389	+	108.605i	0.310498	+	0.113012i	−0.182071	+	0.983285i	$0.558280\pi$
$32$	719.645	+	857.639i	0.702778	+	0.837539i
$33$		0			0
$34$	976.955	−	355.583i	0.845117	−	0.307597i
$35$	−1423.26	−	821.718i	−1.16184	−	0.670790i
$36$		0			0
$37$	−1074.59	−	1861.25i	−0.784946	−	1.35957i	−0.929031	−	0.370001i	$-0.879357\pi$
$37$	−1074.59	−	1861.25i	−0.784946	−	1.35957i	0.144085	−	0.989565i	$-0.453976\pi$
$38$	743.309	−	885.841i	0.514757	−	0.613464i
$39$		0			0
$40$	647.283	+	3670.93i	0.404552	+	2.29433i
$41$	162.159	−	28.5930i	0.0964658	−	0.0170095i	−0.125207	−	0.992131i	$-0.539959\pi$
$41$	162.159	−	28.5930i	0.0964658	−	0.0170095i	0.221673	+	0.975121i	$0.428848\pi$
$42$		0			0
$43$	795.721	+	667.689i	0.430352	+	0.361108i	0.832085	−	0.554649i	$-0.187147\pi$
$43$	795.721	+	667.689i	0.430352	+	0.361108i	−0.401732	+	0.915757i	$0.631592\pi$
$44$	4223.94	−	2438.69i	2.18179	−	1.25966i
$45$		0			0
$46$	−2039.96	+	3533.31i	−0.964064	+	1.66981i
$47$	879.993	+	2417.76i	0.398367	+	1.09450i	0.963080	+	0.269217i	$0.0867649\pi$
$47$	879.993	+	2417.76i	0.398367	+	1.09450i	−0.564712	+	0.825288i	$0.691013\pi$
$48$		0			0
$49$	1358.51	−	1139.93i	0.565810	−	0.474771i
$50$	−54.4228	+	149.525i	−0.0217691	+	0.0598102i
$51$		0			0
$52$	990.071	−	5614.97i	0.366150	−	2.07654i
$53$			422.118i			0.150273i	0.997173	+	0.0751366i	$0.0239393\pi$
$53$			422.118i			0.150273i	−0.997173	+	0.0751366i	$0.976061\pi$
$54$		0			0
$55$	3420.58			1.13077
$56$	−9324.34	−	1644.13i	−2.97332	−	0.524277i
$57$		0			0
$58$	−6411.28	−	2333.52i	−1.90585	−	0.693673i
$59$	−677.524	−	807.441i	−0.194635	−	0.231957i	0.659897	−	0.751356i	$-0.270600\pi$
$59$	−677.524	−	807.441i	−0.194635	−	0.231957i	−0.854531	+	0.519400i	$0.826156\pi$
$60$		0			0
$61$	−3638.45	+	1324.29i	−0.977815	+	0.355896i	−0.780990	−	0.624543i	$-0.785285\pi$
$61$	−3638.45	+	1324.29i	−0.977815	+	0.355896i	−0.196825	+	0.980439i	$0.563063\pi$
$62$	1988.16	+	1147.87i	0.517212	+	0.298612i
$63$		0			0
$64$	213.764	+	370.251i	0.0521886	+	0.0903933i
$65$	2570.26	−	3063.11i	0.608344	−	0.724997i
$66$		0			0
$67$	1308.73	+	7422.17i	0.291541	+	1.65341i	0.680936	+	0.732343i	$0.261573\pi$
$67$	1308.73	+	7422.17i	0.291541	+	1.65341i	−0.389395	+	0.921071i	$0.627316\pi$
$68$	5136.39	−	905.685i	1.11081	−	0.195866i
$69$		0			0
$70$	−9101.88	−	7637.39i	−1.85753	−	1.55865i
$71$	−4732.58	+	2732.36i	−0.938818	+	0.542027i	−0.889590	−	0.456760i	$-0.849010\pi$
$71$	−4732.58	+	2732.36i	−0.938818	+	0.542027i	−0.0492287	+	0.998788i	$0.515676\pi$
$72$		0			0
$73$	2690.68	−	4660.39i	0.504913	−	0.874534i	−0.495071	−	0.868852i	$-0.664858\pi$
$73$	2690.68	−	4660.39i	0.504913	−	0.874534i	0.999984	−	0.00568195i	$-0.00180863\pi$
$74$	−5314.34	−	14601.0i	−0.970478	−	2.66637i
$75$		0			0
$76$	4444.00	−	3728.96i	0.769390	−	0.645595i
$77$	−2971.62	+	8164.47i	−0.501202	+	1.37704i
$78$		0			0
$79$	−714.746	+	4053.52i	−0.114524	+	0.649499i	0.872460	+	0.488685i	$0.162523\pi$
$79$	−714.746	+	4053.52i	−0.114524	+	0.649499i	−0.986985	+	0.160814i	$0.948588\pi$
$80$			12188.3i			1.90442i
$81$		0			0
$82$	1190.46			0.177046
$83$	6700.74	+	1181.52i	0.972673	+	0.171508i	0.637333	−	0.770589i	$-0.280038\pi$
$83$	6700.74	+	1181.52i	0.972673	+	0.171508i	0.335340	+	0.942097i	$0.391149\pi$
$84$		0			0
$85$	3437.20	+	1251.04i	0.475738	+	0.173154i
$86$	4827.24	+	5752.88i	0.652682	+	0.777837i
$87$		0			0
$88$	18518.2	−	6740.08i	2.39130	−	0.870362i
$89$	−145.184	−	83.8223i	−0.0183291	−	0.0105823i	0.490807	−	0.871268i	$-0.336702\pi$
$89$	−145.184	−	83.8223i	−0.0183291	−	0.0105823i	−0.509137	+	0.860686i	$0.670035\pi$
$90$		0			0
$91$	5078.33	+	8795.93i	0.613251	+	1.06218i
$92$	−13156.4	+	15679.2i	−1.55440	+	1.85246i
$93$		0			0
$94$	3230.15	+	18319.1i	0.365567	+	2.07323i
$95$	4006.68	−	706.485i	0.443953	−	0.0782809i
$96$		0			0
$97$	6516.98	+	5468.39i	0.692632	+	0.581188i	0.919667	−	0.392699i	$-0.128459\pi$
$97$	6516.98	+	5468.39i	0.692632	+	0.581188i	−0.227035	+	0.973887i	$0.572903\pi$
$98$	11103.6	−	6410.67i	1.15614	−	0.667500i
$99$		0			0
$100$	−399.132	+	691.318i	−0.0399132	+	0.0691318i
$101$	4276.87	+	11750.6i	0.419260	+	1.15191i	0.952126	+	0.305707i	$0.0988928\pi$
$101$	4276.87	+	11750.6i	0.419260	+	1.15191i	−0.532866	+	0.846200i	$0.678885\pi$
$102$		0			0
$103$	5064.75	−	4249.83i	0.477401	−	0.400587i	−0.372084	−	0.928199i	$-0.621357\pi$
$103$	5064.75	−	4249.83i	0.477401	−	0.400587i	0.849486	+	0.527612i	$0.176912\pi$
$104$	7879.06	−	21647.5i	0.728463	−	2.00144i
$105$		0			0
$106$	−529.942	+	3005.45i	−0.0471646	+	0.267484i
$107$		−	11926.4i		−	1.04170i	−0.853648	−	0.520851i	$-0.825615\pi$
$107$		−	11926.4i		−	1.04170i	0.853648	−	0.520851i	$-0.174385\pi$
$108$		0			0
$109$	−18526.7			−1.55935			−0.779677	−	0.626182i	$-0.784617\pi$
$109$	−18526.7			−1.55935			−0.779677	+	0.626182i	$0.784617\pi$
$110$	24354.3	+	4294.32i	2.01275	+	0.354903i
$111$		0			0
$112$	−29091.9	−	10588.6i	−2.31919	−	0.844115i
$113$	4547.75	+	5419.79i	0.356155	+	0.424449i	0.914138	−	0.405403i	$-0.132869\pi$
$113$	4547.75	+	5419.79i	0.356155	+	0.424449i	−0.557983	+	0.829853i	$0.688424\pi$
$114$		0			0
$115$	−13488.6	+	4909.47i	−1.01994	+	0.371226i
$116$	−29642.0	−	17113.8i	−2.20288	−	1.27184i
$117$		0			0
$118$	−3810.23	−	6599.52i	−0.273645	−	0.473967i
$119$	−5972.13	+	7117.31i	−0.421731	+	0.502599i
$120$		0			0
$121$	−597.834	−	3390.49i	−0.0408329	−	0.231575i
$122$	−27568.1	+	4860.99i	−1.85220	+	0.326592i
$123$		0			0
$124$	8822.53	+	7402.98i	0.573786	+	0.481463i
$125$	13283.0	−	7668.95i	0.850113	−	0.490813i
$126$		0			0
$127$	9865.36	−	17087.3i	0.611653	−	1.05941i	−0.379308	−	0.925270i	$-0.623838\pi$
$127$	9865.36	−	17087.3i	0.611653	−	1.05941i	0.990962	−	0.134145i	$-0.0428286\pi$
$128$	−5069.48	−	13928.3i	−0.309416	−	0.850115i
$129$		0			0
$130$	22145.6	−	18582.4i	1.31039	−	1.09955i
$131$	−1495.58	+	4109.07i	−0.0871499	+	0.239442i	−0.975610	−	0.219512i	$-0.929554\pi$
$131$	−1495.58	+	4109.07i	−0.0871499	+	0.239442i	0.888460	+	0.458954i	$0.151776\pi$
$132$		0			0
$133$	−1794.51	+	10177.2i	−0.101448	+	0.575338i
$134$			54488.4i			3.03455i
$135$		0			0
$136$	21073.3			1.13935
$137$	16547.9	+	2917.84i	0.881662	+	0.155461i	0.596110	−	0.802902i	$-0.296712\pi$
$137$	16547.9	+	2917.84i	0.881662	+	0.155461i	0.285552	+	0.958363i	$0.407823\pi$
$138$		0			0
$139$	−5476.56	−	1993.31i	−0.283451	−	0.103168i	0.196382	−	0.980527i	$-0.437081\pi$
$139$	−5476.56	−	1993.31i	−0.283451	−	0.103168i	−0.479833	+	0.877360i	$0.659303\pi$
$140$	−38314.5	−	45661.4i	−1.95482	−	2.32966i
$141$		0			0
$142$	−37126.0	+	13512.8i	−1.84120	+	0.670142i
$143$	−18307.5	−	10569.8i	−0.895276	−	0.516888i
$144$		0			0
$145$	−12002.2	−	20788.4i	−0.570852	−	0.988745i
$146$	25008.3	−	29803.7i	1.17322	−	1.39819i
$147$		0			0
$148$	−13535.9	−	76765.7i	−0.617963	−	3.50464i
$149$	−22092.9	+	3895.57i	−0.995130	+	0.175468i	−0.647420	−	0.762134i	$-0.724152\pi$
$149$	−22092.9	+	3895.57i	−0.995130	+	0.175468i	−0.347711	+	0.937602i	$0.613041\pi$
$150$		0			0
$151$	8648.32	+	7256.80i	0.379296	+	0.318267i	0.812426	−	0.583064i	$-0.198147\pi$
$151$	8648.32	+	7256.80i	0.379296	+	0.318267i	−0.433130	+	0.901331i	$0.642591\pi$
$152$	20299.1	−	11719.7i	0.878597	−	0.507258i
$153$		0			0
$154$	−31407.7	+	54399.8i	−1.32433	+	2.29380i
$155$	2762.51	+	7589.93i	0.114985	+	0.315918i
$156$		0			0
$157$	−12754.3	+	10702.1i	−0.517436	+	0.434180i	−0.863737	−	0.503943i	$-0.831882\pi$
$157$	−12754.3	+	10702.1i	−0.517436	+	0.434180i	0.346301	+	0.938123i	$0.387438\pi$
$158$	−10177.9	+	27963.5i	−0.407702	+	1.12015i
$159$		0			0
$160$	−4945.11	+	28045.1i	−0.193168	+	1.09551i
$161$		−	36460.7i		−	1.40661i
$162$		0			0
$163$	21562.3			0.811557			0.405779	−	0.913971i	$-0.367000\pi$
$163$	21562.3			0.811557			0.405779	+	0.913971i	$0.367000\pi$
$164$	5881.44	+	1037.06i	0.218673	+	0.0385580i
$165$		0			0
$166$	46225.5	+	16824.7i	1.67751	+	0.610564i
$167$	3007.54	+	3584.25i	0.107840	+	0.128518i	0.817264	−	0.576263i	$-0.195490\pi$
$167$	3007.54	+	3584.25i	0.107840	+	0.128518i	−0.709425	+	0.704781i	$0.751045\pi$
$168$		0			0
$169$	3616.92	−	1316.45i	0.126639	−	0.0460927i
$170$	22902.1	+	13222.5i	0.792459	+	0.457526i
$171$		0			0
$172$	18837.3	+	32627.2i	0.636740	+	1.10287i
$173$	12546.9	−	14952.9i	0.419223	−	0.499611i	−0.514558	−	0.857456i	$-0.672044\pi$
$173$	12546.9	−	14952.9i	0.419223	−	0.499611i	0.933781	+	0.357845i	$0.116488\pi$
$174$		0			0
$175$	−246.929	−	1400.40i	−0.00806299	−	0.0457275i
$176$	63457.7	−	11189.3i	2.04861	−	0.361225i
$177$		0			0
$178$	−928.470	−	779.079i	−0.0293041	−	0.0245890i
$179$	−42317.5	+	24432.0i	−1.32073	+	0.762523i	−0.983845	−	0.179023i	$-0.942706\pi$
$179$	−42317.5	+	24432.0i	−1.32073	+	0.762523i	−0.336884	+	0.941546i	$0.609373\pi$
$180$		0			0
$181$	25257.1	−	43746.6i	0.770951	−	1.33533i	−0.166092	−	0.986110i	$-0.553115\pi$
$181$	25257.1	−	43746.6i	0.770951	−	1.33533i	0.937042	−	0.349216i	$-0.113552\pi$
$182$	25114.7	+	69001.9i	0.758201	+	2.08314i
$183$		0			0
$184$	−63350.5	+	53157.4i	−1.87118	+	1.57010i
$185$	18697.4	−	51370.6i	0.546307	−	1.50097i
$186$		0			0
$187$	3357.99	−	19044.1i	0.0960276	−	0.544600i
$188$			93319.0i			2.64031i
$189$		0			0
$190$	29414.2			0.814798
$191$	−55496.5	−	9785.52i	−1.52124	−	0.268236i	−0.650322	−	0.759659i	$-0.725366\pi$
$191$	−55496.5	−	9785.52i	−1.52124	−	0.268236i	−0.870921	+	0.491423i	$0.836477\pi$
$192$		0			0
$193$	−15733.4	−	5726.48i	−0.422384	−	0.153735i	0.122079	−	0.992520i	$-0.461044\pi$
$193$	−15733.4	−	5726.48i	−0.422384	−	0.153735i	−0.544462	+	0.838785i	$0.683266\pi$
$194$	39535.2	+	47116.2i	1.05046	+	1.25189i
$195$		0			0
$196$	60441.8	−	21999.0i	1.57335	−	0.572652i
$197$	−37267.5	−	21516.4i	−0.960281	−	0.554418i	−0.0640212	−	0.997949i	$-0.520393\pi$
$197$	−37267.5	−	21516.4i	−0.960281	−	0.554418i	−0.896259	+	0.443530i	$0.853726\pi$
$198$		0			0
$199$	−9807.79	−	16987.6i	−0.247665	−	0.428969i	0.715212	−	0.698907i	$-0.246330\pi$
$199$	−9807.79	−	16987.6i	−0.247665	−	0.428969i	−0.962878	+	0.269939i	$0.912997\pi$
$200$	−2073.20	+	2470.74i	−0.0518300	+	0.0617686i
$201$		0			0
$202$	15698.9	+	89032.8i	0.384739	+	2.18196i
$203$	60045.9	−	10587.7i	1.45711	−	0.256927i
$204$		0			0
$205$	3208.48	+	2692.23i	0.0763469	+	0.0640626i
$206$	41396.1	−	23900.0i	0.975494	−	0.563202i
$207$		0			0
$208$	37662.7	−	65233.8i	0.870533	−	1.50781i
$209$	−7356.55	−	20211.9i	−0.168415	−	0.462717i
$210$		0			0
$211$	−22807.2	+	19137.5i	−0.512280	+	0.429854i	−0.861931	−	0.507026i	$-0.830745\pi$
$211$	−22807.2	+	19137.5i	−0.512280	+	0.429854i	0.349650	+	0.936880i	$0.386300\pi$
$212$	−5236.34	+	14386.7i	−0.116508	+	0.320103i
$213$		0			0
$214$	14972.9	−	84915.4i	0.326947	−	1.85421i
$215$			26421.8i			0.571591i
$216$		0			0
$217$	−20516.1			−0.435687
$218$	−131909.	−	23259.1i	−2.77562	−	0.489417i
$219$		0			0
$220$	116581.	+	42432.1i	2.40870	+	0.876695i
$221$	−14530.7	−	17317.0i	−0.297509	−	0.354558i
$222$		0			0
$223$	−63805.7	+	23223.4i	−1.28307	+	0.466998i	−0.891446	−	0.453128i	$-0.850308\pi$
$223$	−63805.7	+	23223.4i	−1.28307	+	0.466998i	−0.391622	+	0.920126i	$0.628086\pi$
$224$	−62643.9	−	36167.5i	−1.24848	−	0.720813i
$225$		0			0
$226$	25575.5	+	44298.0i	0.500733	+	0.867295i
$227$	−26848.4	+	31996.7i	−0.521035	+	0.620946i	−0.960825	−	0.277155i	$-0.910608\pi$
$227$	−26848.4	+	31996.7i	−0.521035	+	0.620946i	0.439790	+	0.898101i	$0.355053\pi$
$228$		0			0
$229$	−16155.0	−	91619.4i	−0.308060	−	1.74710i	−0.608740	−	0.793370i	$-0.708325\pi$
$229$	−16155.0	−	91619.4i	−0.308060	−	1.74710i	0.300680	−	0.953725i	$-0.402786\pi$
$230$	−102202.	+	18020.9i	−1.93198	+	0.340660i
$231$		0			0
$232$	−105939.	−	88893.7i	−1.96826	−	1.65156i
$233$	21030.6	−	12142.0i	0.387381	−	0.223655i	−0.293643	−	0.955915i	$-0.594868\pi$
$233$	21030.6	−	12142.0i	0.387381	−	0.223655i	0.681025	+	0.732260i	$0.261535\pi$
$234$		0			0
$235$	−32723.0	+	56677.9i	−0.592539	+	1.02631i
$236$	−13075.3	−	35924.0i	−0.234762	−	0.645002i
$237$		0			0
$238$	−51456.5	+	43177.1i	−0.908419	+	0.762254i
$239$	−407.704	+	1120.16i	−0.00713755	+	0.0196102i	−0.943210	−	0.332196i	$-0.892210\pi$
$239$	−407.704	+	1120.16i	−0.00713755	+	0.0196102i	0.936073	+	0.351807i	$0.114433\pi$
$240$		0			0
$241$	11258.8	−	63851.8i	0.193846	−	1.09936i	−0.720206	−	0.693761i	$-0.755953\pi$
$241$	11258.8	−	63851.8i	0.193846	−	1.09936i	0.914052	−	0.405597i	$-0.132936\pi$
$242$		−	24890.6i		−	0.425015i
$243$		0			0
$244$	−140434.			−2.35881
$245$	44423.8	+	7833.12i	0.740089	+	0.130498i
$246$		0			0
$247$	−23627.4	−	8599.69i	−0.387278	−	0.140958i
$248$	29911.2	+	35646.7i	0.486329	+	0.579584i
$249$		0			0
$250$	104202.	−	37926.4i	1.66723	−	0.606823i
$251$	90618.3	+	52318.5i	1.43836	+	0.830439i	0.997736	−	0.0672507i	$-0.0214227\pi$
$251$	90618.3	+	52318.5i	1.43836	+	0.830439i	0.440627	+	0.897690i	$0.354756\pi$
$252$		0			0
$253$	37943.9	+	65720.8i	0.592790	+	1.02674i
$254$	91692.7	−	109275.i	1.42124	−	1.69377i
$255$		0			0
$256$	−19796.1	−	112269.i	−0.302065	−	1.71309i
$257$	71229.6	−	12559.7i	1.07844	−	0.190157i	0.393912	−	0.919148i	$-0.371121\pi$
$257$	71229.6	−	12559.7i	1.07844	−	0.190157i	0.684523	+	0.728991i	$0.260010\pi$
$258$		0			0
$259$	106371.	+	89256.2i	1.58572	+	1.33057i
$260$	125598.	−	72513.9i	1.85795	−	1.07269i
$261$		0			0
$262$	−15807.1	+	27378.7i	−0.230277	+	0.398851i
$263$	3335.94	+	9165.43i	0.0482289	+	0.132508i	0.961468	−	0.274915i	$-0.0886498\pi$
$263$	3335.94	+	9165.43i	0.0482289	+	0.132508i	−0.913240	+	0.407423i	$0.866428\pi$
$264$		0			0
$265$	−8225.13	+	6901.70i	−0.117125	+	0.0982798i
$266$	−25553.5	+	70207.8i	−0.361150	+	0.992252i
$267$		0			0
$268$	−47467.1	+	269199.i	−0.660880	+	3.74804i
$269$			50483.0i			0.697655i	0.937187	+	0.348827i	$0.113420\pi$
$269$			50483.0i			0.697655i	−0.937187	+	0.348827i	$0.886580\pi$
$270$		0			0
$271$	122387.			1.66647			0.833237	−	0.552916i	$-0.186485\pi$
$271$	122387.			1.66647			0.833237	+	0.552916i	$0.186485\pi$
$272$	67858.5	+	11965.3i	0.917205	+	0.161728i
$273$		0			0
$274$	114157.	+	41549.7i	1.52055	+	0.553435i
$275$	1902.47	+	2267.27i	0.0251566	+	0.0299804i
$276$		0			0
$277$	−76806.7	+	27955.3i	−1.00101	+	0.364339i	−0.789975	−	0.613139i	$-0.789906\pi$
$277$	−76806.7	+	27955.3i	−1.00101	+	0.364339i	−0.211037	+	0.977478i	$0.567684\pi$
$278$	−36490.3	−	21067.7i	−0.472158	−	0.272601i
$279$		0			0
$280$	−120418.	−	208570.i	−1.53595	−	2.66033i
$281$	−43102.4	+	51367.5i	−0.545870	+	0.650543i	−0.966493	−	0.256693i	$-0.917367\pi$
$281$	−43102.4	+	51367.5i	−0.545870	+	0.650543i	0.420623	+	0.907236i	$0.361812\pi$
$282$		0			0
$283$	12353.7	+	70061.5i	0.154250	+	0.874796i	0.959468	+	0.281817i	$0.0909371\pi$
$283$	12353.7	+	70061.5i	0.154250	+	0.874796i	−0.805218	+	0.592979i	$0.797952\pi$
$284$	−195192.	+	34417.6i	−2.42005	+	0.426721i
$285$		0			0
$286$	−117078.	−	98240.4i	−1.43135	−	1.20104i
$287$	−9213.36	+	5319.33i	−0.111855	+	0.0645793i
$288$		0			0
$289$	−31421.0	+	54422.8i	−0.376205	+	0.651606i
$290$	−59356.2	−	163080.i	−0.705781	−	1.93912i
$291$		0			0
$292$	149516.	−	125459.i	1.75357	−	1.47142i
$293$	10515.9	−	28892.3i	0.122493	−	0.336548i	−0.863256	−	0.504766i	$-0.831579\pi$
$293$	10515.9	−	28892.3i	0.122493	−	0.336548i	0.985750	+	0.168218i	$0.0538011\pi$
$294$		0			0
$295$	4655.67	−	26403.6i	0.0534981	−	0.303403i
$296$		−	314950.i		−	3.59467i
$297$		0			0
$298$	−162191.			−1.82639
$299$	87363.9	+	15404.6i	0.977214	+	0.172309i
$300$		0			0
$301$	−63065.3	−	22953.9i	−0.696077	−	0.253351i
$302$	52465.0	+	62525.4i	0.575249	+	0.685555i
$303$		0			0
$304$	72019.7	−	26213.0i	0.779300	−	0.283642i
$305$	−85293.6	−	49244.3i	−0.916889	−	0.529366i
$306$		0			0
$307$	−35558.1	−	61588.4i	−0.377278	−	0.653465i	0.613387	−	0.789782i	$-0.289807\pi$
$307$	−35558.1	−	61588.4i	−0.377278	−	0.653465i	−0.990665	+	0.136318i	$0.956473\pi$
$308$	−202559.	+	241401.i	−2.13526	+	2.54470i
$309$		0			0
$310$	10140.2	+	57508.0i	0.105517	+	0.598418i
$311$	74518.4	−	13139.6i	0.770447	−	0.135851i	0.225412	−	0.974264i	$-0.427627\pi$
$311$	74518.4	−	13139.6i	0.770447	−	0.135851i	0.545035	+	0.838413i	$0.316516\pi$
$312$		0			0
$313$	98496.9	+	82648.7i	1.00539	+	0.843621i	0.987722	−	0.156223i	$-0.0499319\pi$
$313$	98496.9	+	82648.7i	1.00539	+	0.843621i	0.0176665	+	0.999844i	$0.494376\pi$
$314$	−104245.	+	60186.1i	−1.05730	+	0.610431i
$315$		0			0
$316$	−74643.8	+	129287.i	−0.747514	+	1.29473i
$317$	9129.74	+	25083.8i	0.0908532	+	0.249617i	0.976794	−	0.214181i	$-0.0687084\pi$
$317$	9129.74	+	25083.8i	0.0908532	+	0.249617i	−0.885941	+	0.463798i	$0.846486\pi$
$318$		0			0
$319$	−97215.0	+	81573.1i	−0.955327	+	0.801614i
$320$	−3719.40	+	10219.0i	−0.0363222	+	0.0997945i
$321$		0			0
$322$	45774.1	−	259598.i	0.441477	−	2.50374i
$323$		−	23000.7i		−	0.220464i
$324$		0			0
$325$	3459.86			0.0327560
$326$	153522.	+	27070.0i	1.44456	+	0.254715i
$327$		0			0
$328$	22674.9	+	8252.97i	0.210764	+	0.0767119i
$329$	−106854.	−	127344.i	−0.987190	−	1.17649i
$330$		0			0
$331$	186022.	−	67706.5i	1.69789	−	0.617980i	0.702305	−	0.711876i	$-0.252154\pi$
$331$	186022.	−	67706.5i	1.69789	−	0.617980i	0.995582	+	0.0938957i	$0.0299320\pi$
$332$	213720.	+	123391.i	1.93896	+	1.11946i
$333$		0			0
$334$	16913.7	+	29295.4i	0.151616	+	0.262607i
$335$	−123226.	+	146855.i	−1.09803	+	1.30858i
$336$		0			0
$337$	−9308.32	−	52790.1i	−0.0819618	−	0.464828i	−0.997971	−	0.0636711i	$-0.979719\pi$
$337$	−9308.32	−	52790.1i	−0.0819618	−	0.464828i	0.916009	−	0.401157i	$-0.131392\pi$
$338$	27405.0	−	4832.24i	0.239881	−	0.0422975i
$339$		0			0
$340$	101629.	+	85276.5i	0.879140	+	0.737686i
$341$	36980.4	−	21350.7i	0.318027	−	0.183613i
$342$		0			0
$343$	20274.2	−	35115.9i	0.172328	−	0.298480i
$344$	52062.8	+	143041.i	0.439957	+	1.20877i
$345$		0			0
$346$	108106.	−	90711.4i	0.903018	−	0.757722i
$347$	−65936.4	+	181159.i	−0.547604	+	1.50453i	0.289333	+	0.957228i	$0.406566\pi$
$347$	−65936.4	+	181159.i	−0.547604	+	1.50453i	−0.836937	+	0.547300i	$0.815656\pi$
$348$		0			0
$349$	24859.7	−	140986.i	0.204101	−	1.15751i	−0.694747	−	0.719254i	$-0.744484\pi$
$349$	24859.7	−	140986.i	0.204101	−	1.15751i	0.898848	−	0.438260i	$-0.144405\pi$
$350$		−	10280.8i		−	0.0839248i
$351$		0			0
$352$	150555.			1.21509
$353$	−141463.	−	24943.8i	−1.13526	−	0.200177i	−0.425728	−	0.904851i	$-0.639982\pi$
$353$	−141463.	−	24943.8i	−1.13526	−	0.200177i	−0.709531	+	0.704674i	$0.751093\pi$
$354$		0			0
$355$	−130620.	−	47541.7i	−1.03646	−	0.377240i
$356$	−3908.40	−	4657.85i	−0.0308389	−	0.0367524i
$357$		0			0
$358$	−331970.	+	120827.i	−2.59020	+	0.942756i
$359$	62230.5	+	35928.8i	0.482852	+	0.278775i	0.721604	−	0.692306i	$-0.243405\pi$
$359$	62230.5	+	35928.8i	0.482852	+	0.278775i	−0.238752	+	0.971081i	$0.576738\pi$
$360$		0			0
$361$	52368.9	+	90705.6i	0.401845	+	0.696017i
$362$	234750.	−	279764.i	1.79138	−	2.13489i
$363$		0			0
$364$	63968.1	+	362781.i	0.482793	+	2.73805i
$365$	134803.	−	23769.4i	1.01184	−	0.178415i
$366$		0			0
$367$	153282.	+	128619.i	1.13804	+	0.954931i	0.999373	−	0.0354072i	$-0.0112728\pi$
$367$	153282.	+	128619.i	1.13804	+	0.954931i	0.138670	+	0.990339i	$0.455717\pi$
$368$	−234178.	+	135203.i	−1.72922	+	0.998366i
$369$		0			0
$370$	197616.	−	342282.i	1.44351	−	2.50023i
$371$	−9327.87	−	25628.1i	−0.0677696	−	0.186195i
$372$		0			0
$373$	131103.	−	110009.i	0.942313	−	0.790695i	−0.0356731	−	0.999364i	$-0.511358\pi$
$373$	131103.	−	110009.i	0.942313	−	0.790695i	0.977986	+	0.208669i	$0.0669131\pi$
$374$	47817.3	−	131377.i	0.341855	−	0.939239i
$375$		0			0
$376$	−65473.7	+	371320.i	−0.463117	+	2.62647i
$377$			148350.i			1.04377i
$378$		0			0
$379$	−129847.			−0.903971			−0.451985	−	0.892025i	$-0.649284\pi$
$379$	−129847.			−0.903971			−0.451985	+	0.892025i	$0.649284\pi$
$380$	145320.	+	25623.9i	1.00637	+	0.177451i
$381$		0			0
$382$	−382846.	−	139345.i	−2.62360	−	0.954912i
$383$	−8002.77	−	9537.33i	−0.0545560	−	0.0650173i	0.738076	−	0.674717i	$-0.235734\pi$
$383$	−8002.77	−	9537.33i	−0.0545560	−	0.0650173i	−0.792632	+	0.609700i	$0.791290\pi$
$384$		0			0
$385$	−207675.	+	75587.4i	−1.40108	+	0.509950i
$386$	−104831.	−	60524.4i	−0.703585	−	0.406215i
$387$		0			0
$388$	154278.	+	267218.i	1.02480	+	1.77501i
$389$	90611.4	−	107986.i	0.598803	−	0.713625i	−0.378469	−	0.925614i	$-0.623549\pi$
$389$	90611.4	−	107986.i	0.598803	−	0.713625i	0.977272	+	0.211988i	$0.0679939\pi$
$390$		0			0
$391$	14091.6	+	79917.7i	0.0921740	+	0.522745i
$392$	255935.	−	45128.2i	1.66555	−	0.293681i
$393$		0			0
$394$	−238330.	−	199982.i	−1.53527	−	1.28825i
$395$	−90670.7	+	52348.8i	−0.581129	+	0.335515i
$396$		0			0
$397$	16565.0	−	28691.4i	0.105102	−	0.182042i	−0.808678	−	0.588252i	$-0.799817\pi$
$397$	16565.0	−	28691.4i	0.105102	−	0.182042i	0.913780	+	0.406210i	$0.133150\pi$
$398$	−48504.0	−	133264.i	−0.306204	−	0.841289i
$399$		0			0
$400$	−8078.80	+	6778.92i	−0.0504925	+	0.0423682i
$401$	39602.8	−	108808.i	0.246285	−	0.676662i	−0.753530	−	0.657414i	$-0.771650\pi$
$401$	39602.8	−	108808.i	0.246285	−	0.676662i	0.999815	−	0.0192483i	$-0.00612732\pi$
$402$		0			0
$403$	8668.03	−	49158.9i	0.0533716	−	0.302686i
$404$			453541.i			2.77878i
$405$		0			0
$406$	440815.			2.67427
$407$	−284623.	−	50186.6i	−1.71823	−	0.302970i
$408$		0			0
$409$	165867.	+	60370.7i	0.991548	+	0.360894i	0.786320	−	0.617820i	$-0.211984\pi$
$409$	165867.	+	60370.7i	0.991548	+	0.360894i	0.205229	+	0.978714i	$0.434206\pi$
$410$	19464.2	+	23196.6i	0.115790	+	0.137993i
$411$		0			0
$412$	225337.	−	82015.9i	1.32751	−	0.483174i
$413$	58977.3	+	34050.6i	0.345768	+	0.199629i
$414$		0			0
$415$	86536.0	+	149885.i	0.502459	+	0.870284i
$416$	113128.	−	134821.i	0.653710	−	0.779061i
$417$		0			0
$418$	−27003.3	−	153143.i	−0.154548	−	0.876487i
$419$	−262487.	+	46283.6i	−1.49513	+	0.263632i	−0.860607	−	0.509269i	$-0.829916\pi$
$419$	−262487.	+	46283.6i	−1.49513	+	0.263632i	−0.634526	+	0.772901i	$0.718805\pi$
$420$		0			0
$421$	−236361.	−	198330.i	−1.33356	−	1.11899i	−0.983232	−	0.182360i	$-0.941626\pi$
$421$	−236361.	−	198330.i	−1.33356	−	1.11899i	−0.350326	−	0.936628i	$-0.613929\pi$
$422$	−186412.	+	107625.i	−1.04676	+	0.604349i
$423$		0			0
$424$	−30929.5	+	53571.4i	−0.172044	+	0.297990i
$425$	1082.48	+	2974.09i	0.00599298	+	0.0164656i
$426$		0			0
$427$	191638.	−	160804.i	1.05106	−	0.881942i
$428$	147947.	−	406480.i	0.807639	−	2.21897i
$429$		0			0
$430$	−33170.9	+	188121.i	−0.179399	+	1.01742i
$431$		−	275720.i		−	1.48427i	−0.670249	−	0.742137i	$-0.733813\pi$
$431$		−	275720.i		−	1.48427i	0.670249	−	0.742137i	$-0.266187\pi$
$432$		0			0
$433$	176040.			0.938933			0.469467	−	0.882950i	$-0.344446\pi$
$433$	176040.			0.938933			0.469467	+	0.882950i	$0.344446\pi$
$434$	−146073.	−	25756.6i	−0.775516	−	0.136744i
$435$		0			0
$436$	−631431.	−	229822.i	−3.32164	−	1.20898i
$437$	58019.3	+	69144.7i	0.303815	+	0.362073i
$438$		0			0
$439$	−146875.	+	53458.3i	−0.762114	+	0.277387i	−0.693694	−	0.720270i	$-0.744018\pi$
$439$	−146875.	+	53458.3i	−0.762114	+	0.277387i	−0.0684202	+	0.997657i	$0.521796\pi$
$440$	434110.	+	250633.i	2.24230	+	1.29459i
$441$		0			0
$442$	−81717.0	−	141538.i	−0.418281	−	0.724483i
$443$	189936.	−	226357.i	0.967831	−	1.15342i	−0.0202982	−	0.999794i	$-0.506462\pi$
$443$	189936.	−	226357.i	0.967831	−	1.15342i	0.988130	−	0.153623i	$-0.0490940\pi$
$444$		0			0
$445$	−740.483	−	4199.49i	−0.00373934	−	0.0212069i
$446$	−483447.	+	85244.8i	−2.43041	+	0.428547i
$447$		0			0
$448$	−21160.1	−	17755.4i	−0.105429	−	0.0884656i
$449$	−39669.7	+	22903.3i	−0.196773	+	0.113607i	−0.595150	−	0.803615i	$-0.702907\pi$
$449$	−39669.7	+	22903.3i	−0.196773	+	0.113607i	0.398376	+	0.917222i	$0.369574\pi$
$450$		0			0
$451$	11071.4	−	19176.3i	0.0544316	−	0.0942784i
$452$	87765.3	+	241133.i	0.429582	+	1.18027i
$453$		0			0
$454$	−231329.	+	194108.i	−1.12232	+	0.941741i
$455$	−88360.5	+	242768.i	−0.426811	+	1.17265i
$456$		0			0
$457$	36843.1	−	208948.i	0.176410	−	1.00047i	−0.760093	−	0.649814i	$-0.774847\pi$
$457$	36843.1	−	208948.i	0.176410	−	1.00047i	0.936504	−	0.350658i	$-0.114042\pi$
$458$		−	672606.i		−	3.20649i
$459$		0			0
$460$	−520625.			−2.46042
$461$	279504.	+	49284.1i	1.31518	+	0.231902i	0.786855	−	0.617138i	$-0.211708\pi$
$461$	279504.	+	49284.1i	1.31518	+	0.231902i	0.528328	+	0.849040i	$0.322819\pi$
$462$		0			0
$463$	100368.	+	36530.9i	0.468201	+	0.170411i	0.565337	−	0.824860i	$-0.308746\pi$
$463$	100368.	+	36530.9i	0.468201	+	0.170411i	−0.0971364	+	0.995271i	$0.530968\pi$
$464$	−290663.	−	346399.i	−1.35006	−	1.60894i
$465$		0			0
$466$	164980.	−	60047.7i	0.759729	−	0.276519i
$467$	−139206.	−	80370.9i	−0.638301	−	0.368523i	0.145659	−	0.989335i	$-0.453470\pi$
$467$	−139206.	−	80370.9i	−0.638301	−	0.368523i	−0.783960	+	0.620812i	$0.786803\pi$
$468$		0			0
$469$	−243471.	−	421704.i	−1.10688	−	1.91718i
$470$	−304141.	+	362461.i	−1.37683	+	1.64084i
$471$		0			0
$472$	−26822.3	−	152117.i	−0.120396	−	0.682800i
$473$	137563.	−	24256.1i	0.614866	−	0.108418i
$474$		0			0
$475$	2696.72	+	2262.82i	0.0119522	+	0.0100291i
$476$	−291833.	+	168490.i	−1.28802	+	0.743636i
$477$		0			0
$478$	−4309.11	+	7463.60i	−0.0188596	+	0.0326657i
$479$	73210.5	+	201144.i	0.319082	+	0.876670i	0.990736	+	0.135805i	$0.0433620\pi$
$479$	73210.5	+	201144.i	0.319082	+	0.876670i	−0.671654	+	0.740865i	$0.734416\pi$
$480$		0			0
$481$	−258810.	+	217167.i	−1.11864	+	0.938651i
$482$	160324.	−	440486.i	0.690087	−	1.89600i
$483$		0			0
$484$	21683.2	−	122971.i	0.0925619	−	0.524945i
$485$			216395.i			0.919950i
$486$		0			0
$487$	−55350.1			−0.233378			−0.116689	−	0.993168i	$-0.537228\pi$
$487$	−55350.1			−0.233378			−0.116689	+	0.993168i	$0.537228\pi$
$488$	−558793.	−	98530.3i	−2.34645	−	0.413742i
$489$		0			0
$490$	306461.	+	111543.i	1.27639	+	0.464567i
$491$	−12022.5	−	14327.8i	−0.0498690	−	0.0594316i	0.740533	−	0.672020i	$-0.234573\pi$
$491$	−12022.5	−	14327.8i	−0.0498690	−	0.0594316i	−0.790402	+	0.612588i	$0.790129\pi$
$492$		0			0
$493$	−127522.	+	46414.2i	−0.524676	+	0.190966i
$494$	−157429.	−	90892.0i	−0.645108	−	0.372453i
$495$		0			0
$496$	76077.3	+	131770.i	0.309237	+	0.535614i
$497$	226951.	−	270470.i	0.918798	−	1.09498i
$498$		0			0
$499$	60131.6	+	341023.i	0.241492	+	1.36957i	0.828501	+	0.559987i	$0.189194\pi$
$499$	60131.6	+	341023.i	0.241492	+	1.36957i	−0.587010	+	0.809580i	$0.699695\pi$
$500$	547848.	−	96600.3i	2.19139	−	0.386401i
$501$		0			0
$502$	579514.	+	486270.i	2.29962	+	1.92961i
$503$	186309.	−	107566.i	0.736374	−	0.425146i	−0.0843753	−	0.996434i	$-0.526889\pi$
$503$	186309.	−	107566.i	0.736374	−	0.425146i	0.820750	+	0.571288i	$0.193556\pi$
$504$		0			0
$505$	−159038.	+	275461.i	−0.623615	+	1.08013i
$506$	187650.	+	515564.i	0.732904	+	2.01364i
$507$		0			0
$508$	548200.	−	459995.i	2.12428	−	1.78248i
$509$	−125785.	+	345591.i	−0.485503	+	1.33391i	0.419210	+	0.907889i	$0.362307\pi$
$509$	−125785.	+	345591.i	−0.485503	+	1.33391i	−0.904714	+	0.426020i	$0.859915\pi$
$510$		0			0
$511$	−60375.4	+	342406.i	−0.231216	+	1.31129i
$512$		−	587049.i		−	2.23941i
$513$		0			0
$514$	522918.			1.97928
$515$	165619.	+	29203.1i	0.624448	+	0.110107i
$516$		0			0
$517$	325131.	+	118338.i	1.21640	+	0.442734i
$518$	645302.	+	769040.i	2.40493	+	2.86609i
$519$		0			0
$520$	550635.	−	200415.i	2.03637	−	0.741178i
$521$	29333.5	+	16935.7i	0.108066	+	0.0623919i	0.553059	−	0.833142i	$-0.313460\pi$
$521$	29333.5	+	16935.7i	0.108066	+	0.0623919i	−0.444993	+	0.895534i	$0.646794\pi$
$522$		0			0
$523$	−205272.	−	355541.i	−0.750456	−	1.29983i	−0.947602	−	0.319454i	$-0.896500\pi$
$523$	−205272.	−	355541.i	−0.750456	−	1.29983i	0.197145	−	0.980374i	$-0.436833\pi$
$524$	−101945.	+	121494.i	−0.371283	+	0.442478i
$525$		0			0
$526$	12245.1	+	69445.3i	0.0442578	+	0.250999i
$527$	44968.9	−	7929.24i	0.161917	−	0.0285503i
$528$		0			0
$529$	−29583.7	−	24823.6i	−0.105716	−	0.0887062i
$530$	−67227.0	+	38813.5i	−0.239327	+	0.138176i
$531$		0			0
$532$	−187408.	+	324600.i	−0.662162	+	1.14690i
$533$	−8853.09	−	24323.7i	−0.0311631	−	0.0856199i
$534$		0			0
$535$	232391.	−	194999.i	0.811918	−	0.681280i
$536$	−377746.	+	1.03785e6i	−1.31483	+	3.61247i
$537$		0			0
$538$	−63378.2	+	359436.i	−0.218965	+	1.24181i
$539$		−	238481.i		−	0.820874i
$540$		0			0
$541$	−210371.			−0.718772			−0.359386	−	0.933189i	$-0.617014\pi$
$541$	−210371.			−0.718772			−0.359386	+	0.933189i	$0.617014\pi$
$542$	871391.	+	153650.i	2.96629	+	0.523038i
$543$		0			0
$544$	151287.	+	55063.9i	0.511214	+	0.186067i
$545$	−302915.	−	361000.i	−1.01983	−	1.21538i
$546$		0			0
$547$	−162076.	+	58990.7i	−0.541680	+	0.197155i	−0.598346	−	0.801238i	$-0.704175\pi$
$547$	−162076.	+	58990.7i	−0.541680	+	0.197155i	0.0566659	+	0.998393i	$0.481953\pi$
$548$	527795.	+	304722.i	1.75753	+	1.01471i
$549$		0			0
$550$	10699.0	+	18531.2i	0.0353686	+	0.0612603i
$551$	−97024.1	+	115629.i	−0.319578	+	0.380858i
$552$		0			0
$553$	−46179.5	−	261897.i	−0.151008	−	0.856407i
$554$	−581955.	+	102614.i	−1.89614	+	0.334340i
$555$		0			0
$556$	−161927.	−	135873.i	−0.523804	−	0.439524i
$557$	127707.	−	73731.6i	0.411627	−	0.237653i	−0.279862	−	0.960040i	$-0.590289\pi$
$557$	127707.	−	73731.6i	0.411627	−	0.237653i	0.691489	+	0.722387i	$0.256955\pi$
$558$		0			0
$559$	81645.1	−	141414.i	0.261280	−	0.452551i
$560$	−269335.	−	739992.i	−0.858849	−	2.35967i
$561$		0			0
$562$	−371375.	+	311621.i	−1.17582	+	0.986629i
$563$	91822.0	−	252279.i	0.289688	−	0.795911i	−0.706422	−	0.707791i	$-0.749692\pi$
$563$	91822.0	−	252279.i	0.289688	−	0.795911i	0.996110	−	0.0881198i	$-0.0280858\pi$
$564$		0			0
$565$	−31250.3	+	177229.i	−0.0978943	+	0.555186i
$566$			514343.i			1.60553i
$567$		0			0
$568$	−800823.			−2.48222
$569$	169548.	+	29895.9i	0.523684	+	0.0923396i	0.429240	−	0.903191i	$-0.358782\pi$
$569$	169548.	+	29895.9i	0.523684	+	0.0923396i	0.0944440	+	0.995530i	$0.469893\pi$
$570$		0			0
$571$	−66547.8	−	24221.4i	−0.204109	−	0.0742895i	0.237943	−	0.971279i	$-0.423527\pi$
$571$	−66547.8	−	24221.4i	−0.204109	−	0.0742895i	−0.442051	+	0.896990i	$0.645749\pi$
$572$	−492842.	−	587347.i	−1.50632	−	1.79516i
$573$		0			0
$574$	−72276.6	+	26306.5i	−0.219368	+	0.0798435i
$575$	−10756.3	−	6210.15i	−0.0325332	−	0.0187831i
$576$		0			0
$577$	267806.	+	463853.i	0.804393	+	1.39325i	0.916700	+	0.399577i	$0.130843\pi$
$577$	267806.	+	463853.i	0.804393	+	1.39325i	−0.112306	+	0.993674i	$0.535824\pi$
$578$	−292040.	+	348040.i	−0.874151	+	1.04177i
$579$		0			0
$580$	−151183.	−	857400.i	−0.449414	−	2.54875i
$581$	−432933.	+	76337.7i	−1.28253	+	0.226145i
$582$		0			0
$583$	43484.3	+	36487.6i	0.127937	+	0.107352i
$584$	682954.	−	394304.i	2.00247	−	1.15613i
$585$		0			0
$586$	111145.	−	192509.i	0.323665	−	0.560604i
$587$	−153583.	−	421967.i	−0.445726	−	1.22462i	−0.935672	−	0.352870i	$-0.885206\pi$
$587$	−153583.	−	421967.i	−0.445726	−	1.22462i	0.489946	−	0.871753i	$-0.337017\pi$
$588$		0			0
$589$	38907.0	−	32646.9i	0.112150	−	0.0941047i
$590$	66296.2	−	182147.i	0.190451	−	0.523261i
$591$		0			0
$592$	178826.	−	1.01417e6i	0.510256	−	2.89381i
$593$			240988.i			0.685310i	0.939461	+	0.342655i	$0.111326\pi$
$593$			240988.i			0.685310i	−0.939461	+	0.342655i	$0.888674\pi$
$594$		0			0
$595$	−236329.			−0.667549
$596$	−801299.	−	141291.i	−2.25581	−	0.397760i
$597$		0			0
$598$	602686.	+	219360.i	1.68534	+	0.613415i
$599$	260613.	+	310587.i	0.726345	+	0.865624i	0.995231	−	0.0975482i	$-0.0311000\pi$
$599$	260613.	+	310587.i	0.726345	+	0.865624i	−0.268886	+	0.963172i	$0.586656\pi$
$600$		0			0
$601$	217746.	−	79253.1i	0.602839	−	0.219415i	−0.0225280	−	0.999746i	$-0.507172\pi$
$601$	217746.	−	79253.1i	0.602839	−	0.219415i	0.625367	+	0.780331i	$0.284949\pi$
$602$	−420203.	−	242605.i	−1.15949	−	0.669431i
$603$		0			0
$604$	204734.	+	354610.i	0.561198	+	0.972024i
$605$	56290.3	−	67084.1i	0.153788	−	0.183277i
$606$		0			0
$607$	−26009.7	−	147508.i	−0.0705924	−	0.400350i	−0.999545	−	0.0301517i	$-0.990401\pi$
$607$	−26009.7	−	147508.i	−0.0705924	−	0.400350i	0.928953	−	0.370198i	$-0.120710\pi$
$608$	176352.	−	31095.6i	0.477060	−	0.0841185i
$609$		0			0
$610$	−545462.	−	457697.i	−1.46590	−	1.23004i
$611$	350277.	−	202233.i	0.938273	−	0.541712i
$612$		0			0
$613$	43415.0	−	75197.0i	0.115536	−	0.200115i	−0.802458	−	0.596709i	$-0.796475\pi$
$613$	43415.0	−	75197.0i	0.115536	−	0.200115i	0.917994	+	0.396594i	$0.129808\pi$
$614$	−175851.	−	483146.i	−0.466453	−	1.28157i
$615$		0			0
$616$	−975361.	+	818425.i	−2.57042	+	2.15684i
$617$	−212153.	+	582885.i	−0.557286	+	1.53113i	0.266271	+	0.963898i	$0.414208\pi$
$617$	−212153.	+	582885.i	−0.557286	+	1.53113i	−0.823557	+	0.567233i	$0.808014\pi$
$618$		0			0
$619$	74877.2	−	424650.i	0.195420	−	1.10828i	−0.716400	−	0.697689i	$-0.754212\pi$
$619$	74877.2	−	424650.i	0.195420	−	1.10828i	0.911820	−	0.410590i	$-0.134677\pi$
$620$			292951.i			0.762098i
$621$		0			0
$622$	547062.			1.41402
$623$	10666.9	+	1880.86i	0.0274829	+	0.00484598i
$624$		0			0
$625$	379538.	+	138141.i	0.971618	+	0.353640i
$626$	597531.	+	712110.i	1.52480	+	1.81718i
$627$		0			0
$628$	−567453.	+	206536.i	−1.43883	+	0.523692i
$629$	−267651.	−	154528.i	−0.676499	−	0.390577i
$630$		0			0
$631$	113366.	+	196356.i	0.284724	+	0.493156i	0.972542	−	0.232727i	$-0.0747647\pi$
$631$	113366.	+	196356.i	0.284724	+	0.493156i	−0.687818	+	0.725883i	$0.741431\pi$
$632$	−387720.	+	462066.i	−0.970697	+	1.15683i
$633$		0			0
$634$	33512.1	+	190057.i	0.0833725	+	0.472829i
$635$	494253.	−	87150.2i	1.22575	−	0.216133i
$636$		0			0
$637$	−213558.	−	179197.i	−0.526305	−	0.441623i
$638$	−794574.	+	458747.i	−1.95206	+	1.12702i
$639$		0			0
$640$	188511.	−	326511.i	0.460232	−	0.797145i
$641$	−135909.	−	373408.i	−0.330775	−	0.908797i	−0.987911	−	0.155025i	$-0.950454\pi$
$641$	−135909.	−	373408.i	−0.330775	−	0.908797i	0.657135	−	0.753773i	$-0.271768\pi$
$642$		0			0
$643$	−106086.	+	89016.4i	−0.256587	+	0.215302i	−0.762003	−	0.647574i	$-0.775784\pi$
$643$	−106086.	+	89016.4i	−0.256587	+	0.215302i	0.505416	+	0.862876i	$0.331339\pi$
$644$	452292.	−	1.24266e6i	1.09055	−	2.99627i
$645$		0			0
$646$	28876.0	−	163764.i	0.0691945	−	0.392421i
$647$		−	303133.i		−	0.724144i	−0.932150	−	0.362072i	$-0.882069\pi$
$647$		−	303133.i		−	0.724144i	0.932150	−	0.362072i	$-0.117931\pi$
$648$		0			0
$649$	−141743.			−0.336521
$650$	24633.9	+	4343.63i	0.0583052	+	0.0102808i
$651$		0			0
$652$	734890.	+	267478.i	1.72873	+	0.629207i
$653$	−291500.	−	347396.i	−0.683615	−	0.814701i	0.306953	−	0.951725i	$-0.400691\pi$
$653$	−291500.	−	347396.i	−0.683615	−	0.814701i	−0.990568	+	0.137024i	$0.956246\pi$
$654$		0			0
$655$	−104520.	+	38042.1i	−0.243622	+	0.0886711i
$656$	68329.6	+	39450.1i	0.158782	+	0.0916728i
$657$		0			0
$658$	−600924.	−	1.04083e6i	−1.38793	−	2.40397i
$659$	−182083.	+	216998.i	−0.419274	+	0.499671i	−0.933796	−	0.357806i	$-0.883525\pi$
$659$	−182083.	+	216998.i	−0.419274	+	0.499671i	0.514522	+	0.857477i	$0.327969\pi$
$660$		0			0
$661$	84714.7	+	480441.i	0.193890	+	1.09961i	0.913991	+	0.405736i	$0.132985\pi$
$661$	84714.7	+	480441.i	0.193890	+	1.09961i	−0.720100	+	0.693870i	$0.755904\pi$
$662$	1.40947e6	−	248527.i	3.21617	−	0.567097i
$663$		0			0
$664$	763826.	+	640926.i	1.73244	+	1.45369i
$665$	−227646.	+	131432.i	−0.514775	+	0.297206i
$666$		0			0
$667$	266276.	−	461203.i	0.598522	−	1.03667i
$668$	58041.4	+	159468.i	0.130072	+	0.357371i
$669$		0			0
$670$	−1.06173e6	+	890896.i	−2.36518	+	1.98462i
$671$	−178085.	+	489284.i	−0.395532	+	1.08672i
$672$		0			0
$673$	61594.7	−	349321.i	0.135992	−	0.771248i	−0.838172	−	0.545406i	$-0.816375\pi$
$673$	61594.7	−	349321.i	0.135992	−	0.771248i	0.974164	−	0.225842i	$-0.0725134\pi$
$674$		−	387548.i		−	0.853111i
$675$		0			0
$676$	139603.			0.305494
$677$	−120244.	−	21202.3i	−0.262353	−	0.0462599i	0.0409243	−	0.999162i	$-0.486970\pi$
$677$	−120244.	−	21202.3i	−0.262353	−	0.0462599i	−0.303277	+	0.952902i	$0.598081\pi$
$678$		0			0
$679$	−516506.	−	187993.i	−1.12030	−	0.407757i
$680$	344553.	+	410622.i	0.745141	+	0.888024i
$681$		0			0
$682$	290103.	−	105589.i	0.623710	−	0.227012i
$683$	439872.	+	253960.i	0.942942	+	0.544408i	0.890881	−	0.454236i	$-0.150088\pi$
$683$	439872.	+	253960.i	0.942942	+	0.544408i	0.0520609	+	0.998644i	$0.483421\pi$
$684$		0			0
$685$	213706.	+	370150.i	0.455445	+	0.788854i
$686$	188437.	−	224570.i	0.400421	−	0.477204i
$687$		0			0
$688$	86430.2	+	490170.i	0.182595	+	1.03555i
$689$	65348.9	−	11522.8i	0.137658	−	0.0242727i
$690$		0			0
$691$	−306096.	−	256845.i	−0.641065	−	0.537917i	0.263280	−	0.964719i	$-0.415196\pi$
$691$	−306096.	−	256845.i	−0.641065	−	0.537917i	−0.904345	+	0.426802i	$0.859640\pi$
$692$	613117.	−	353983.i	1.28036	−	0.739214i
$693$		0			0
$694$	−696896.	+	1.20706e6i	−1.44694	+	2.50616i
$695$	−50702.5	−	139304.i	−0.104969	−	0.288399i
$696$		0			0
$697$	18138.8	−	15220.2i	0.0373373	−	0.0313297i
$698$	353999.	−	972604.i	0.726593	−	1.99630i
$699$		0			0
$700$	8956.01	−	50792.1i	0.0182776	−	0.103657i
$701$		−	51063.9i		−	0.103915i	−0.998649	−	0.0519574i	$-0.983454\pi$
$701$		−	51063.9i		−	0.103915i	0.998649	−	0.0519574i	$-0.0165460\pi$
$702$		0			0
$703$	−343756.			−0.695569
$704$	56618.9	+	9983.44i	0.114239	+	0.0201435i
$705$		0			0
$706$	−975895.	−	355197.i	−1.95791	−	0.712623i
$707$	−519325.	−	618908.i	−1.03896	−	1.23819i
$708$		0			0
$709$	219521.	−	79899.1i	0.436701	−	0.158946i	−0.114308	−	0.993445i	$-0.536465\pi$
$709$	219521.	−	79899.1i	0.436701	−	0.158946i	0.551009	+	0.834499i	$0.314243\pi$
$710$	−870318.	−	502478.i	−1.72648	−	0.996783i
$711$		0			0
$712$	−12283.7	−	21276.0i	−0.0242308	−	0.0419690i
$713$	−115184.	+	137271.i	−0.226575	+	0.270022i
$714$		0			0
$715$	−93373.5	−	529548.i	−0.182647	−	1.03584i
$716$	−1.74535e6	+	307753.i	−3.40453	+	0.600310i
$717$		0			0
$718$	397971.	+	333937.i	0.771973	+	0.647762i
$719$	−390392.	+	225393.i	−0.755167	+	0.435996i	−0.827558	−	0.561380i	$-0.810270\pi$
$719$	−390392.	+	225393.i	−0.755167	+	0.435996i	0.0723907	+	0.997376i	$0.476937\pi$
$720$		0			0
$721$	−213585.	+	369941.i	−0.410867	+	0.711642i
$722$	258988.	+	711564.i	0.496827	+	1.36502i
$723$		0			0
$724$	1.40349e6	−	1.17767e6i	2.67752	−	2.24671i
$725$	7103.80	−	19517.5i	0.0135150	−	0.0371321i
$726$		0			0
$727$	−42168.2	+	239148.i	−0.0797841	+	0.452478i	0.918577	+	0.395243i	$0.129340\pi$
$727$	−42168.2	+	239148.i	−0.0797841	+	0.452478i	−0.998361	+	0.0572351i	$0.981772\pi$
$728$			1.48840e6i			2.80839i
$729$		0			0
$730$	989627.			1.85706
$731$	147103.	+	25938.3i	0.275288	+	0.0485408i
$732$		0			0
$733$	553098.	+	201311.i	1.02942	+	0.374679i	0.800861	−	0.598850i	$-0.204375\pi$
$733$	553098.	+	201311.i	1.02942	+	0.374679i	0.228562	+	0.973529i	$0.426598\pi$
$734$	929884.	+	1.10819e6i	1.72598	+	2.05695i
$735$		0			0
$736$	−593696.	+	216088.i	−1.09599	+	0.398909i
$737$	877718.	+	506751.i	1.61592	+	0.932952i
$738$		0			0
$739$	−193191.	−	334617.i	−0.353751	−	0.612716i	0.633152	−	0.774027i	$-0.281761\pi$
$739$	−193191.	−	334617.i	−0.353751	−	0.612716i	−0.986903	+	0.161312i	$0.948427\pi$
$740$	1.27450e6	−	1.51888e6i	2.32742	−	2.77371i
$741$		0			0
$742$	−34239.4	−	194181.i	−0.0621896	−	0.352695i
$743$	679396.	−	119796.i	1.23068	−	0.217002i	0.479763	−	0.877398i	$-0.340723\pi$
$743$	679396.	−	119796.i	1.23068	−	0.217002i	0.750918	+	0.660396i	$0.229612\pi$
$744$		0			0
$745$	−437130.	−	366795.i	−0.787585	−	0.660863i
$746$	1.07155e6	−	618662.i	1.92547	−	1.11167i
$747$		0			0
$748$	350688.	−	607410.i	0.626785	−	1.08562i
$749$	263548.	+	724092.i	0.469782	+	1.29072i
$750$		0			0
$751$	−314821.	+	264166.i	−0.558193	+	0.468379i	−0.877704	−	0.479203i	$-0.840926\pi$
$751$	−314821.	+	264166.i	−0.558193	+	0.468379i	0.319511	+	0.947582i	$0.396481\pi$
$752$	−421665.	+	1.15851e6i	−0.745644	+	2.04864i
$753$		0			0
$754$	−186244.	+	1.05624e6i	−0.327597	+	1.85790i
$755$			287166.i			0.503778i
$756$		0			0
$757$	235863.			0.411594			0.205797	−	0.978595i	$-0.434021\pi$
$757$	235863.			0.411594			0.205797	+	0.978595i	$0.434021\pi$
$758$	−924504.	−	163015.i	−1.60905	−	0.283719i
$759$		0			0
$760$	560257.	+	203917.i	0.969975	+	0.353042i
$761$	−458695.	−	546651.i	−0.792053	−	0.943932i	0.207357	−	0.978265i	$-0.433514\pi$
$761$	−458695.	−	546651.i	−0.792053	−	0.943932i	−0.999410	+	0.0343333i	$0.989069\pi$
$762$		0			0
$763$	1.12481e6	−	409399.i	1.93211	−	0.703230i
$764$	−1.77006e6	−	1.02194e6i	−3.03250	−	1.75081i
$765$		0			0
$766$	−45005.7	−	77952.1i	−0.0767025	−	0.132853i
$767$	−106507.	+	126930.i	−0.181045	+	0.215761i
$768$		0			0
$769$	−167796.	−	951617.i	−0.283745	−	1.60920i	−0.709734	−	0.704469i	$-0.751185\pi$
$769$	−167796.	−	951617.i	−0.283745	−	1.60920i	0.425989	−	0.904728i	$-0.359926\pi$
$770$	−1.57352e6	+	277455.i	−2.65395	+	0.467962i
$771$		0			0
$772$	−465192.	−	390342.i	−0.780544	−	0.654954i
$773$	−730930.	+	422003.i	−1.22325	+	0.706246i	−0.965610	−	0.259993i	$-0.916280\pi$
$773$	−730930.	+	422003.i	−1.22325	+	0.706246i	−0.257644	+	0.966240i	$0.582946\pi$
$774$		0			0
$775$	−3494.39	+	6052.46i	−0.00581792	+	0.0100769i
$776$	426396.	+	1.17151e6i	0.708092	+	1.94547i
$777$		0			0
$778$	780717.	−	655100.i	1.28984	−	1.08230i
$779$	9007.80	−	24748.7i	0.0148438	−	0.0407829i
$780$		0			0
$781$	−127609.	+	723709.i	−0.209209	+	1.18648i
$782$			586700.i			0.959406i
$783$		0			0
$784$	849762.			1.38250
$785$	−417069.	−	73540.6i	−0.676813	−	0.119340i
$786$		0			0
$787$	−349313.	−	127140.i	−0.563982	−	0.205273i	0.0442659	−	0.999020i	$-0.485905\pi$
$787$	−349313.	−	127140.i	−0.563982	−	0.205273i	−0.608248	+	0.793747i	$0.708127\pi$
$788$	−1.00325e6	−	1.19563e6i	−1.61569	−	1.92550i
$789$		0			0
$790$	−711290.	+	258888.i	−1.13971	+	0.414819i
$791$	−395874.	−	228558.i	−0.632709	−	0.365295i
$792$		0			0
$793$	304336.	+	527126.i	0.483958	+	0.838240i
$794$	153962.	−	183485.i	0.244215	−	0.291044i
$795$		0			0
$796$	−123542.	−	700640.i	−0.194979	−	1.10578i
$797$	−465192.	+	82025.9i	−0.732345	+	0.129132i	−0.527371	−	0.849635i	$-0.676822\pi$
$797$	−465192.	+	82025.9i	−0.732345	+	0.129132i	−0.204974	+	0.978767i	$0.565711\pi$
$798$		0			0
$799$	283430.	+	237826.i	0.443969	+	0.372534i
$800$	−21339.6	+	12320.4i	−0.0333431	+	0.0192507i
$801$		0			0
$802$	418571.	−	724986.i	0.650759	−	1.12715i
$803$	−247508.	−	680021.i	−0.383846	−	1.05461i
$804$		0			0
$805$	710451.	−	596139.i	1.09633	−	0.919932i
$806$	123432.	−	339126.i	0.190001	−	0.522024i
$807$		0			0
$808$	−318210.	+	1.80466e6i	−0.487406	+	2.76422i
$809$			712287.i			1.08832i	0.838980	+	0.544162i	$0.183152\pi$
$809$			712287.i			1.08832i	−0.838980	+	0.544162i	$0.816848\pi$
$810$		0			0
$811$	169586.			0.257839			0.128919	−	0.991655i	$-0.458849\pi$
$811$	169586.			0.257839			0.128919	+	0.991655i	$0.458849\pi$
$812$	2.17784e6	+	384012.i	3.30304	+	0.582415i
$813$		0			0
$814$	−1.96349e6	−	714651.i	−2.96333	−	1.07856i
$815$	352547.	+	420149.i	0.530764	+	0.632540i
$816$		0			0
$817$	156124.	−	56824.6i	0.233898	−	0.0851318i
$818$	1.10517e6	+	638071.i	1.65167	+	0.953592i
$819$		0			0
$820$	75955.2	+	131558.i	0.112961	+	0.195655i
$821$	464808.	−	553937.i	0.689584	−	0.821815i	−0.301721	−	0.953396i	$-0.597561\pi$
$821$	464808.	−	553937.i	0.689584	−	0.821815i	0.991305	+	0.131582i	$0.0420056\pi$
$822$		0			0
$823$	198478.	+	1.12563e6i	0.293031	+	1.66186i	0.675099	+	0.737727i	$0.264101\pi$
$823$	198478.	+	1.12563e6i	0.293031	+	1.66186i	−0.382068	+	0.924134i	$0.624788\pi$
$824$	954167.	−	168245.i	1.40530	−	0.247793i
$825$		0			0
$826$	377166.	+	316480.i	0.552806	+	0.463859i
$827$	1.06404e6	−	614325.i	1.55578	−	0.898229i	0.558126	−	0.829756i	$-0.311521\pi$
$827$	1.06404e6	−	614325.i	1.55578	−	0.898229i	0.997653	−	0.0684732i	$-0.0218128\pi$
$828$		0			0
$829$	−678194.	+	1.17467e6i	−0.986836	+	1.70925i	−0.353361	+	0.935487i	$0.614961\pi$
$829$	−678194.	+	1.17467e6i	−0.986836	+	1.70925i	−0.633475	+	0.773763i	$0.718372\pi$
$830$	427960.	+	1.17581e6i	0.621222	+	1.70679i
$831$		0			0
$832$	51484.1	−	43200.3i	0.0743749	−	0.0624079i
$833$	87221.8	−	239640.i	0.125700	−	0.345358i
$834$		0			0
$835$	−20666.6	+	117206.i	−0.0296413	+	0.168104i
$836$		−	780126.i		−	1.11623i
$837$		0			0
$838$	−1.92700e6			−2.74406
$839$	−746116.	−	131560.i	−1.05994	−	0.186897i	−0.383612	−	0.923494i	$-0.625320\pi$
$839$	−746116.	−	131560.i	−1.05994	−	0.186897i	−0.676331	+	0.736598i	$0.736431\pi$
$840$		0			0
$841$	172237.	+	62689.2i	0.243520	+	0.0886341i
$842$	−1.43388e6	−	1.70884e6i	−2.02251	−	2.41033i
$843$		0			0
$844$	−1.01472e6	+	369328.i	−1.42450	+	0.518475i
$845$	84789.0	+	48952.9i	0.118748	+	0.0685591i
$846$		0			0
$847$	111219.	+	192637.i	0.155028	+	0.268517i
$848$	−130014.	+	154944.i	−0.180800	+	0.215469i
$849$		0			0
$850$	3973.41	+	22534.3i	0.00549953	+	0.0311894i
$851$	1.19441e6	−	210606.i	1.64927	−	0.290811i
$852$		0			0
$853$	601574.	+	504780.i	0.826782	+	0.693752i	0.954550	−	0.298052i	$-0.0963369\pi$
$853$	601574.	+	504780.i	0.826782	+	0.693752i	−0.127768	+	0.991804i	$0.540781\pi$
$854$	1.56633e6	−	904321.i	2.14767	−	1.23996i
$855$		0			0
$856$	873876.	−	1.51360e6i	1.19262	−	2.06568i
$857$	351199.	+	964912.i	0.478180	+	1.31379i	0.911036	+	0.412327i	$0.135284\pi$
$857$	351199.	+	964912.i	0.478180	+	1.31379i	−0.432856	+	0.901463i	$0.642494\pi$
$858$		0			0
$859$	−805269.	+	675701.i	−1.09133	+	0.915732i	−0.996812	−	0.0797913i	$-0.974575\pi$
$859$	−805269.	+	675701.i	−1.09133	+	0.915732i	−0.0945154	+	0.995523i	$0.530130\pi$
$860$	−327760.	+	900514.i	−0.443159	+	1.21757i
$861$		0			0
$862$	346149.	−	1.96311e6i	0.465853	−	2.64198i
$863$			369062.i			0.495539i	0.968819	+	0.247770i	$0.0796976\pi$
$863$			369062.i			0.495539i	−0.968819	+	0.247770i	$0.920302\pi$
$864$		0			0
$865$	496507.			0.663580
$866$	1.25339e6	+	221007.i	1.67129	+	0.294693i
$867$		0			0
$868$	−699234.	−	254500.i	−0.928075	−	0.337792i
$869$	355790.	+	424014.i	0.471144	+	0.561488i
$870$		0			0
$871$	1.11332e6	−	405214.i	1.46752	−	0.534132i
$872$	−2.35124e6	−	1.35749e6i	−3.09218	−	1.78527i
$873$		0			0
$874$	326287.	+	565145.i	0.427146	+	0.739839i
$875$	−636988.	+	759132.i	−0.831984	+	0.991520i
$876$		0			0
$877$	213744.	+	1.21220e6i	0.277904	+	1.57607i	0.729583	+	0.683892i	$0.239714\pi$
$877$	213744.	+	1.21220e6i	0.277904	+	1.57607i	−0.451679	+	0.892180i	$0.649175\pi$
$878$	−1.11286e6	+	196227.i	−1.44361	+	0.254548i
$879$		0			0
$880$	1.25557e6	+	1.05355e6i	1.62135	+	1.36047i
$881$	−495635.	+	286155.i	−0.638572	+	0.368680i	−0.784064	−	0.620679i	$-0.786857\pi$
$881$	−495635.	+	286155.i	−0.638572	+	0.368680i	0.145492	+	0.989359i	$0.453524\pi$
$882$		0			0
$883$	353760.	−	612730.i	0.453719	−	0.785864i	−0.544895	−	0.838504i	$-0.683430\pi$
$883$	353760.	−	612730.i	0.453719	−	0.785864i	0.998614	+	0.0526404i	$0.0167637\pi$
$884$	−280422.	−	770453.i	−0.358845	−	0.985920i
$885$		0			0
$886$	1.63651e6	−	1.37319e6i	2.08473	−	1.74930i
$887$	−141090.	+	387641.i	−0.179328	+	0.492700i	−0.996490	−	0.0837080i	$-0.973324\pi$
$887$	−141090.	+	387641.i	−0.179328	+	0.492700i	0.817162	+	0.576408i	$0.195546\pi$
$888$		0			0
$889$	−221366.	+	1.25543e6i	−0.280096	+	1.58850i
$890$		−	30829.7i		−	0.0389215i
$891$		0			0
$892$	−2.46272e6			−3.09518
$893$	405281.	+	71462.0i	0.508222	+	0.0896133i
$894$		0			0
$895$	−1.16797e6	−	425105.i	−1.45809	−	0.530701i
$896$	615569.	+	733607.i	0.766762	+	0.913792i
$897$		0			0
$898$	−311199.	+	113267.i	−0.385910	+	0.140460i
$899$	−259515.	−	149831.i	−0.321102	−	0.185388i
$900$		0			0
$901$	30350.6	+	52568.8i	0.0373868	+	0.0647558i
$902$	102903.	−	122635.i	0.126478	−	0.150730i
$903$		0			0
$904$	180040.	+	1.02106e6i	0.220308	+	1.24943i
$905$	1.26538e6	−	223120.i	1.54498	−	0.272422i
$906$		0			0
$907$	−1.20036e6	−	1.00722e6i	−1.45914	−	1.22436i	−0.925552	−	0.378620i	$-0.876399\pi$
$907$	−1.20036e6	−	1.00722e6i	−1.45914	−	1.22436i	−0.533588	−	0.845745i	$-0.679157\pi$
$908$	−1.31197e6	+	757467.i	−1.59130	+	0.918739i
$909$		0			0
$910$	−933901.	+	1.61756e6i	−1.12776	+	1.95334i
$911$	−93821.4	−	257772.i	−0.113049	−	0.310598i	0.870247	−	0.492616i	$-0.163959\pi$
$911$	−93821.4	−	257772.i	−0.113049	−	0.310598i	−0.983295	+	0.182018i	$0.941737\pi$
$912$		0			0
$913$	700923.	−	588144.i	0.840869	−	0.705573i
$914$	524641.	−	1.44144e6i	0.628015	−	1.72546i
$915$		0			0
$916$	585934.	−	3.32300e6i	0.698325	−	3.96040i
$917$		−	282524.i		−	0.335983i
$918$		0			0
$919$	833152.			0.986491			0.493246	−	0.869890i	$-0.335810\pi$
$919$	833152.			0.986491			0.493246	+	0.869890i	$0.335810\pi$
$920$	−2.07159e6	−	365276.i	−2.44753	−	0.431565i
$921$		0			0
$922$	1.92818e6	+	701799.i	2.26822	+	0.825565i
$923$	552190.	+	658075.i	0.648165	+	0.772452i
$924$		0			0
$925$	44449.2	−	16178.2i	0.0519494	−	0.0189080i
$926$	668749.	+	386103.i	0.779905	+	0.450278i
$927$		0			0
$928$	−528269.	−	914989.i	−0.613422	−	1.06248i
$929$	−413834.	+	493188.i	−0.479507	+	0.571454i	−0.950516	−	0.310674i	$-0.899445\pi$
$929$	−413834.	+	493188.i	−0.479507	+	0.571454i	0.471010	+	0.882128i	$0.343890\pi$
$930$		0			0
$931$	−49255.7	−	279343.i	−0.0568274	−	0.322284i
$932$	867389.	−	152944.i	0.998578	−	0.176076i
$933$		0			0
$934$	−890240.	−	747000.i	−1.02050	−	0.856302i
$935$	425986.	−	245943.i	0.487272	−	0.281327i
$936$		0			0
$937$	−174761.	+	302695.i	−0.199051	+	0.344767i	−0.948221	−	0.317611i	$-0.897119\pi$
$937$	−174761.	+	302695.i	−0.199051	+	0.344767i	0.749170	+	0.662378i	$0.230453\pi$
$938$	−1.20407e6	−	3.30817e6i	−1.36851	−	3.75995i
$939$		0			0
$940$	−1.81836e6	+	1.52578e6i	−2.05790	+	1.72678i
$941$	239502.	−	658026.i	0.270477	−	0.743128i	−0.727874	−	0.685711i	$-0.759491\pi$
$941$	239502.	−	658026.i	0.270477	−	0.743128i	0.998350	−	0.0574171i	$-0.0182865\pi$
$942$		0			0
$943$	−16135.7	+	91510.0i	−0.0181453	+	0.102907i
$944$		−	505063.i		−	0.566763i
$945$		0			0
$946$	1.00989e6			1.12848
$947$	−764050.	−	134723.i	−0.851965	−	0.150224i	−0.269420	−	0.963023i	$-0.586832\pi$
$947$	−764050.	−	134723.i	−0.851965	−	0.150224i	−0.582545	+	0.812798i	$0.697943\pi$
$948$		0			0
$949$	−794934.	−	289332.i	−0.882671	−	0.321266i
$950$	16359.7	+	19496.7i	0.0181270	+	0.0216030i
$951$		0			0
$952$	−1.27943e6	+	465675.i	−1.41170	+	0.513817i
$953$	42843.8	+	24735.9i	0.0471740	+	0.0272359i	0.523401	−	0.852086i	$-0.324663\pi$
$953$	42843.8	+	24735.9i	0.0471740	+	0.0272359i	−0.476228	+	0.879322i	$0.657996\pi$
$954$		0			0
$955$	−716703.	−	1.24137e6i	−0.785837	−	1.36111i
$956$	−27790.9	+	33119.9i	−0.0304079	+	0.0362388i
$957$		0			0
$958$	268730.	+	1.52404e6i	0.292809	+	1.66060i
$959$	−1.06916e6	+	188521.i	−1.16253	+	0.204985i
$960$		0			0
$961$	−630217.	−	528815.i	−0.682407	−	0.572607i
$962$	−2.11535e6	+	1.22130e6i	−2.28577	+	1.31969i
$963$		0			0
$964$	1.17580e6	−	2.03655e6i	1.26526	−	2.19150i
$965$	−145661.	−	400200.i	−0.156419	−	0.429756i
$966$		0			0
$967$	−702808.	+	589726.i	−0.751595	+	0.630663i	−0.935924	−	0.352202i	$-0.885433\pi$
$967$	−702808.	+	589726.i	−0.751595	+	0.630663i	0.184329	+	0.982865i	$0.440989\pi$
$968$	172556.	−	474095.i	0.184154	−	0.505958i
$969$		0			0
$970$	−271670.	+	1.54072e6i	−0.288735	+	1.63749i
$971$		−	498736.i		−	0.528972i	−0.964390	−	0.264486i	$-0.914798\pi$
$971$		−	498736.i		−	0.528972i	0.964390	−	0.264486i	$-0.0852023\pi$
$972$		0			0
$973$	376547.			0.397735
$974$	−394089.	−	69488.5i	−0.415410	−	0.0732479i
$975$		0			0
$976$	−1.74343e6	−	634557.i	−1.83023	−	0.666148i
$977$	−483694.	−	576444.i	−0.506736	−	0.603904i	0.450655	−	0.892698i	$-0.351190\pi$
$977$	−483694.	−	576444.i	−0.506736	−	0.603904i	−0.957391	+	0.288794i	$0.906746\pi$
$978$		0			0
$979$	−21184.6	+	7710.56i	−0.0221032	+	0.00804490i
$980$	1.41689e6	+	818044.i	1.47532	+	0.851775i
$981$		0			0
$982$	−67611.5	−	117107.i	−0.0701129	−	0.121439i
$983$	320924.	−	382463.i	0.332120	−	0.395806i	−0.573979	−	0.818870i	$-0.694601\pi$
$983$	320924.	−	382463.i	0.332120	−	0.395806i	0.906100	+	0.423064i	$0.139045\pi$
$984$		0			0
$985$	−190075.	−	1.07797e6i	−0.195908	−	1.11105i
$986$	−966217.	+	170370.i	−0.993850	+	0.175243i
$987$		0			0
$988$	−698598.	−	586193.i	−0.715671	−	0.600519i
$989$	−507650.	+	293092.i	−0.519006	+	0.299648i
$990$		0			0
$991$	−7420.51	+	12852.7i	−0.00755591	+	0.0130872i	−0.869779	−	0.493442i	$-0.835738\pi$
$991$	−7420.51	+	12852.7i	−0.00755591	+	0.0130872i	0.862223	+	0.506529i	$0.169072\pi$
$992$	121590.	+	334067.i	0.123559	+	0.339477i
$993$		0			0
$994$	1.95544e6	−	1.64081e6i	1.97911	−	1.66067i
$995$	170651.	−	468859.i	0.172370	−	0.473583i
$996$		0			0
$997$	11310.5	−	64145.1i	0.0113787	−	0.0645317i	−0.978590	−	0.205821i	$-0.934014\pi$
$997$	11310.5	−	64145.1i	0.0113787	−	0.0645317i	0.989968	+	0.141289i	$0.0451247\pi$
$998$			2.50356e6i			2.51360i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.5.f.a.8.11		66
3.2	odd	2		27.5.f.a.2.1	✓	66
27.13	even	9		27.5.f.a.14.1	yes	66
27.14	odd	18	inner	81.5.f.a.71.11		66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.5.f.a.2.1	✓	66	3.2	odd	2
27.5.f.a.14.1	yes	66	27.13	even	9
81.5.f.a.8.11		66	1.1	even	1	trivial
81.5.f.a.71.11		66	27.14	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)

\(f(q)\)	\(=\)	\(q+(7.11993 + 1.25544i) q^{2} +(34.0822 + 12.4049i) q^{4} +(16.3502 + 19.4854i) q^{5} +(-60.7132 + 22.0978i) q^{7} +(126.911 + 73.2722i) q^{8} +(91.9496 + 159.261i) q^{10} +(86.4395 - 103.015i) q^{11} +(-27.2976 - 154.812i) q^{13} +(-460.017 + 81.1133i) q^{14} +(367.064 + 308.004i) q^{16} +(124.536 - 71.9009i) q^{17} +(79.9738 - 138.519i) q^{19} +(315.536 + 866.929i) q^{20} +(744.772 - 624.938i) q^{22} +(-193.010 + 530.290i) q^{23} +(-3.82186 + 21.6748i) q^{25} -1136.52i q^{26} -2343.37 q^{28} +(-929.364 - 163.872i) q^{29} +(298.389 + 108.605i) q^{31} +(719.645 + 857.639i) q^{32} +(976.955 - 355.583i) q^{34} +(-1423.26 - 821.718i) q^{35} +(-1074.59 - 1861.25i) q^{37} +(743.309 - 885.841i) q^{38} +(647.283 + 3670.93i) q^{40} +(162.159 - 28.5930i) q^{41} +(795.721 + 667.689i) q^{43} +(4223.94 - 2438.69i) q^{44} +(-2039.96 + 3533.31i) q^{46} +(879.993 + 2417.76i) q^{47} +(1358.51 - 1139.93i) q^{49} +(-54.4228 + 149.525i) q^{50} +(990.071 - 5614.97i) q^{52} +422.118i q^{53} +3420.58 q^{55} +(-9324.34 - 1644.13i) q^{56} +(-6411.28 - 2333.52i) q^{58} +(-677.524 - 807.441i) q^{59} +(-3638.45 + 1324.29i) q^{61} +(1988.16 + 1147.87i) q^{62} +(213.764 + 370.251i) q^{64} +(2570.26 - 3063.11i) q^{65} +(1308.73 + 7422.17i) q^{67} +(5136.39 - 905.685i) q^{68} +(-9101.88 - 7637.39i) q^{70} +(-4732.58 + 2732.36i) q^{71} +(2690.68 - 4660.39i) q^{73} +(-5314.34 - 14601.0i) q^{74} +(4444.00 - 3728.96i) q^{76} +(-2971.62 + 8164.47i) q^{77} +(-714.746 + 4053.52i) q^{79} +12188.3i q^{80} +1190.46 q^{82} +(6700.74 + 1181.52i) q^{83} +(3437.20 + 1251.04i) q^{85} +(4827.24 + 5752.88i) q^{86} +(18518.2 - 6740.08i) q^{88} +(-145.184 - 83.8223i) q^{89} +(5078.33 + 8795.93i) q^{91} +(-13156.4 + 15679.2i) q^{92} +(3230.15 + 18319.1i) q^{94} +(4006.68 - 706.485i) q^{95} +(6516.98 + 5468.39i) q^{97} +(11103.6 - 6410.67i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q + 6 q^{2} - 6 q^{4} - 3 q^{5} - 6 q^{7} + 9 q^{8} - 3 q^{10} + 492 q^{11} - 6 q^{13} - 1137 q^{14} - 54 q^{16} + 9 q^{17} - 3 q^{19} + 2487 q^{20} + 1002 q^{22} + 2724 q^{23} + 435 q^{25} - 12 q^{28}+ \cdots + 259938 q^{98}+O(q^{100}) \) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more