LMFDB - Embedded newform 81.5.f.a.17.2

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			17.2
Character	$\chi$	$=$	81.17
Dual form			81.5.f.a.62.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.28985 + 6.29131i) q^{2} +(-22.0805 - 18.5277i) q^{4} +(25.7110 + 4.53354i) q^{5} +(68.4999 - 57.4782i) q^{7} +(74.3553 - 42.9290i) q^{8} +(-87.3962 + 151.375i) q^{10} +(114.832 - 20.2479i) q^{11} +(79.4001 - 28.8993i) q^{13} +(204.759 + 562.571i) q^{14} +(19.7336 + 111.915i) q^{16} +(-177.240 - 102.329i) q^{17} +(29.8600 + 51.7191i) q^{19} +(-483.715 - 576.469i) q^{20} +(-135.561 + 768.806i) q^{22} +(-197.425 + 235.282i) q^{23} +(53.1928 + 19.3606i) q^{25} +565.706i q^{26} -2577.45 q^{28} +(-118.070 + 324.395i) q^{29} +(913.317 + 766.364i) q^{31} +(603.579 + 106.427i) q^{32} +(1049.64 - 880.751i) q^{34} +(2021.78 - 1167.27i) q^{35} +(765.910 - 1326.59i) q^{37} +(-393.756 + 69.4298i) q^{38} +(2106.37 - 766.655i) q^{40} +(172.539 + 474.046i) q^{41} +(409.482 + 2322.29i) q^{43} +(-2910.69 - 1680.49i) q^{44} +(-1028.16 - 1780.82i) q^{46} +(-856.572 - 1020.82i) q^{47} +(971.558 - 5509.98i) q^{49} +(-243.607 + 290.320i) q^{50} +(-2288.63 - 832.994i) q^{52} +2366.23i q^{53} +3044.22 q^{55} +(2625.84 - 7214.44i) q^{56} +(-1770.51 - 1485.63i) q^{58} +(1320.08 + 232.766i) q^{59} +(1145.64 - 961.305i) q^{61} +(-6912.80 + 3991.10i) q^{62} +(-2960.81 + 5128.27i) q^{64} +(2172.47 - 383.065i) q^{65} +(-3328.14 + 1211.34i) q^{67} +(2017.61 + 5543.33i) q^{68} +(2714.12 + 15392.5i) q^{70} +(-8066.81 - 4657.37i) q^{71} +(1018.24 + 1763.64i) q^{73} +(6592.21 + 7856.28i) q^{74} +(298.914 - 1695.22i) q^{76} +(6702.13 - 7987.29i) q^{77} +(-6418.45 - 2336.12i) q^{79} +2966.91i q^{80} -3377.46 q^{82} +(-866.863 + 2381.69i) q^{83} +(-4093.09 - 3434.51i) q^{85} +(-15547.9 - 2741.51i) q^{86} +(7669.11 - 6435.15i) q^{88} +(-5059.72 + 2921.23i) q^{89} +(3777.82 - 6543.37i) q^{91} +(8718.50 - 1537.31i) q^{92} +(8383.74 - 3051.43i) q^{94} +(533.260 + 1465.12i) q^{95} +(1671.44 + 9479.22i) q^{97} +(32440.3 + 18729.4i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.28985	+	6.29131i	−0.572463	+	1.57283i	0.228137	+	0.973629i	$0.426737\pi$
$2$	−2.28985	+	6.29131i	−0.572463	+	1.57283i	−0.800600	+	0.599200i	$0.795486\pi$
$3$		0			0
$3$		0			0
$4$	−22.0805	−	18.5277i	−1.38003	−	1.15798i
$5$	25.7110	+	4.53354i	1.02844	+	0.181341i	0.662316	−	0.749225i	$-0.269574\pi$
$5$	25.7110	+	4.53354i	1.02844	+	0.181341i	0.366123	+	0.930566i	$0.380685\pi$
$6$		0			0
$7$	68.4999	−	57.4782i	1.39796	−	1.17302i	0.435959	−	0.899966i	$-0.356409\pi$
$7$	68.4999	−	57.4782i	1.39796	−	1.17302i	0.961997	−	0.273058i	$-0.0880352\pi$
$8$	74.3553	−	42.9290i	1.16180	−	0.670766i
$9$		0			0
$10$	−87.3962	+	151.375i	−0.873962	+	1.51375i
$11$	114.832	−	20.2479i	0.949021	−	0.167338i	0.322349	−	0.946621i	$-0.395528\pi$
$11$	114.832	−	20.2479i	0.949021	−	0.167338i	0.626672	+	0.779283i	$0.284416\pi$
$12$		0			0
$13$	79.4001	−	28.8993i	0.469823	−	0.171002i	−0.0962491	−	0.995357i	$-0.530685\pi$
$13$	79.4001	−	28.8993i	0.469823	−	0.171002i	0.566072	+	0.824356i	$0.308462\pi$
$14$	204.759	+	562.571i	1.04469	+	2.87026i
$15$		0			0
$16$	19.7336	+	111.915i	0.0770845	+	0.437168i
$17$	−177.240	−	102.329i	−0.613286	−	0.354081i	0.160965	−	0.986960i	$-0.448539\pi$
$17$	−177.240	−	102.329i	−0.613286	−	0.354081i	−0.774250	+	0.632880i	$0.781873\pi$
$18$		0			0
$19$	29.8600	+	51.7191i	0.0827147	+	0.143266i	0.904415	−	0.426654i	$-0.140308\pi$
$19$	29.8600	+	51.7191i	0.0827147	+	0.143266i	−0.821700	+	0.569920i	$0.806974\pi$
$20$	−483.715	−	576.469i	−1.20929	−	1.44117i
$21$		0			0
$22$	−135.561	+	768.806i	−0.280085	+	1.58844i
$23$	−197.425	+	235.282i	−0.373204	+	0.444768i	−0.919657	−	0.392722i	$-0.871533\pi$
$23$	−197.425	+	235.282i	−0.373204	+	0.444768i	0.546453	+	0.837490i	$0.315978\pi$
$24$		0			0
$25$	53.1928	+	19.3606i	0.0851084	+	0.0309769i
$26$			565.706i			0.836843i
$27$		0			0
$28$	−2577.45			−3.28757
$29$	−118.070	+	324.395i	−0.140392	+	0.385725i	−0.989884	−	0.141877i	$-0.954686\pi$
$29$	−118.070	+	324.395i	−0.140392	+	0.385725i	0.849492	+	0.527602i	$0.176909\pi$
$30$		0			0
$31$	913.317	+	766.364i	0.950382	+	0.797465i	0.979362	−	0.202115i	$-0.0647815\pi$
$31$	913.317	+	766.364i	0.950382	+	0.797465i	−0.0289801	+	0.999580i	$0.509226\pi$
$32$	603.579	+	106.427i	0.589433	+	0.103933i
$33$		0			0
$34$	1049.64	−	880.751i	0.907991	−	0.761895i
$35$	2021.78	−	1167.27i	1.65043	−	0.952876i
$36$		0			0
$37$	765.910	−	1326.59i	0.559467	−	0.969025i	−0.438074	−	0.898939i	$-0.644339\pi$
$37$	765.910	−	1326.59i	0.559467	−	0.969025i	0.997541	−	0.0700859i	$-0.0223273\pi$
$38$	−393.756	+	69.4298i	−0.272684	+	0.0480816i
$39$		0			0
$40$	2106.37	−	766.655i	1.31648	−	0.479159i
$41$	172.539	+	474.046i	0.102640	+	0.282002i	0.980374	−	0.197147i	$-0.0631676\pi$
$41$	172.539	+	474.046i	0.102640	+	0.282002i	−0.877734	+	0.479149i	$0.840945\pi$
$42$		0			0
$43$	409.482	+	2322.29i	0.221461	+	1.25597i	0.869335	+	0.494222i	$0.164547\pi$
$43$	409.482	+	2322.29i	0.221461	+	1.25597i	−0.647874	+	0.761747i	$0.724342\pi$
$44$	−2910.69	−	1680.49i	−1.50345	−	0.868020i
$45$		0			0
$46$	−1028.16	−	1780.82i	−0.485898	−	0.841600i
$47$	−856.572	−	1020.82i	−0.387764	−	0.462120i	0.536484	−	0.843910i	$-0.319752\pi$
$47$	−856.572	−	1020.82i	−0.387764	−	0.462120i	−0.924249	+	0.381791i	$0.875308\pi$
$48$		0			0
$49$	971.558	−	5509.98i	0.404647	−	2.29487i
$50$	−243.607	+	290.320i	−0.0974428	+	0.116128i
$51$		0			0
$52$	−2288.63	−	832.994i	−0.846388	−	0.308060i
$53$			2366.23i			0.842375i	0.906974	+	0.421187i	$0.138387\pi$
$53$			2366.23i			0.842375i	−0.906974	+	0.421187i	$0.861613\pi$
$54$		0			0
$55$	3044.22			1.00636
$56$	2625.84	−	7214.44i	0.837322	−	2.30052i
$57$		0			0
$58$	−1770.51	−	1485.63i	−0.526310	−	0.441627i
$59$	1320.08	+	232.766i	0.379225	+	0.0668677i	0.360012	−	0.932948i	$-0.382773\pi$
$59$	1320.08	+	232.766i	0.379225	+	0.0668677i	0.0192136	+	0.999815i	$0.493884\pi$
$60$		0			0
$61$	1145.64	−	961.305i	0.307885	−	0.258346i	−0.475732	−	0.879590i	$-0.657817\pi$
$61$	1145.64	−	961.305i	0.307885	−	0.258346i	0.783617	+	0.621244i	$0.213372\pi$
$62$	−6912.80	+	3991.10i	−1.79833	+	1.03827i
$63$		0			0
$64$	−2960.81	+	5128.27i	−0.722853	+	1.25202i
$65$	2172.47	−	383.065i	0.514194	−	0.0906663i
$66$		0			0
$67$	−3328.14	+	1211.34i	−0.741400	+	0.269847i	−0.684982	−	0.728560i	$-0.740190\pi$
$67$	−3328.14	+	1211.34i	−0.741400	+	0.269847i	−0.0564175	+	0.998407i	$0.517968\pi$
$68$	2017.61	+	5543.33i	0.436334	+	1.19882i
$69$		0			0
$70$	2714.12	+	15392.5i	0.553901	+	3.14133i
$71$	−8066.81	−	4657.37i	−1.60024	−	0.923899i	−0.991438	−	0.130575i	$-0.958318\pi$
$71$	−8066.81	−	4657.37i	−1.60024	−	0.923899i	−0.608801	−	0.793323i	$-0.708349\pi$
$72$		0			0
$73$	1018.24	+	1763.64i	0.191075	+	0.330952i	0.945607	−	0.325312i	$-0.105469\pi$
$73$	1018.24	+	1763.64i	0.191075	+	0.330952i	−0.754532	+	0.656264i	$0.772136\pi$
$74$	6592.21	+	7856.28i	1.20384	+	1.43468i
$75$		0			0
$76$	298.914	−	1695.22i	0.0517510	−	0.293494i
$77$	6702.13	−	7987.29i	1.13040	−	1.34716i
$78$		0			0
$79$	−6418.45	−	2336.12i	−1.02843	−	0.374319i	−0.227949	−	0.973673i	$-0.573202\pi$
$79$	−6418.45	−	2336.12i	−1.02843	−	0.374319i	−0.800484	+	0.599354i	$0.795424\pi$
$80$			2966.91i			0.463579i
$81$		0			0
$82$	−3377.46			−0.502299
$83$	−866.863	+	2381.69i	−0.125833	+	0.345723i	−0.986573	−	0.163322i	$-0.947779\pi$
$83$	−866.863	+	2381.69i	−0.125833	+	0.345723i	0.860740	+	0.509045i	$0.170001\pi$
$84$		0			0
$85$	−4093.09	−	3434.51i	−0.566517	−	0.475364i
$86$	−15547.9	−	2741.51i	−2.10220	−	0.370675i
$87$		0			0
$88$	7669.11	−	6435.15i	0.990329	−	0.830985i
$89$	−5059.72	+	2921.23i	−0.638773	+	0.368796i	−0.784142	−	0.620582i	$-0.786897\pi$
$89$	−5059.72	+	2921.23i	−0.638773	+	0.368796i	0.145369	+	0.989378i	$0.453563\pi$
$90$		0			0
$91$	3777.82	−	6543.37i	0.456203	−	0.790167i
$92$	8718.50	−	1537.31i	1.03007	−	0.181629i
$93$		0			0
$94$	8383.74	−	3051.43i	0.948816	−	0.345341i
$95$	533.260	+	1465.12i	0.0590869	+	0.162340i
$96$		0			0
$97$	1671.44	+	9479.22i	0.177643	+	1.00746i	0.935049	+	0.354519i	$0.115355\pi$
$97$	1671.44	+	9479.22i	0.177643	+	1.00746i	−0.757406	+	0.652944i	$0.773534\pi$
$98$	32440.3	+	18729.4i	3.37779	+	1.95017i
$99$		0			0
$100$	−815.816	−	1413.03i	−0.0815816	−	0.141303i
$101$	−5351.94	−	6378.20i	−0.524649	−	0.625252i	0.437025	−	0.899450i	$-0.356032\pi$
$101$	−5351.94	−	6378.20i	−0.524649	−	0.625252i	−0.961673	+	0.274197i	$0.911588\pi$
$102$		0			0
$103$	−2148.25	+	12183.3i	−0.202493	+	1.14840i	0.698843	+	0.715275i	$0.253699\pi$
$103$	−2148.25	+	12183.3i	−0.202493	+	1.14840i	−0.901336	+	0.433121i	$0.857412\pi$
$104$	4663.20	−	5557.38i	0.431139	−	0.513811i
$105$		0			0
$106$	−14886.7	−	5418.32i	−1.32491	−	0.482228i
$107$		−	18289.2i		−	1.59745i	−0.601695	−	0.798726i	$-0.705508\pi$
$107$		−	18289.2i		−	1.59745i	0.601695	−	0.798726i	$-0.294492\pi$
$108$		0			0
$109$	15025.2			1.26464			0.632320	−	0.774707i	$-0.282103\pi$
$109$	15025.2			1.26464			0.632320	+	0.774707i	$0.282103\pi$
$110$	−6970.82	+	19152.2i	−0.576101	+	1.58282i
$111$		0			0
$112$	7784.43	+	6531.91i	0.620570	+	0.520720i
$113$	16147.7	+	2847.27i	1.26460	+	0.222983i	0.765429	−	0.643520i	$-0.222527\pi$
$113$	16147.7	+	2847.27i	1.26460	+	0.222983i	0.499171	+	0.866504i	$0.333638\pi$
$114$		0			0
$115$	−6142.65	+	5154.30i	−0.464473	+	0.389739i
$116$	8617.35	−	4975.23i	0.640410	−	0.369741i
$117$		0			0
$118$	−4487.20	+	7772.06i	−0.322264	+	0.558177i
$119$	−18022.6	+	3177.87i	−1.27269	+	0.224410i
$120$		0			0
$121$	−981.730	+	357.320i	−0.0670535	+	0.0244055i
$122$	3424.53	+	9408.82i	0.230081	+	0.632143i
$123$		0			0
$124$	−5967.51	−	33843.4i	−0.388105	−	2.20105i
$125$	−12851.3	−	7419.69i	−0.822482	−	0.474860i
$126$		0			0
$127$	−10486.5	−	18163.1i	−0.650163	−	1.12612i	−0.983083	−	0.183160i	$-0.941367\pi$
$127$	−10486.5	−	18163.1i	−0.650163	−	1.12612i	0.332920	−	0.942955i	$-0.391966\pi$
$128$	−19180.4	−	22858.3i	−1.17068	−	1.39516i
$129$		0			0
$130$	−2564.65	+	14544.8i	−0.151754	+	0.860642i
$131$	−8641.82	+	10298.9i	−0.503574	+	0.600136i	−0.956615	−	0.291354i	$-0.905894\pi$
$131$	−8641.82	+	10298.9i	−0.503574	+	0.600136i	0.453042	+	0.891489i	$0.350339\pi$
$132$		0			0
$133$	5018.13	+	1826.45i	0.283686	+	0.103253i
$134$		−	23712.2i		−	1.32057i
$135$		0			0
$136$	−17571.6			−0.950021
$137$	284.313	−	781.142i	0.0151480	−	0.0416188i	−0.931888	−	0.362746i	$-0.881839\pi$
$137$	284.313	−	781.142i	0.0151480	−	0.0416188i	0.947036	+	0.321127i	$0.104062\pi$
$138$		0			0
$139$	8787.22	+	7373.35i	0.454801	+	0.381624i	0.841214	−	0.540702i	$-0.181841\pi$
$139$	8787.22	+	7373.35i	0.454801	+	0.381624i	−0.386413	+	0.922326i	$0.626286\pi$
$140$	−66268.8	−	11685.0i	−3.38106	−	0.596173i
$141$		0			0
$142$	47772.8	−	40086.1i	2.36921	−	1.98800i
$143$	8532.49	−	4926.23i	0.417257	−	0.240903i
$144$		0			0
$145$	−4506.35	+	7805.23i	−0.214333	+	0.371236i
$146$	−13427.3	+	2367.59i	−0.629914	+	0.111071i
$147$		0			0
$148$	−41490.5	+	15101.3i	−1.89420	+	0.689431i
$149$	5305.67	+	14577.2i	0.238983	+	0.656602i	0.999969	+	0.00783318i	$0.00249340\pi$
$149$	5305.67	+	14577.2i	0.238983	+	0.656602i	−0.760986	+	0.648768i	$0.775284\pi$
$150$		0			0
$151$	−675.777	−	3832.52i	−0.0296381	−	0.168086i	0.966396	−	0.257058i	$-0.0827530\pi$
$151$	−675.777	−	3832.52i	−0.0296381	−	0.168086i	−0.996034	+	0.0889718i	$0.971642\pi$
$152$	4440.50	+	2563.72i	0.192196	+	0.110965i
$153$		0			0
$154$	34903.7	+	60454.9i	1.47174	+	2.54912i
$155$	20007.9	+	23844.5i	0.832796	+	0.992487i
$156$		0			0
$157$	4167.47	−	23634.9i	0.169072	−	0.958858i	−0.775693	−	0.631110i	$-0.782599\pi$
$157$	4167.47	−	23634.9i	0.169072	−	0.958858i	0.944765	−	0.327747i	$-0.106289\pi$
$158$	29394.6	−	35031.1i	1.17748	−	1.40326i
$159$		0			0
$160$	15036.1	+	5472.70i	0.587348	+	0.213777i
$161$			27464.4i			1.05954i
$162$		0			0
$163$	3197.22			0.120336			0.0601682	−	0.998188i	$-0.480836\pi$
$163$	3197.22			0.120336			0.0601682	+	0.998188i	$0.480836\pi$
$164$	4973.26	−	13663.9i	0.184907	−	0.508028i
$165$		0			0
$166$	−12999.0	−	10907.4i	−0.471729	−	0.395827i
$167$	15221.2	+	2683.90i	0.545776	+	0.0962351i	0.439737	−	0.898127i	$-0.355072\pi$
$167$	15221.2	+	2683.90i	0.545776	+	0.0962351i	0.106040	+	0.994362i	$0.466183\pi$
$168$		0			0
$169$	−16409.8	+	13769.4i	−0.574552	+	0.482107i
$170$	30980.1	−	17886.4i	1.07198	−	0.618906i
$171$		0			0
$172$	33985.2	−	58864.1i	1.14877	−	1.98973i
$173$	2896.29	−	510.694i	0.0967720	−	0.0170635i	−0.125052	−	0.992150i	$-0.539910\pi$
$173$	2896.29	−	510.694i	0.0967720	−	0.0170635i	0.221824	+	0.975087i	$0.428799\pi$
$174$		0			0
$175$	4756.51	−	1731.23i	0.155315	−	0.0565299i
$176$	4532.09	+	12451.8i	0.146310	+	0.401983i
$177$		0			0
$178$	−6792.38	−	38521.5i	−0.214379	−	1.21580i
$179$	15637.7	+	9028.43i	0.488053	+	0.281778i	0.723766	−	0.690045i	$-0.242409\pi$
$179$	15637.7	+	9028.43i	0.488053	+	0.281778i	−0.235713	+	0.971823i	$0.575743\pi$
$180$		0			0
$181$	−12607.6	−	21837.1i	−0.384837	−	0.666557i	0.606910	−	0.794771i	$-0.292409\pi$
$181$	−12607.6	−	21837.1i	−0.384837	−	0.666557i	−0.991747	+	0.128214i	$0.959076\pi$
$182$	32515.8	+	38750.8i	0.981638	+	1.16987i
$183$		0			0
$184$	−4579.17	+	25969.7i	−0.135254	+	0.767065i
$185$	25706.4	−	30635.7i	0.751101	−	0.895128i
$186$		0			0
$187$	−22424.6	−	8161.90i	−0.641272	−	0.233404i
$188$			38410.6i			1.08677i
$189$		0			0
$190$	−10438.6			−0.289158
$191$	4428.43	−	12167.0i	0.121390	−	0.333517i	−0.864083	−	0.503350i	$-0.832101\pi$
$191$	4428.43	−	12167.0i	0.121390	−	0.333517i	0.985473	+	0.169833i	$0.0543229\pi$
$192$		0			0
$193$	21097.8	+	17703.2i	0.566400	+	0.475266i	0.880449	−	0.474141i	$-0.157241\pi$
$193$	21097.8	+	17703.2i	0.566400	+	0.475266i	−0.314049	+	0.949407i	$0.601686\pi$
$194$	−63464.1	−	11190.4i	−1.68626	−	0.297333i
$195$		0			0
$196$	−123540.	+	103662.i	−3.21585	+	2.69842i
$197$	−25871.2	+	14936.7i	−0.666628	+	0.384878i	−0.794798	−	0.606874i	$-0.792423\pi$
$197$	−25871.2	+	14936.7i	−0.666628	+	0.384878i	0.128169	+	0.991752i	$0.459090\pi$
$198$		0			0
$199$	−1874.31	+	3246.39i	−0.0473298	+	0.0819776i	−0.888720	−	0.458451i	$-0.848404\pi$
$199$	−1874.31	+	3246.39i	−0.0473298	+	0.0819776i	0.841390	+	0.540428i	$0.181738\pi$
$200$	4786.29	−	843.953i	0.119657	−	0.0210988i
$201$		0			0
$202$	52382.4	−	19065.6i	1.28376	−	0.467249i
$203$	10557.9	+	29007.5i	0.256203	+	0.703911i
$204$		0			0
$205$	2287.03	+	12970.4i	0.0544207	+	0.308635i
$206$	−71730.0	−	41413.3i	−1.69031	−	0.975901i
$207$		0			0
$208$	4801.12	+	8315.78i	0.110973	+	0.192210i
$209$	4476.08	+	5334.38i	0.102472	+	0.122121i
$210$		0			0
$211$	−2992.43	+	16970.9i	−0.0672138	+	0.381188i	0.932582	+	0.360959i	$0.117551\pi$
$211$	−2992.43	+	16970.9i	−0.0672138	+	0.381188i	−0.999795	+	0.0202291i	$0.993560\pi$
$212$	43840.9	−	52247.6i	0.975457	−	1.16250i
$213$		0			0
$214$	115063.	+	41879.6i	2.51252	+	0.914482i
$215$			61564.7i			1.33185i
$216$		0			0
$217$	106611.			2.26404
$218$	−34405.5	+	94528.3i	−0.723960	+	1.98906i
$219$		0			0
$220$	−67218.0	−	56402.6i	−1.38880	−	1.16534i
$221$	−17030.1	−	3002.86i	−0.348684	−	0.0614824i
$222$		0			0
$223$	−52469.8	+	44027.4i	−1.05511	+	0.885346i	−0.993622	−	0.112761i	$-0.964030\pi$
$223$	−52469.8	+	44027.4i	−1.05511	+	0.885346i	−0.0614925	+	0.998108i	$0.519586\pi$
$224$	47462.4	−	27402.4i	0.945918	−	0.546126i
$225$		0			0
$226$	−54888.9	+	95070.3i	−1.07465	+	1.86135i
$227$	−2085.83	+	367.788i	−0.0404787	+	0.00713749i	−0.193851	−	0.981031i	$-0.562098\pi$
$227$	−2085.83	+	367.788i	−0.0404787	+	0.00713749i	0.153372	+	0.988169i	$0.450987\pi$
$228$		0			0
$229$	−55758.2	+	20294.3i	−1.06326	+	0.386993i	−0.813650	−	0.581354i	$-0.802523\pi$
$229$	−55758.2	+	20294.3i	−1.06326	+	0.386993i	−0.249605	+	0.968348i	$0.580301\pi$
$230$	−18361.5	−	50447.9i	−0.347099	−	0.953647i
$231$		0			0
$232$	5146.83	+	29189.1i	0.0956233	+	0.542306i
$233$	−859.319	−	496.128i	−0.0158286	−	0.00913865i	0.492065	−	0.870559i	$-0.336242\pi$
$233$	−859.319	−	496.128i	−0.0158286	−	0.00913865i	−0.507893	+	0.861420i	$0.669576\pi$
$234$		0			0
$235$	−17395.3	−	30129.6i	−0.314990	−	0.545579i
$236$	−24835.5	−	29597.8i	−0.445912	−	0.531417i
$237$		0			0
$238$	21276.1	−	120663.i	0.375610	−	2.13019i
$239$	−65023.4	+	77491.9i	−1.13835	+	1.35663i	−0.213203	+	0.977008i	$0.568390\pi$
$239$	−65023.4	+	77491.9i	−1.13835	+	1.35663i	−0.925143	+	0.379620i	$0.876055\pi$
$240$		0			0
$241$	−8987.19	−	3271.07i	−0.154735	−	0.0563191i	0.263491	−	0.964662i	$-0.415126\pi$
$241$	−8987.19	−	3271.07i	−0.154735	−	0.0563191i	−0.418227	+	0.908343i	$0.637348\pi$
$242$		−	6994.58i		−	0.119435i
$243$		0			0
$244$	−43107.1			−0.724051
$245$	49959.4	−	137262.i	0.832309	−	2.28675i
$246$		0			0
$247$	3865.53	+	3243.57i	0.0633600	+	0.0531654i
$248$	100809.	+	17775.4i	1.63907	+	0.289012i
$249$		0			0
$250$	76107.2	−	63861.5i	1.21771	−	1.02178i
$251$	−99454.3	+	57420.0i	−1.57862	+	0.911414i	−0.583562	+	0.812068i	$0.698342\pi$
$251$	−99454.3	+	57420.0i	−1.57862	+	0.911414i	−0.995053	+	0.0993455i	$0.968325\pi$
$252$		0			0
$253$	−17906.7	+	31015.3i	−0.279752	+	0.484545i
$254$	138282.	−	24382.9i	2.14338	−	0.377936i
$255$		0			0
$256$	98697.2	−	35922.8i	1.50600	−	0.548139i
$257$	10228.5	+	28102.5i	0.154862	+	0.425479i	0.992725	−	0.120400i	$-0.0384179\pi$
$257$	10228.5	+	28102.5i	0.154862	+	0.425479i	−0.837864	+	0.545880i	$0.816196\pi$
$258$		0			0
$259$	−23785.6	−	134895.i	−0.354580	−	2.01092i
$260$	−55066.6	−	31792.7i	−0.814594	−	0.470306i
$261$		0			0
$262$	−45005.3	−	77951.5i	−0.655633	−	1.13559i
$263$	−69051.5	−	82292.4i	−0.998301	−	1.18973i	−0.981810	−	0.189865i	$-0.939195\pi$
$263$	−69051.5	−	82292.4i	−0.998301	−	1.18973i	−0.0164913	−	0.999864i	$-0.505250\pi$
$264$		0			0
$265$	−10727.4	+	60838.1i	−0.152758	+	0.866331i
$266$	−22981.5	+	27388.3i	−0.324800	+	0.387081i
$267$		0			0
$268$	95930.6	+	34915.9i	1.33563	+	0.486131i
$269$		−	93032.6i		−	1.28567i	−0.766003	−	0.642837i	$-0.777757\pi$
$269$		−	93032.6i		−	1.28567i	0.766003	−	0.642837i	$-0.222243\pi$
$270$		0			0
$271$	−116322.			−1.58389			−0.791943	−	0.610595i	$-0.790930\pi$
$271$	−116322.			−1.58389			−0.791943	+	0.610595i	$0.790930\pi$
$272$	7954.61	−	21855.1i	0.107518	−	0.295403i
$273$		0			0
$274$	4263.38	+	3577.40i	0.0567875	+	0.0476504i
$275$	6500.22	+	1146.16i	0.0859533	+	0.0151559i
$276$		0			0
$277$	35882.2	−	30108.7i	0.467648	−	0.392404i	−0.378288	−	0.925688i	$-0.623487\pi$
$277$	35882.2	−	30108.7i	0.467648	−	0.392404i	0.845936	+	0.533285i	$0.179042\pi$
$278$	−66509.5	+	38399.3i	−0.860586	+	0.496859i
$279$		0			0
$280$	100220.	−	173586.i	1.27831	−	2.21411i
$281$	47538.9	−	8382.39i	0.602055	−	0.106159i	0.135691	−	0.990751i	$-0.456675\pi$
$281$	47538.9	−	8382.39i	0.602055	−	0.106159i	0.466364	+	0.884593i	$0.345564\pi$
$282$		0			0
$283$	61394.4	−	22345.7i	0.766577	−	0.279011i	0.0710129	−	0.997475i	$-0.477377\pi$
$283$	61394.4	−	22345.7i	0.766577	−	0.279011i	0.695564	+	0.718464i	$0.255155\pi$
$284$	91828.6	+	252297.i	1.13852	+	3.12806i
$285$		0			0
$286$	11454.4	+	64960.9i	0.140036	+	0.794182i
$287$	39066.2	+	22554.9i	0.474283	+	0.273827i
$288$		0			0
$289$	−20817.9	−	36057.7i	−0.249254	−	0.431720i
$290$	−38786.3	−	46223.7i	−0.461192	−	0.549628i
$291$		0			0
$292$	10193.1	−	57807.9i	0.119547	−	0.677987i
$293$	81822.2	−	97512.0i	0.953095	−	1.13585i	−0.0375370	−	0.999295i	$-0.511951\pi$
$293$	81822.2	−	97512.0i	0.953095	−	1.13585i	0.990632	−	0.136559i	$-0.0436043\pi$
$294$		0			0
$295$	32885.4	+	11969.3i	0.377884	+	0.137539i
$296$		−	131519.i		−	1.50109i
$297$		0			0
$298$	−103859.			−1.16953
$299$	−8876.09	+	24386.9i	−0.0992841	+	0.272781i
$300$		0			0
$301$	161530.	+	135540.i	1.78288	+	1.49601i
$302$	25659.0	+	4524.38i	0.281337	+	0.0496073i
$303$		0			0
$304$	−5198.90	+	4362.39i	−0.0562554	+	0.0472039i
$305$	33813.6	−	19522.3i	0.363489	−	0.209861i
$306$		0			0
$307$	−84380.8	+	146152.i	−0.895297	+	1.55070i	−0.0618593	+	0.998085i	$0.519703\pi$
$307$	−84380.8	+	146152.i	−0.895297	+	1.55070i	−0.833437	+	0.552614i	$0.813630\pi$
$308$	−295973.	+	52188.0i	−3.11997	+	0.550135i
$309$		0			0
$310$	−195828.	+	71275.7i	−2.03776	+	0.741683i
$311$	−40368.2	−	110911.i	−0.417368	−	1.14671i	−0.953188	−	0.302377i	$-0.902220\pi$
$311$	−40368.2	−	110911.i	−0.417368	−	1.14671i	0.535821	−	0.844332i	$-0.320002\pi$
$312$		0			0
$313$	−192.485	−	1091.64i	−0.00196476	−	0.0111427i	0.983810	−	0.179217i	$-0.0573563\pi$
$313$	−192.485	−	1091.64i	−0.00196476	−	0.0111427i	−0.985774	+	0.168074i	$0.946245\pi$
$314$	139152.	+	80339.2i	1.41133	+	0.814832i
$315$		0			0
$316$	98439.5	+	170502.i	0.985815	+	1.70748i
$317$	−13432.5	−	16008.2i	−0.133671	−	0.159303i	0.695057	−	0.718955i	$-0.255379\pi$
$317$	−13432.5	−	16008.2i	−0.133671	−	0.159303i	−0.828728	+	0.559652i	$0.810935\pi$
$318$		0			0
$319$	−6989.85	+	39641.4i	−0.0686889	+	0.389554i
$320$	−99374.4	+	118430.i	−0.970453	+	1.15654i
$321$		0			0
$322$	−172787.	−	62889.5i	−1.66648	−	0.606550i
$323$		−	12222.2i		−	0.117151i
$324$		0			0
$325$	4783.02			0.0452830
$326$	−7321.15	+	20114.7i	−0.0688881	+	0.189269i
$327$		0			0
$328$	33179.5	+	27840.9i	0.308405	+	0.258783i
$329$	−117350.	−	20692.0i	−1.08416	−	0.191166i
$330$		0			0
$331$	29579.5	−	24820.1i	0.269982	−	0.226542i	−0.497738	−	0.867328i	$-0.665836\pi$
$331$	29579.5	−	24820.1i	0.269982	−	0.226542i	0.767720	+	0.640786i	$0.221391\pi$
$332$	63268.1	−	36527.8i	0.573996	−	0.331397i
$333$		0			0
$334$	−51739.5	+	89615.4i	−0.463798	+	0.803322i
$335$	−91061.4	+	16056.6i	−0.811418	+	0.143075i
$336$		0			0
$337$	204490.	−	74428.4i	1.80058	−	0.655358i	0.802290	−	0.596934i	$-0.203615\pi$
$337$	204490.	−	74428.4i	1.80058	−	0.655358i	0.998292	−	0.0584241i	$-0.0186076\pi$
$338$	−49051.9	−	134769.i	−0.429361	−	1.17966i
$339$		0			0
$340$	26743.7	+	151671.i	0.231347	+	1.31204i
$341$	120395.	+	69510.0i	1.03538	+	0.597776i
$342$		0			0
$343$	−142803.	−	247342.i	−1.21381	−	2.10237i
$344$	130141.	+	155096.i	1.09976	+	1.31064i
$345$		0			0
$346$	−3419.13	+	19390.9i	−0.0285604	+	0.161974i
$347$	−91221.8	+	108714.i	−0.757599	+	0.902872i	−0.997694	−	0.0678779i	$-0.978377\pi$
$347$	−91221.8	+	108714.i	−0.757599	+	0.902872i	0.240094	+	0.970750i	$0.422822\pi$
$348$		0			0
$349$	−106148.	−	38634.6i	−0.871484	−	0.317194i	−0.132716	−	0.991154i	$-0.542370\pi$
$349$	−106148.	−	38634.6i	−0.871484	−	0.317194i	−0.738768	+	0.673960i	$0.764592\pi$
$350$			33889.0i			0.276645i
$351$		0			0
$352$	71464.9			0.576776
$353$	−6289.31	+	17279.7i	−0.0504724	+	0.138672i	−0.962367	−	0.271752i	$-0.912397\pi$
$353$	−6289.31	+	17279.7i	−0.0504724	+	0.138672i	0.911895	+	0.410424i	$0.134619\pi$
$354$		0			0
$355$	−186291.	−	156317.i	−1.47821	−	1.24036i
$356$	165845.	+	29243.0i	1.30859	+	0.230739i
$357$		0			0
$358$	−92608.8	+	77708.0i	−0.722580	+	0.606317i
$359$	−13604.2	+	7854.36i	−0.105556	+	0.0609427i	−0.551849	−	0.833944i	$-0.686077\pi$
$359$	−13604.2	+	7854.36i	−0.105556	+	0.0609427i	0.446293	+	0.894887i	$0.352744\pi$
$360$		0			0
$361$	63377.3	−	109773.i	0.486317	−	0.842325i
$362$	166254.	−	29315.0i	1.26869	−	0.223703i
$363$		0			0
$364$	−204650.	+	74486.6i	−1.54458	+	0.562180i
$365$	18184.4	+	49961.2i	0.136494	+	0.375014i
$366$		0			0
$367$	33676.1	+	190987.i	0.250029	+	1.41798i	0.808518	+	0.588472i	$0.200270\pi$
$367$	33676.1	+	190987.i	0.250029	+	1.41798i	−0.558489	+	0.829512i	$0.688619\pi$
$368$	−30227.5	−	17451.9i	−0.223207	−	0.128868i
$369$		0			0
$370$	133875.	+	231879.i	0.977905	+	1.69378i
$371$	136007.	+	162087.i	0.988127	+	1.17760i
$372$		0			0
$373$	−23955.5	+	135858.i	−0.172182	+	0.976493i	0.769164	+	0.639051i	$0.220673\pi$
$373$	−23955.5	+	135858.i	−0.172182	+	0.976493i	−0.941346	+	0.337442i	$0.890438\pi$
$374$	102698.	−	122391.i	0.734209	−	0.874996i
$375$		0			0
$376$	−107514.	−	39131.7i	−0.760479	−	0.276792i
$377$			29169.1i			0.205230i
$378$		0			0
$379$	252626.			1.75873			0.879367	−	0.476145i	$-0.157966\pi$
$379$	252626.			1.75873			0.879367	+	0.476145i	$0.157966\pi$
$380$	15370.7	−	42230.7i	0.106445	−	0.292456i
$381$		0			0
$382$	66406.1	+	55721.3i	0.455073	+	0.381852i
$383$	214247.	+	37777.5i	1.46055	+	0.257535i	0.846778	−	0.531947i	$-0.178539\pi$
$383$	214247.	+	37777.5i	1.46055	+	0.257535i	0.613774	+	0.789481i	$0.289650\pi$
$384$		0			0
$385$	208529.	−	174977.i	1.40684	−	1.18048i
$386$	−159687.	+	92195.5i	−1.07175	+	0.618778i
$387$		0			0
$388$	138722.	−	240274.i	0.921473	−	1.59604i
$389$	138469.	−	24415.8i	0.915069	−	0.161351i	0.303765	−	0.952747i	$-0.401756\pi$
$389$	138469.	−	24415.8i	0.915069	−	0.161351i	0.611304	+	0.791396i	$0.290645\pi$
$390$		0			0
$391$	59067.8	−	21498.9i	0.386365	−	0.140625i
$392$	−164298.	−	451404.i	−1.06920	−	2.93760i
$393$		0			0
$394$	−34730.5	−	196967.i	−0.223727	−	1.26882i
$395$	−154434.	−	89162.3i	−0.989800	−	0.571461i
$396$		0			0
$397$	84254.1	+	145932.i	0.534577	+	0.925914i	0.999184	+	0.0403969i	$0.0128622\pi$
$397$	84254.1	+	145932.i	0.534577	+	0.925914i	−0.464607	+	0.885517i	$0.653804\pi$
$398$	−16132.2	−	19225.6i	−0.101842	−	0.121371i
$399$		0			0
$400$	−1117.05	+	6335.13i	−0.00698159	+	0.0395945i
$401$	8280.32	−	9868.10i	0.0514942	−	0.0613684i	−0.739683	−	0.672956i	$-0.765024\pi$
$401$	8280.32	−	9868.10i	0.0514942	−	0.0613684i	0.791177	+	0.611588i	$0.209469\pi$
$402$		0			0
$403$	94664.8	+	34455.2i	0.582879	+	0.212151i
$404$			239993.i			1.47040i
$405$		0			0
$406$	−206671.			−1.25380
$407$	61089.9	−	167843.i	0.368791	−	1.01324i
$408$		0			0
$409$	−163827.	−	137468.i	−0.979354	−	0.821776i	0.00463745	−	0.999989i	$-0.498524\pi$
$409$	−163827.	−	137468.i	−0.979354	−	0.821776i	−0.983992	+	0.178213i	$0.942968\pi$
$410$	−86837.7	−	15311.8i	−0.516584	−	0.0910876i
$411$		0			0
$412$	273164.	−	229212.i	1.60927	−	1.35034i
$413$	103805.	−	59931.6i	0.608578	−	0.351363i
$414$		0			0
$415$	−33085.4	+	57305.5i	−0.192105	+	0.332736i
$416$	50999.9	−	8992.66i	0.294702	−	0.0519639i
$417$		0			0
$418$	−43809.8	+	15945.5i	−0.250737	+	0.0912609i
$419$	−51671.9	−	141967.i	−0.294325	−	0.808650i	−0.995421	−	0.0955842i	$-0.969528\pi$
$419$	−51671.9	−	141967.i	−0.294325	−	0.808650i	0.701097	−	0.713066i	$-0.252694\pi$
$420$		0			0
$421$	−8285.29	−	46988.2i	−0.0467459	−	0.265109i	0.952473	−	0.304623i	$-0.0985303\pi$
$421$	−8285.29	−	46988.2i	−0.0467459	−	0.265109i	−0.999219	+	0.0395134i	$0.987419\pi$
$422$	−99917.0	−	57687.1i	−0.561067	−	0.323932i
$423$		0			0
$424$	101580.	+	175942.i	0.565037	+	0.978672i
$425$	−7446.71	−	8874.64i	−0.0412274	−	0.0491330i
$426$		0			0
$427$	23222.0	−	131699.i	0.127363	−	0.722313i
$428$	−338858.	+	403836.i	−1.84982	+	2.20454i
$429$		0			0
$430$	−387323.	−	140974.i	−2.09477	−	0.762433i
$431$			178097.i			0.958744i	0.877612	+	0.479372i	$0.159136\pi$
$431$			178097.i			0.958744i	−0.877612	+	0.479372i	$0.840864\pi$
$432$		0			0
$433$	245595.			1.30992			0.654960	−	0.755664i	$-0.272686\pi$
$433$	245595.			1.30992			0.654960	+	0.755664i	$0.272686\pi$
$434$	−244124.	+	670725.i	−1.29608	+	3.56094i
$435$		0			0
$436$	−331764.	−	278383.i	−1.74524	−	1.46443i
$437$	−18063.7	−	3185.12i	−0.0945897	−	0.0166787i
$438$		0			0
$439$	−135369.	+	113588.i	−0.702407	+	0.589390i	−0.922457	−	0.386099i	$-0.873822\pi$
$439$	−135369.	+	113588.i	−0.702407	+	0.589390i	0.220050	+	0.975489i	$0.429378\pi$
$440$	226354.	−	130686.i	1.16918	−	0.675029i
$441$		0			0
$442$	57888.3	−	100265.i	0.296310	−	0.513224i
$443$	−84669.8	+	14929.6i	−0.431441	+	0.0760746i	−0.385151	−	0.922853i	$-0.625851\pi$
$443$	−84669.8	+	14929.6i	−0.431441	+	0.0760746i	−0.0462894	+	0.998928i	$0.514740\pi$
$444$		0			0
$445$	−143334.	+	52169.3i	−0.723817	+	0.263448i
$446$	−156842.	−	430920.i	−0.788484	−	2.16634i
$447$		0			0
$448$	91948.8	+	521468.i	0.458131	+	2.59819i
$449$	−327830.	−	189273.i	−1.62613	−	0.938847i	−0.985232	−	0.171222i	$-0.945228\pi$
$449$	−327830.	−	189273.i	−1.62613	−	0.938847i	−0.640899	−	0.767625i	$-0.721438\pi$
$450$		0			0
$451$	29411.3	+	50941.9i	0.144598	+	0.250450i
$452$	−303795.	−	362049.i	−1.48698	−	1.77211i
$453$		0			0
$454$	2462.37	−	13964.8i	0.0119465	−	0.0677521i
$455$	126796.	−	151110.i	0.612467	−	0.729910i
$456$		0			0
$457$	−200123.	−	72838.8i	−0.958218	−	0.348763i	−0.184883	−	0.982761i	$-0.559191\pi$
$457$	−200123.	−	72838.8i	−0.958218	−	0.348763i	−0.773335	+	0.633998i	$0.781413\pi$
$458$		−	397263.i		−	1.89386i
$459$		0			0
$460$	231130.			1.09230
$461$	36759.6	−	100996.i	0.172969	−	0.475229i	−0.822670	−	0.568520i	$-0.807516\pi$
$461$	36759.6	−	100996.i	0.172969	−	0.475229i	0.995639	+	0.0932907i	$0.0297386\pi$
$462$		0			0
$463$	210371.	+	176523.i	0.981352	+	0.823452i	0.984293	−	0.176543i	$-0.0564916\pi$
$463$	210371.	+	176523.i	0.981352	+	0.823452i	−0.00294065	+	0.999996i	$0.500936\pi$
$464$	−38634.6	−	6812.33i	−0.179449	−	0.0316417i
$465$		0			0
$466$	5089.01	−	4270.19i	0.0234348	−	0.0196641i
$467$	305797.	−	176552.i	1.40217	−	0.809540i	0.407551	−	0.913183i	$-0.366383\pi$
$467$	305797.	−	176552.i	1.40217	−	0.809540i	0.994615	+	0.103642i	$0.0330497\pi$
$468$		0			0
$469$	−158351.	+	274273.i	−0.719907	+	1.24691i
$470$	229388.	−	40447.2i	1.03842	−	0.183102i
$471$		0			0
$472$	108148.	−	39362.5i	0.485437	−	0.176685i
$473$	94042.9	+	258381.i	0.420343	+	1.15488i
$474$		0			0
$475$	587.026	+	3329.19i	0.00260178	+	0.0147554i
$476$	456827.	+	263749.i	2.01622	+	1.16406i
$477$		0			0
$478$	−338632.	−	586528.i	−1.48208	−	2.56704i
$479$	198315.	+	236343.i	0.864341	+	1.03008i	0.999231	+	0.0392207i	$0.0124875\pi$
$479$	198315.	+	236343.i	0.864341	+	1.03008i	−0.134890	+	0.990861i	$0.543068\pi$
$480$		0			0
$481$	22475.7	−	127466.i	0.0971456	−	0.550940i
$482$	41158.7	−	49051.0i	0.177161	−	0.211132i
$483$		0			0
$484$	28297.4	+	10299.4i	0.120797	+	0.0439665i
$485$			251297.i			1.06833i
$486$		0			0
$487$	28076.8			0.118383			0.0591915	−	0.998247i	$-0.481148\pi$
$487$	28076.8			0.118383			0.0591915	+	0.998247i	$0.481148\pi$
$488$	43916.4	−	120659.i	0.184411	−	0.506665i
$489$		0			0
$490$	749160.	+	628620.i	3.12020	+	2.61816i
$491$	−330288.	−	58238.8i	−1.37003	−	0.241573i	−0.560259	−	0.828318i	$-0.689298\pi$
$491$	−330288.	−	58238.8i	−1.37003	−	0.241573i	−0.809772	+	0.586744i	$0.800409\pi$
$492$		0			0
$493$	54121.8	−	45413.6i	0.222678	−	0.186849i
$494$	−29257.8	+	16892.0i	−0.119891	+	0.0692193i
$495$		0			0
$496$	−67744.6	+	117337.i	−0.275367	+	0.476949i
$497$	−820273.	+	144636.i	−3.32082	+	0.585550i
$498$		0			0
$499$	−286659.	+	104335.i	−1.15123	+	0.419015i	−0.845958	−	0.533249i	$-0.820971\pi$
$499$	−286659.	+	104335.i	−1.15123	+	0.419015i	−0.305276	+	0.952264i	$0.598749\pi$
$500$	146293.	+	401936.i	0.585171	+	1.60774i
$501$		0			0
$502$	−133512.	−	757182.i	−0.529799	−	3.00464i
$503$	169836.	+	98054.7i	0.671264	+	0.387554i	0.796555	−	0.604566i	$-0.206653\pi$
$503$	169836.	+	98054.7i	0.671264	+	0.387554i	−0.125292	+	0.992120i	$0.539987\pi$
$504$		0			0
$505$	−108688.	−	188253.i	−0.426185	−	0.738174i
$506$	−154123.	−	183677.i	−0.601959	−	0.717387i
$507$		0			0
$508$	−104975.	+	595342.i	−0.406778	+	2.30695i
$509$	14669.5	−	17482.4i	0.0566211	−	0.0674784i	−0.736991	−	0.675903i	$-0.763754\pi$
$509$	14669.5	−	17482.4i	0.0566211	−	0.0674784i	0.793612	+	0.608425i	$0.208198\pi$
$510$		0			0
$511$	171120.	+	62282.7i	0.655330	+	0.238521i
$512$			225763.i			0.861216i
$513$		0			0
$514$	−200223.			−0.757858
$515$	−110467.	+	303506.i	−0.416504	+	1.14433i
$516$		0			0
$517$	−119031.	−	99878.8i	−0.445327	−	0.373674i
$518$	903130.	+	159246.i	3.36582	+	0.593485i
$519$		0			0
$520$	145090.	−	121745.i	0.536575	−	0.450240i
$521$	−45748.9	+	26413.1i	−0.168541	+	0.0973070i	−0.581898	−	0.813262i	$-0.697690\pi$
$521$	−45748.9	+	26413.1i	−0.168541	+	0.0973070i	0.413357	+	0.910569i	$0.364356\pi$
$522$		0			0
$523$	−3648.58	+	6319.53i	−0.0133389	+	0.0231037i	−0.872618	−	0.488404i	$-0.837579\pi$
$523$	−3648.58	+	6319.53i	−0.0133389	+	0.0231037i	0.859279	+	0.511507i	$0.170913\pi$
$524$	381632.	−	67292.0i	1.38990	−	0.245076i
$525$		0			0
$526$	675845.	−	245987.i	2.44273	−	0.889081i
$527$	−83454.4	−	229289.i	−0.300489	−	0.825585i
$528$		0			0
$529$	32212.9	+	182688.i	0.115111	+	0.652829i
$530$	−358187.	−	206800.i	−1.27514	−	0.736204i
$531$		0			0
$532$	−76962.8	−	133304.i	−0.271930	−	0.470997i
$533$	27399.2	+	32653.0i	0.0964457	+	0.114939i
$534$		0			0
$535$	82914.9	−	470234.i	0.289684	−	1.64288i
$536$	−195463.	+	232944.i	−0.680354	+	0.810815i
$537$		0			0
$538$	585298.	+	213031.i	2.02214	+	0.736000i
$539$		−	652391.i		−	2.24559i
$540$		0			0
$541$	−168037.			−0.574132			−0.287066	−	0.957911i	$-0.592680\pi$
$541$	−168037.			−0.574132			−0.287066	+	0.957911i	$0.592680\pi$
$542$	266360.	−	731819.i	0.906716	−	2.49118i
$543$		0			0
$544$	−96087.5	−	80627.0i	−0.324690	−	0.272447i
$545$	386312.	+	68117.3i	1.30061	+	0.229332i
$546$		0			0
$547$	−418801.	+	351416.i	−1.39969	+	1.17448i	−0.438461	+	0.898750i	$0.644476\pi$
$547$	−418801.	+	351416.i	−1.39969	+	1.17448i	−0.961234	+	0.275733i	$0.911079\pi$
$548$	−20750.6	+	11980.4i	−0.0690986	+	0.0398941i
$549$		0			0
$550$	−22095.4	+	38270.4i	−0.0730427	+	0.126514i
$551$	−20303.0	+	3579.96i	−0.0668739	+	0.0117917i
$552$		0			0
$553$	−573939.	+	208897.i	−1.87679	+	0.683096i
$554$	107259.	+	294691.i	0.349472	+	0.960167i
$555$		0			0
$556$	−57414.7	−	325615.i	−0.185726	−	1.05331i
$557$	175084.	+	101085.i	0.564333	+	0.325818i	0.754883	−	0.655860i	$-0.227694\pi$
$557$	175084.	+	101085.i	0.564333	+	0.325818i	−0.190550	+	0.981678i	$0.561027\pi$
$558$		0			0
$559$	99625.4	+	172556.i	0.318821	+	0.552213i
$560$	170533.	+	203233.i	0.543790	+	0.648064i
$561$		0			0
$562$	−56120.7	+	318276.i	−0.177685	+	1.00770i
$563$	−357122.	+	425602.i	−1.12668	+	1.34272i	−0.194426	+	0.980917i	$0.562284\pi$
$563$	−357122.	+	425602.i	−1.12668	+	1.34272i	−0.932253	+	0.361806i	$0.882160\pi$
$564$		0			0
$565$	402264.	+	146412.i	1.26013	+	0.458649i
$566$			437420.i			1.36542i
$567$		0			0
$568$	−799746.			−2.47888
$569$	83421.8	−	229199.i	0.257665	−	0.707928i	−0.741646	−	0.670792i	$-0.765954\pi$
$569$	83421.8	−	229199.i	0.257665	−	0.707928i	0.999310	−	0.0371359i	$-0.0118234\pi$
$570$		0			0
$571$	−242431.	−	203424.i	−0.743561	−	0.623922i	0.190230	−	0.981740i	$-0.439077\pi$
$571$	−242431.	−	203424.i	−0.743561	−	0.623922i	−0.933792	+	0.357817i	$0.883521\pi$
$572$	−279674.	−	49314.0i	−0.854790	−	0.150723i
$573$		0			0
$574$	−231356.	+	194130.i	−0.702192	+	0.589209i
$575$	−15056.8	+	8693.04i	−0.0455404	+	0.0262928i
$576$		0			0
$577$	−61386.3	+	106324.i	−0.184383	+	0.319360i	−0.943368	−	0.331747i	$-0.892362\pi$
$577$	−61386.3	+	106324.i	−0.184383	+	0.319360i	0.758986	+	0.651107i	$0.225695\pi$
$578$	274520.	−	48405.4i	0.821711	−	0.144890i
$579$		0			0
$580$	244116.	−	88850.9i	0.725671	−	0.264123i
$581$	77515.1	+	212971.i	0.229633	+	0.630911i
$582$		0			0
$583$	47911.2	+	271718.i	0.140961	+	0.799432i
$584$	151423.	+	87424.2i	0.443983	+	0.256334i
$585$		0			0
$586$	426118.	+	738057.i	1.24089	+	2.14929i
$587$	260872.	+	310895.i	0.757096	+	0.902272i	0.997661	−	0.0683614i	$-0.0217771\pi$
$587$	260872.	+	310895.i	0.757096	+	0.902272i	−0.240565	+	0.970633i	$0.577333\pi$
$588$		0			0
$589$	−12364.0	+	70119.5i	−0.0356391	+	0.202120i
$590$	−150605.	+	179484.i	−0.432649	+	0.515611i
$591$		0			0
$592$	163580.	+	59538.3i	0.466753	+	0.169884i
$593$		−	165039.i		−	0.469327i	−0.972077	−	0.234664i	$-0.924601\pi$
$593$		−	165039.i		−	0.469327i	0.972077	−	0.234664i	$-0.0753989\pi$
$594$		0			0
$595$	−477785.			−1.34958
$596$	152931.	−	420174.i	0.430530	−	1.18287i
$597$		0			0
$598$	−133101.	−	111685.i	−0.372201	−	0.312314i
$599$	−67800.8	−	11955.1i	−0.188965	−	0.0333196i	0.0783647	−	0.996925i	$-0.475030\pi$
$599$	−67800.8	−	11955.1i	−0.188965	−	0.0333196i	−0.267330	+	0.963605i	$0.586141\pi$
$600$		0			0
$601$	211057.	−	177098.i	0.584320	−	0.490302i	−0.302043	−	0.953294i	$-0.597669\pi$
$601$	211057.	−	177098.i	0.584320	−	0.490302i	0.886362	+	0.462992i	$0.153224\pi$
$602$	−1.22261e6	+	705872.i	−3.37360	+	1.94775i
$603$		0			0
$604$	−56086.5	+	97144.7i	−0.153739	+	0.266284i
$605$	−26861.1	+	4736.35i	−0.0733861	+	0.0129400i
$606$		0			0
$607$	366203.	−	133287.i	0.993905	−	0.361752i	0.206674	−	0.978410i	$-0.433736\pi$
$607$	366203.	−	133287.i	0.993905	−	0.361752i	0.787231	+	0.616658i	$0.211514\pi$
$608$	12518.6	+	34394.5i	0.0338647	+	0.0930426i
$609$		0			0
$610$	45392.7	+	257435.i	0.121991	+	0.691844i
$611$	−97512.9	−	56299.1i	−0.261204	−	0.150806i
$612$		0			0
$613$	91256.0	+	158060.i	0.242851	+	0.420631i	0.961525	−	0.274716i	$-0.0885839\pi$
$613$	91256.0	+	158060.i	0.242851	+	0.420631i	−0.718674	+	0.695347i	$0.755251\pi$
$614$	−726268.	−	865532.i	−1.92646	−	2.29587i
$615$		0			0
$616$	155452.	−	881614.i	0.409671	−	2.32336i
$617$	306777.	−	365602.i	0.805846	−	0.960369i	−0.193941	−	0.981013i	$-0.562127\pi$
$617$	306777.	−	365602.i	0.805846	−	0.960369i	0.999787	+	0.0206438i	$0.00657159\pi$
$618$		0			0
$619$	−77561.0	−	28229.9i	−0.202424	−	0.0736763i	0.238818	−	0.971064i	$-0.423240\pi$
$619$	−77561.0	−	28229.9i	−0.202424	−	0.0736763i	−0.441242	+	0.897388i	$0.645462\pi$
$620$		−	897201.i		−	2.33403i
$621$		0			0
$622$	790212.			2.04250
$623$	−178683.	+	490928.i	−0.460371	+	1.26486i
$624$		0			0
$625$	−323883.	−	271770.i	−0.829142	−	0.695732i
$626$	7308.60	+	1288.70i	0.0186503	+	0.00328855i
$627$		0			0
$628$	−529921.	+	444656.i	−1.34367	+	1.12747i
$629$	−271499.	+	156750.i	−0.686226	+	0.396193i
$630$		0			0
$631$	229945.	−	398277.i	0.577518	−	1.00029i	−0.418245	−	0.908334i	$-0.637355\pi$
$631$	229945.	−	398277.i	0.577518	−	1.00029i	0.995763	−	0.0919568i	$-0.0293122\pi$
$632$	−577533.	+	101835.i	−1.44591	+	0.254954i
$633$		0			0
$634$	131471.	−	47851.5i	0.327078	−	0.119047i
$635$	−187274.	−	514532.i	−0.464441	−	1.27604i
$636$		0			0
$637$	−82092.6	−	465570.i	−0.202314	−	1.14738i
$638$	−233391.	−	134748.i	−0.573380	−	0.331041i
$639$		0			0
$640$	−389518.	−	674664.i	−0.950971	−	1.64713i
$641$	436643.	+	520371.i	1.06270	+	1.26648i	0.962434	+	0.271515i	$0.0875246\pi$
$641$	436643.	+	520371.i	1.06270	+	1.26648i	0.100265	+	0.994961i	$0.468031\pi$
$642$		0			0
$643$	−44266.2	+	251046.i	−0.107066	+	0.607200i	0.883309	+	0.468791i	$0.155310\pi$
$643$	−44266.2	+	251046.i	−0.107066	+	0.607200i	−0.990375	+	0.138410i	$0.955801\pi$
$644$	508854.	−	606429.i	1.22694	−	1.46220i
$645$		0			0
$646$	76893.8	+	27987.1i	0.184258	+	0.0670644i
$647$		−	468446.i		−	1.11905i	−0.828812	−	0.559527i	$-0.810983\pi$
$647$		−	468446.i		−	1.11905i	0.828812	−	0.559527i	$-0.189017\pi$
$648$		0			0
$649$	156300.			0.371082
$650$	−10952.4	+	30091.5i	−0.0259228	+	0.0712224i
$651$		0			0
$652$	−70596.2	−	59237.2i	−0.166068	−	0.139348i
$653$	44397.4	+	7828.46i	0.104119	+	0.0183590i	0.225465	−	0.974251i	$-0.427610\pi$
$653$	44397.4	+	7828.46i	0.104119	+	0.0183590i	−0.121346	+	0.992610i	$0.538721\pi$
$654$		0			0
$655$	−268880.	+	225617.i	−0.626724	+	0.525884i
$656$	−49648.0	+	28664.3i	−0.115370	+	0.0666091i
$657$		0			0
$658$	398894.	−	690905.i	0.921310	−	1.59576i
$659$	274558.	−	48412.1i	0.632214	−	0.111476i	0.151647	−	0.988435i	$-0.451542\pi$
$659$	274558.	−	48412.1i	0.632214	−	0.111476i	0.480566	+	0.876958i	$0.340431\pi$
$660$		0			0
$661$	314216.	−	114365.i	0.719160	−	0.261753i	0.0435909	−	0.999049i	$-0.486120\pi$
$661$	314216.	−	114365.i	0.719160	−	0.261753i	0.675569	+	0.737297i	$0.263898\pi$
$662$	88418.7	+	242928.i	0.201757	+	0.554322i
$663$		0			0
$664$	37787.7	+	214305.i	0.0857066	+	0.486066i
$665$	120741.	+	69709.6i	0.273030	+	0.157634i
$666$		0			0
$667$	−53014.3	−	91823.5i	−0.119163	−	0.206396i
$668$	−286364.	−	341276.i	−0.641750	−	0.764808i
$669$		0			0
$670$	107500.	−	609663.i	0.239474	−	1.35813i
$671$	112091.	−	133585.i	0.248958	−	0.296697i
$672$		0			0
$673$	128784.	+	46873.7i	0.284337	+	0.103490i	0.480252	−	0.877131i	$-0.340545\pi$
$673$	128784.	+	46873.7i	0.284337	+	0.103490i	−0.195915	+	0.980621i	$0.562768\pi$
$674$			1.45694e6i			3.20718i
$675$		0			0
$676$	617453.			1.35117
$677$	27499.5	−	75554.3i	0.0599995	−	0.164847i	−0.906071	−	0.423126i	$-0.860933\pi$
$677$	27499.5	−	75554.3i	0.0599995	−	0.164847i	0.966071	+	0.258278i	$0.0831551\pi$
$678$		0			0
$679$	659342.	+	553254.i	1.43012	+	1.20001i
$680$	−451783.	−	79661.5i	−0.977038	−	0.172278i
$681$		0			0
$682$	−712996.	+	598274.i	−1.53292	+	1.28627i
$683$	19492.1	−	11253.8i	0.0417846	−	0.0241244i	−0.478962	−	0.877836i	$-0.658987\pi$
$683$	19492.1	−	11253.8i	0.0417846	−	0.0241244i	0.520747	+	0.853711i	$0.325654\pi$
$684$		0			0
$685$	10851.3	−	18795.0i	0.0231260	−	0.0400554i
$686$	1.88311e6	−	332042.i	4.00153	−	0.705578i
$687$		0			0
$688$	−251818.	+	91654.4i	−0.531999	+	0.193632i
$689$	68382.4	+	187879.i	0.144047	+	0.395767i
$690$		0			0
$691$	−100053.	−	567432.i	−0.209544	−	1.18839i	−0.890126	−	0.455714i	$-0.849384\pi$
$691$	−100053.	−	567432.i	−0.209544	−	1.18839i	0.680582	−	0.732672i	$-0.261727\pi$
$692$	−73413.5	−	42385.3i	−0.153308	−	0.0885122i
$693$		0			0
$694$	−475069.	−	822844.i	−0.986365	−	1.70843i
$695$	192501.	+	229413.i	0.398531	+	0.474951i
$696$		0			0
$697$	17928.1	−	101675.i	0.0369036	−	0.209291i
$698$	486125.	−	579341.i	0.997784	−	1.18911i
$699$		0			0
$700$	−137102.	−	49901.0i	−0.279800	−	0.101839i
$701$			678935.i			1.38163i	0.723030	+	0.690816i	$0.242749\pi$
$701$			678935.i			1.38163i	−0.723030	+	0.690816i	$0.757251\pi$
$702$		0			0
$703$	91480.3			0.185105
$704$	−236157.	+	648837.i	−0.476493	+	1.30915i
$705$		0			0
$706$	−94310.7	−	79136.1i	−0.189213	−	0.158769i
$707$	−733215.	−	129286.i	−1.46687	−	0.258649i
$708$		0			0
$709$	241064.	−	202277.i	0.479557	−	0.402396i	−0.370709	−	0.928749i	$-0.620885\pi$
$709$	241064.	−	202277.i	0.479557	−	0.402396i	0.850266	+	0.526353i	$0.176441\pi$
$710$	1.41002e6	−	814073.i	2.79710	−	1.61490i
$711$		0			0
$712$	−250811.	+	434418.i	−0.494752	+	0.856935i
$713$	−360623.	+	63587.6i	−0.709373	+	0.125082i
$714$		0			0
$715$	241712.	−	87975.9i	0.472809	−	0.172088i
$716$	−178012.	−	489084.i	−0.347235	−	0.954020i
$717$		0			0
$718$	−18262.8	−	103573.i	−0.0354256	−	0.200909i
$719$	677863.	+	391365.i	1.31125	+	0.757049i	0.982303	−	0.187301i	$-0.0599739\pi$
$719$	677863.	+	391365.i	1.31125	+	0.757049i	0.328944	+	0.944349i	$0.393307\pi$
$720$		0			0
$721$	553122.	+	958035.i	1.06402	+	1.84294i
$722$	545490.	+	650089.i	1.04643	+	1.24709i
$723$		0			0
$724$	−126209.	+	715765.i	−0.240775	+	1.36551i
$725$	−12560.9	+	14969.6i	−0.0238972	+	0.0284795i
$726$		0			0
$727$	795962.	+	289706.i	1.50599	+	0.548137i	0.957605	−	0.288086i	$-0.0930188\pi$
$727$	795962.	+	289706.i	1.50599	+	0.548137i	0.548390	+	0.836223i	$0.315241\pi$
$728$		−	648712.i		−	1.22402i
$729$		0			0
$730$	−355961.			−0.667970
$731$	165062.	−	453503.i	0.308896	−	0.848683i
$732$		0			0
$733$	−420921.	−	353195.i	−0.783417	−	0.657365i	0.160689	−	0.987005i	$-0.448628\pi$
$733$	−420921.	−	353195.i	−0.783417	−	0.657365i	−0.944107	+	0.329640i	$0.893073\pi$
$734$	−1.27867e6	−	225464.i	−2.37338	−	0.418491i
$735$		0			0
$736$	−144202.	+	121000.i	−0.266205	+	0.223373i
$737$	−357649.	+	206489.i	−0.658448	+	0.380155i
$738$		0			0
$739$	93328.8	−	161650.i	0.170894	−	0.295997i	−0.767839	−	0.640643i	$-0.778668\pi$
$739$	93328.8	−	161650.i	0.170894	−	0.295997i	0.938733	+	0.344646i	$0.112001\pi$
$740$	−1.13522e6	+	200170.i	−2.07309	+	0.365541i
$741$		0			0
$742$	−1.33117e6	+	484507.i	−2.41783	+	0.880020i
$743$	215328.	+	591610.i	0.390053	+	1.07166i	0.966977	+	0.254864i	$0.0820307\pi$
$743$	215328.	+	591610.i	0.390053	+	1.07166i	−0.576924	+	0.816798i	$0.695747\pi$
$744$		0			0
$745$	70327.6	+	398848.i	0.126711	+	0.718612i
$746$	−799874.	−	461807.i	−1.43729	−	0.829819i
$747$		0			0
$748$	343926.	+	595697.i	0.614698	+	1.06469i
$749$	−1.05123e6	−	1.25281e6i	−1.87385	−	2.23317i
$750$		0			0
$751$	51308.4	−	290985.i	0.0909722	−	0.515929i	−0.904935	−	0.425550i	$-0.860081\pi$
$751$	51308.4	−	290985.i	0.0909722	−	0.515929i	0.995907	−	0.0903797i	$-0.0288081\pi$
$752$	97342.1	−	116008.i	0.172133	−	0.205141i
$753$		0			0
$754$	−183512.	−	66793.0i	−0.322791	−	0.117486i
$755$		−	101602.i		−	0.178240i
$756$		0			0
$757$	−608815.			−1.06241			−0.531207	−	0.847242i	$-0.678261\pi$
$757$	−608815.			−1.06241			−0.531207	+	0.847242i	$0.678261\pi$
$758$	−578476.	+	1.58935e6i	−1.00681	+	2.76619i
$759$		0			0
$760$	102547.	+	86047.0i	0.177539	+	0.148973i
$761$	316069.	+	55731.5i	0.545774	+	0.0962346i	0.439735	−	0.898127i	$-0.355072\pi$
$761$	316069.	+	55731.5i	0.545774	+	0.0962346i	0.106038	+	0.994362i	$0.466183\pi$
$762$		0			0
$763$	1.02922e6	−	863622.i	1.76791	−	1.48346i
$764$	−323210.	+	186605.i	−0.553729	+	0.319696i
$765$		0			0
$766$	−728264.	+	1.26139e6i	−1.24117	+	2.14977i
$767$	111542.	−	19667.8i	0.189603	−	0.0334322i
$768$		0			0
$769$	−671028.	+	244234.i	−1.13472	+	0.413004i	−0.840003	−	0.542582i	$-0.817447\pi$
$769$	−671028.	+	244234.i	−1.13472	+	0.413004i	−0.294715	+	0.955585i	$0.595225\pi$
$770$	623333.	+	1.71259e6i	1.05133	+	2.88850i
$771$		0			0
$772$	−137851.	−	781791.i	−0.231299	−	1.31176i
$773$	−417603.	−	241103.i	−0.698883	−	0.403500i	0.108048	−	0.994146i	$-0.465540\pi$
$773$	−417603.	−	241103.i	−0.698883	−	0.403500i	−0.806931	+	0.590645i	$0.798873\pi$
$774$		0			0
$775$	33744.6	+	58447.4i	0.0561825	+	0.0973109i
$776$	531214.	+	633076.i	0.882158	+	1.05131i
$777$		0			0
$778$	−163466.	+	927061.i	−0.270065	+	1.53161i
$779$	−19365.2	+	23078.6i	−0.0319115	+	0.0380306i
$780$		0			0
$781$	−1.02063e6	−	371477.i	−1.67326	−	0.609018i
$782$			420843.i			0.688188i
$783$		0			0
$784$	635822.			1.03444
$785$	214299.	−	588782.i	0.347761	−	0.955466i
$786$		0			0
$787$	308970.	+	259257.i	0.498846	+	0.418582i	0.857184	−	0.515010i	$-0.172212\pi$
$787$	308970.	+	259257.i	0.498846	+	0.418582i	−0.358338	+	0.933592i	$0.616656\pi$
$788$	847993.	+	149524.i	1.36565	+	0.240801i
$789$		0			0
$790$	914578.	−	767422.i	1.46543	−	1.22965i
$791$	1.26977e6	−	733102.i	2.02942	−	1.17169i
$792$		0			0
$793$	63182.8	−	109436.i	0.100474	−	0.174026i
$794$	−1.11104e6	+	195906.i	−1.76233	+	0.310746i
$795$		0			0
$796$	101534.	−	36955.4i	0.160245	−	0.0583245i
$797$	−409182.	−	1.12422e6i	−0.644169	−	1.76984i	−0.638217	−	0.769856i	$-0.720328\pi$
$797$	−409182.	−	1.12422e6i	−0.644169	−	1.76984i	−0.00595131	−	0.999982i	$-0.501894\pi$
$798$		0			0
$799$	47358.3	+	268582.i	0.0741827	+	0.420711i
$800$	30045.6	+	17346.8i	0.0469462	+	0.0271044i
$801$		0			0
$802$	43122.6	+	74690.6i	0.0670435	+	0.116123i
$803$	152636.	+	181905.i	0.236715	+	0.282106i
$804$		0			0
$805$	−124511.	+	706137.i	−0.192139	+	1.08968i
$806$	−433537.	+	516669.i	−0.667353	+	0.795321i
$807$		0			0
$808$	−671755.	−	244499.i	−1.02894	−	0.374502i
$809$			249260.i			0.380852i	0.981702	+	0.190426i	$0.0609869\pi$
$809$			249260.i			0.380852i	−0.981702	+	0.190426i	$0.939013\pi$
$810$		0			0
$811$	−573638.			−0.872160			−0.436080	−	0.899908i	$-0.643634\pi$
$811$	−573638.			−0.872160			−0.436080	+	0.899908i	$0.643634\pi$
$812$	304320.	−	836113.i	0.461550	−	1.26810i
$813$		0			0
$814$	916066.	+	768671.i	1.38254	+	1.16009i
$815$	82203.5	+	14494.7i	0.123759	+	0.0218220i
$816$		0			0
$817$	−107879.	+	90521.6i	−0.161620	+	0.135615i
$818$	1.23999e6	−	715910.i	1.85316	−	1.06992i
$819$		0			0
$820$	189813.	−	328766.i	0.282292	−	0.488944i
$821$	409959.	−	72286.8i	0.608211	−	0.107244i	0.138944	−	0.990300i	$-0.455629\pi$
$821$	409959.	−	72286.8i	0.608211	−	0.107244i	0.469267	+	0.883056i	$0.344518\pi$
$822$		0			0
$823$	683645.	−	248827.i	1.00933	−	0.367364i	0.216152	−	0.976360i	$-0.430649\pi$
$823$	683645.	−	248827.i	1.00933	−	0.367364i	0.793174	+	0.608995i	$0.208427\pi$
$824$	363285.	+	998118.i	0.535049	+	1.47003i
$825$		0			0
$826$	139352.	+	790302.i	0.204245	+	1.15833i
$827$	340056.	+	196331.i	0.497209	+	0.287064i	0.727560	−	0.686044i	$-0.240654\pi$
$827$	340056.	+	196331.i	0.497209	+	0.287064i	−0.230351	+	0.973108i	$0.573987\pi$
$828$		0			0
$829$	−36689.1	−	63547.4i	−0.0533860	−	0.0924673i	0.838097	−	0.545521i	$-0.183668\pi$
$829$	−36689.1	−	63547.4i	−0.0533860	−	0.0924673i	−0.891483	+	0.453053i	$0.850335\pi$
$830$	−284767.	−	339372.i	−0.413364	−	0.492628i
$831$		0			0
$832$	−86885.2	+	492750.i	−0.125516	+	0.711836i
$833$	−736031.	+	877167.i	−1.06073	+	1.26413i
$834$		0			0
$835$	379183.	+	138011.i	0.543846	+	0.197944i
$836$		−	200717.i		−	0.287192i
$837$		0			0
$838$	1.01148e6			1.44036
$839$	389586.	−	1.07038e6i	0.553452	−	1.52060i	−0.275515	−	0.961297i	$-0.588848\pi$
$839$	389586.	−	1.07038e6i	0.553452	−	1.52060i	0.828966	−	0.559299i	$-0.188930\pi$
$840$		0			0
$841$	450517.	+	378029.i	0.636971	+	0.534482i
$842$	314590.	+	55470.7i	0.443732	+	0.0782419i
$843$		0			0
$844$	380507.	−	319283.i	0.534167	−	0.448220i
$845$	−484336.	+	279631.i	−0.678318	+	0.391627i
$846$		0			0
$847$	−46710.2	+	80904.5i	−0.0651096	+	0.112773i
$848$	−264817.	+	46694.4i	−0.368260	+	0.0649341i
$849$		0			0
$850$	72885.0	−	26528.0i	0.100879	−	0.0367169i
$851$	160914.	+	442108.i	0.222195	+	0.610477i
$852$		0			0
$853$	−195430.	−	1.10834e6i	−0.268592	−	1.52326i	−0.758609	−	0.651546i	$-0.774121\pi$
$853$	−195430.	−	1.10834e6i	−0.268592	−	1.52326i	0.490018	−	0.871712i	$-0.336990\pi$
$854$	775382.	+	447667.i	1.06316	+	0.613818i
$855$		0			0
$856$	−785139.	−	1.35990e6i	−1.07152	−	1.85592i
$857$	425954.	+	507632.i	0.579964	+	0.691174i	0.973644	−	0.228073i	$-0.0732426\pi$
$857$	425954.	+	507632.i	0.579964	+	0.691174i	−0.393680	+	0.919248i	$0.628798\pi$
$858$		0			0
$859$	96383.6	−	546618.i	0.130622	−	0.740795i	−0.847187	−	0.531295i	$-0.821705\pi$
$859$	96383.6	−	546618.i	0.130622	−	0.740795i	0.977809	−	0.209499i	$-0.0671834\pi$
$860$	1.14065e6	−	1.35938e6i	1.54226	−	1.83799i
$861$		0			0
$862$	−1.12047e6	−	407816.i	−1.50794	−	0.548845i
$863$		−	246831.i		−	0.331419i	−0.986175	−	0.165710i	$-0.947009\pi$
$863$		−	246831.i		−	0.331419i	0.986175	−	0.165710i	$-0.0529915\pi$
$864$		0			0
$865$	76781.6			0.102618
$866$	−562377.	+	1.54512e6i	−0.749880	+	2.06028i
$867$		0			0
$868$	−2.35403e6	−	1.97527e6i	−3.12445	−	2.62172i
$869$	−784342.	−	138301.i	−1.03864	−	0.183141i
$870$		0			0
$871$	−229248.	+	192362.i	−0.302182	+	0.253561i
$872$	1.11720e6	−	645017.i	1.46926	−	0.848278i
$873$		0			0
$874$	61401.7	−	106351.i	0.0803818	−	0.139225i
$875$	−1.30678e6	+	230421.i	−1.70682	+	0.300958i
$876$		0			0
$877$	−15899.4	+	5786.89i	−0.0206719	+	0.00752395i	−0.352335	−	0.935874i	$-0.614612\pi$
$877$	−15899.4	+	5786.89i	−0.0206719	+	0.00752395i	0.331664	+	0.943398i	$0.392390\pi$
$878$	−404642.	−	1.11175e6i	−0.524907	−	1.44217i
$879$		0			0
$880$	60073.6	+	340695.i	0.0775744	+	0.439946i
$881$	−3640.78	−	2102.01i	−0.00469076	−	0.00270821i	0.497653	−	0.867376i	$-0.334195\pi$
$881$	−3640.78	−	2102.01i	−0.00469076	−	0.00270821i	−0.502344	+	0.864668i	$0.667529\pi$
$882$		0			0
$883$	−479018.	−	829683.i	−0.614370	−	1.06412i	−0.990495	−	0.137551i	$-0.956077\pi$
$883$	−479018.	−	829683.i	−0.614370	−	1.06412i	0.376124	−	0.926569i	$-0.377256\pi$
$884$	320397.	+	381834.i	0.410000	+	0.488618i
$885$		0			0
$886$	99954.6	−	566871.i	0.127331	−	0.722132i
$887$	776929.	−	925908.i	0.987493	−	1.17685i	0.00325556	−	0.999995i	$-0.498964\pi$
$887$	776929.	−	925908.i	0.987493	−	1.17685i	0.984237	−	0.176853i	$-0.0565918\pi$
$888$		0			0
$889$	−1.76231e6	−	641427.i	−2.22986	−	0.811603i
$890$		−	1.02122e6i		−	1.28925i
$891$		0			0
$892$	1.97429e6			2.48131
$893$	27218.7	−	74782.9i	0.0341323	−	0.0937776i
$894$		0			0
$895$	361130.	+	303024.i	0.450835	+	0.378295i
$896$	−2.62771e6	−	463336.i	−3.27312	−	0.577139i
$897$		0			0
$898$	1.94145e6	−	1.62907e6i	2.40755	−	2.02017i
$899$	−356440.	+	205791.i	−0.441029	+	0.254628i
$900$		0			0
$901$	242135.	−	419390.i	0.298269	−	0.516616i
$902$	−387839.	+	68386.5i	−0.476692	+	0.0840537i
$903$		0			0
$904$	1.32290e6	−	481495.i	1.61878	−	0.589189i
$905$	−225156.	−	618610.i	−0.274907	−	0.755300i
$906$		0			0
$907$	121229.	+	687525.i	0.147365	+	0.835746i	0.965438	+	0.260632i	$0.0839310\pi$
$907$	121229.	+	687525.i	0.147365	+	0.835746i	−0.818074	+	0.575113i	$0.804958\pi$
$908$	52870.5	+	30524.8i	0.0641271	+	0.0370238i
$909$		0			0
$910$	660334.	+	1.14373e6i	0.797408	+	1.38115i
$911$	244464.	+	291341.i	0.294563	+	0.351047i	0.892946	−	0.450163i	$-0.148634\pi$
$911$	244464.	+	291341.i	0.294563	+	0.351047i	−0.598383	+	0.801210i	$0.704190\pi$
$912$		0			0
$913$	−51319.1	+	291045.i	−0.0615655	+	0.349155i
$914$	916503.	−	1.09225e6i	1.09709	−	1.30746i
$915$		0			0
$916$	1.60718e6	+	584965.i	1.91546	+	0.697170i
$917$			1.20219e6i			1.42967i
$918$		0			0
$919$	−1.55045e6			−1.83580			−0.917901	−	0.396810i	$-0.870117\pi$
$919$	−1.55045e6			−1.83580			−0.917901	+	0.396810i	$0.870117\pi$
$920$	−235470.	+	646947.i	−0.278201	+	0.764352i
$921$		0			0
$922$	551224.	+	462532.i	0.648435	+	0.544102i
$923$	−775100.	−	136671.i	−0.909817	−	0.160425i
$924$		0			0
$925$	66424.5	−	55736.8i	0.0776327	−	0.0651416i
$926$	−1.59228e6	+	919303.i	−1.85694	+	1.07210i
$927$		0			0
$928$	−105789.	+	183232.i	−0.122841	+	0.212768i
$929$	471397.	−	83119.9i	0.546204	−	0.0963105i	0.106265	−	0.994338i	$-0.466111\pi$
$929$	471397.	−	83119.9i	0.546204	−	0.0963105i	0.439940	+	0.898027i	$0.355000\pi$
$930$		0			0
$931$	313982.	−	114280.i	0.362247	−	0.131847i
$932$	9782.07	+	26876.0i	0.0112616	+	0.0309409i
$933$		0			0
$934$	410514.	+	2.32814e6i	0.470581	+	2.66880i
$935$	−539557.	−	311513.i	−0.617183	−	0.356331i
$936$		0			0
$937$	231373.	+	400750.i	0.263532	+	0.456451i	0.967178	−	0.254100i	$-0.0817792\pi$
$937$	231373.	+	400750.i	0.263532	+	0.456451i	−0.703646	+	0.710551i	$0.748446\pi$
$938$	−1.36293e6	−	1.62428e6i	−1.54906	−	1.84610i
$939$		0			0
$940$	−174136.	+	987574.i	−0.197076	+	1.11767i
$941$	−597872.	+	712516.i	−0.675195	+	0.804666i	−0.989481	−	0.144663i	$-0.953790\pi$
$941$	−597872.	+	712516.i	−0.675195	+	0.804666i	0.314286	+	0.949328i	$0.398235\pi$
$942$		0			0
$943$	−145598.	−	52993.3i	−0.163731	−	0.0595933i
$944$			152331.i			0.170940i
$945$		0			0
$946$	−1.84090e6			−2.05706
$947$	105465.	−	289762.i	0.117600	−	0.323104i	−0.866901	−	0.498480i	$-0.833892\pi$
$947$	105465.	−	289762.i	0.117600	−	0.323104i	0.984502	+	0.175376i	$0.0561141\pi$
$948$		0			0
$949$	131816.	+	110607.i	0.146365	+	0.122815i
$950$	−22289.2	−	3930.18i	−0.0246971	−	0.00435477i
$951$		0			0
$952$	−1.20365e6	+	1.00998e6i	−1.32809	+	1.11440i
$953$	−421824.	+	243540.i	−0.464457	+	0.268154i	−0.713917	−	0.700231i	$-0.753080\pi$
$953$	−421824.	+	243540.i	−0.464457	+	0.268154i	0.249459	+	0.968385i	$0.419747\pi$
$954$		0			0
$955$	169019.	−	292749.i	0.185323	−	0.320988i
$956$	2.87150e6	−	506323.i	3.14191	−	0.554003i
$957$		0			0
$958$	−1.94102e6	+	706473.i	−2.11494	+	0.769777i
$959$	−25423.3	−	69849.9i	−0.0276436	−	0.0759502i
$960$		0			0
$961$	86466.4	+	490375.i	0.0936269	+	0.530984i
$962$	750463.	+	433280.i	0.810922	+	0.468186i
$963$		0			0
$964$	137836.	+	238739.i	0.148323	+	0.256903i
$965$	462188.	+	550814.i	0.496322	+	0.591494i
$966$		0			0
$967$	−98732.1	+	559938.i	−0.105586	+	0.598807i	0.885399	+	0.464832i	$0.153885\pi$
$967$	−98732.1	+	559938.i	−0.105586	+	0.598807i	−0.990985	+	0.133975i	$0.957226\pi$
$968$	−57657.4	+	68713.4i	−0.0615325	+	0.0733315i
$969$		0			0
$970$	−1.58099e6	−	575433.i	−1.68030	−	0.611578i
$971$		−	570591.i		−	0.605183i	−0.953120	−	0.302591i	$-0.902148\pi$
$971$		−	570591.i		−	0.605183i	0.953120	−	0.302591i	$-0.0978518\pi$
$972$		0			0
$973$	1.02573e6			1.08345
$974$	−64291.7	+	176640.i	−0.0677699	+	0.186196i
$975$		0			0
$976$	130192.	+	109244.i	0.136674	+	0.114683i
$977$	1.42905e6	+	251981.i	1.49713	+	0.263984i	0.861400	−	0.507928i	$-0.169588\pi$
$977$	1.42905e6	+	251981.i	1.49713	+	0.263984i	0.635729	+	0.771912i	$0.280700\pi$
$978$		0			0
$979$	−521867.	+	437899.i	−0.544496	+	0.456886i
$980$	−3.64629e6	+	2.10519e6i	−3.79664	+	2.19199i
$981$		0			0
$982$	1.12271e6	−	1.94459e6i	1.16425	−	2.01653i
$983$	338266.	−	59645.3i	0.350067	−	0.0617262i	0.00414985	−	0.999991i	$-0.498679\pi$
$983$	338266.	−	59645.3i	0.350067	−	0.0617262i	0.345917	+	0.938265i	$0.387568\pi$
$984$		0			0
$985$	−732889.	+	266750.i	−0.755381	+	0.274936i
$986$	161780.	+	444487.i	0.166407	+	0.457199i
$987$		0			0
$988$	−25256.9	−	143239.i	−0.0258742	−	0.146740i
$989$	−627235.	−	362134.i	−0.641265	−	0.370235i
$990$		0			0
$991$	886474.	+	1.53542e6i	0.902649	+	1.56343i	0.824042	+	0.566528i	$0.191714\pi$
$991$	886474.	+	1.53542e6i	0.902649	+	1.56343i	0.0786066	+	0.996906i	$0.474953\pi$
$992$	469697.	+	559763.i	0.477303	+	0.568828i
$993$		0			0
$994$	968351.	−	5.49179e6i	0.980076	−	5.55829i
$995$	−62907.9	+	74970.7i	−0.0635417	+	0.0757260i
$996$		0			0
$997$	1.13454e6	+	412938.i	1.14138	+	0.415427i	0.842410	−	0.538837i	$-0.181136\pi$
$997$	1.13454e6	+	412938.i	1.14138	+	0.415427i	0.298966	+	0.954264i	$0.403358\pi$
$998$		−	2.04237e6i		−	2.05057i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.5.f.a.17.2		66
3.2	odd	2		27.5.f.a.23.10	yes	66
27.7	even	9		27.5.f.a.20.10	✓	66
27.20	odd	18	inner	81.5.f.a.62.2		66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.5.f.a.20.10	✓	66	27.7	even	9
27.5.f.a.23.10	yes	66	3.2	odd	2
81.5.f.a.17.2		66	1.1	even	1	trivial
81.5.f.a.62.2		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)

\(f(q)\)	\(=\)	\(q+(-2.28985 + 6.29131i) q^{2} +(-22.0805 - 18.5277i) q^{4} +(25.7110 + 4.53354i) q^{5} +(68.4999 - 57.4782i) q^{7} +(74.3553 - 42.9290i) q^{8} +(-87.3962 + 151.375i) q^{10} +(114.832 - 20.2479i) q^{11} +(79.4001 - 28.8993i) q^{13} +(204.759 + 562.571i) q^{14} +(19.7336 + 111.915i) q^{16} +(-177.240 - 102.329i) q^{17} +(29.8600 + 51.7191i) q^{19} +(-483.715 - 576.469i) q^{20} +(-135.561 + 768.806i) q^{22} +(-197.425 + 235.282i) q^{23} +(53.1928 + 19.3606i) q^{25} +565.706i q^{26} -2577.45 q^{28} +(-118.070 + 324.395i) q^{29} +(913.317 + 766.364i) q^{31} +(603.579 + 106.427i) q^{32} +(1049.64 - 880.751i) q^{34} +(2021.78 - 1167.27i) q^{35} +(765.910 - 1326.59i) q^{37} +(-393.756 + 69.4298i) q^{38} +(2106.37 - 766.655i) q^{40} +(172.539 + 474.046i) q^{41} +(409.482 + 2322.29i) q^{43} +(-2910.69 - 1680.49i) q^{44} +(-1028.16 - 1780.82i) q^{46} +(-856.572 - 1020.82i) q^{47} +(971.558 - 5509.98i) q^{49} +(-243.607 + 290.320i) q^{50} +(-2288.63 - 832.994i) q^{52} +2366.23i q^{53} +3044.22 q^{55} +(2625.84 - 7214.44i) q^{56} +(-1770.51 - 1485.63i) q^{58} +(1320.08 + 232.766i) q^{59} +(1145.64 - 961.305i) q^{61} +(-6912.80 + 3991.10i) q^{62} +(-2960.81 + 5128.27i) q^{64} +(2172.47 - 383.065i) q^{65} +(-3328.14 + 1211.34i) q^{67} +(2017.61 + 5543.33i) q^{68} +(2714.12 + 15392.5i) q^{70} +(-8066.81 - 4657.37i) q^{71} +(1018.24 + 1763.64i) q^{73} +(6592.21 + 7856.28i) q^{74} +(298.914 - 1695.22i) q^{76} +(6702.13 - 7987.29i) q^{77} +(-6418.45 - 2336.12i) q^{79} +2966.91i q^{80} -3377.46 q^{82} +(-866.863 + 2381.69i) q^{83} +(-4093.09 - 3434.51i) q^{85} +(-15547.9 - 2741.51i) q^{86} +(7669.11 - 6435.15i) q^{88} +(-5059.72 + 2921.23i) q^{89} +(3777.82 - 6543.37i) q^{91} +(8718.50 - 1537.31i) q^{92} +(8383.74 - 3051.43i) q^{94} +(533.260 + 1465.12i) q^{95} +(1671.44 + 9479.22i) q^{97} +(32440.3 + 18729.4i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q + 6 q^{2} - 6 q^{4} - 3 q^{5} - 6 q^{7} + 9 q^{8} - 3 q^{10} + 492 q^{11} - 6 q^{13} - 1137 q^{14} - 54 q^{16} + 9 q^{17} - 3 q^{19} + 2487 q^{20} + 1002 q^{22} + 2724 q^{23} + 435 q^{25} - 12 q^{28}+ \cdots + 259938 q^{98}+O(q^{100}) \) 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

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