LMFDB - Embedded newform 81.5.f.a.8.8

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			8.8
Character	$\chi$	$=$	81.8
Dual form			81.5.f.a.71.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.58910 + 0.632855i) q^{2} +(-2.55397 - 0.929568i) q^{4} +(-12.8585 - 15.3241i) q^{5} +(75.5885 - 27.5120i) q^{7} +(-59.0773 - 34.1083i) q^{8} +(-36.4523 - 63.1373i) q^{10} +(73.4332 - 87.5142i) q^{11} +(-36.1566 - 205.054i) q^{13} +(288.705 - 50.9066i) q^{14} +(-157.137 - 131.853i) q^{16} +(163.954 - 94.6591i) q^{17} +(-227.463 + 393.977i) q^{19} +(18.5953 + 51.0902i) q^{20} +(318.943 - 267.625i) q^{22} +(-216.433 + 594.644i) q^{23} +(39.0415 - 221.415i) q^{25} -758.841i q^{26} -218.625 q^{28} +(598.503 + 105.532i) q^{29} +(-320.106 - 116.509i) q^{31} +(221.047 + 263.433i) q^{32} +(648.354 - 235.981i) q^{34} +(-1393.55 - 804.566i) q^{35} +(551.400 + 955.053i) q^{37} +(-1065.72 + 1270.07i) q^{38} +(236.964 + 1343.89i) q^{40} +(894.918 - 157.798i) q^{41} +(-987.620 - 828.712i) q^{43} +(-268.896 + 155.247i) q^{44} +(-1153.12 + 1997.26i) q^{46} +(161.256 + 443.048i) q^{47} +(3117.44 - 2615.84i) q^{49} +(280.247 - 769.973i) q^{50} +(-98.2691 + 557.312i) q^{52} -293.218i q^{53} -2285.32 q^{55} +(-5403.95 - 952.863i) q^{56} +(2081.30 + 757.531i) q^{58} +(3379.85 + 4027.95i) q^{59} +(-2379.12 + 865.931i) q^{61} +(-1075.16 - 620.743i) q^{62} +(2267.66 + 3927.70i) q^{64} +(-2677.36 + 3190.75i) q^{65} +(933.925 + 5296.55i) q^{67} +(-506.726 + 89.3495i) q^{68} +(-4492.41 - 3769.58i) q^{70} +(4919.78 - 2840.43i) q^{71} +(1385.76 - 2400.21i) q^{73} +(1374.62 + 3776.73i) q^{74} +(947.162 - 794.763i) q^{76} +(3143.01 - 8635.36i) q^{77} +(1459.18 - 8275.44i) q^{79} +4103.41i q^{80} +3311.81 q^{82} +(6331.63 + 1116.44i) q^{83} +(-3558.77 - 1295.29i) q^{85} +(-3020.21 - 3599.35i) q^{86} +(-7323.20 + 2665.43i) q^{88} +(-6738.82 - 3890.66i) q^{89} +(-8374.46 - 14505.0i) q^{91} +(1105.52 - 1317.51i) q^{92} +(298.379 + 1692.19i) q^{94} +(8962.18 - 1580.27i) q^{95} +(8458.98 + 7097.93i) q^{97} +(12844.2 - 7415.62i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	3.58910	+	0.632855i	0.897274	+	0.158214i	0.603220	−	0.797575i	$-0.293884\pi$
$2$	3.58910	+	0.632855i	0.897274	+	0.158214i	0.294054	+	0.955789i	$0.404995\pi$
$3$		0			0
$3$		0			0
$4$	−2.55397	−	0.929568i	−0.159623	−	0.0580980i
$5$	−12.8585	−	15.3241i	−0.514339	−	0.612965i	0.444894	−	0.895583i	$-0.353241\pi$
$5$	−12.8585	−	15.3241i	−0.514339	−	0.612965i	−0.959232	+	0.282618i	$0.908797\pi$
$6$		0			0
$7$	75.5885	−	27.5120i	1.54262	−	0.561469i	0.575950	−	0.817485i	$-0.304632\pi$
$7$	75.5885	−	27.5120i	1.54262	−	0.561469i	0.966672	+	0.256017i	$0.0824102\pi$
$8$	−59.0773	−	34.1083i	−0.923083	−	0.532943i
$9$		0			0
$10$	−36.4523	−	63.1373i	−0.364523	−	0.631373i
$11$	73.4332	−	87.5142i	0.606886	−	0.723258i	−0.371871	−	0.928285i	$-0.621284\pi$
$11$	73.4332	−	87.5142i	0.606886	−	0.723258i	0.978756	+	0.205026i	$0.0657280\pi$
$12$		0			0
$13$	−36.1566	−	205.054i	−0.213944	−	1.21334i	−0.882729	−	0.469882i	$-0.844296\pi$
$13$	−36.1566	−	205.054i	−0.213944	−	1.21334i	0.668785	−	0.743456i	$-0.266815\pi$
$14$	288.705	−	50.9066i	1.47299	−	0.259727i
$15$		0			0
$16$	−157.137	−	131.853i	−0.613814	−	0.515051i
$17$	163.954	−	94.6591i	0.567316	−	0.327540i	−0.188760	−	0.982023i	$-0.560447\pi$
$17$	163.954	−	94.6591i	0.567316	−	0.327540i	0.756077	+	0.654483i	$0.227114\pi$
$18$		0			0
$19$	−227.463	+	393.977i	−0.630091	+	1.09135i	0.357441	+	0.933936i	$0.383649\pi$
$19$	−227.463	+	393.977i	−0.630091	+	1.09135i	−0.987533	+	0.157414i	$0.949684\pi$
$20$	18.5953	+	51.0902i	0.0464882	+	0.127725i
$21$		0			0
$22$	318.943	−	267.625i	0.658972	−	0.552943i
$23$	−216.433	+	594.644i	−0.409135	+	1.12409i	0.548511	+	0.836143i	$0.315195\pi$
$23$	−216.433	+	594.644i	−0.409135	+	1.12409i	−0.957646	+	0.287947i	$0.907027\pi$
$24$		0			0
$25$	39.0415	−	221.415i	0.0624664	−	0.354264i
$26$		−	758.841i		−	1.12255i
$27$		0			0
$28$	−218.625			−0.278858
$29$	598.503	+	105.532i	0.711657	+	0.125484i	0.517745	−	0.855535i	$-0.326771\pi$
$29$	598.503	+	105.532i	0.711657	+	0.125484i	0.193911	+	0.981019i	$0.437883\pi$
$30$		0			0
$31$	−320.106	−	116.509i	−0.333097	−	0.121237i	0.170057	−	0.985434i	$-0.445605\pi$
$31$	−320.106	−	116.509i	−0.333097	−	0.121237i	−0.503154	+	0.864197i	$0.667827\pi$
$32$	221.047	+	263.433i	0.215866	+	0.257259i
$33$		0			0
$34$	648.354	−	235.981i	0.560860	−	0.204136i
$35$	−1393.55	−	804.566i	−1.13759	−	0.656788i
$36$		0			0
$37$	551.400	+	955.053i	0.402776	+	0.697628i	0.994060	−	0.108835i	$-0.0347121\pi$
$37$	551.400	+	955.053i	0.402776	+	0.697628i	−0.591284	+	0.806463i	$0.701379\pi$
$38$	−1065.72	+	1270.07i	−0.738031	+	0.879551i
$39$		0			0
$40$	236.964	+	1343.89i	0.148102	+	0.839931i
$41$	894.918	−	157.798i	0.532372	−	0.0938716i	0.0990014	−	0.995087i	$-0.468435\pi$
$41$	894.918	−	157.798i	0.532372	−	0.0938716i	0.433371	+	0.901216i	$0.357324\pi$
$42$		0			0
$43$	−987.620	−	828.712i	−0.534137	−	0.448194i	0.335390	−	0.942079i	$-0.391132\pi$
$43$	−987.620	−	828.712i	−0.534137	−	0.448194i	−0.869527	+	0.493885i	$0.835576\pi$
$44$	−268.896	+	155.247i	−0.138893	+	0.0801898i
$45$		0			0
$46$	−1153.12	+	1997.26i	−0.544953	+	0.943886i
$47$	161.256	+	443.048i	0.0729997	+	0.200565i	0.970826	−	0.239785i	$-0.0770768\pi$
$47$	161.256	+	443.048i	0.0729997	+	0.200565i	−0.897826	+	0.440349i	$0.854855\pi$
$48$		0			0
$49$	3117.44	−	2615.84i	1.29839	−	1.08948i
$50$	280.247	−	769.973i	0.112099	−	0.307989i
$51$		0			0
$52$	−98.2691	+	557.312i	−0.0363421	+	0.206106i
$53$		−	293.218i		−	0.104385i	−0.998637	−	0.0521927i	$-0.983379\pi$
$53$		−	293.218i		−	0.104385i	0.998637	−	0.0521927i	$-0.0166210\pi$
$54$		0			0
$55$	−2285.32			−0.755477
$56$	−5403.95	−	952.863i	−1.72320	−	0.303847i
$57$		0			0
$58$	2081.30	+	757.531i	0.618698	+	0.225188i
$59$	3379.85	+	4027.95i	0.970943	+	1.15713i	0.987557	+	0.157263i	$0.0502671\pi$
$59$	3379.85	+	4027.95i	0.970943	+	1.15713i	−0.0166134	+	0.999862i	$0.505288\pi$
$60$		0			0
$61$	−2379.12	+	865.931i	−0.639378	+	0.232714i	−0.641308	−	0.767284i	$-0.721608\pi$
$61$	−2379.12	+	865.931i	−0.639378	+	0.232714i	0.00193010	+	0.999998i	$0.499386\pi$
$62$	−1075.16	−	620.743i	−0.279698	−	0.161484i
$63$		0			0
$64$	2267.66	+	3927.70i	0.553628	+	0.958912i
$65$	−2677.36	+	3190.75i	−0.633694	+	0.755207i
$66$		0			0
$67$	933.925	+	5296.55i	0.208047	+	1.17990i	0.892572	+	0.450905i	$0.148899\pi$
$67$	933.925	+	5296.55i	0.208047	+	1.17990i	−0.684524	+	0.728990i	$0.739990\pi$
$68$	−506.726	+	89.3495i	−0.109586	+	0.0193230i
$69$		0			0
$70$	−4492.41	−	3769.58i	−0.916818	−	0.769302i
$71$	4919.78	−	2840.43i	0.975952	−	0.563466i	0.0749067	−	0.997191i	$-0.476134\pi$
$71$	4919.78	−	2840.43i	0.975952	−	0.563466i	0.901046	+	0.433724i	$0.142801\pi$
$72$		0			0
$73$	1385.76	−	2400.21i	0.260041	−	0.450404i	−0.706211	−	0.708001i	$-0.749597\pi$
$73$	1385.76	−	2400.21i	0.260041	−	0.450404i	0.966253	+	0.257597i	$0.0829305\pi$
$74$	1374.62	+	3776.73i	0.251026	+	0.689689i
$75$		0			0
$76$	947.162	−	794.763i	0.163982	−	0.137598i
$77$	3143.01	−	8635.36i	0.530109	−	1.45646i
$78$		0			0
$79$	1459.18	−	8275.44i	0.233806	−	1.32598i	−0.611308	−	0.791393i	$-0.709356\pi$
$79$	1459.18	−	8275.44i	0.233806	−	1.32598i	0.845114	−	0.534587i	$-0.179533\pi$
$80$			4103.41i			0.641158i
$81$		0			0
$82$	3311.81			0.492536
$83$	6331.63	+	1116.44i	0.919093	+	0.162061i	0.613129	−	0.789983i	$-0.289910\pi$
$83$	6331.63	+	1116.44i	0.919093	+	0.162061i	0.305963	+	0.952043i	$0.401022\pi$
$84$		0			0
$85$	−3558.77	−	1295.29i	−0.492563	−	0.179278i
$86$	−3020.21	−	3599.35i	−0.408357	−	0.486661i
$87$		0			0
$88$	−7323.20	+	2665.43i	−0.945661	+	0.344193i
$89$	−6738.82	−	3890.66i	−0.850753	−	0.491183i	0.0101517	−	0.999948i	$-0.496769\pi$
$89$	−6738.82	−	3890.66i	−0.850753	−	0.491183i	−0.860905	+	0.508766i	$0.830102\pi$
$90$		0			0
$91$	−8374.46	−	14505.0i	−1.01129	−	1.75160i
$92$	1105.52	−	1317.51i	0.130615	−	0.155661i
$93$		0			0
$94$	298.379	+	1692.19i	0.0337686	+	0.191511i
$95$	8962.18	−	1580.27i	0.993040	−	0.175100i
$96$		0			0
$97$	8458.98	+	7097.93i	0.899031	+	0.754377i	0.970001	−	0.243102i	$-0.0781649\pi$
$97$	8458.98	+	7097.93i	0.899031	+	0.754377i	−0.0709696	+	0.997478i	$0.522609\pi$
$98$	12844.2	−	7415.62i	1.33738	−	0.772139i
$99$		0			0
$100$	−305.531	+	529.196i	−0.0305531	+	0.0529196i
$101$	−3965.48	−	10895.1i	−0.388734	−	1.06804i	−0.967572	−	0.252596i	$-0.918716\pi$
$101$	−3965.48	−	10895.1i	−0.388734	−	1.06804i	0.578838	−	0.815443i	$-0.303506\pi$
$102$		0			0
$103$	10494.0	−	8805.50i	0.989159	−	0.830003i	0.00371311	−	0.999993i	$-0.498818\pi$
$103$	10494.0	−	8805.50i	0.989159	−	0.830003i	0.985446	+	0.169990i	$0.0543736\pi$
$104$	−4858.02	+	13347.3i	−0.449151	+	1.23403i
$105$		0			0
$106$	185.565	−	1052.39i	0.0165152	−	0.0936623i
$107$			9783.48i			0.854527i	0.904127	+	0.427264i	$0.140522\pi$
$107$			9783.48i			0.854527i	−0.904127	+	0.427264i	$0.859478\pi$
$108$		0			0
$109$	5416.41			0.455888			0.227944	−	0.973674i	$-0.426800\pi$
$109$	5416.41			0.455888			0.227944	+	0.973674i	$0.426800\pi$
$110$	−8202.23	−	1446.27i	−0.677870	−	0.119527i
$111$		0			0
$112$	−15505.2	−	5643.45i	−1.23607	−	0.449892i
$113$	−6637.56	−	7910.34i	−0.519818	−	0.619495i	0.440719	−	0.897645i	$-0.354723\pi$
$113$	−6637.56	−	7910.34i	−0.519818	−	0.619495i	−0.960538	+	0.278150i	$0.910279\pi$
$114$		0			0
$115$	11895.4	−	4329.57i	0.899462	−	0.327377i
$116$	−1430.46	−	825.876i	−0.106306	−	0.0613760i
$117$		0			0
$118$	9581.52	+	16595.7i	0.688130	+	1.19188i
$119$	9788.81	−	11665.8i	0.691251	−	0.823801i
$120$		0			0
$121$	276.071	+	1565.67i	0.0188560	+	0.106938i
$122$	−9086.92	+	1602.27i	−0.610516	+	0.107650i
$123$		0			0
$124$	709.238	+	595.121i	0.0461263	+	0.0387045i
$125$	−14722.6	+	8500.11i	−0.942247	+	0.544007i
$126$		0			0
$127$	−4578.46	+	7930.12i	−0.283865	+	0.491668i	−0.972333	−	0.233598i	$-0.924950\pi$
$127$	−4578.46	+	7930.12i	−0.283865	+	0.491668i	0.688468	+	0.725266i	$0.258283\pi$
$128$	3771.32	+	10361.6i	0.230183	+	0.632424i
$129$		0			0
$130$	−11628.6	+	9757.54i	−0.688082	+	0.577369i
$131$	−7733.68	+	21248.1i	−0.450654	+	1.23816i	0.481611	+	0.876385i	$0.340052\pi$
$131$	−7733.68	+	21248.1i	−0.450654	+	1.23816i	−0.932265	+	0.361777i	$0.882170\pi$
$132$		0			0
$133$	−6354.49	+	36038.1i	−0.359234	+	2.03732i
$134$			19600.9i			1.09161i
$135$		0			0
$136$	−12914.7			−0.698240
$137$	23306.1	+	4109.50i	1.24173	+	0.218951i	0.755659	−	0.654965i	$-0.227317\pi$
$137$	23306.1	+	4109.50i	1.24173	+	0.218951i	0.486076	+	0.873917i	$0.338428\pi$
$138$		0			0
$139$	−11956.2	−	4351.70i	−0.618819	−	0.225232i	0.0135387	−	0.999908i	$-0.495690\pi$
$139$	−11956.2	−	4351.70i	−0.618819	−	0.225232i	−0.632357	+	0.774677i	$0.717913\pi$
$140$	2811.18	+	3350.23i	0.143428	+	0.170930i
$141$		0			0
$142$	19455.1	−	7081.09i	0.964845	−	0.351175i
$143$	−20600.3	−	11893.6i	−1.00740	−	0.581621i
$144$		0			0
$145$	−6078.65	−	10528.5i	−0.289115	−	0.500762i
$146$	6492.61	−	7737.59i	0.304588	−	0.362994i
$147$		0			0
$148$	−520.471	−	2951.74i	−0.0237615	−	0.134758i
$149$	−28007.9	+	4938.55i	−1.26156	+	0.222447i	−0.764134	−	0.645058i	$-0.776833\pi$
$149$	−28007.9	+	4938.55i	−1.26156	+	0.222447i	−0.497428	+	0.867505i	$0.665722\pi$
$150$		0			0
$151$	23369.1	+	19609.0i	1.02492	+	0.860008i	0.990237	−	0.139391i	$-0.0445143\pi$
$151$	23369.1	+	19609.0i	1.02492	+	0.860008i	0.0346800	+	0.999398i	$0.488959\pi$
$152$	26875.8	−	15516.8i	1.16325	−	0.671605i
$153$		0			0
$154$	16745.5	−	29004.1i	0.706085	−	1.22297i
$155$	2330.67	+	6403.48i	0.0970104	+	0.266534i
$156$		0			0
$157$	−33200.8	+	27858.8i	−1.34695	+	1.13022i	−0.367162	+	0.930157i	$0.619671\pi$
$157$	−33200.8	+	27858.8i	−1.34695	+	1.13022i	−0.979783	+	0.200064i	$0.935885\pi$
$158$	10474.3	−	28777.9i	0.419576	−	1.15278i
$159$		0			0
$160$	1194.56	−	6774.70i	0.0466626	−	0.264637i
$161$			50902.7i			1.96376i
$162$		0			0
$163$	2612.38			0.0983243			0.0491622	−	0.998791i	$-0.484345\pi$
$163$	2612.38			0.0983243			0.0491622	+	0.998791i	$0.484345\pi$
$164$	−2432.27	−	428.876i	−0.0904326	−	0.0159457i
$165$		0			0
$166$	22018.3	+	8014.00i	0.799038	+	0.290826i
$167$	−10495.0	−	12507.5i	−0.376314	−	0.448474i	0.544333	−	0.838869i	$-0.316783\pi$
$167$	−10495.0	−	12507.5i	−0.376314	−	0.448474i	−0.920647	+	0.390395i	$0.872338\pi$
$168$		0			0
$169$	−13901.4	+	5059.68i	−0.486725	+	0.177153i
$170$	−11953.0	−	6901.09i	−0.413600	−	0.238792i
$171$		0			0
$172$	1752.01	+	3034.56i	0.0592214	+	0.102574i
$173$	1963.78	−	2340.34i	0.0656146	−	0.0781964i	−0.732239	−	0.681048i	$-0.761524\pi$
$173$	1963.78	−	2340.34i	0.0656146	−	0.0781964i	0.797853	+	0.602852i	$0.205969\pi$
$174$		0			0
$175$	−3140.48	−	17810.5i	−0.102546	−	0.581569i
$176$	−23078.1	+	4069.29i	−0.745030	+	0.131369i
$177$		0			0
$178$	−21724.0	−	18228.6i	−0.685647	−	0.575326i
$179$	29485.4	−	17023.4i	0.920241	−	0.531302i	0.0365292	−	0.999333i	$-0.488370\pi$
$179$	29485.4	−	17023.4i	0.920241	−	0.531302i	0.883712	+	0.468031i	$0.155036\pi$
$180$		0			0
$181$	11868.0	−	20555.9i	0.362259	−	0.627451i	−0.626073	−	0.779764i	$-0.715339\pi$
$181$	11868.0	−	20555.9i	0.362259	−	0.627451i	0.988332	+	0.152313i	$0.0486722\pi$
$182$	−20877.2	−	57359.7i	−0.630274	−	1.73166i
$183$		0			0
$184$	33068.6	−	27747.8i	0.976742	−	0.819583i
$185$	7545.19	−	20730.2i	0.220459	−	0.605705i
$186$		0			0
$187$	3755.67	−	21299.5i	0.107400	−	0.609096i
$188$		−	1281.43i		−	0.0362559i
$189$		0			0
$190$	33166.2			0.918732
$191$	−8026.32	−	1415.26i	−0.220014	−	0.0387944i	0.0625545	−	0.998042i	$-0.480075\pi$
$191$	−8026.32	−	1415.26i	−0.220014	−	0.0387944i	−0.282568	+	0.959247i	$0.591186\pi$
$192$		0			0
$193$	13058.7	+	4752.99i	0.350580	+	0.127601i	0.511307	−	0.859398i	$-0.329162\pi$
$193$	13058.7	+	4752.99i	0.350580	+	0.127601i	−0.160727	+	0.986999i	$0.551384\pi$
$194$	25868.2	+	30828.5i	0.687325	+	0.819122i
$195$		0			0
$196$	−10393.4	+	3782.90i	−0.270550	+	0.0984721i
$197$	−7299.39	−	4214.30i	−0.188085	−	0.108591i	0.403001	−	0.915200i	$-0.367967\pi$
$197$	−7299.39	−	4214.30i	−0.188085	−	0.108591i	−0.591086	+	0.806609i	$0.701301\pi$
$198$		0			0
$199$	−10447.1	−	18094.8i	−0.263808	−	0.456929i	0.703443	−	0.710752i	$-0.251645\pi$
$199$	−10447.1	−	18094.8i	−0.263808	−	0.456929i	−0.967251	+	0.253823i	$0.918312\pi$
$200$	−9858.57	+	11749.0i	−0.246464	+	0.293725i
$201$		0			0
$202$	−7337.49	−	41613.0i	−0.179823	−	1.01983i
$203$	48143.4	−	8488.97i	1.16827	−	0.205998i
$204$		0			0
$205$	−13925.4	−	11684.8i	−0.331360	−	0.278044i
$206$	43236.5	−	24962.6i	1.01886	−	0.588242i
$207$		0			0
$208$	−21355.5	+	36988.9i	−0.493610	+	0.854957i
$209$	17775.3	+	48837.2i	0.406934	+	1.11804i
$210$		0			0
$211$	−59352.0	+	49802.2i	−1.33312	+	1.11862i	−0.349786	+	0.936830i	$0.613746\pi$
$211$	−59352.0	+	49802.2i	−1.33312	+	1.11862i	−0.983337	+	0.181793i	$0.941810\pi$
$212$	−272.566	+	748.870i	−0.00606458	+	0.0166623i
$213$		0			0
$214$	−6191.52	+	35113.9i	−0.135198	+	0.766745i
$215$			25790.4i			0.557931i
$216$		0			0
$217$	−27401.7			−0.581914
$218$	19440.0	+	3427.80i	0.409057	+	0.0721277i
$219$		0			0
$220$	5836.63	+	2124.36i	0.120591	+	0.0438917i
$221$	−25338.3	−	30197.0i	−0.518791	−	0.618271i
$222$		0			0
$223$	11279.7	−	4105.47i	0.226823	−	0.0825568i	−0.226109	−	0.974102i	$-0.572600\pi$
$223$	11279.7	−	4105.47i	0.226823	−	0.0825568i	0.452932	+	0.891545i	$0.350378\pi$
$224$	23956.1	+	13831.1i	0.477442	+	0.275651i
$225$		0			0
$226$	−18816.8	−	32591.6i	−0.368407	−	0.638100i
$227$	−16872.7	+	20108.1i	−0.327441	+	0.390229i	−0.904500	−	0.426474i	$-0.859756\pi$
$227$	−16872.7	+	20108.1i	−0.327441	+	0.390229i	0.577059	+	0.816702i	$0.304200\pi$
$228$		0			0
$229$	10216.5	+	57940.6i	0.194819	+	1.10487i	0.912676	+	0.408683i	$0.134012\pi$
$229$	10216.5	+	57940.6i	0.194819	+	1.10487i	−0.717858	+	0.696190i	$0.754877\pi$
$230$	45433.7	−	8011.19i	0.858860	−	0.151440i
$231$		0			0
$232$	−31758.5	−	26648.5i	−0.590043	−	0.495105i
$233$	−38277.1	+	22099.3i	−0.705062	+	0.407068i	−0.809230	−	0.587492i	$-0.800115\pi$
$233$	−38277.1	+	22099.3i	−0.705062	+	0.407068i	0.104168	+	0.994560i	$0.466782\pi$
$234$		0			0
$235$	4715.81	−	8168.03i	0.0853927	−	0.147905i
$236$	−4887.78	−	13429.1i	−0.0877582	−	0.241114i
$237$		0			0
$238$	42515.8	−	35675.0i	0.750578	−	0.629810i
$239$	9592.71	−	26355.7i	0.167937	−	0.461402i	−0.826965	−	0.562254i	$-0.809934\pi$
$239$	9592.71	−	26355.7i	0.167937	−	0.461402i	0.994901	+	0.100852i	$0.0321567\pi$
$240$		0			0
$241$	12199.4	−	69186.4i	0.210042	−	1.19121i	−0.679264	−	0.733894i	$-0.737701\pi$
$241$	12199.4	−	69186.4i	0.210042	−	1.19121i	0.889306	−	0.457312i	$-0.151188\pi$
$242$			5794.07i			0.0989357i
$243$		0			0
$244$	6881.15			0.115580
$245$	−80171.0	−	14136.3i	−1.33563	−	0.235507i
$246$		0			0
$247$	89011.0	+	32397.3i	1.45898	+	0.531026i
$248$	14937.1	+	17801.3i	0.242864	+	0.289434i
$249$		0			0
$250$	−58220.2	+	21190.4i	−0.931524	+	0.339047i
$251$	−98020.2	−	56592.0i	−1.55585	−	0.898272i	−0.997646	−	0.0685690i	$-0.978157\pi$
$251$	−98020.2	−	56592.0i	−1.55585	−	0.898272i	−0.558206	−	0.829703i	$-0.688510\pi$
$252$		0			0
$253$	36146.5	+	62607.5i	0.564709	+	0.978105i
$254$	−21451.1	+	25564.5i	−0.332493	+	0.396250i
$255$		0			0
$256$	−5622.56	−	31887.1i	−0.0857934	−	0.486559i
$257$	14639.9	−	2581.41i	0.221652	−	0.0390832i	−0.0617192	−	0.998094i	$-0.519658\pi$
$257$	14639.9	−	2581.41i	0.221652	−	0.0390832i	0.283371	+	0.959010i	$0.408547\pi$
$258$		0			0
$259$	67954.9	+	57020.9i	1.01303	+	0.850031i
$260$	9803.91	−	5660.29i	0.145028	−	0.0837321i
$261$		0			0
$262$	−41203.9	+	71367.2i	−0.600255	+	1.03967i
$263$	31408.8	+	86295.1i	0.454088	+	1.24760i	0.929822	+	0.368008i	$0.119960\pi$
$263$	31408.8	+	86295.1i	0.454088	+	1.24760i	−0.475734	+	0.879589i	$0.657818\pi$
$264$		0			0
$265$	−4493.31	+	3770.34i	−0.0639845	+	0.0536894i
$266$	−45613.8	+	125323.i	−0.644663	+	1.77120i
$267$		0			0
$268$	2538.29	−	14395.4i	0.0353404	−	0.200426i
$269$		−	96636.1i		−	1.33547i	−0.744398	−	0.667736i	$-0.767264\pi$
$269$		−	96636.1i		−	1.33547i	0.744398	−	0.667736i	$-0.232736\pi$
$270$		0			0
$271$	12128.1			0.165140			0.0825701	−	0.996585i	$-0.473687\pi$
$271$	12128.1			0.165140			0.0825701	+	0.996585i	$0.473687\pi$
$272$	−38244.3	−	6743.51i	−0.516927	−	0.0911482i
$273$		0			0
$274$	81047.2	+	29498.8i	1.07954	+	0.392919i
$275$	−16510.0	−	19675.9i	−0.218315	−	0.260177i
$276$		0			0
$277$	−34773.7	+	12656.6i	−0.453201	+	0.164952i	−0.558527	−	0.829486i	$-0.688633\pi$
$277$	−34773.7	+	12656.6i	−0.453201	+	0.164952i	0.105327	+	0.994438i	$0.466411\pi$
$278$	−40158.0	−	23185.2i	−0.519615	−	0.300000i
$279$		0			0
$280$	54884.8	+	95063.2i	0.700061	+	1.21254i
$281$	−15897.6	+	18946.0i	−0.201335	+	0.239941i	−0.857259	−	0.514885i	$-0.827835\pi$
$281$	−15897.6	+	18946.0i	−0.201335	+	0.239941i	0.655924	+	0.754827i	$0.272279\pi$
$282$		0			0
$283$	−13223.6	−	74994.8i	−0.165111	−	0.936393i	−0.948950	−	0.315428i	$-0.897852\pi$
$283$	−13223.6	−	74994.8i	−0.165111	−	0.936393i	0.783838	−	0.620965i	$-0.213259\pi$
$284$	−15205.3	+	2681.11i	−0.188521	+	0.0332413i
$285$		0			0
$286$	−66409.4	−	55724.1i	−0.811891	−	0.681257i
$287$	63304.1	−	36548.7i	0.768543	−	0.443719i
$288$		0			0
$289$	−23839.8	+	41291.8i	−0.285435	+	0.494388i
$290$	−15153.8	−	41634.8i	−0.180188	−	0.495063i
$291$		0			0
$292$	−5770.34	+	4841.89i	−0.0676762	+	0.0567870i
$293$	−11979.5	+	32913.3i	−0.139541	+	0.383386i	−0.989703	−	0.143135i	$-0.954282\pi$
$293$	−11979.5	+	32913.3i	−0.139541	+	0.383386i	0.850162	+	0.526521i	$0.176504\pi$
$294$		0			0
$295$	18265.1	−	103587.i	0.209884	−	1.19031i
$296$		−	75229.3i		−	0.858626i
$297$		0			0
$298$	−103649.			−1.16716
$299$	129760.	+	22880.1i	1.45143	+	0.255927i
$300$		0			0
$301$	−97452.2	−	35469.7i	−1.07562	−	0.391493i
$302$	71464.5	+	85168.0i	0.783567	+	0.933819i
$303$		0			0
$304$	87689.9	−	31916.5i	0.948861	−	0.345357i
$305$	43861.5	+	25323.5i	0.471503	+	0.272222i
$306$		0			0
$307$	−9364.32	−	16219.5i	−0.0993572	−	0.172092i	0.812062	−	0.583572i	$-0.198345\pi$
$307$	−9364.32	−	16219.5i	−0.0993572	−	0.172092i	−0.911419	+	0.411480i	$0.865012\pi$
$308$	−16054.3	+	19132.8i	−0.169235	+	0.201686i
$309$		0			0
$310$	4312.55	+	24457.7i	0.0448756	+	0.254502i
$311$	47860.6	−	8439.12i	0.494832	−	0.0872522i	0.0793371	−	0.996848i	$-0.474720\pi$
$311$	47860.6	−	8439.12i	0.494832	−	0.0872522i	0.415495	+	0.909596i	$0.363609\pi$
$312$		0			0
$313$	34100.2	+	28613.5i	0.348071	+	0.292066i	0.800015	−	0.599980i	$-0.204825\pi$
$313$	34100.2	+	28613.5i	0.348071	+	0.292066i	−0.451944	+	0.892046i	$0.649269\pi$
$314$	−136792.	+	78976.7i	−1.38740	+	0.801013i
$315$		0			0
$316$	−11419.3	+	19778.8i	−0.114358	+	0.198073i
$317$	−21930.6	−	60253.9i	−0.218239	−	0.599607i	0.781465	−	0.623950i	$-0.214473\pi$
$317$	−21930.6	−	60253.9i	−0.218239	−	0.599607i	−0.999704	+	0.0243426i	$0.992251\pi$
$318$		0			0
$319$	53185.6	−	44628.0i	0.522652	−	0.438557i
$320$	31030.0	−	85254.2i	0.303027	−	0.832560i
$321$		0			0
$322$	−32214.0	+	182695.i	−0.310694	+	1.76203i
$323$			86125.8i			0.825521i
$324$		0			0
$325$	−46813.7			−0.443207
$326$	9376.08	+	1653.26i	0.0882239	+	0.0155563i
$327$		0			0
$328$	−58251.6	−	21201.8i	−0.541452	−	0.197072i
$329$	24378.2	+	29052.8i	0.225222	+	0.268409i
$330$		0			0
$331$	38407.2	−	13979.1i	0.350555	−	0.127592i	−0.160740	−	0.986997i	$-0.551388\pi$
$331$	38407.2	−	13979.1i	0.350555	−	0.127592i	0.511295	+	0.859405i	$0.329166\pi$
$332$	−15133.0	−	8737.03i	−0.137293	−	0.0792661i
$333$		0			0
$334$	−29752.3	−	51532.4i	−0.266703	−	0.461942i
$335$	69156.2	−	82417.1i	0.616228	−	0.734392i
$336$		0			0
$337$	6145.73	+	34854.2i	0.0541145	+	0.306899i	0.999837	−	0.0180778i	$-0.00575467\pi$
$337$	6145.73	+	34854.2i	0.0541145	+	0.306899i	−0.945722	+	0.324977i	$0.894644\pi$
$338$	−53095.4	+	9362.15i	−0.464754	+	0.0819487i
$339$		0			0
$340$	7884.93	+	6616.24i	0.0682087	+	0.0572339i
$341$	−33702.6	+	19458.2i	−0.289838	+	0.167338i
$342$		0			0
$343$	67107.8	−	116234.i	0.570407	−	0.987973i
$344$	30080.0	+	82644.1i	0.254191	+	0.698385i
$345$		0			0
$346$	8529.29	−	7156.93i	0.0712460	−	0.0597825i
$347$	47338.2	−	130061.i	0.393145	−	1.08016i	−0.572412	−	0.819966i	$-0.693992\pi$
$347$	47338.2	−	130061.i	0.393145	−	1.08016i	0.965557	−	0.260191i	$-0.0837857\pi$
$348$		0			0
$349$	29.9066	−	169.609i	0.000245537	−	0.00139251i	−0.984685	−	0.174344i	$-0.944219\pi$
$349$	29.9066	−	169.609i	0.000245537	−	0.00139251i	0.984930	+	0.172952i	$0.0553305\pi$
$350$		−	65911.3i		−	0.538051i
$351$		0			0
$352$	39286.3			0.317071
$353$	−83193.1	−	14669.2i	−0.667633	−	0.117722i	−0.170449	−	0.985367i	$-0.554522\pi$
$353$	−83193.1	−	14669.2i	−0.667633	−	0.117722i	−0.497185	+	0.867645i	$0.665633\pi$
$354$		0			0
$355$	−106788.	−	38867.6i	−0.847355	−	0.308412i
$356$	13594.1	+	16200.8i	0.107263	+	0.127831i
$357$		0			0
$358$	116600.	−	42438.7i	0.909768	−	0.331128i
$359$	190874.	+	110201.i	1.48101	+	0.855060i	0.999768	−	0.0215290i	$-0.00685342\pi$
$359$	190874.	+	110201.i	1.48101	+	0.855060i	0.481239	+	0.876589i	$0.340187\pi$
$360$		0			0
$361$	−38318.3	−	66369.2i	−0.294030	−	0.509275i
$362$	55604.2	−	66266.5i	0.424317	−	0.505681i
$363$		0			0
$364$	7904.73	+	44829.9i	0.0596601	+	0.338349i
$365$	−54599.8	+	9627.42i	−0.409831	+	0.0722643i
$366$		0			0
$367$	−115293.	−	96742.6i	−0.855996	−	0.718266i	0.105105	−	0.994461i	$-0.466482\pi$
$367$	−115293.	−	96742.6i	−0.855996	−	0.718266i	−0.961102	+	0.276195i	$0.910926\pi$
$368$	112415.	−	64902.9i	0.830098	−	0.479257i
$369$		0			0
$370$	40199.7	−	69627.9i	0.293643	−	0.508604i
$371$	−8067.01	−	22163.9i	−0.0586091	−	0.161027i
$372$		0			0
$373$	95850.7	−	80428.3i	0.688934	−	0.578084i	−0.229668	−	0.973269i	$-0.573764\pi$
$373$	95850.7	−	80428.3i	0.688934	−	0.578084i	0.918602	+	0.395185i	$0.129319\pi$
$374$	26958.9	−	74069.1i	0.192734	−	0.529534i
$375$		0			0
$376$	5585.03	−	31674.3i	0.0395048	−	0.224043i
$377$		−	126541.i		−	0.890327i
$378$		0			0
$379$	168468.			1.17284			0.586419	−	0.810008i	$-0.300537\pi$
$379$	168468.			1.17284			0.586419	+	0.810008i	$0.300537\pi$
$380$	−24358.1	−	4294.99i	−0.168685	−	0.0297437i
$381$		0			0
$382$	−27911.6	−	10159.0i	−0.191275	−	0.0696184i
$383$	−100371.	−	119618.i	−0.684245	−	0.815452i	0.306402	−	0.951902i	$-0.400875\pi$
$383$	−100371.	−	119618.i	−0.684245	−	0.815452i	−0.990647	+	0.136451i	$0.956431\pi$
$384$		0			0
$385$	−172744.	+	62873.6i	−1.16542	+	0.424176i
$386$	43861.1	+	25323.2i	0.294378	+	0.169959i
$387$		0			0
$388$	−15006.0	−	25991.1i	−0.0996783	−	0.172648i
$389$	−3006.53	+	3583.04i	−0.0198686	+	0.0236784i	−0.775887	−	0.630872i	$-0.782697\pi$
$389$	−3006.53	+	3583.04i	−0.0198686	+	0.0236784i	0.756019	+	0.654550i	$0.227142\pi$
$390$		0			0
$391$	20803.4	+	117982.i	0.136076	+	0.771723i
$392$	−273392.	+	48206.4i	−1.77915	+	0.313713i
$393$		0			0
$394$	−23531.2	−	19745.0i	−0.151583	−	0.127193i
$395$	−145577.	+	84048.8i	−0.933035	+	0.538688i
$396$		0			0
$397$	16900.1	−	29271.7i	0.107228	−	0.185724i	−0.807418	−	0.589979i	$-0.799136\pi$
$397$	16900.1	−	29271.7i	0.107228	−	0.185724i	0.914646	+	0.404255i	$0.132469\pi$
$398$	−26044.1	−	71555.6i	−0.164416	−	0.451728i
$399$		0			0
$400$	−35329.1	+	29644.7i	−0.220807	+	0.185279i
$401$	−56821.5	+	156116.i	−0.353366	+	0.970864i	0.627915	+	0.778282i	$0.283908\pi$
$401$	−56821.5	+	156116.i	−0.353366	+	0.970864i	−0.981281	+	0.192582i	$0.938314\pi$
$402$		0			0
$403$	−12316.7	+	69851.7i	−0.0758378	+	0.430097i
$404$			31511.8i			0.193068i
$405$		0			0
$406$	178163.			1.08085
$407$	124072.	+	21877.2i	0.749004	+	0.132070i
$408$		0			0
$409$	−118234.	−	43033.6i	−0.706798	−	0.257254i	−0.0364877	−	0.999334i	$-0.511617\pi$
$409$	−118234.	−	43033.6i	−0.706798	−	0.257254i	−0.670311	+	0.742080i	$0.733839\pi$
$410$	−42584.8	−	50750.6i	−0.253330	−	0.301907i
$411$		0			0
$412$	−34986.6	+	12734.1i	−0.206114	+	0.0750194i
$413$	366295.	+	211480.i	2.14749	+	1.23985i
$414$		0			0
$415$	−64306.6	−	111382.i	−0.373387	−	0.646726i
$416$	46025.8	−	54851.4i	0.265959	−	0.316957i
$417$		0			0
$418$	32890.4	+	186531.i	0.188242	+	1.06757i
$419$	284781.	−	50214.6i	1.62212	−	0.286023i	0.712565	−	0.701607i	$-0.247534\pi$
$419$	284781.	−	50214.6i	1.62212	−	0.286023i	0.909555	+	0.415583i	$0.136422\pi$
$420$		0			0
$421$	162213.	+	136113.i	0.915210	+	0.767952i	0.973103	−	0.230371i	$-0.0739938\pi$
$421$	162213.	+	136113.i	0.915210	+	0.767952i	−0.0578932	+	0.998323i	$0.518438\pi$
$422$	−244538.	+	141184.i	−1.37316	+	0.792793i
$423$		0			0
$424$	−10001.2	+	17322.6i	−0.0556314	+	0.0963564i
$425$	−14557.9	−	39997.6i	−0.0805976	−	0.221440i
$426$		0			0
$427$	−156011.	+	130909.i	−0.855656	+	0.717981i
$428$	9094.41	−	24986.7i	0.0496463	−	0.136402i
$429$		0			0
$430$	−16321.6	+	92564.2i	−0.0882724	+	0.500617i
$431$			1455.79i			0.00783688i	0.999992	+	0.00391844i	$0.00124728\pi$
$431$			1455.79i			0.00783688i	−0.999992	+	0.00391844i	$0.998753\pi$
$432$		0			0
$433$	−85562.0			−0.456357			−0.228179	−	0.973619i	$-0.573277\pi$
$433$	−85562.0			−0.456357			−0.228179	+	0.973619i	$0.573277\pi$
$434$	−98347.5	−	17341.3i	−0.522136	−	0.0920667i
$435$		0			0
$436$	−13833.3	−	5034.92i	−0.0727702	−	0.0264862i
$437$	−185046.	−	220529.i	−0.968983	−	1.15479i
$438$		0			0
$439$	65703.4	−	23914.1i	0.340925	−	0.124087i	−0.165883	−	0.986145i	$-0.553047\pi$
$439$	65703.4	−	23914.1i	0.340925	−	0.124087i	0.506808	+	0.862059i	$0.330825\pi$
$440$	135010.	+	77948.3i	0.697368	+	0.402626i
$441$		0			0
$442$	−71831.2	−	124415.i	−0.367679	−	0.636839i
$443$	−201497.	+	240135.i	−1.02674	+	1.22363i	−0.0523843	+	0.998627i	$0.516682\pi$
$443$	−201497.	+	240135.i	−1.02674	+	1.22363i	−0.974359	+	0.224998i	$0.927762\pi$
$444$		0			0
$445$	27029.9	+	153294.i	0.136498	+	0.774116i
$446$	43082.0	−	7596.52i	0.216584	−	0.0381896i
$447$		0			0
$448$	279468.	+	234501.i	1.39244	+	1.16839i
$449$	−249646.	+	144133.i	−1.23832	+	0.714943i	−0.968750	−	0.248039i	$-0.920214\pi$
$449$	−249646.	+	144133.i	−1.23832	+	0.714943i	−0.269567	+	0.962982i	$0.586880\pi$
$450$		0			0
$451$	51907.0	−	89905.6i	0.255196	−	0.442012i
$452$	9598.92	+	26372.8i	0.0469835	+	0.129086i
$453$		0			0
$454$	−73283.3	+	61492.0i	−0.355544	+	0.298337i
$455$	−114594.	+	314843.i	−0.553525	+	1.52080i
$456$		0			0
$457$	−9696.26	+	54990.2i	−0.0464271	+	0.263301i	−0.999182	−	0.0404389i	$-0.987124\pi$
$457$	−9696.26	+	54990.2i	−0.0464271	+	0.263301i	0.952755	+	0.303740i	$0.0982355\pi$
$458$			214420.i			1.02220i
$459$		0			0
$460$	−34405.1			−0.162595
$461$	125241.	+	22083.3i	0.589309	+	0.103911i	0.460348	−	0.887739i	$-0.347725\pi$
$461$	125241.	+	22083.3i	0.589309	+	0.103911i	0.128961	+	0.991650i	$0.458836\pi$
$462$		0			0
$463$	100428.	+	36552.9i	0.468483	+	0.170514i	0.565465	−	0.824772i	$-0.308697\pi$
$463$	100428.	+	36552.9i	0.468483	+	0.170514i	−0.0969821	+	0.995286i	$0.530919\pi$
$464$	−80131.9	−	95497.5i	−0.372194	−	0.443564i
$465$		0			0
$466$	−151366.	+	55092.7i	−0.697038	+	0.253701i
$467$	−319824.	−	184650.i	−1.46648	−	0.846674i	−0.467185	−	0.884159i	$-0.654732\pi$
$467$	−319824.	−	184650.i	−1.46648	−	0.846674i	−0.999297	+	0.0374855i	$0.988065\pi$
$468$		0			0
$469$	216312.	+	374664.i	0.983412	+	1.70332i
$470$	22094.7	−	26331.4i	0.100021	−	0.119201i
$471$		0			0
$472$	−62286.1	−	353242.i	−0.279581	−	1.58558i
$473$	−145048.	+	25575.9i	−0.648321	+	0.114316i
$474$		0			0
$475$	78352.1	+	65745.2i	0.347267	+	0.291392i
$476$	−35844.5	+	20694.8i	−0.158201	+	0.0913373i
$477$		0			0
$478$	51108.5	−	88522.5i	0.223685	−	0.387434i
$479$	−68595.4	−	188464.i	−0.298968	−	0.821406i	−0.994673	−	0.103079i	$-0.967130\pi$
$479$	−68595.4	−	188464.i	−0.298968	−	0.821406i	0.695706	−	0.718327i	$-0.255092\pi$
$480$		0			0
$481$	175901.	−	147598.i	0.760288	−	0.637957i
$482$	87569.9	−	240596.i	0.376930	−	1.03561i
$483$		0			0
$484$	750.326	−	4255.31i	0.00320302	−	0.0181652i
$485$		−	220895.i		−	0.939080i
$486$		0			0
$487$	−355215.			−1.49773			−0.748865	−	0.662722i	$-0.769401\pi$
$487$	−355215.			−1.49773			−0.748865	+	0.662722i	$0.769401\pi$
$488$	170088.	+	29991.1i	0.714223	+	0.125937i
$489$		0			0
$490$	−278795.	−	101473.i	−1.16116	−	0.422629i
$491$	218986.	+	260977.i	0.908349	+	1.08253i	0.996261	+	0.0863997i	$0.0275362\pi$
$491$	218986.	+	260977.i	0.908349	+	1.08253i	−0.0879117	+	0.996128i	$0.528019\pi$
$492$		0			0
$493$	108117.	−	39351.3i	0.444836	−	0.161907i
$494$	298966.	+	172608.i	1.22509	+	0.707307i
$495$		0			0
$496$	34938.3	+	60514.8i	0.142016	+	0.245979i
$497$	293733.	−	350057.i	1.18916	−	1.41718i
$498$		0			0
$499$	−24501.9	−	138957.i	−0.0984006	−	0.558058i	−0.993652	−	0.112496i	$-0.964115\pi$
$499$	−24501.9	−	138957.i	−0.0984006	−	0.558058i	0.895252	−	0.445561i	$-0.146996\pi$
$500$	45502.5	−	8023.32i	0.182010	−	0.0320933i
$501$		0			0
$502$	−315990.	−	265147.i	−1.25391	−	1.05215i
$503$	368754.	−	212900.i	1.45747	−	0.841473i	0.458588	−	0.888649i	$-0.348356\pi$
$503$	368754.	−	212900.i	1.45747	−	0.841473i	0.998887	+	0.0471760i	$0.0150222\pi$
$504$		0			0
$505$	−115967.	+	200861.i	−0.454729	+	0.787614i
$506$	90111.7	+	247580.i	0.351949	+	0.966973i
$507$		0			0
$508$	19064.8	−	15997.3i	0.0738763	−	0.0619896i
$509$	−119089.	+	327195.i	−0.459661	+	1.26291i	0.466078	+	0.884743i	$0.345667\pi$
$509$	−119089.	+	327195.i	−0.459661	+	1.26291i	−0.925739	+	0.378164i	$0.876556\pi$
$510$		0			0
$511$	38713.1	−	219553.i	0.148257	−	0.840809i
$512$		−	294430.i		−	1.12316i
$513$		0			0
$514$	54177.6			0.205066
$515$	−269873.	−	47585.9i	−1.01753	−	0.179417i
$516$		0			0
$517$	50614.6	+	18422.2i	0.189363	+	0.0689224i
$518$	207811.	+	247659.i	0.774477	+	0.922986i
$519$		0			0
$520$	267002.	−	97180.9i	0.987435	−	0.359397i
$521$	−190108.	−	109759.i	−0.700365	−	0.404356i	0.107119	−	0.994246i	$-0.465838\pi$
$521$	−190108.	−	109759.i	−0.700365	−	0.404356i	−0.807483	+	0.589891i	$0.799171\pi$
$522$		0			0
$523$	−58738.0	−	101737.i	−0.214741	−	0.371943i	0.738451	−	0.674307i	$-0.235557\pi$
$523$	−58738.0	−	101737.i	−0.214741	−	0.371943i	−0.953193	+	0.302364i	$0.902224\pi$
$524$	39503.1	−	47078.0i	0.143870	−	0.171457i
$525$		0			0
$526$	58117.1	+	329599.i	0.210055	+	1.19128i
$527$	−63511.5	+	11198.8i	−0.228681	+	0.0403227i
$528$		0			0
$529$	−92387.4	−	77522.2i	−0.330143	−	0.277022i
$530$	−18513.0	+	10688.5i	−0.0659061	+	0.0380509i
$531$		0			0
$532$	49729.0	−	86133.2i	0.175706	−	0.304332i
$533$	−64714.3	−	177801.i	−0.227796	−	0.625864i
$534$		0			0
$535$	149923.	−	125801.i	0.523795	−	0.439516i
$536$	125483.	−	344761.i	0.436771	−	1.20002i
$537$		0			0
$538$	61156.6	−	346836.i	0.211290	−	1.19828i
$539$		−	464910.i		−	1.60026i
$540$		0			0
$541$	421114.			1.43882			0.719408	−	0.694588i	$-0.244413\pi$
$541$	421114.			1.43882			0.719408	+	0.694588i	$0.244413\pi$
$542$	43528.8	+	7675.30i	0.148176	+	0.0261274i
$543$		0			0
$544$	61177.9	+	22266.9i	0.206727	+	0.0752424i
$545$	−69646.7	−	83001.7i	−0.234481	−	0.279444i
$546$		0			0
$547$	−301567.	+	109761.i	−1.00788	+	0.366839i	−0.792619	−	0.609718i	$-0.791283\pi$
$547$	−301567.	+	109761.i	−1.00788	+	0.366839i	−0.215262	+	0.976556i	$0.569061\pi$
$548$	−55703.0	−	32160.2i	−0.185489	−	0.107092i
$549$		0			0
$550$	−46804.2	−	81067.2i	−0.154725	−	0.267991i
$551$	−177715.	+	211792.i	−0.585356	+	0.697600i
$552$		0			0
$553$	−117376.	−	665673.i	−0.383822	−	2.17676i
$554$	−132816.	+	23419.0i	−0.432743	+	0.0763043i
$555$		0			0
$556$	26490.5	+	22228.2i	0.0856922	+	0.0719043i
$557$	−246377.	+	142246.i	−0.794127	+	0.458489i	−0.841413	−	0.540392i	$-0.818276\pi$
$557$	−246377.	+	142246.i	−0.794127	+	0.458489i	0.0472867	+	0.998881i	$0.484943\pi$
$558$		0			0
$559$	−134222.	+	232479.i	−0.429536	+	0.743978i
$560$	112893.	+	310170.i	0.359990	+	0.989064i
$561$		0			0
$562$	−69048.1	+	57938.2i	−0.218614	+	0.183439i
$563$	58933.8	−	161919.i	0.185929	−	0.510836i	−0.811349	−	0.584561i	$-0.801267\pi$
$563$	58933.8	−	161919.i	0.185929	−	0.510836i	0.997279	+	0.0737253i	$0.0234888\pi$
$564$		0			0
$565$	−35870.1	+	203430.i	−0.112366	+	0.637261i
$566$		−	277532.i		−	0.866324i
$567$		0			0
$568$	−387530.			−1.20118
$569$	148034.	+	26102.4i	0.457232	+	0.0806224i	0.397520	−	0.917593i	$-0.369871\pi$
$569$	148034.	+	26102.4i	0.457232	+	0.0806224i	0.0597116	+	0.998216i	$0.480982\pi$
$570$		0			0
$571$	362690.	+	132008.i	1.11241	+	0.404883i	0.831876	−	0.554962i	$-0.187267\pi$
$571$	362690.	+	132008.i	1.11241	+	0.404883i	0.280531	+	0.959845i	$0.409489\pi$
$572$	41556.5	+	49525.1i	0.127013	+	0.151368i
$573$		0			0
$574$	250335.	−	91114.4i	0.759796	−	0.276543i
$575$	123213.	+	71137.3i	0.372668	+	0.215160i
$576$		0			0
$577$	12415.1	+	21503.6i	0.0372906	+	0.0645892i	0.884068	−	0.467358i	$-0.154794\pi$
$577$	12415.1	+	21503.6i	0.0372906	+	0.0645892i	−0.846778	+	0.531947i	$0.821461\pi$
$578$	−111695.	+	133113.i	−0.334332	+	0.398442i
$579$		0			0
$580$	5737.68	+	32540.0i	0.0170561	+	0.0967302i
$581$	509314.	−	89805.7i	1.50880	−	0.266043i
$582$		0			0
$583$	−25660.8	−	21532.0i	−0.0754975	−	0.0633499i
$584$	−163734.	+	94531.8i	−0.480079	+	0.277174i
$585$		0			0
$586$	−63824.8	+	110548.i	−0.185864	+	0.321925i
$587$	66760.6	+	183423.i	0.193751	+	0.532327i	0.998085	−	0.0618503i	$-0.0197001\pi$
$587$	66760.6	+	183423.i	0.193751	+	0.532327i	−0.804334	+	0.594177i	$0.797478\pi$
$588$		0			0
$589$	118714.	−	99613.1i	0.342194	−	0.287135i
$590$	131111.	−	360223.i	0.376646	−	1.03483i
$591$		0			0
$592$	39281.7	−	222778.i	0.112085	−	0.635665i
$593$			421811.i			1.19952i	0.800179	+	0.599761i	$0.204738\pi$
$593$			421811.i			1.19952i	−0.800179	+	0.599761i	$0.795262\pi$
$594$		0			0
$595$	−304638.			−0.860498
$596$	76122.1	+	13422.4i	0.214298	+	0.0377865i
$597$		0			0
$598$	451240.	+	164238.i	1.26184	+	0.459273i
$599$	308462.	+	367610.i	0.859701	+	1.02455i	0.999410	+	0.0343593i	$0.0109391\pi$
$599$	308462.	+	367610.i	0.859701	+	1.02455i	−0.139708	+	0.990193i	$0.544616\pi$
$600$		0			0
$601$	−489106.	+	178020.i	−1.35411	+	0.492856i	−0.914228	−	0.405199i	$-0.867202\pi$
$601$	−489106.	+	178020.i	−1.35411	+	0.492856i	−0.439882	+	0.898055i	$0.644980\pi$
$602$	−327318.	−	188977.i	−0.903186	−	0.521455i
$603$		0			0
$604$	−41456.1	−	71804.1i	−0.113636	−	0.196823i
$605$	20442.7	−	24362.7i	0.0558507	−	0.0665603i
$606$		0			0
$607$	51395.7	+	291480.i	0.139492	+	0.791099i	0.971626	+	0.236524i	$0.0760081\pi$
$607$	51395.7	+	291480.i	0.139492	+	0.791099i	−0.832134	+	0.554575i	$0.812881\pi$
$608$	−154067.	+	27166.1i	−0.416775	+	0.0734886i
$609$		0			0
$610$	141397.	+	118646.i	0.379998	+	0.318856i
$611$	85018.3	−	49085.4i	0.227735	−	0.131483i
$612$		0			0
$613$	−226603.	+	392488.i	−0.603038	+	1.04449i	0.389321	+	0.921102i	$0.372710\pi$
$613$	−226603.	+	392488.i	−0.603038	+	1.04449i	−0.992358	+	0.123390i	$0.960624\pi$
$614$	−23344.9	−	64139.5i	−0.0619234	−	0.170133i
$615$		0			0
$616$	−480218.	+	402951.i	−1.26554	+	1.06192i
$617$	−183856.	+	505140.i	−0.482956	+	1.32691i	0.423991	+	0.905666i	$0.360629\pi$
$617$	−183856.	+	505140.i	−0.482956	+	1.32691i	−0.906947	+	0.421244i	$0.861594\pi$
$618$		0			0
$619$	−12278.3	+	69633.5i	−0.0320447	+	0.181734i	−0.996629	−	0.0820403i	$-0.973856\pi$
$619$	−12278.3	+	69633.5i	−0.0320447	+	0.181734i	0.964584	+	0.263775i	$0.0849675\pi$
$620$		−	18520.8i		−	0.0481810i
$621$		0			0
$622$	177117.			0.457804
$623$	−616416.	−	108691.i	−1.58817	−	0.280038i
$624$		0			0
$625$	187522.	+	68252.4i	0.480056	+	0.174726i
$626$	104281.	+	124277.i	0.266106	+	0.317133i
$627$		0			0
$628$	110691.	−	40288.1i	0.280667	−	0.102154i
$629$	180809.	+	104390.i	0.457003	+	0.263851i
$630$		0			0
$631$	205642.	+	356183.i	0.516481	+	0.894571i	0.999817	+	0.0191360i	$0.00609154\pi$
$631$	205642.	+	356183.i	0.516481	+	0.894571i	−0.483336	+	0.875435i	$0.660575\pi$
$632$	−368466.	+	439121.i	−0.922493	+	1.09938i
$633$		0			0
$634$	−40579.2	−	230136.i	−0.100954	−	0.572540i
$635$	180394.	−	31808.4i	0.447378	−	0.0788849i
$636$		0			0
$637$	−649105.	−	544664.i	−1.59969	−	1.34230i
$638$	219131.	−	126515.i	0.538348	−	0.310815i
$639$		0			0
$640$	110289.	−	191027.i	0.269261	−	0.466374i
$641$	−112303.	−	308550.i	−0.273323	−	0.750948i	−0.998080	−	0.0619434i	$-0.980270\pi$
$641$	−112303.	−	308550.i	−0.273323	−	0.750948i	0.724757	−	0.689005i	$-0.241952\pi$
$642$		0			0
$643$	−217884.	+	182826.i	−0.526990	+	0.442197i	−0.867061	−	0.498203i	$-0.833994\pi$
$643$	−217884.	+	182826.i	−0.526990	+	0.442197i	0.340070	+	0.940400i	$0.389549\pi$
$644$	47317.5	−	130004.i	0.114091	−	0.313462i
$645$		0			0
$646$	−54505.1	+	309114.i	−0.130609	+	0.740719i
$647$			338284.i			0.808114i	0.914734	+	0.404057i	$0.132400\pi$
$647$			338284.i			0.808114i	−0.914734	+	0.404057i	$0.867600\pi$
$648$		0			0
$649$	600697.			1.42615
$650$	−168019.	−	29626.3i	−0.397678	−	0.0701214i
$651$		0			0
$652$	−6671.93	−	2428.38i	−0.0156948	−	0.00571245i
$653$	−410668.	−	489416.i	−0.963086	−	1.14776i	−0.988973	−	0.148096i	$-0.952686\pi$
$653$	−410668.	−	489416.i	−0.963086	−	1.14776i	0.0258872	−	0.999665i	$-0.491759\pi$
$654$		0			0
$655$	425052.	−	154706.i	0.990739	−	0.360600i
$656$	−161430.	−	93201.9i	−0.375126	−	0.216579i
$657$		0			0
$658$	69109.6	+	119701.i	0.159620	+	0.276469i
$659$	−306063.	+	364752.i	−0.704759	+	0.839899i	−0.993056	−	0.117642i	$-0.962466\pi$
$659$	−306063.	+	364752.i	−0.704759	+	0.839899i	0.288297	+	0.957541i	$0.406911\pi$
$660$		0			0
$661$	−56228.4	−	318887.i	−0.128692	−	0.729851i	−0.979046	−	0.203639i	$-0.934723\pi$
$661$	−56228.4	−	318887.i	−0.128692	−	0.729851i	0.850354	−	0.526212i	$-0.176388\pi$
$662$	146694.	−	25866.1i	0.334731	−	0.0590221i
$663$		0			0
$664$	−335976.	−	281917.i	−0.762030	−	0.639419i
$665$	633961.	−	366018.i	1.43357	−	0.827673i
$666$		0			0
$667$	−192290.	+	333056.i	−0.432220	+	0.748626i
$668$	15177.4	+	41699.6i	0.0340130	+	0.0934499i
$669$		0			0
$670$	300366.	−	252037.i	0.669116	−	0.561455i
$671$	−98925.4	+	271795.i	−0.219717	+	0.603666i
$672$		0			0
$673$	−68023.9	+	385783.i	−0.150187	+	0.851751i	0.812869	+	0.582447i	$0.197905\pi$
$673$	−68023.9	+	385783.i	−0.150187	+	0.851751i	−0.963055	+	0.269304i	$0.913206\pi$
$674$			128984.i			0.283934i
$675$		0			0
$676$	40206.9			0.0879848
$677$	−301876.	−	53228.9i	−0.658645	−	0.116137i	−0.165671	−	0.986181i	$-0.552979\pi$
$677$	−301876.	−	53228.9i	−0.658645	−	0.116137i	−0.492974	+	0.870044i	$0.664090\pi$
$678$		0			0
$679$	834680.	+	303799.i	1.81042	+	0.658940i
$680$	166063.	+	197906.i	0.359132	+	0.427997i
$681$		0			0
$682$	−133276.	+	48508.6i	−0.286539	+	0.104292i
$683$	−399708.	−	230772.i	−0.856844	−	0.494699i	0.00611018	−	0.999981i	$-0.498055\pi$
$683$	−399708.	−	230772.i	−0.856844	−	0.494699i	−0.862954	+	0.505282i	$0.831388\pi$
$684$		0			0
$685$	−236707.	−	409988.i	−0.504463	−	0.873755i
$686$	314416.	−	374706.i	0.668122	−	0.796237i
$687$		0			0
$688$	45922.9	+	260442.i	0.0970180	+	0.550216i
$689$	−60125.6	+	10601.8i	−0.126655	+	0.0223326i
$690$		0			0
$691$	52014.2	+	43645.1i	0.108935	+	0.0914071i	0.695628	−	0.718402i	$-0.255126\pi$
$691$	52014.2	+	43645.1i	0.108935	+	0.0914071i	−0.586693	+	0.809809i	$0.699571\pi$
$692$	−7190.94	+	4151.69i	−0.0150167	+	0.00866987i
$693$		0			0
$694$	252211.	−	436842.i	0.523655	−	0.906997i
$695$	87052.4	+	239174.i	0.180223	+	0.495160i
$696$		0			0
$697$	131789.	−	110584.i	0.271277	−	0.227628i
$698$	214.676	−	589.816i	0.000440628	−	0.00121061i
$699$		0			0
$700$	−8535.44	+	48406.9i	−0.0174193	+	0.0987895i
$701$			124351.i			0.253054i	0.991963	+	0.126527i	$0.0403830\pi$
$701$			124351.i			0.253054i	−0.991963	+	0.126527i	$0.959617\pi$
$702$		0			0
$703$	−501692.			−1.01514
$704$	510251.	+	89971.1i	1.02953	+	0.181534i
$705$		0			0
$706$	−289305.	−	105298.i	−0.580425	−	0.211257i
$707$	−599489.	−	714443.i	−1.19934	−	1.42932i
$708$		0			0
$709$	−243010.	+	88448.3i	−0.483427	+	0.175953i	−0.572225	−	0.820097i	$-0.693920\pi$
$709$	−243010.	+	88448.3i	−0.483427	+	0.175953i	0.0887980	+	0.996050i	$0.471697\pi$
$710$	−358675.	−	207081.i	−0.711515	−	0.410793i
$711$		0			0
$712$	265408.	+	459699.i	0.523544	+	0.906805i
$713$	138563.	−	165133.i	0.272563	−	0.324828i
$714$		0			0
$715$	82629.3	+	468614.i	0.161630	+	0.916649i
$716$	−91129.3	+	16068.6i	−0.177759	+	0.0313437i
$717$		0			0
$718$	615323.	+	516317.i	1.19359	+	1.00154i
$719$	−360037.	+	207867.i	−0.696449	+	0.402095i	−0.806023	−	0.591884i	$-0.798384\pi$
$719$	−360037.	+	207867.i	−0.696449	+	0.402095i	0.109575	+	0.993979i	$0.465051\pi$
$720$		0			0
$721$	550968.	−	954304.i	1.05988	−	1.83576i
$722$	−95525.9	−	262455.i	−0.183251	−	0.503479i
$723$		0			0
$724$	−49418.5	+	41467.1i	−0.0942785	+	0.0791091i
$725$	46732.9	−	128398.i	0.0889092	−	0.244276i
$726$		0			0
$727$	50277.5	−	285138.i	0.0951271	−	0.539493i	−0.899581	−	0.436754i	$-0.856128\pi$
$727$	50277.5	−	285138.i	0.0951271	−	0.539493i	0.994708	−	0.102739i	$-0.0327607\pi$
$728$			1.14256e6i			2.15583i
$729$		0			0
$730$	−202057.			−0.379164
$731$	−240370.	−	42383.7i	−0.449826	−	0.0793165i
$732$		0			0
$733$	−617196.	−	224641.i	−1.14872	−	0.418101i	−0.303666	−	0.952778i	$-0.598211\pi$
$733$	−617196.	−	224641.i	−1.14872	−	0.418101i	−0.845056	+	0.534678i	$0.820433\pi$
$734$	−352575.	−	420182.i	−0.654424	−	0.779912i
$735$		0			0
$736$	−204491.	+	74428.5i	−0.377501	+	0.137399i
$737$	532105.	+	307211.i	0.979630	+	0.565590i
$738$		0			0
$739$	−255257.	−	442119.i	−0.467401	−	0.809562i	0.531906	−	0.846804i	$-0.321476\pi$
$739$	−255257.	−	442119.i	−0.467401	−	0.809562i	−0.999306	+	0.0372420i	$0.988143\pi$
$740$	−38540.4	+	45930.6i	−0.0703805	+	0.0838762i
$741$		0			0
$742$	−14926.7	−	84653.7i	−0.0271117	−	0.153758i
$743$	576592.	−	101669.i	1.04446	−	0.184166i	0.375007	−	0.927022i	$-0.377640\pi$
$743$	576592.	−	101669.i	1.04446	−	0.184166i	0.669451	+	0.742856i	$0.266529\pi$
$744$		0			0
$745$	435818.	+	365695.i	0.785222	+	0.658880i
$746$	394917.	−	228005.i	0.709624	−	0.409701i
$747$		0			0
$748$	−29391.2	+	50907.0i	−0.0525308	+	0.0909859i
$749$	269163.	+	739519.i	0.479790	+	1.31821i
$750$		0			0
$751$	−748006.	+	627652.i	−1.32625	+	1.11286i	−0.341311	+	0.939950i	$0.610871\pi$
$751$	−748006.	+	627652.i	−1.32625	+	1.11286i	−0.984938	+	0.172905i	$0.944685\pi$
$752$	33078.0	−	90881.1i	0.0584930	−	0.160708i
$753$		0			0
$754$	80082.2	−	454169.i	0.140862	−	0.798868i
$755$		−	610254.i		−	1.07057i
$756$		0			0
$757$	644723.			1.12507			0.562537	−	0.826772i	$-0.309825\pi$
$757$	644723.			1.12507			0.562537	+	0.826772i	$0.309825\pi$
$758$	604647.	+	106616.i	1.05236	+	0.185559i
$759$		0			0
$760$	−583363.	−	212327.i	−1.00998	−	0.367601i
$761$	619111.	+	737828.i	1.06905	+	1.27405i	0.959997	+	0.280012i	$0.0903384\pi$
$761$	619111.	+	737828.i	1.06905	+	1.27405i	0.109056	+	0.994036i	$0.465217\pi$
$762$		0			0
$763$	409418.	−	149016.i	0.703263	−	0.255967i
$764$	19183.4	+	11075.5i	0.0328654	+	0.0189748i
$765$		0			0
$766$	−284542.	−	492840.i	−0.484940	−	0.839941i
$767$	703745.	−	838690.i	1.19626	−	1.42564i
$768$		0			0
$769$	−79070.3	−	448430.i	−0.133709	−	0.758302i	−0.975750	−	0.218888i	$-0.929757\pi$
$769$	−79070.3	−	448430.i	−0.133709	−	0.758302i	0.842041	−	0.539414i	$-0.181354\pi$
$770$	−659784.	+	116338.i	−1.11281	+	0.196218i
$771$		0			0
$772$	−28933.4	−	24278.0i	−0.0485472	−	0.0407360i
$773$	841371.	−	485766.i	1.40808	−	0.812957i	0.412880	−	0.910785i	$-0.364523\pi$
$773$	841371.	−	485766.i	1.40808	−	0.812957i	0.995203	+	0.0978280i	$0.0311895\pi$
$774$		0			0
$775$	−38294.3	+	66327.7i	−0.0637574	+	0.110431i
$776$	−257636.	−	707849.i	−0.427841	−	1.17548i
$777$		0			0
$778$	−13058.3	+	10957.2i	−0.0215738	+	0.0181026i
$779$	−141392.	+	388470.i	−0.232996	+	0.640152i
$780$		0			0
$781$	112696.	−	639133.i	0.184760	−	1.04783i
$782$			436614.i			0.713976i
$783$		0			0
$784$	−834770.			−1.35811
$785$	853824.	+	150552.i	1.38557	+	0.244314i
$786$		0			0
$787$	−1.06229e6	−	386642.i	−1.71512	−	0.624251i	−0.717717	−	0.696335i	$-0.754813\pi$
$787$	−1.06229e6	−	386642.i	−1.71512	−	0.624251i	−0.997399	+	0.0720836i	$0.977035\pi$
$788$	14724.9	+	17548.5i	0.0237138	+	0.0282610i
$789$		0			0
$790$	−575680.	+	209530.i	−0.922416	+	0.335732i
$791$	−719352.	−	415318.i	−1.14971	−	0.663786i
$792$		0			0
$793$	263584.	+	456540.i	0.419153	+	0.725994i
$794$	79180.7	−	94363.9i	0.125597	−	0.149680i
$795$		0			0
$796$	9861.06	+	55924.9i	0.0155632	+	0.0882630i
$797$	−169413.	+	29872.1i	−0.266704	+	0.0470272i	−0.305401	−	0.952224i	$-0.598791\pi$
$797$	−169413.	+	29872.1i	−0.266704	+	0.0470272i	0.0386966	+	0.999251i	$0.487679\pi$
$798$		0			0
$799$	68377.2	+	57375.3i	0.107107	+	0.0898734i
$800$	66958.1	−	38658.3i	0.104622	−	0.0604036i
$801$		0			0
$802$	−302737.	+	524355.i	−0.470670	+	0.815224i
$803$	−108291.	−	297528.i	−0.167943	−	0.461421i
$804$		0			0
$805$	780039.	−	654531.i	1.20372	−	1.01004i
$806$	−88411.9	+	242910.i	−0.136095	+	0.373917i
$807$		0			0
$808$	−137342.	+	778907.i	−0.210369	+	1.19306i
$809$			1.07946e6i			1.64933i	0.565621	+	0.824666i	$0.308637\pi$
$809$			1.07946e6i			1.64933i	−0.565621	+	0.824666i	$0.691363\pi$
$810$		0			0
$811$	−113522.			−0.172599			−0.0862995	−	0.996269i	$-0.527504\pi$
$811$	−113522.			−0.172599			−0.0862995	+	0.996269i	$0.527504\pi$
$812$	−130848.	−	23072.0i	−0.198451	−	0.0349923i
$813$		0			0
$814$	431461.	+	157039.i	0.651167	+	0.237005i
$815$	−33591.2	−	40032.4i	−0.0505720	−	0.0602694i
$816$		0			0
$817$	551140.	−	200599.i	0.825692	−	0.300527i
$818$	−397119.	−	229277.i	−0.593491	−	0.342652i
$819$		0			0
$820$	24703.2	+	42787.2i	0.0367388	+	0.0636335i
$821$	336695.	−	401258.i	0.499517	−	0.595301i	−0.456094	−	0.889932i	$-0.650752\pi$
$821$	336695.	−	401258.i	0.499517	−	0.595301i	0.955611	+	0.294630i	$0.0951964\pi$
$822$		0			0
$823$	−108163.	−	613424.i	−0.159691	−	0.905652i	−0.954371	−	0.298624i	$-0.903472\pi$
$823$	−108163.	−	613424.i	−0.159691	−	0.905652i	0.794680	−	0.607028i	$-0.207639\pi$
$824$	−920298.	+	162273.i	−1.35542	+	0.238997i
$825$		0			0
$826$	1.18083e6	+	990835.i	1.73072	+	1.45225i
$827$	−80950.5	+	46736.8i	−0.118361	+	0.0683357i	−0.558012	−	0.829833i	$-0.688436\pi$
$827$	−80950.5	+	46736.8i	−0.118361	+	0.0683357i	0.439651	+	0.898169i	$0.355102\pi$
$828$		0			0
$829$	−92504.3	+	160222.i	−0.134602	+	0.233138i	−0.925446	−	0.378881i	$-0.876309\pi$
$829$	−92504.3	+	160222.i	−0.134602	+	0.233138i	0.790843	+	0.612019i	$0.209642\pi$
$830$	−160314.	−	440459.i	−0.232710	−	0.639365i
$831$		0			0
$832$	723401.	−	607006.i	1.04504	−	0.876892i
$833$	263504.	−	723973.i	0.379750	−	1.04335i
$834$		0			0
$835$	−56716.4	+	321654.i	−0.0813458	+	0.461335i
$836$		−	141252.i		−	0.202108i
$837$		0			0
$838$	1.05389e6			1.50074
$839$	345551.	+	60930.0i	0.490895	+	0.0865580i	0.413616	−	0.910451i	$-0.364266\pi$
$839$	345551.	+	60930.0i	0.490895	+	0.0865580i	0.0772790	+	0.997010i	$0.475377\pi$
$840$		0			0
$841$	−317558.	−	115582.i	−0.448984	−	0.163417i
$842$	496058.	+	591178.i	0.699694	+	0.833862i
$843$		0			0
$844$	197878.	−	72021.5i	0.277787	−	0.101106i
$845$	256285.	+	147966.i	0.358930	+	0.207229i
$846$		0			0
$847$	63942.5	+	110752.i	0.0891298	+	0.154377i
$848$	−38661.8	+	46075.3i	−0.0537638	+	0.0640732i
$849$		0			0
$850$	−26937.2	−	152768.i	−0.0372833	−	0.211444i
$851$	−687257.	+	121182.i	−0.948987	+	0.167332i
$852$		0			0
$853$	−875689.	−	734790.i	−1.20352	−	1.00987i	−0.999523	−	0.0308968i	$-0.990164\pi$
$853$	−875689.	−	734790.i	−1.20352	−	1.00987i	−0.203993	−	0.978972i	$-0.565392\pi$
$854$	−642785.	+	371112.i	−0.881353	+	0.508849i
$855$		0			0
$856$	333698.	−	577982.i	0.455414	−	0.788800i
$857$	−174673.	−	479909.i	−0.237828	−	0.653428i	−0.999982	−	0.00603135i	$-0.998080\pi$
$857$	−174673.	−	479909.i	−0.237828	−	0.653428i	0.762154	−	0.647396i	$-0.224142\pi$
$858$		0			0
$859$	−632238.	+	530511.i	−0.856830	+	0.718965i	−0.961283	−	0.275564i	$-0.911135\pi$
$859$	−632238.	+	530511.i	−0.856830	+	0.718965i	0.104453	+	0.994530i	$0.466691\pi$
$860$	23973.9	−	65867.8i	0.0324147	−	0.0890587i
$861$		0			0
$862$	−921.302	+	5224.96i	−0.00123990	+	0.00703183i
$863$		−	314595.i		−	0.422406i	−0.977442	−	0.211203i	$-0.932262\pi$
$863$		−	314595.i		−	0.422406i	0.977442	−	0.211203i	$-0.0677381\pi$
$864$		0			0
$865$	−61114.9			−0.0816798
$866$	−307090.	−	54148.3i	−0.409478	−	0.0722020i
$867$		0			0
$868$	69983.1	+	25471.8i	0.0928868	+	0.0338080i
$869$	−617066.	−	735391.i	−0.817132	−	0.973820i
$870$		0			0
$871$	1.05231e6	−	383010.i	1.38710	−	0.504864i
$872$	−319987.	−	184745.i	−0.420823	−	0.242962i
$873$		0			0
$874$	−524584.	−	908607.i	−0.686740	−	1.18947i
$875$	−879005.	+	1.04756e6i	−1.14809	+	1.36824i
$876$		0			0
$877$	189340.	+	1.07380e6i	0.246175	+	1.39613i	0.817749	+	0.575575i	$0.195222\pi$
$877$	189340.	+	1.07380e6i	0.246175	+	1.39613i	−0.571575	+	0.820550i	$0.693667\pi$
$878$	250950.	−	44249.3i	0.325536	−	0.0574007i
$879$		0			0
$880$	359107.	+	301326.i	0.463723	+	0.389109i
$881$	705767.	−	407475.i	0.909304	−	0.524987i	0.0290971	−	0.999577i	$-0.490737\pi$
$881$	705767.	−	407475.i	0.909304	−	0.524987i	0.880207	+	0.474589i	$0.157403\pi$
$882$		0			0
$883$	290090.	−	502451.i	0.372059	−	0.644425i	−0.617823	−	0.786317i	$-0.711985\pi$
$883$	290090.	−	502451.i	0.372059	−	0.644425i	0.989882	+	0.141892i	$0.0453187\pi$
$884$	36643.0	+	100676.i	0.0468907	+	0.128831i
$885$		0			0
$886$	−875164.	+	734350.i	−1.11486	+	0.935483i
$887$	149005.	−	409387.i	0.189388	−	0.520340i	−0.808264	−	0.588820i	$-0.799593\pi$
$887$	149005.	−	409387.i	0.189388	−	0.520340i	0.997652	+	0.0684799i	$0.0218149\pi$
$888$		0			0
$889$	−127905.	+	725388.i	−0.161840	+	0.917840i
$890$			567294.i			0.716190i
$891$		0			0
$892$	−32624.3			−0.0410025
$893$	−211231.	−	37245.7i	−0.264883	−	0.0467060i
$894$		0			0
$895$	−640007.	−	232943.i	−0.798985	−	0.290807i
$896$	570137.	+	679463.i	0.710172	+	0.846350i
$897$		0			0
$898$	−987219.	+	359318.i	−1.22422	+	0.445581i
$899$	−179289.	−	103513.i	−0.221837	−	0.128078i
$900$		0			0
$901$	−27755.8	−	48074.4i	−0.0341904	−	0.0592195i
$902$	243197.	−	289830.i	0.298913	−	0.356230i
$903$		0			0
$904$	122321.	+	693718.i	0.149680	+	0.848879i
$905$	−467605.	+	82451.5i	−0.570929	+	0.100670i
$906$		0			0
$907$	435560.	+	365478.i	0.529460	+	0.444270i	0.867915	−	0.496713i	$-0.165460\pi$
$907$	435560.	+	365478.i	0.529460	+	0.444270i	−0.338455	+	0.940983i	$0.609904\pi$
$908$	61784.2	−	35671.1i	0.0749386	−	0.0432658i
$909$		0			0
$910$	−610538.	+	1.05748e6i	−0.737275	+	1.27700i
$911$	335275.	+	921160.i	0.403984	+	1.10994i	0.960301	+	0.278967i	$0.0899919\pi$
$911$	335275.	+	921160.i	0.403984	+	1.10994i	−0.556317	+	0.830970i	$0.687786\pi$
$912$		0			0
$913$	562656.	−	472124.i	0.674996	−	0.566389i
$914$	−69601.6	+	191229.i	−0.0833157	+	0.228908i
$915$		0			0
$916$	27767.2	−	157475.i	0.0330933	−	0.187682i
$917$			1.81888e6i			2.16304i
$918$		0			0
$919$	930154.			1.10135			0.550673	−	0.834721i	$-0.314371\pi$
$919$	930154.			1.10135			0.550673	+	0.834721i	$0.314371\pi$
$920$	−850422.	−	149952.i	−1.00475	−	0.177165i
$921$		0			0
$922$	435525.	+	158518.i	0.512332	+	0.186474i
$923$	−760325.	−	906120.i	−0.892475	−	1.06361i
$924$		0			0
$925$	232991.	−	84801.7i	0.272305	−	0.0991109i
$926$	337314.	+	194748.i	0.393380	+	0.227118i
$927$		0			0
$928$	104496.	+	180993.i	0.121340	+	0.210168i
$929$	485187.	−	578223.i	0.562183	−	0.669983i	−0.407824	−	0.913060i	$-0.633712\pi$
$929$	485187.	−	578223.i	0.562183	−	0.669983i	0.970007	+	0.243077i	$0.0781569\pi$
$930$		0			0
$931$	321481.	+	1.82321e6i	0.370899	+	2.10347i
$932$	118301.	−	20859.7i	0.136194	−	0.0240147i
$933$		0			0
$934$	−1.03102e6	−	865130.i	−1.18188	−	0.991716i
$935$	−374688.	+	216326.i	−0.428594	+	0.247449i
$936$		0			0
$937$	−14627.9	+	25336.2i	−0.0166610	+	0.0288577i	−0.874236	−	0.485502i	$-0.838637\pi$
$937$	−14627.9	+	25336.2i	−0.0166610	+	0.0288577i	0.857575	+	0.514359i	$0.171970\pi$
$938$	539258.	+	1.48160e6i	0.612902	+	1.68393i
$939$		0			0
$940$	−19636.8	+	16477.2i	−0.0222236	+	0.0186478i
$941$	−444219.	+	1.22048e6i	−0.501670	+	1.37833i	0.387974	+	0.921670i	$0.373175\pi$
$941$	−444219.	+	1.22048e6i	−0.501670	+	1.37833i	−0.889643	+	0.456656i	$0.849047\pi$
$942$		0			0
$943$	−99855.7	+	566310.i	−0.112292	+	0.636840i
$944$		−	1.07858e6i		−	1.21035i
$945$		0			0
$946$	−536778.			−0.599808
$947$	1.23922e6	+	218507.i	1.38181	+	0.243650i	0.814647	−	0.579958i	$-0.196931\pi$
$947$	1.23922e6	+	218507.i	1.38181	+	0.243650i	0.567160	+	0.823607i	$0.308042\pi$
$948$		0			0
$949$	−542277.	−	197373.i	−0.602127	−	0.219156i
$950$	239606.	+	285551.i	0.265492	+	0.316401i
$951$		0			0
$952$	−976199.	+	355307.i	−1.07712	+	0.392040i
$953$	−556515.	−	321304.i	−0.612761	−	0.353778i	0.161284	−	0.986908i	$-0.448436\pi$
$953$	−556515.	−	321304.i	−0.612761	−	0.353778i	−0.774045	+	0.633130i	$0.781770\pi$
$954$		0			0
$955$	81518.7	+	141194.i	0.0893820	+	0.154814i
$956$	−48998.9	+	58394.6i	−0.0536131	+	0.0638936i
$957$		0			0
$958$	−126925.	−	719828.i	−0.138298	−	0.784328i
$959$	1.87473e6	−	330566.i	2.03846	−	0.359436i
$960$		0			0
$961$	−618565.	−	519037.i	−0.669789	−	0.562020i
$962$	724734.	−	418425.i	0.783120	−	0.452135i
$963$		0			0
$964$	−95470.5	+	165360.i	−0.102734	+	0.177941i
$965$	−95079.9	−	261230.i	−0.102102	−	0.280523i
$966$		0			0
$967$	903515.	−	758139.i	0.966234	−	0.810766i	−0.0157221	−	0.999876i	$-0.505005\pi$
$967$	903515.	−	758139.i	0.966234	−	0.810766i	0.981956	+	0.189110i	$0.0605603\pi$
$968$	37093.0	−	101912.i	0.0395860	−	0.108762i
$969$		0			0
$970$	139794.	−	792814.i	0.148575	−	0.842612i
$971$		−	423403.i		−	0.449072i	−0.974466	−	0.224536i	$-0.927913\pi$
$971$		−	423403.i		−	0.449072i	0.974466	−	0.224536i	$-0.0720866\pi$
$972$		0			0
$973$	−1.02347e6			−1.08106
$974$	−1.27490e6	−	224800.i	−1.34387	−	0.236961i
$975$		0			0
$976$	488023.	+	177626.i	0.512319	+	0.186469i
$977$	−619524.	−	738320.i	−0.649037	−	0.773492i	0.336732	−	0.941601i	$-0.390678\pi$
$977$	−619524.	−	738320.i	−0.649037	−	0.773492i	−0.985768	+	0.168109i	$0.946234\pi$
$978$		0			0
$979$	−835341.	+	304039.i	−0.871562	+	0.317223i
$980$	191613.	+	110628.i	0.199514	+	0.115190i
$981$		0			0
$982$	620800.	+	1.07526e6i	0.643767	+	1.11504i
$983$	−994517.	+	1.18522e6i	−1.02921	+	1.22657i	−0.0555777	+	0.998454i	$0.517700\pi$
$983$	−994517.	+	1.18522e6i	−1.02921	+	1.22657i	−0.973635	+	0.228113i	$0.926744\pi$
$984$		0			0
$985$	29278.4	+	166046.i	0.0301769	+	0.171142i
$986$	412946.	−	72813.4i	0.424755	−	0.0748958i
$987$		0			0
$988$	−197216.	−	165484.i	−0.202035	−	0.169528i
$989$	706541.	−	407922.i	0.722345	−	0.417046i
$990$		0			0
$991$	668136.	−	1.15725e6i	0.680327	−	1.17836i	−0.294554	−	0.955635i	$-0.595171\pi$
$991$	668136.	−	1.15725e6i	0.680327	−	1.17836i	0.974881	−	0.222726i	$-0.0714955\pi$
$992$	−40066.0	−	110081.i	−0.0407149	−	0.111863i
$993$		0			0
$994$	1.27577e6	−	1.07050e6i	1.29122	−	1.08346i
$995$	−142954.	+	392764.i	−0.144395	+	0.396721i
$996$		0			0
$997$	71152.1	−	403524.i	0.0715809	−	0.405956i	−0.927872	−	0.372898i	$-0.878364\pi$
$997$	71152.1	−	403524.i	0.0715809	−	0.405956i	0.999453	−	0.0330581i	$-0.0105246\pi$
$998$		−	514236.i		−	0.516299i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.5.f.a.8.8		66
3.2	odd	2		27.5.f.a.2.4	✓	66
27.13	even	9		27.5.f.a.14.4	yes	66
27.14	odd	18	inner	81.5.f.a.71.8		66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.5.f.a.2.4	✓	66	3.2	odd	2
27.5.f.a.14.4	yes	66	27.13	even	9
81.5.f.a.8.8		66	1.1	even	1	trivial
81.5.f.a.71.8		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)

\(f(q)\)	\(=\)	\(q+(3.58910 + 0.632855i) q^{2} +(-2.55397 - 0.929568i) q^{4} +(-12.8585 - 15.3241i) q^{5} +(75.5885 - 27.5120i) q^{7} +(-59.0773 - 34.1083i) q^{8} +(-36.4523 - 63.1373i) q^{10} +(73.4332 - 87.5142i) q^{11} +(-36.1566 - 205.054i) q^{13} +(288.705 - 50.9066i) q^{14} +(-157.137 - 131.853i) q^{16} +(163.954 - 94.6591i) q^{17} +(-227.463 + 393.977i) q^{19} +(18.5953 + 51.0902i) q^{20} +(318.943 - 267.625i) q^{22} +(-216.433 + 594.644i) q^{23} +(39.0415 - 221.415i) q^{25} -758.841i q^{26} -218.625 q^{28} +(598.503 + 105.532i) q^{29} +(-320.106 - 116.509i) q^{31} +(221.047 + 263.433i) q^{32} +(648.354 - 235.981i) q^{34} +(-1393.55 - 804.566i) q^{35} +(551.400 + 955.053i) q^{37} +(-1065.72 + 1270.07i) q^{38} +(236.964 + 1343.89i) q^{40} +(894.918 - 157.798i) q^{41} +(-987.620 - 828.712i) q^{43} +(-268.896 + 155.247i) q^{44} +(-1153.12 + 1997.26i) q^{46} +(161.256 + 443.048i) q^{47} +(3117.44 - 2615.84i) q^{49} +(280.247 - 769.973i) q^{50} +(-98.2691 + 557.312i) q^{52} -293.218i q^{53} -2285.32 q^{55} +(-5403.95 - 952.863i) q^{56} +(2081.30 + 757.531i) q^{58} +(3379.85 + 4027.95i) q^{59} +(-2379.12 + 865.931i) q^{61} +(-1075.16 - 620.743i) q^{62} +(2267.66 + 3927.70i) q^{64} +(-2677.36 + 3190.75i) q^{65} +(933.925 + 5296.55i) q^{67} +(-506.726 + 89.3495i) q^{68} +(-4492.41 - 3769.58i) q^{70} +(4919.78 - 2840.43i) q^{71} +(1385.76 - 2400.21i) q^{73} +(1374.62 + 3776.73i) q^{74} +(947.162 - 794.763i) q^{76} +(3143.01 - 8635.36i) q^{77} +(1459.18 - 8275.44i) q^{79} +4103.41i q^{80} +3311.81 q^{82} +(6331.63 + 1116.44i) q^{83} +(-3558.77 - 1295.29i) q^{85} +(-3020.21 - 3599.35i) q^{86} +(-7323.20 + 2665.43i) q^{88} +(-6738.82 - 3890.66i) q^{89} +(-8374.46 - 14505.0i) q^{91} +(1105.52 - 1317.51i) q^{92} +(298.379 + 1692.19i) q^{94} +(8962.18 - 1580.27i) q^{95} +(8458.98 + 7097.93i) q^{97} +(12844.2 - 7415.62i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q + 6 q^{2} - 6 q^{4} - 3 q^{5} - 6 q^{7} + 9 q^{8} - 3 q^{10} + 492 q^{11} - 6 q^{13} - 1137 q^{14} - 54 q^{16} + 9 q^{17} - 3 q^{19} + 2487 q^{20} + 1002 q^{22} + 2724 q^{23} + 435 q^{25} - 12 q^{28}+ \cdots + 259938 q^{98}+O(q^{100}) \) 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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