LMFDB - Embedded newform 324.5.d.f.163.22

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,5,Mod(163,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("324.163");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	324.d (of order $2$, degree $1$, 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:	$33.4918680392$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			163.22
Character	$\chi$	$=$	324.163
Dual form			324.5.d.f.163.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.99662 + 0.164298i) q^{2} +(15.9460 + 1.31328i) q^{4} +29.7694 q^{5} -59.8988i q^{7} +(63.5145 + 7.86857i) q^{8} +O(q^{10})$	\(q+(3.99662 + 0.164298i) q^{2} +(15.9460 + 1.31328i) q^{4} +29.7694 q^{5} -59.8988i q^{7} +(63.5145 + 7.86857i) q^{8} +(118.977 + 4.89106i) q^{10} +225.488i q^{11} +171.765 q^{13} +(9.84126 - 239.393i) q^{14} +(252.551 + 41.8830i) q^{16} -99.0725 q^{17} -169.267i q^{19} +(474.703 + 39.0954i) q^{20} +(-37.0472 + 901.189i) q^{22} -358.855i q^{23} +261.217 q^{25} +(686.480 + 28.2206i) q^{26} +(78.6636 - 955.147i) q^{28} -18.0327 q^{29} -775.841i q^{31} +(1002.47 + 208.884i) q^{32} +(-395.956 - 16.2774i) q^{34} -1783.15i q^{35} +609.762 q^{37} +(27.8102 - 676.496i) q^{38} +(1890.79 + 234.243i) q^{40} -413.091 q^{41} +306.571i q^{43} +(-296.127 + 3595.63i) q^{44} +(58.9591 - 1434.21i) q^{46} +2621.85i q^{47} -1186.86 q^{49} +(1043.99 + 42.9175i) q^{50} +(2738.96 + 225.575i) q^{52} +2034.30 q^{53} +6712.63i q^{55} +(471.318 - 3804.44i) q^{56} +(-72.0699 - 2.96274i) q^{58} +2598.63i q^{59} -1417.36 q^{61} +(127.469 - 3100.74i) q^{62} +(3972.17 + 999.536i) q^{64} +5113.34 q^{65} -5995.13i q^{67} +(-1579.81 - 130.110i) q^{68} +(292.968 - 7126.58i) q^{70} -1239.44i q^{71} -5060.60 q^{73} +(2436.99 + 100.183i) q^{74} +(222.294 - 2699.13i) q^{76} +13506.4 q^{77} +1889.08i q^{79} +(7518.28 + 1246.83i) q^{80} +(-1650.97 - 67.8700i) q^{82} -6733.68i q^{83} -2949.33 q^{85} +(-50.3691 + 1225.25i) q^{86} +(-1774.27 + 14321.7i) q^{88} +9436.67 q^{89} -10288.5i q^{91} +(471.275 - 5722.30i) q^{92} +(-430.765 + 10478.6i) q^{94} -5038.98i q^{95} -14595.8 q^{97} +(-4743.45 - 195.000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + q^{2} + q^{4} + 2 q^{5} + 61 q^{8}+O(q^{10}) $ 22 * q + q^2 + q^4 + 2 * q^5 + 61 * q^8	$ 22 q + q^{2} + q^{4} + 2 q^{5} + 61 q^{8} + 14 q^{10} + 2 q^{13} - 252 q^{14} + q^{16} - 28 q^{17} + 140 q^{20} + 33 q^{22} + 1752 q^{25} + 548 q^{26} - 258 q^{28} - 526 q^{29} + 121 q^{32} - 385 q^{34} - 4 q^{37} - 1395 q^{38} + 2276 q^{40} + 2762 q^{41} + 3357 q^{44} + 1788 q^{46} - 3428 q^{49} - 6375 q^{50} - 1438 q^{52} - 5044 q^{53} + 7506 q^{56} + 4064 q^{58} + 2 q^{61} - 9162 q^{62} + 4513 q^{64} + 2014 q^{65} + 11405 q^{68} - 3666 q^{70} - 1708 q^{73} - 14620 q^{74} - 1581 q^{76} + 3942 q^{77} + 22760 q^{80} - 4243 q^{82} + 1252 q^{85} - 22113 q^{86} - 1995 q^{88} + 6524 q^{89} + 30294 q^{92} - 7524 q^{94} - 5638 q^{97} - 46469 q^{98}+O(q^{100}) $ 22 * q + q^2 + q^4 + 2 * q^5 + 61 * q^8 + 14 * q^10 + 2 * q^13 - 252 * q^14 + q^16 - 28 * q^17 + 140 * q^20 + 33 * q^22 + 1752 * q^25 + 548 * q^26 - 258 * q^28 - 526 * q^29 + 121 * q^32 - 385 * q^34 - 4 * q^37 - 1395 * q^38 + 2276 * q^40 + 2762 * q^41 + 3357 * q^44 + 1788 * q^46 - 3428 * q^49 - 6375 * q^50 - 1438 * q^52 - 5044 * q^53 + 7506 * q^56 + 4064 * q^58 + 2 * q^61 - 9162 * q^62 + 4513 * q^64 + 2014 * q^65 + 11405 * q^68 - 3666 * q^70 - 1708 * q^73 - 14620 * q^74 - 1581 * q^76 + 3942 * q^77 + 22760 * q^80 - 4243 * q^82 + 1252 * q^85 - 22113 * q^86 - 1995 * q^88 + 6524 * q^89 + 30294 * q^92 - 7524 * q^94 - 5638 * q^97 - 46469 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$	3.99662	+	0.164298i	0.999156	+	0.0410745i
$2$	3.99662	+	0.164298i	0.999156	+	0.0410745i
$3$		0			0
$3$		0			0
$4$	15.9460	+	1.31328i	0.996626	+	0.0820797i
$5$	29.7694			1.19078			0.595388	−	0.803438i	$-0.296998\pi$
$5$	29.7694			1.19078			0.595388	+	0.803438i	$0.296998\pi$
$6$		0			0
$7$		−	59.8988i		−	1.22242i	−0.791467	−	0.611212i	$-0.790682\pi$
$7$		−	59.8988i		−	1.22242i	0.791467	−	0.611212i	$-0.209318\pi$
$8$	63.5145	+	7.86857i	0.992413	+	0.122946i
$9$		0			0
$10$	118.977	+	4.89106i	1.18977	+	0.0489106i
$11$			225.488i			1.86353i	0.363057	+	0.931767i	$0.381733\pi$
$11$			225.488i			1.86353i	−0.363057	+	0.931767i	$0.618267\pi$
$12$		0			0
$13$	171.765			1.01636			0.508180	−	0.861251i	$-0.330318\pi$
$13$	171.765			1.01636			0.508180	+	0.861251i	$0.330318\pi$
$14$	9.84126	−	239.393i	0.0502105	−	1.22139i
$15$		0			0
$16$	252.551	+	41.8830i	0.986526	+	0.163606i
$17$	−99.0725			−0.342812			−0.171406	−	0.985201i	$-0.554831\pi$
$17$	−99.0725			−0.342812			−0.171406	+	0.985201i	$0.554831\pi$
$18$		0			0
$19$		−	169.267i		−	0.468884i	−0.972130	−	0.234442i	$-0.924674\pi$
$19$		−	169.267i		−	0.468884i	0.972130	−	0.234442i	$-0.0753262\pi$
$20$	474.703	+	39.0954i	1.18676	+	0.0977386i
$21$		0			0
$22$	−37.0472	+	901.189i	−0.0765438	+	1.86196i
$23$		−	358.855i		−	0.678364i	−0.940721	−	0.339182i	$-0.889850\pi$
$23$		−	358.855i		−	0.678364i	0.940721	−	0.339182i	$-0.110150\pi$
$24$		0			0
$25$	261.217			0.417948
$26$	686.480	+	28.2206i	1.01550	+	0.0417465i
$27$		0			0
$28$	78.6636	−	955.147i	0.100336	−	1.21830i
$29$	−18.0327			−0.0214420			−0.0107210	−	0.999943i	$-0.503413\pi$
$29$	−18.0327			−0.0214420			−0.0107210	+	0.999943i	$0.503413\pi$
$30$		0			0
$31$		−	775.841i		−	0.807326i	−0.914908	−	0.403663i	$-0.867737\pi$
$31$		−	775.841i		−	0.807326i	0.914908	−	0.403663i	$-0.132263\pi$
$32$	1002.47	+	208.884i	0.978973	+	0.203989i
$33$		0			0
$34$	−395.956	−	16.2774i	−0.342522	−	0.0140808i
$35$		−	1783.15i		−	1.45563i
$36$		0			0
$37$	609.762			0.445407			0.222703	−	0.974886i	$-0.428512\pi$
$37$	609.762			0.445407			0.222703	+	0.974886i	$0.428512\pi$
$38$	27.8102	−	676.496i	0.0192592	−	0.468488i
$39$		0			0
$40$	1890.79	+	234.243i	1.18174	+	0.146402i
$41$	−413.091			−0.245741			−0.122871	−	0.992423i	$-0.539210\pi$
$41$	−413.091			−0.245741			−0.122871	+	0.992423i	$0.539210\pi$
$42$		0			0
$43$			306.571i			0.165804i	0.996558	+	0.0829019i	$0.0264188\pi$
$43$			306.571i			0.165804i	−0.996558	+	0.0829019i	$0.973581\pi$
$44$	−296.127	+	3595.63i	−0.152958	+	1.85725i
$45$		0			0
$46$	58.9591	−	1434.21i	0.0278635	−	0.677791i
$47$			2621.85i			1.18689i	0.804873	+	0.593447i	$0.202233\pi$
$47$			2621.85i			1.18689i	−0.804873	+	0.593447i	$0.797767\pi$
$48$		0			0
$49$	−1186.86			−0.494321
$50$	1043.99	+	42.9175i	0.417595	+	0.0171670i
$51$		0			0
$52$	2738.96	+	225.575i	1.01293	+	0.0834226i
$53$	2034.30			0.724209			0.362104	−	0.932138i	$-0.382058\pi$
$53$	2034.30			0.724209			0.362104	+	0.932138i	$0.382058\pi$
$54$		0			0
$55$			6712.63i			2.21905i
$56$	471.318	−	3804.44i	0.150293	−	1.21315i
$57$		0			0
$58$	−72.0699	−	2.96274i	−0.0214239	−	0.000880719i
$59$			2598.63i			0.746520i	0.927727	+	0.373260i	$0.121760\pi$
$59$			2598.63i			0.746520i	−0.927727	+	0.373260i	$0.878240\pi$
$60$		0			0
$61$	−1417.36			−0.380909			−0.190455	−	0.981696i	$-0.560996\pi$
$61$	−1417.36			−0.380909			−0.190455	+	0.981696i	$0.560996\pi$
$62$	127.469	−	3100.74i	0.0331606	−	0.806645i
$63$		0			0
$64$	3972.17	+	999.536i	0.969768	+	0.244027i
$65$	5113.34			1.21026
$66$		0			0
$67$		−	5995.13i		−	1.33552i	−0.744379	−	0.667758i	$-0.767254\pi$
$67$		−	5995.13i		−	1.33552i	0.744379	−	0.667758i	$-0.232746\pi$
$68$	−1579.81	−	130.110i	−0.341655	−	0.0281379i
$69$		0			0
$70$	292.968	−	7126.58i	0.0597895	−	1.45441i
$71$		−	1239.44i		−	0.245872i	−0.992415	−	0.122936i	$-0.960769\pi$
$71$		−	1239.44i		−	0.245872i	0.992415	−	0.122936i	$-0.0392310\pi$
$72$		0			0
$73$	−5060.60			−0.949633			−0.474817	−	0.880085i	$-0.657486\pi$
$73$	−5060.60			−0.949633			−0.474817	+	0.880085i	$0.657486\pi$
$74$	2436.99	+	100.183i	0.445031	+	0.0182949i
$75$		0			0
$76$	222.294	−	2699.13i	0.0384858	−	0.467301i
$77$	13506.4			2.27803
$78$		0			0
$79$			1889.08i			0.302688i	0.988481	+	0.151344i	$0.0483601\pi$
$79$			1889.08i			0.302688i	−0.988481	+	0.151344i	$0.951640\pi$
$80$	7518.28	+	1246.83i	1.17473	+	0.194818i
$81$		0			0
$82$	−1650.97	−	67.8700i	−0.245534	−	0.0100937i
$83$		−	6733.68i		−	0.977455i	−0.872437	−	0.488727i	$-0.837461\pi$
$83$		−	6733.68i		−	0.977455i	0.872437	−	0.488727i	$-0.162539\pi$
$84$		0			0
$85$	−2949.33			−0.408212
$86$	−50.3691	+	1225.25i	−0.00681031	+	0.165664i
$87$		0			0
$88$	−1774.27	+	14321.7i	−0.229115	+	1.84940i
$89$	9436.67			1.19135			0.595674	−	0.803226i	$-0.296885\pi$
$89$	9436.67			1.19135			0.595674	+	0.803226i	$0.296885\pi$
$90$		0			0
$91$		−	10288.5i		−	1.24242i
$92$	471.275	−	5722.30i	0.0556799	−	0.676075i
$93$		0			0
$94$	−430.765	+	10478.6i	−0.0487511	+	1.18589i
$95$		−	5038.98i		−	0.558335i
$96$		0			0
$97$	−14595.8			−1.55126			−0.775631	−	0.631186i	$-0.782568\pi$
$97$	−14595.8			−1.55126			−0.775631	+	0.631186i	$0.782568\pi$
$98$	−4743.45	−	195.000i	−0.493904	−	0.0203040i
$99$		0			0
$100$	4165.37	+	343.050i	0.416537	+	0.0343050i
$101$	6461.42			0.633411			0.316705	−	0.948524i	$-0.397423\pi$
$101$	6461.42			0.633411			0.316705	+	0.948524i	$0.397423\pi$
$102$		0			0
$103$			16156.1i			1.52286i	0.648244	+	0.761432i	$0.275504\pi$
$103$			16156.1i			1.52286i	−0.648244	+	0.761432i	$0.724496\pi$
$104$	10909.6	+	1351.54i	1.00865	+	0.124958i
$105$		0			0
$106$	8130.34	+	334.232i	0.723597	+	0.0297465i
$107$			3065.27i			0.267732i	0.990999	+	0.133866i	$0.0427392\pi$
$107$			3065.27i			0.267732i	−0.990999	+	0.133866i	$0.957261\pi$
$108$		0			0
$109$	−17728.8			−1.49220			−0.746098	−	0.665836i	$-0.768075\pi$
$109$	−17728.8			−1.49220			−0.746098	+	0.665836i	$0.768075\pi$
$110$	−1102.87	+	26827.9i	−0.0911465	+	2.21718i
$111$		0			0
$112$	2508.74	−	15127.5i	0.199995	−	1.20595i
$113$	−14793.1			−1.15852			−0.579259	−	0.815143i	$-0.696658\pi$
$113$	−14793.1			−1.15852			−0.579259	+	0.815143i	$0.696658\pi$
$114$		0			0
$115$		−	10682.9i		−	0.807780i
$116$	−287.550	−	23.6819i	−0.0213696	−	0.00175995i
$117$		0			0
$118$	−426.951	+	10385.8i	−0.0306629	+	0.745890i
$119$			5934.32i			0.419061i
$120$		0			0
$121$	−36203.7			−2.47276
$122$	−5664.67	−	232.870i	−0.380588	−	0.0156457i
$123$		0			0
$124$	1018.89	−	12371.6i	0.0662651	−	0.804602i
$125$	−10829.6			−0.693094
$126$		0			0
$127$		−	18478.7i		−	1.14568i	−0.819667	−	0.572841i	$-0.805841\pi$
$127$		−	18478.7i		−	1.14568i	0.819667	−	0.572841i	$-0.194159\pi$
$128$	15711.1	+	4647.39i	0.958927	+	0.283654i
$129$		0			0
$130$	20436.1	+	840.112i	1.20924	+	0.0497108i
$131$		−	8320.71i		−	0.484862i	−0.970169	−	0.242431i	$-0.922055\pi$
$131$		−	8320.71i		−	0.484862i	0.970169	−	0.242431i	$-0.0779447\pi$
$132$		0			0
$133$	−10138.9			−0.573175
$134$	984.989	−	23960.3i	0.0548557	−	1.33439i
$135$		0			0
$136$	−6292.54	−	779.559i	−0.340211	−	0.0421474i
$137$	−21406.7			−1.14054			−0.570268	−	0.821459i	$-0.693160\pi$
$137$	−21406.7			−1.14054			−0.570268	+	0.821459i	$0.693160\pi$
$138$		0			0
$139$			18225.3i			0.943292i	0.881788	+	0.471646i	$0.156340\pi$
$139$			18225.3i			0.943292i	−0.881788	+	0.471646i	$0.843660\pi$
$140$	2341.77	−	28434.1i	0.119478	−	1.45072i
$141$		0			0
$142$	203.638	−	4953.59i	0.0100991	−	0.245665i
$143$			38730.8i			1.89402i
$144$		0			0
$145$	−536.823			−0.0255326
$146$	−20225.3	−	831.446i	−0.948832	−	0.0390057i
$147$		0			0
$148$	9723.27	+	800.785i	0.443904	+	0.0365589i
$149$	−16239.4			−0.731473			−0.365736	−	0.930718i	$-0.619183\pi$
$149$	−16239.4			−0.731473			−0.365736	+	0.930718i	$0.619183\pi$
$150$		0			0
$151$			24526.3i			1.07567i	0.843050	+	0.537835i	$0.180758\pi$
$151$			24526.3i			1.07567i	−0.843050	+	0.537835i	$0.819242\pi$
$152$	1331.89	−	10750.9i	0.0576476	−	0.465326i
$153$		0			0
$154$	53980.1	+	2219.08i	2.27611	+	0.0935690i
$155$		−	23096.3i		−	0.961345i
$156$		0			0
$157$	39654.1			1.60875			0.804375	−	0.594122i	$-0.202500\pi$
$157$	39654.1			1.60875			0.804375	+	0.594122i	$0.202500\pi$
$158$	−310.372	+	7549.92i	−0.0124328	+	0.302432i
$159$		0			0
$160$	29842.9	+	6218.36i	1.16574	+	0.242905i
$161$	−21494.9			−0.829248
$162$		0			0
$163$			25324.6i			0.953162i	0.879130	+	0.476581i	$0.158124\pi$
$163$			25324.6i			0.953162i	−0.879130	+	0.476581i	$0.841876\pi$
$164$	−6587.15	−	542.502i	−0.244912	−	0.0201704i
$165$		0			0
$166$	1106.33	−	26912.0i	0.0401485	−	0.976630i
$167$			27839.5i			0.998226i	0.866537	+	0.499113i	$0.166341\pi$
$167$			27839.5i			0.998226i	−0.866537	+	0.499113i	$0.833659\pi$
$168$		0			0
$169$	942.163			0.0329877
$170$	−11787.4	−	484.569i	−0.407867	−	0.0167671i
$171$		0			0
$172$	−402.612	+	4888.59i	−0.0136091	+	0.165244i
$173$	−22054.5			−0.736895			−0.368448	−	0.929648i	$-0.620111\pi$
$173$	−22054.5			−0.736895			−0.368448	+	0.929648i	$0.620111\pi$
$174$		0			0
$175$		−	15646.6i		−	0.510909i
$176$	−9444.10	+	56947.0i	−0.304885	+	1.83842i
$177$		0			0
$178$	37714.8	+	1550.43i	1.19034	+	0.0489341i
$179$		−	52513.4i		−	1.63895i	−0.573118	−	0.819473i	$-0.694266\pi$
$179$		−	52513.4i		−	1.63895i	0.573118	−	0.819473i	$-0.305734\pi$
$180$		0			0
$181$	−7223.25			−0.220483			−0.110242	−	0.993905i	$-0.535162\pi$
$181$	−7223.25			−0.220483			−0.110242	+	0.993905i	$0.535162\pi$
$182$	1690.38	−	41119.3i	0.0510319	−	1.24137i
$183$		0			0
$184$	2823.67	−	22792.4i	0.0834024	−	0.673217i
$185$	18152.2			0.530380
$186$		0			0
$187$		−	22339.6i		−	0.638841i
$188$	−3443.21	+	41808.1i	−0.0974200	+	1.18289i
$189$		0			0
$190$	827.894	−	20138.9i	0.0229334	−	0.557864i
$191$		−	10582.8i		−	0.290090i	−0.989425	−	0.145045i	$-0.953667\pi$
$191$		−	10582.8i		−	0.290090i	0.989425	−	0.145045i	$-0.0463326\pi$
$192$		0			0
$193$	−39086.5			−1.04933			−0.524665	−	0.851309i	$-0.675809\pi$
$193$	−39086.5			−1.04933			−0.524665	+	0.851309i	$0.675809\pi$
$194$	−58334.0	−	2398.07i	−1.54995	−	0.0637174i
$195$		0			0
$196$	−18925.7	−	1558.68i	−0.492653	−	0.0405737i
$197$	−10820.0			−0.278802			−0.139401	−	0.990236i	$-0.544518\pi$
$197$	−10820.0			−0.278802			−0.139401	+	0.990236i	$0.544518\pi$
$198$		0			0
$199$		−	807.389i		−	0.0203881i	−0.999948	−	0.0101940i	$-0.996755\pi$
$199$		−	807.389i		−	0.0203881i	0.999948	−	0.0101940i	$-0.00324492\pi$
$200$	16591.1	+	2055.41i	0.414777	+	0.0513852i
$201$		0			0
$202$	25823.9	+	1061.60i	0.632876	+	0.0260171i
$203$			1080.14i			0.0262112i
$204$		0			0
$205$	−12297.5			−0.292623
$206$	−2654.41	+	64569.8i	−0.0625510	+	1.52158i
$207$		0			0
$208$	43379.3	+	7194.03i	1.00267	+	0.166282i
$209$	38167.6			0.873780
$210$		0			0
$211$		−	60834.1i		−	1.36641i	−0.730225	−	0.683207i	$-0.760585\pi$
$211$		−	60834.1i		−	1.36641i	0.730225	−	0.683207i	$-0.239415\pi$
$212$	32439.0	+	2671.60i	0.721765	+	0.0594429i
$213$		0			0
$214$	−503.618	+	12250.7i	−0.0109970	+	0.267506i
$215$			9126.44i			0.197435i
$216$		0			0
$217$	−46471.9			−0.986895
$218$	−70855.3	−	2912.81i	−1.49094	−	0.0612913i
$219$		0			0
$220$	−8815.54	+	107040.i	−0.182139	+	2.21156i
$221$	−17017.2			−0.348420
$222$		0			0
$223$			10729.6i			0.215762i	0.994164	+	0.107881i	$0.0344065\pi$
$223$			10729.6i			0.215762i	−0.994164	+	0.107881i	$0.965594\pi$
$224$	12511.9	−	60046.6i	0.249361	−	1.19672i
$225$		0			0
$226$	−59122.5	−	2430.48i	−1.15754	−	0.0475856i
$227$			75731.3i			1.46968i	0.678239	+	0.734842i	$0.262744\pi$
$227$			75731.3i			1.46968i	−0.678239	+	0.734842i	$0.737256\pi$
$228$		0			0
$229$	−53366.6			−1.01765			−0.508825	−	0.860870i	$-0.669920\pi$
$229$	−53366.6			−1.01765			−0.508825	+	0.860870i	$0.669920\pi$
$230$	1755.18	−	42695.5i	0.0331792	−	0.807098i
$231$		0			0
$232$	−1145.34	−	141.892i	−0.0212793	−	0.00263621i
$233$	56485.5			1.04046			0.520230	−	0.854026i	$-0.325846\pi$
$233$	56485.5			1.04046			0.520230	+	0.854026i	$0.325846\pi$
$234$		0			0
$235$			78050.9i			1.41333i
$236$	−3412.72	+	41437.9i	−0.0612741	+	0.744001i
$237$		0			0
$238$	−974.998	+	23717.3i	−0.0172127	+	0.418707i
$239$		−	47991.4i		−	0.840171i	−0.907484	−	0.420086i	$-0.862000\pi$
$239$		−	47991.4i		−	0.840171i	0.907484	−	0.420086i	$-0.138000\pi$
$240$		0			0
$241$	−64150.1			−1.10449			−0.552247	−	0.833681i	$-0.686229\pi$
$241$	−64150.1			−1.10449			−0.552247	+	0.833681i	$0.686229\pi$
$242$	−144692.	−	5948.19i	−2.47067	−	0.101567i
$243$		0			0
$244$	−22601.3	−	1861.39i	−0.379624	−	0.0312649i
$245$	−35332.2			−0.588625
$246$		0			0
$247$		−	29074.1i		−	0.476555i
$248$	6104.76	−	49277.1i	0.0992579	−	0.801201i
$249$		0			0
$250$	−43281.8	−	1779.28i	−0.692509	−	0.0284685i
$251$		−	65230.8i		−	1.03539i	−0.855564	−	0.517696i	$-0.826790\pi$
$251$		−	65230.8i		−	1.03539i	0.855564	−	0.517696i	$-0.173210\pi$
$252$		0			0
$253$	80917.3			1.26415
$254$	3036.02	−	73852.4i	0.0470583	−	1.14471i
$255$		0			0
$256$	62027.6	+	21155.2i	0.946466	+	0.322802i
$257$	−43315.8			−0.655813			−0.327907	−	0.944710i	$-0.606343\pi$
$257$	−43315.8			−0.655813			−0.327907	+	0.944710i	$0.606343\pi$
$258$		0			0
$259$		−	36524.0i		−	0.544476i
$260$	81537.3	+	6715.22i	1.20617	+	0.0993376i
$261$		0			0
$262$	1367.08	−	33254.7i	0.0199155	−	0.484452i
$263$			84805.2i			1.22606i	0.790061	+	0.613029i	$0.210049\pi$
$263$			84805.2i			1.22606i	−0.790061	+	0.613029i	$0.789951\pi$
$264$		0			0
$265$	60560.0			0.862370
$266$	−40521.3	−	1665.80i	−0.572691	−	0.0235429i
$267$		0			0
$268$	7873.26	−	95598.4i	0.109619	−	1.33101i
$269$	−66685.5			−0.921567			−0.460784	−	0.887513i	$-0.652432\pi$
$269$	−66685.5			−0.921567			−0.460784	+	0.887513i	$0.652432\pi$
$270$		0			0
$271$		−	122426.i		−	1.66700i	−0.552516	−	0.833502i	$-0.686332\pi$
$271$		−	122426.i		−	1.66700i	0.552516	−	0.833502i	$-0.313668\pi$
$272$	−25020.8	−	4149.46i	−0.338192	−	0.0560859i
$273$		0			0
$274$	−85554.5	−	3517.08i	−1.13957	−	0.0468469i
$275$			58901.3i			0.778860i
$276$		0			0
$277$	137452.			1.79140			0.895699	−	0.444661i	$-0.146676\pi$
$277$	137452.			1.79140			0.895699	+	0.444661i	$0.146676\pi$
$278$	−2994.39	+	72839.8i	−0.0387453	+	0.942496i
$279$		0			0
$280$	14030.8	−	113256.i	0.178965	−	1.44459i
$281$	14003.2			0.177344			0.0886718	−	0.996061i	$-0.471738\pi$
$281$	14003.2			0.177344			0.0886718	+	0.996061i	$0.471738\pi$
$282$		0			0
$283$			115048.i			1.43650i	0.695786	+	0.718249i	$0.255056\pi$
$283$			115048.i			1.43650i	−0.695786	+	0.718249i	$0.744944\pi$
$284$	1627.73	−	19764.2i	0.0201811	−	0.245043i
$285$		0			0
$286$	−6363.41	+	154793.i	−0.0777961	+	1.89242i
$287$			24743.6i			0.300400i
$288$		0			0
$289$	−73705.6			−0.882480
$290$	−2145.48	−	88.1990i	−0.0255110	−	0.00104874i
$291$		0			0
$292$	−80696.3	−	6645.96i	−0.946429	−	0.0779457i
$293$	28518.6			0.332195			0.166097	−	0.986109i	$-0.446883\pi$
$293$	28518.6			0.332195			0.166097	+	0.986109i	$0.446883\pi$
$294$		0			0
$295$			77359.8i			0.888938i
$296$	38728.7	+	4797.95i	0.442027	+	0.0547611i
$297$		0			0
$298$	−64902.9	−	2668.11i	−0.730856	−	0.0300449i
$299$		−	61638.6i		−	0.689462i
$300$		0			0
$301$	18363.2			0.202682
$302$	−4029.63	+	98022.5i	−0.0441826	+	1.07476i
$303$		0			0
$304$	7089.41	−	42748.5i	0.0767120	−	0.462566i
$305$	−42194.0			−0.453577
$306$		0			0
$307$			115338.i			1.22376i	0.790952	+	0.611879i	$0.209586\pi$
$307$			115338.i			1.22376i	−0.790952	+	0.611879i	$0.790414\pi$
$308$	215374.	+	17737.7i	2.27034	+	0.186980i
$309$		0			0
$310$	3794.68	−	92307.3i	0.0394868	−	0.960534i
$311$		−	98803.8i		−	1.02153i	−0.859719	−	0.510767i	$-0.829361\pi$
$311$		−	98803.8i		−	1.02153i	0.859719	−	0.510767i	$-0.170639\pi$
$312$		0			0
$313$	−74132.1			−0.756690			−0.378345	−	0.925665i	$-0.623507\pi$
$313$	−74132.1			−0.756690			−0.378345	+	0.925665i	$0.623507\pi$
$314$	158482.	+	6515.09i	1.60739	+	0.0660786i
$315$		0			0
$316$	−2480.88	+	30123.2i	−0.0248445	+	0.301667i
$317$	−2114.59			−0.0210430			−0.0105215	−	0.999945i	$-0.503349\pi$
$317$	−2114.59			−0.0210430			−0.0105215	+	0.999945i	$0.503349\pi$
$318$		0			0
$319$		−	4066.15i		−	0.0399579i
$320$	118249.	+	29755.6i	1.15478	+	0.290582i
$321$		0			0
$322$	−85907.2	−	3531.58i	−0.828549	−	0.0340610i
$323$			16769.7i			0.160739i
$324$		0			0
$325$	44868.0			0.424785
$326$	−4160.78	+	101213.i	−0.0391507	+	0.952358i
$327$		0			0
$328$	−26237.2	−	3250.43i	−0.243877	−	0.0302130i
$329$	157046.			1.45089
$330$		0			0
$331$			14242.0i			0.129992i	0.997886	+	0.0649960i	$0.0207034\pi$
$331$			14242.0i			0.129992i	−0.997886	+	0.0649960i	$0.979297\pi$
$332$	8843.19	−	107375.i	0.0802292	−	0.974156i
$333$		0			0
$334$	−4573.98	+	111264.i	−0.0410017	+	0.997384i
$335$		−	178471.i		−	1.59030i
$336$		0			0
$337$	75423.6			0.664121			0.332061	−	0.943258i	$-0.392256\pi$
$337$	75423.6			0.664121			0.332061	+	0.943258i	$0.392256\pi$
$338$	3765.47	+	154.796i	0.0329599	+	0.00135496i
$339$		0			0
$340$	−47030.1	−	3873.28i	−0.406834	−	0.0335059i
$341$	174942.			1.50448
$342$		0			0
$343$		−	72725.3i		−	0.618155i
$344$	−2412.28	+	19471.7i	−0.0203850	+	0.164546i
$345$		0			0
$346$	−88143.7	−	3623.52i	−0.736274	−	0.0302676i
$347$			148440.i			1.23280i	0.787432	+	0.616401i	$0.211410\pi$
$347$			148440.i			1.23280i	−0.787432	+	0.616401i	$0.788590\pi$
$348$		0			0
$349$	−23330.9			−0.191549			−0.0957745	−	0.995403i	$-0.530533\pi$
$349$	−23330.9			−0.191549			−0.0957745	+	0.995403i	$0.530533\pi$
$350$	2570.71	−	62533.6i	0.0209854	−	0.510478i
$351$		0			0
$352$	−47100.8	+	226044.i	−0.380140	+	1.82435i
$353$	19374.4			0.155482			0.0777409	−	0.996974i	$-0.475229\pi$
$353$	19374.4			0.155482			0.0777409	+	0.996974i	$0.475229\pi$
$354$		0			0
$355$		−	36897.5i		−	0.292779i
$356$	150477.	+	12393.0i	1.18733	+	0.0977856i
$357$		0			0
$358$	8627.86	−	209877.i	0.0673189	−	1.63756i
$359$			139927.i			1.08571i	0.839827	+	0.542854i	$0.182656\pi$
$359$			139927.i			1.08571i	−0.839827	+	0.542854i	$0.817344\pi$
$360$		0			0
$361$	101670.			0.780148
$362$	−28868.6	−	1186.77i	−0.220297	−	0.00905625i
$363$		0			0
$364$	13511.6	−	164061.i	0.101978	−	1.23823i
$365$	−150651.			−1.13080
$366$		0			0
$367$		−	91572.9i		−	0.679884i	−0.940446	−	0.339942i	$-0.889593\pi$
$367$		−	91572.9i		−	0.679884i	0.940446	−	0.339942i	$-0.110407\pi$
$368$	15029.9	−	90628.9i	0.110984	−	0.669224i
$369$		0			0
$370$	72547.7	+	2982.38i	0.529932	+	0.0217851i
$371$		−	121852.i		−	0.885290i
$372$		0			0
$373$	85580.8			0.615118			0.307559	−	0.951529i	$-0.400488\pi$
$373$	85580.8			0.615118			0.307559	+	0.951529i	$0.400488\pi$
$374$	3670.36	−	89283.1i	0.0262401	−	0.638302i
$375$		0			0
$376$	−20630.2	+	166525.i	−0.145924	+	1.17789i
$377$	−3097.38			−0.0217928
$378$		0			0
$379$		−	39838.1i		−	0.277345i	−0.990338	−	0.138672i	$-0.955716\pi$
$379$		−	39838.1i		−	0.277345i	0.990338	−	0.138672i	$-0.0442835\pi$
$380$	6617.57	−	80351.6i	0.0458280	−	0.556451i
$381$		0			0
$382$	1738.73	−	42295.3i	0.0119153	−	0.289845i
$383$		−	170684.i		−	1.16357i	−0.813341	−	0.581787i	$-0.802354\pi$
$383$		−	170684.i		−	1.16357i	0.813341	−	0.581787i	$-0.197646\pi$
$384$		0			0
$385$	402078.			2.71262
$386$	−156214.	−	6421.84i	−1.04844	−	0.0431007i
$387$		0			0
$388$	−232745.	−	19168.3i	−1.54603	−	0.127327i
$389$	215815.			1.42621			0.713103	−	0.701059i	$-0.247289\pi$
$389$	215815.			1.42621			0.713103	+	0.701059i	$0.247289\pi$
$390$		0			0
$391$			35552.6i			0.232551i
$392$	−75383.0	−	9338.92i	−0.490570	−	0.0607750i
$393$		0			0
$394$	−43243.6	−	1777.71i	−0.278567	−	0.0114517i
$395$			56236.6i			0.360434i
$396$		0			0
$397$	292553.			1.85620			0.928098	−	0.372336i	$-0.121443\pi$
$397$	292553.			1.85620			0.928098	+	0.372336i	$0.121443\pi$
$398$	132.652	−	3226.83i	0.000837431	−	0.0203709i
$399$		0			0
$400$	65970.6	+	10940.6i	0.412316	+	0.0683786i
$401$	204314.			1.27060			0.635300	−	0.772266i	$-0.280877\pi$
$401$	204314.			1.27060			0.635300	+	0.772266i	$0.280877\pi$
$402$		0			0
$403$		−	133262.i		−	0.820534i
$404$	103034.	+	8485.63i	0.631274	+	0.0519902i
$405$		0			0
$406$	−177.464	+	4316.90i	−0.00107661	+	0.0261891i
$407$			137494.i			0.830030i
$408$		0			0
$409$	34728.8			0.207607			0.103804	−	0.994598i	$-0.466899\pi$
$409$	34728.8			0.207607			0.103804	+	0.994598i	$0.466899\pi$
$410$	−49148.3	−	2020.45i	−0.292376	−	0.0120193i
$411$		0			0
$412$	−21217.4	+	257625.i	−0.124996	+	1.51773i
$413$	155655.			0.912564
$414$		0			0
$415$		−	200458.i		−	1.16393i
$416$	172189.	+	35879.0i	0.994989	+	0.207326i
$417$		0			0
$418$	152542.	+	6270.87i	0.873043	+	0.0358901i
$419$			320640.i			1.82637i	0.407541	+	0.913187i	$0.366386\pi$
$419$			320640.i			1.82637i	−0.407541	+	0.913187i	$0.633614\pi$
$420$		0			0
$421$	135771.			0.766028			0.383014	−	0.923743i	$-0.374886\pi$
$421$	135771.			0.766028			0.383014	+	0.923743i	$0.374886\pi$
$422$	9994.93	−	243131.i	0.0561248	−	1.36526i
$423$		0			0
$424$	129208.	+	16007.0i	0.718714	+	0.0890388i
$425$	−25879.5			−0.143277
$426$		0			0
$427$			84898.3i			0.465632i
$428$	−4025.54	+	48878.8i	−0.0219754	+	0.266829i
$429$		0			0
$430$	−1499.46	+	36474.9i	−0.00810955	+	0.197268i
$431$			31343.0i			0.168728i	0.996435	+	0.0843638i	$0.0268858\pi$
$431$			31343.0i			0.168728i	−0.996435	+	0.0843638i	$0.973114\pi$
$432$		0			0
$433$	101022.			0.538815			0.269407	−	0.963026i	$-0.413172\pi$
$433$	101022.			0.538815			0.269407	+	0.963026i	$0.413172\pi$
$434$	−185731.	−	7635.25i	−0.986062	−	0.0405363i
$435$		0			0
$436$	−282704.	−	23282.8i	−1.48716	−	0.122479i
$437$	−60742.2			−0.318074
$438$		0			0
$439$			181972.i			0.944227i	0.881538	+	0.472113i	$0.156509\pi$
$439$			181972.i			0.944227i	−0.881538	+	0.472113i	$0.843491\pi$
$440$	−52818.8	+	426349.i	−0.272824	+	2.20222i
$441$		0			0
$442$	−68011.3	−	2795.89i	−0.348126	−	0.0143112i
$443$			37188.8i			0.189498i	0.995501	+	0.0947490i	$0.0302049\pi$
$443$			37188.8i			0.189498i	−0.995501	+	0.0947490i	$0.969795\pi$
$444$		0			0
$445$	280924.			1.41863
$446$	−1762.85	+	42882.2i	−0.00886231	+	0.215580i
$447$		0			0
$448$	59871.0	−	237928.i	0.298305	−	1.18547i
$449$	−20385.0			−0.101115			−0.0505577	−	0.998721i	$-0.516100\pi$
$449$	−20385.0			−0.101115			−0.0505577	+	0.998721i	$0.516100\pi$
$450$		0			0
$451$		−	93146.9i		−	0.457947i
$452$	−235891.	−	19427.4i	−1.15461	−	0.0950909i
$453$		0			0
$454$	−12442.5	+	302670.i	−0.0603666	+	1.46844i
$455$		−	306283.i		−	1.47945i
$456$		0			0
$457$	−279658.			−1.33904			−0.669521	−	0.742793i	$-0.733501\pi$
$457$	−279658.			−1.33904			−0.669521	+	0.742793i	$0.733501\pi$
$458$	−213286.	−	8768.03i	−1.01679	−	0.0417995i
$459$		0			0
$460$	14029.6	−	170349.i	0.0663023	−	0.805054i
$461$	−160597.			−0.755675			−0.377838	−	0.925872i	$-0.623332\pi$
$461$	−160597.			−0.755675			−0.377838	+	0.925872i	$0.623332\pi$
$462$		0			0
$463$			99153.6i			0.462537i	0.972890	+	0.231268i	$0.0742876\pi$
$463$			99153.6i			0.462537i	−0.972890	+	0.231268i	$0.925712\pi$
$464$	−4554.17	−	755.264i	−0.0211531	−	0.00350803i
$465$		0			0
$466$	225752.	+	9280.47i	1.03958	+	0.0427364i
$467$		−	278790.i		−	1.27833i	−0.769068	−	0.639167i	$-0.779279\pi$
$467$		−	278790.i		−	1.27833i	0.769068	−	0.639167i	$-0.220721\pi$
$468$		0			0
$469$	−359101.			−1.63257
$470$	−12823.6	+	311940.i	−0.0580517	+	1.41213i
$471$		0			0
$472$	−20447.5	+	165051.i	−0.0917819	+	0.740856i
$473$	−69128.0			−0.308981
$474$		0			0
$475$		−	44215.5i		−	0.195969i
$476$	−7793.40	+	94628.8i	−0.0343964	+	0.417647i
$477$		0			0
$478$	7884.90	−	191804.i	0.0345096	−	0.839462i
$479$		−	31991.6i		−	0.139433i	−0.997567	−	0.0697163i	$-0.977791\pi$
$479$		−	31991.6i		−	0.139433i	0.997567	−	0.0697163i	$-0.0222094\pi$
$480$		0			0
$481$	104736.			0.452693
$482$	−256384.	−	10539.7i	−1.10356	−	0.0453666i
$483$		0			0
$484$	−577304.	−	47545.4i	−2.46442	−	0.202963i
$485$	−434509.			−1.84721
$486$		0			0
$487$			346823.i			1.46235i	0.682192	+	0.731173i	$0.261027\pi$
$487$			346823.i			1.46235i	−0.682192	+	0.731173i	$0.738973\pi$
$488$	−90023.0	−	11152.6i	−0.378019	−	0.0468314i
$489$		0			0
$490$	−141210.	−	5805.02i	−0.588129	−	0.0241775i
$491$		−	239982.i		−	0.995440i	−0.867338	−	0.497720i	$-0.834171\pi$
$491$		−	239982.i		−	0.995440i	0.867338	−	0.497720i	$-0.165829\pi$
$492$		0			0
$493$	1786.55			0.00735056
$494$	4776.82	−	116198.i	0.0195743	−	0.476152i
$495$		0			0
$496$	32494.6	−	195939.i	0.132083	−	0.796448i
$497$	−74241.1			−0.300560
$498$		0			0
$499$		−	341046.i		−	1.36966i	−0.728705	−	0.684828i	$-0.759877\pi$
$499$		−	341046.i		−	1.36966i	0.728705	−	0.684828i	$-0.240123\pi$
$500$	−172689.	−	14222.2i	−0.690755	−	0.0568890i
$501$		0			0
$502$	10717.3	−	260703.i	0.0425283	−	1.03452i
$503$			3886.22i			0.0153600i	0.999971	+	0.00768001i	$0.00244465\pi$
$503$			3886.22i			0.0153600i	−0.999971	+	0.00768001i	$0.997555\pi$
$504$		0			0
$505$	192353.			0.754250
$506$	323396.	+	13294.6i	1.26309	+	0.0519245i
$507$		0			0
$508$	24267.6	−	294662.i	0.0940373	−	1.14182i
$509$	197346.			0.761717			0.380858	−	0.924633i	$-0.375629\pi$
$509$	197346.			0.761717			0.380858	+	0.924633i	$0.375629\pi$
$510$		0			0
$511$			303124.i			1.16085i
$512$	244425.	+	94740.3i	0.932409	+	0.361405i
$513$		0			0
$514$	−173117.	−	7116.71i	−0.655260	−	0.0269372i
$515$			480957.i			1.81339i
$516$		0			0
$517$	−591195.			−2.21182
$518$	6000.82	−	145973.i	0.0223641	−	0.544016i
$519$		0			0
$520$	324771.	+	40234.7i	1.20108	+	0.148797i
$521$	229165.			0.844255			0.422127	−	0.906536i	$-0.361283\pi$
$521$	229165.			0.844255			0.422127	+	0.906536i	$0.361283\pi$
$522$		0			0
$523$			346673.i			1.26741i	0.773575	+	0.633705i	$0.218467\pi$
$523$			346673.i			1.26741i	−0.773575	+	0.633705i	$0.781533\pi$
$524$	10927.4	−	132682.i	0.0397973	−	0.483226i
$525$		0			0
$526$	−13933.3	+	338934.i	−0.0503597	+	1.22502i
$527$			76864.5i			0.276761i
$528$		0			0
$529$	151064.			0.539822
$530$	242035.	+	9949.89i	0.861642	+	0.0354215i
$531$		0			0
$532$	−161675.	−	13315.2i	−0.571241	−	0.0470460i
$533$	−70954.5			−0.249761
$534$		0			0
$535$			91251.2i			0.318809i
$536$	47173.1	−	380777.i	0.164197	−	1.32538i
$537$		0			0
$538$	−266517.	−	10956.3i	−0.920789	−	0.0378529i
$539$		−	267623.i		−	0.921184i
$540$		0			0
$541$	−287354.			−0.981799			−0.490900	−	0.871216i	$-0.663332\pi$
$541$	−287354.			−0.981799			−0.490900	+	0.871216i	$0.663332\pi$
$542$	20114.4	−	489293.i	0.0684714	−	1.66560i
$543$		0			0
$544$	−99317.1	−	20694.7i	−0.335603	−	0.0699296i
$545$	−527776.			−1.77687
$546$		0			0
$547$		−	561865.i		−	1.87783i	−0.344144	−	0.938917i	$-0.611831\pi$
$547$		−	561865.i		−	1.87783i	0.344144	−	0.938917i	$-0.388169\pi$
$548$	−341352.	−	28112.9i	−1.13669	−	0.0936148i
$549$		0			0
$550$	−9677.37	+	235406.i	−0.0319913	+	0.778203i
$551$			3052.34i			0.0100538i
$552$		0			0
$553$	113153.			0.370013
$554$	549345.	+	22583.1i	1.78989	+	0.0735808i
$555$		0			0
$556$	−23934.9	+	290621.i	−0.0774251	+	0.940109i
$557$	−393303.			−1.26770			−0.633850	−	0.773456i	$-0.718526\pi$
$557$	−393303.			−1.26770			−0.633850	+	0.773456i	$0.718526\pi$
$558$		0			0
$559$			52658.1i			0.168516i
$560$	74683.8	−	450336.i	0.238150	−	1.43602i
$561$		0			0
$562$	55965.6	+	2300.70i	0.177194	+	0.00728431i
$563$			556412.i			1.75541i	0.479198	+	0.877707i	$0.340928\pi$
$563$			556412.i			1.75541i	−0.479198	+	0.877707i	$0.659072\pi$
$564$		0			0
$565$	−440382.			−1.37954
$566$	−18902.1	+	459802.i	−0.0590035	+	1.43529i
$567$		0			0
$568$	9752.64	−	78722.5i	0.0302291	−	0.244007i
$569$	182062.			0.562333			0.281167	−	0.959659i	$-0.409279\pi$
$569$	182062.			0.562333			0.281167	+	0.959659i	$0.409279\pi$
$570$		0			0
$571$		−	219715.i		−	0.673888i	−0.941525	−	0.336944i	$-0.890607\pi$
$571$		−	219715.i		−	0.673888i	0.941525	−	0.336944i	$-0.109393\pi$
$572$	−50864.3	+	617603.i	−0.155461	+	1.88763i
$573$		0			0
$574$	−4065.33	+	98891.0i	−0.0123388	+	0.300146i
$575$		−	93739.0i		−	0.283521i
$576$		0			0
$577$	9527.81			0.0286181			0.0143091	−	0.999898i	$-0.495445\pi$
$577$	9527.81			0.0286181			0.0143091	+	0.999898i	$0.495445\pi$
$578$	−294574.	−	12109.7i	−0.881736	−	0.0362475i
$579$		0			0
$580$	−8560.18	−	704.996i	−0.0254464	−	0.00209571i
$581$	−403339.			−1.19486
$582$		0			0
$583$			458710.i			1.34959i
$584$	−321421.	−	39819.7i	−0.942429	−	0.116754i
$585$		0			0
$586$	113978.	+	4685.55i	0.331914	+	0.0136447i
$587$			10333.0i			0.0299882i	0.999888	+	0.0149941i	$0.00477294\pi$
$587$			10333.0i			0.0299882i	−0.999888	+	0.0149941i	$0.995227\pi$
$588$		0			0
$589$	−131324.			−0.378542
$590$	−12710.1	+	309178.i	−0.0365127	+	0.888188i
$591$		0			0
$592$	153996.	+	25538.7i	0.439405	+	0.0728710i
$593$	143639.			0.408473			0.204236	−	0.978922i	$-0.434529\pi$
$593$	143639.			0.408473			0.204236	+	0.978922i	$0.434529\pi$
$594$		0			0
$595$			176661.i			0.499008i
$596$	−258954.	−	21326.9i	−0.729005	−	0.0600391i
$597$		0			0
$598$	10127.1	−	246346.i	0.0283193	−	0.688880i
$599$			352934.i			0.983649i	0.870694	+	0.491824i	$0.163670\pi$
$599$			352934.i			0.983649i	−0.870694	+	0.491824i	$0.836330\pi$
$600$		0			0
$601$	35467.7			0.0981937			0.0490969	−	0.998794i	$-0.484366\pi$
$601$	35467.7			0.0981937			0.0490969	+	0.998794i	$0.484366\pi$
$602$	73390.9	+	3017.04i	0.202511	+	0.00832509i
$603$		0			0
$604$	−32209.8	+	391097.i	−0.0882907	+	1.07204i
$605$	−1.07776e6			−2.94450
$606$		0			0
$607$		−	489950.i		−	1.32976i	−0.746949	−	0.664881i	$-0.768482\pi$
$607$		−	489950.i		−	1.32976i	0.746949	−	0.664881i	$-0.231518\pi$
$608$	35357.2	−	169685.i	0.0956469	−	0.459024i
$609$		0			0
$610$	−168634.	−	6932.40i	−0.453195	−	0.0186305i
$611$			450342.i			1.20631i
$612$		0			0
$613$	284390.			0.756821			0.378410	−	0.925638i	$-0.376471\pi$
$613$	284390.			0.756821			0.378410	+	0.925638i	$0.376471\pi$
$614$	−18949.8	+	460962.i	−0.0502653	+	1.22272i
$615$		0			0
$616$	857854.	+	106276.i	2.26075	+	0.280075i
$617$	196475.			0.516103			0.258052	−	0.966131i	$-0.416920\pi$
$617$	196475.			0.516103			0.258052	+	0.966131i	$0.416920\pi$
$618$		0			0
$619$		−	67817.0i		−	0.176993i	−0.996076	−	0.0884967i	$-0.971794\pi$
$619$		−	67817.0i		−	0.176993i	0.996076	−	0.0884967i	$-0.0282063\pi$
$620$	30331.8	−	368294.i	0.0789069	−	0.958101i
$621$		0			0
$622$	16233.3	−	394882.i	0.0419590	−	1.02067i
$623$		−	565245.i		−	1.45633i
$624$		0			0
$625$	−485651.			−1.24327
$626$	−296278.	−	12179.8i	−0.756051	−	0.0310807i
$627$		0			0
$628$	632324.	+	52076.7i	1.60332	+	0.132046i
$629$	−60410.6			−0.152691
$630$		0			0
$631$		−	716972.i		−	1.80071i	−0.435158	−	0.900354i	$-0.643308\pi$
$631$		−	716972.i		−	1.80071i	0.435158	−	0.900354i	$-0.356692\pi$
$632$	−14864.3	+	119984.i	−0.0372144	+	0.300392i
$633$		0			0
$634$	−8451.23	−	347.423i	−0.0210253	−	0.000864332i
$635$		−	550100.i		−	1.36425i
$636$		0			0
$637$	−203862.			−0.502408
$638$	668.061	−	16250.9i	0.00164125	−	0.0399241i
$639$		0			0
$640$	467709.	+	138350.i	1.14187	+	0.337769i
$641$	642891.			1.56466			0.782332	−	0.622861i	$-0.214030\pi$
$641$	642891.			1.56466			0.782332	+	0.622861i	$0.214030\pi$
$642$		0			0
$643$		−	1531.82i		−	0.00370498i	−0.999998	−	0.00185249i	$-0.999410\pi$
$643$		−	1531.82i		−	0.00370498i	0.999998	−	0.00185249i	$-0.000589666\pi$
$644$	−342759.	−	28228.8i	−0.826450	−	0.0680645i
$645$		0			0
$646$	−2755.23	+	67022.2i	−0.00660227	+	0.160603i
$647$			106720.i			0.254938i	0.991843	+	0.127469i	$0.0406854\pi$
$647$			106720.i			0.254938i	−0.991843	+	0.127469i	$0.959315\pi$
$648$		0			0
$649$	−585960.			−1.39116
$650$	179320.	+	7371.72i	0.424427	+	0.0174479i
$651$		0			0
$652$	−33258.1	+	403826.i	−0.0782353	+	0.949946i
$653$	229665.			0.538603			0.269301	−	0.963056i	$-0.413207\pi$
$653$	229665.			0.538603			0.269301	+	0.963056i	$0.413207\pi$
$654$		0			0
$655$		−	247703.i		−	0.577362i
$656$	−104326.	−	17301.5i	−0.242430	−	0.0402046i
$657$		0			0
$658$	627652.	+	25802.3i	1.44966	+	0.0595946i
$659$		−	390184.i		−	0.898460i	−0.893416	−	0.449230i	$-0.851698\pi$
$659$		−	390184.i		−	0.898460i	0.893416	−	0.449230i	$-0.148302\pi$
$660$		0			0
$661$	446886.			1.02281			0.511403	−	0.859341i	$-0.329126\pi$
$661$	446886.			1.02281			0.511403	+	0.859341i	$0.329126\pi$
$662$	−2339.94	+	56920.1i	−0.00533936	+	0.129882i
$663$		0			0
$664$	52984.5	−	427686.i	0.120175	−	0.970039i
$665$	−301829.			−0.682523
$666$		0			0
$667$			6471.12i			0.0145455i
$668$	−36561.0	+	443930.i	−0.0819342	+	0.994858i
$669$		0			0
$670$	29322.5	−	713283.i	0.0653208	−	1.58896i
$671$		−	319598.i		−	0.709837i
$672$		0			0
$673$	339492.			0.749548			0.374774	−	0.927116i	$-0.377720\pi$
$673$	339492.			0.749548			0.374774	+	0.927116i	$0.377720\pi$
$674$	301440.	+	12392.0i	0.663561	+	0.0272785i
$675$		0			0
$676$	15023.7	+	1237.32i	0.0328764	+	0.00270762i
$677$	533403.			1.16380			0.581900	−	0.813260i	$-0.302310\pi$
$677$	533403.			1.16380			0.581900	+	0.813260i	$0.302310\pi$
$678$		0			0
$679$			874272.i			1.89630i
$680$	−187325.	−	23207.0i	−0.405115	−	0.0501882i
$681$		0			0
$682$	699179.	+	28742.7i	1.50321	+	0.0617958i
$683$		−	175866.i		−	0.376999i	−0.982073	−	0.188500i	$-0.939638\pi$
$683$		−	175866.i		−	0.376999i	0.982073	−	0.188500i	$-0.0603624\pi$
$684$		0			0
$685$	−637265.			−1.35812
$686$	11948.6	−	290656.i	0.0253904	−	0.617633i
$687$		0			0
$688$	−12840.1	+	77424.7i	−0.0271264	+	0.163570i
$689$	349422.			0.736057
$690$		0			0
$691$			234536.i			0.491194i	0.969372	+	0.245597i	$0.0789840\pi$
$691$			234536.i			0.491194i	−0.969372	+	0.245597i	$0.921016\pi$
$692$	−351682.	−	28963.7i	−0.734409	−	0.0604842i
$693$		0			0
$694$	−24388.5	+	593261.i	−0.0506368	+	1.23176i
$695$			542557.i			1.12325i
$696$		0			0
$697$	40925.9			0.0842429
$698$	−93244.6	−	3833.22i	−0.191387	−	0.00786778i
$699$		0			0
$700$	20548.3	−	249501.i	0.0419353	−	0.509185i
$701$	192485.			0.391707			0.195853	−	0.980633i	$-0.437252\pi$
$701$	192485.			0.391707			0.195853	+	0.980633i	$0.437252\pi$
$702$		0			0
$703$		−	103213.i		−	0.208844i
$704$	−225383.	+	895675.i	−0.454753	+	1.80720i
$705$		0			0
$706$	77432.3	+	3183.18i	0.155351	+	0.00638634i
$707$		−	387031.i		−	0.774297i
$708$		0			0
$709$	−600879.			−1.19535			−0.597674	−	0.801739i	$-0.703908\pi$
$709$	−600879.			−1.19535			−0.597674	+	0.801739i	$0.703908\pi$
$710$	6062.18	−	147465.i	0.0120258	−	0.292532i
$711$		0			0
$712$	599365.	+	74253.1i	1.18231	+	0.146472i
$713$	−278414.			−0.547661
$714$		0			0
$715$			1.15299e6i			2.25536i
$716$	68964.6	−	837380.i	0.134524	−	1.63342i
$717$		0			0
$718$	−22989.8	+	559236.i	−0.0445950	+	1.08479i
$719$			37302.4i			0.0721571i	0.999349	+	0.0360786i	$0.0114867\pi$
$719$			37302.4i			0.0721571i	−0.999349	+	0.0360786i	$0.988513\pi$
$720$		0			0
$721$	967729.			1.86159
$722$	406336.	+	16704.1i	0.779490	+	0.0320442i
$723$		0			0
$724$	−115182.	−	9486.12i	−0.219739	−	0.0180972i
$725$	−4710.45			−0.00896163
$726$		0			0
$727$		−	748065.i		−	1.41537i	−0.706527	−	0.707686i	$-0.749739\pi$
$727$		−	748065.i		−	1.41537i	0.706527	−	0.707686i	$-0.250261\pi$
$728$	80955.8	−	653469.i	0.152751	−	1.23300i
$729$		0			0
$730$	−602095.	−	24751.7i	−1.12985	−	0.0464471i
$731$		−	30372.8i		−	0.0568394i
$732$		0			0
$733$	−263418.			−0.490272			−0.245136	−	0.969489i	$-0.578833\pi$
$733$	−263418.			−0.490272			−0.245136	+	0.969489i	$0.578833\pi$
$734$	15045.3	−	365983.i	0.0279259	−	0.679310i
$735$		0			0
$736$	74959.1	−	359740.i	0.138379	−	0.664100i
$737$	1.35183e6			2.48878
$738$		0			0
$739$		−	288908.i		−	0.529018i	−0.964383	−	0.264509i	$-0.914790\pi$
$739$		−	288908.i		−	0.529018i	0.964383	−	0.264509i	$-0.0852099\pi$
$740$	289456.	+	23838.9i	0.528590	+	0.0435334i
$741$		0			0
$742$	20020.1	−	486997.i	0.0363629	−	0.884543i
$743$			313404.i			0.567710i	0.958867	+	0.283855i	$0.0916134\pi$
$743$			313404.i			0.567710i	−0.958867	+	0.283855i	$0.908387\pi$
$744$		0			0
$745$	−483438.			−0.871020
$746$	342034.	+	14060.8i	0.614599	+	0.0252657i
$747$		0			0
$748$	29338.1	−	356228.i	0.0524359	−	0.636685i
$749$	183606.			0.327282
$750$		0			0
$751$		−	236182.i		−	0.418761i	−0.977834	−	0.209381i	$-0.932855\pi$
$751$		−	236182.i		−	0.418761i	0.977834	−	0.209381i	$-0.0671447\pi$
$752$	−109811.	+	662150.i	−0.194183	+	1.17090i
$753$		0			0
$754$	−12379.1	−	508.894i	−0.0217744	−	0.000895128i
$755$			730134.i			1.28088i
$756$		0			0
$757$	−1.00219e6			−1.74888			−0.874438	−	0.485137i	$-0.838770\pi$
$757$	−1.00219e6			−1.74888			−0.874438	+	0.485137i	$0.838770\pi$
$758$	6545.33	−	159218.i	0.0113918	−	0.277111i
$759$		0			0
$760$	39649.5	−	320048.i	0.0686453	−	0.554099i
$761$	912825.			1.57622			0.788112	−	0.615532i	$-0.211059\pi$
$761$	912825.			1.57622			0.788112	+	0.615532i	$0.211059\pi$
$762$		0			0
$763$			1.06193e6i			1.82410i
$764$	13898.1	−	168753.i	0.0238105	−	0.289111i
$765$		0			0
$766$	28043.0	−	682158.i	0.0477933	−	1.16259i
$767$			446354.i			0.758733i
$768$		0			0
$769$	−208651.			−0.352831			−0.176416	−	0.984316i	$-0.556450\pi$
$769$	−208651.			−0.352831			−0.176416	+	0.984316i	$0.556450\pi$
$770$	1.60696e6	+	66060.7i	2.71033	+	0.111420i
$771$		0			0
$772$	−623274.	−	51331.3i	−1.04579	−	0.0861287i
$773$	−661279.			−1.10669			−0.553345	−	0.832952i	$-0.686649\pi$
$773$	−661279.			−1.10669			−0.553345	+	0.832952i	$0.686649\pi$
$774$		0			0
$775$		−	202663.i		−	0.337420i
$776$	−927046.	−	114848.i	−1.53949	−	0.190722i
$777$		0			0
$778$	862531.	+	35458.0i	1.42500	+	0.0585808i
$779$			69922.6i			0.115224i
$780$		0			0
$781$	279479.			0.458191
$782$	−5841.23	+	142090.i	−0.00955192	+	0.232355i
$783$		0			0
$784$	−299743.	−	49709.5i	−0.487660	−	0.0808736i
$785$	1.18048e6			1.91566
$786$		0			0
$787$			38862.8i			0.0627459i	0.999508	+	0.0313729i	$0.00998795\pi$
$787$			38862.8i			0.0627459i	−0.999508	+	0.0313729i	$0.990012\pi$
$788$	−172536.	−	14209.7i	−0.277861	−	0.0228840i
$789$		0			0
$790$	−9239.58	+	224757.i	−0.0148046	+	0.360129i
$791$			886090.i			1.41620i
$792$		0			0
$793$	−243453.			−0.387141
$794$	1.16923e6	+	48065.9i	1.85463	+	0.0762424i
$795$		0			0
$796$	1060.32	−	12874.6i	0.00167345	−	0.0203193i
$797$	−642602.			−1.01164			−0.505820	−	0.862639i	$-0.668810\pi$
$797$	−642602.			−1.01164			−0.505820	+	0.862639i	$0.668810\pi$
$798$		0			0
$799$		−	259753.i		−	0.406881i
$800$	261862.	+	54564.2i	0.409160	+	0.0852566i
$801$		0			0
$802$	816565.	+	33568.3i	1.26953	+	0.0521893i
$803$		−	1.14110e6i		−	1.76967i
$804$		0			0
$805$	−639892.			−0.987449
$806$	21894.7	−	532599.i	0.0337031	−	0.819842i
$807$		0			0
$808$	410394.	+	50842.2i	0.628605	+	0.0778756i
$809$	737297.			1.12654			0.563269	−	0.826274i	$-0.309544\pi$
$809$	737297.			1.12654			0.563269	+	0.826274i	$0.309544\pi$
$810$		0			0
$811$		−	823394.i		−	1.25189i	−0.779867	−	0.625945i	$-0.784714\pi$
$811$		−	823394.i		−	1.25189i	0.779867	−	0.625945i	$-0.215286\pi$
$812$	−1418.52	+	17223.9i	−0.00215141	+	0.0261227i
$813$		0			0
$814$	−22590.0	+	549511.i	−0.0340931	+	0.829330i
$815$			753897.i			1.13500i
$816$		0			0
$817$	51892.4			0.0777426
$818$	138798.	+	5705.87i	0.207432	+	0.00852738i
$819$		0			0
$820$	−196096.	−	16150.0i	−0.291635	−	0.0240184i
$821$	−580247.			−0.860848			−0.430424	−	0.902627i	$-0.641636\pi$
$821$	−580247.			−0.860848			−0.430424	+	0.902627i	$0.641636\pi$
$822$		0			0
$823$		−	461966.i		−	0.682040i	−0.940056	−	0.341020i	$-0.889228\pi$
$823$		−	461966.i		−	0.682040i	0.940056	−	0.341020i	$-0.110772\pi$
$824$	−127125.	+	1.02614e6i	−0.187231	+	1.51131i
$825$		0			0
$826$	622095.	+	25573.8i	0.911793	+	0.0374831i
$827$		−	1.11437e6i		−	1.62936i	−0.579912	−	0.814679i	$-0.696913\pi$
$827$		−	1.11437e6i		−	1.62936i	0.579912	−	0.814679i	$-0.303087\pi$
$828$		0			0
$829$	915553.			1.33222			0.666108	−	0.745856i	$-0.267959\pi$
$829$	915553.			1.33222			0.666108	+	0.745856i	$0.267959\pi$
$830$	32934.8	−	801154.i	0.0478079	−	1.16295i
$831$		0			0
$832$	682279.	+	171685.i	0.985634	+	0.248020i
$833$	117586.			0.169459
$834$		0			0
$835$			828766.i			1.18866i
$836$	608621.	+	50124.6i	0.870832	+	0.0717197i
$837$		0			0
$838$	−52680.6	+	1.28148e6i	−0.0750175	+	1.82483i
$839$		−	565403.i		−	0.803219i	−0.915811	−	0.401610i	$-0.868451\pi$
$839$		−	565403.i		−	0.803219i	0.915811	−	0.401610i	$-0.131549\pi$
$840$		0			0
$841$	−706956.			−0.999540
$842$	542628.	+	22307.0i	0.765381	+	0.0314642i
$843$		0			0
$844$	79891.9	−	970061.i	0.112155	−	1.36180i
$845$	28047.6			0.0392810
$846$		0			0
$847$			2.16856e6i			3.02276i
$848$	513764.	+	85202.7i	0.714450	+	0.118485i
$849$		0			0
$850$	−103430.	−	4251.95i	−0.143156	−	0.00588505i
$851$		−	218816.i		−	0.302148i
$852$		0			0
$853$	201979.			0.277593			0.138796	−	0.990321i	$-0.455677\pi$
$853$	201979.			0.277593			0.138796	+	0.990321i	$0.455677\pi$
$854$	−13948.6	+	339307.i	−0.0191256	+	0.465240i
$855$		0			0
$856$	−24119.3	+	194689.i	−0.0329167	+	0.265701i
$857$	−504329.			−0.686676			−0.343338	−	0.939212i	$-0.611558\pi$
$857$	−504329.			−0.686676			−0.343338	+	0.939212i	$0.611558\pi$
$858$		0			0
$859$		−	764695.i		−	1.03634i	−0.855278	−	0.518170i	$-0.826614\pi$
$859$		−	764695.i		−	1.03634i	0.855278	−	0.518170i	$-0.173386\pi$
$860$	−11985.5	+	145530.i	−0.0162054	+	0.196769i
$861$		0			0
$862$	−5149.60	+	125266.i	−0.00693041	+	0.168585i
$863$		−	1.21817e6i		−	1.63564i	−0.575477	−	0.817818i	$-0.695183\pi$
$863$		−	1.21817e6i		−	1.63564i	0.575477	−	0.817818i	$-0.304817\pi$
$864$		0			0
$865$	−656551.			−0.877477
$866$	403746.	+	16597.7i	0.538360	+	0.0221316i
$867$		0			0
$868$	−741042.	−	61030.4i	−0.983565	−	0.0810041i
$869$	−425963.			−0.564069
$870$		0			0
$871$		−	1.02975e6i		−	1.35736i
$872$	−1.12603e6	−	139500.i	−1.48088	−	0.183460i
$873$		0			0
$874$	−242764.	−	9979.83i	−0.317805	−	0.0130647i
$875$			648679.i			0.847255i
$876$		0			0
$877$	450910.			0.586260			0.293130	−	0.956073i	$-0.405303\pi$
$877$	450910.			0.586260			0.293130	+	0.956073i	$0.405303\pi$
$878$	−29897.7	+	727275.i	−0.0387837	+	0.943430i
$879$		0			0
$880$	−281145.	+	1.69528e6i	−0.363049	+	2.18915i
$881$	−1.04312e6			−1.34395			−0.671974	−	0.740575i	$-0.734553\pi$
$881$	−1.04312e6			−1.34395			−0.671974	+	0.740575i	$0.734553\pi$
$882$		0			0
$883$			303710.i			0.389527i	0.980850	+	0.194763i	$0.0623939\pi$
$883$			303710.i			0.389527i	−0.980850	+	0.194763i	$0.937606\pi$
$884$	−271356.	−	22348.2i	−0.347244	−	0.0285982i
$885$		0			0
$886$	−6110.05	+	148630.i	−0.00778354	+	0.189338i
$887$		−	678530.i		−	0.862426i	−0.902250	−	0.431213i	$-0.858086\pi$
$887$		−	678530.i		−	0.862426i	0.902250	−	0.431213i	$-0.141914\pi$
$888$		0			0
$889$	−1.10685e6			−1.40051
$890$	1.12275e6	+	46155.3i	1.41743	+	0.0582696i
$891$		0			0
$892$	−14090.9	+	171094.i	−0.0177097	+	0.215034i
$893$	443793.			0.556515
$894$		0			0
$895$		−	1.56329e6i		−	1.95162i
$896$	278373.	−	941073.i	0.346746	−	1.17222i
$897$		0			0
$898$	−81471.0	−	3349.21i	−0.101030	−	0.00415327i
$899$			13990.5i			0.0173107i
$900$		0			0
$901$	−201543.			−0.248267
$902$	15303.9	−	372273.i	0.0188100	−	0.457560i
$903$		0			0
$904$	−939577.	−	116401.i	−1.14973	−	0.142436i
$905$	−215032.			−0.262546
$906$		0			0
$907$		−	1.18664e6i		−	1.44247i	−0.692692	−	0.721233i	$-0.743576\pi$
$907$		−	1.18664e6i		−	1.44247i	0.692692	−	0.721233i	$-0.256424\pi$
$908$	−99456.1	+	1.20761e6i	−0.120631	+	1.46472i
$909$		0			0
$910$	50321.7	−	1.22410e6i	0.0607676	−	1.47820i
$911$			870726.i			1.04917i	0.851359	+	0.524584i	$0.175779\pi$
$911$			870726.i			1.04917i	−0.851359	+	0.524584i	$0.824221\pi$
$912$		0			0
$913$	1.51836e6			1.82152
$914$	−1.11769e6	−	45947.2i	−1.33791	−	0.0550005i
$915$		0			0
$916$	−850984.	−	70085.0i	−1.01422	−	0.0835284i
$917$	−498400.			−0.592706
$918$		0			0
$919$		−	60879.9i		−	0.0720847i	−0.999350	−	0.0360423i	$-0.988525\pi$
$919$		−	60879.9i		−	0.0720847i	0.999350	−	0.0360423i	$-0.0114751\pi$
$920$	84059.0	−	678518.i	0.0993136	−	0.801651i
$921$		0			0
$922$	−641845.	−	26385.8i	−0.755038	−	0.0310390i
$923$		−	212893.i		−	0.249895i
$924$		0			0
$925$	159280.			0.186157
$926$	−16290.7	+	396280.i	−0.0189985	+	0.462147i
$927$		0			0
$928$	−18077.2	−	3766.75i	−0.0209911	−	0.00437392i
$929$	−940810.			−1.09011			−0.545055	−	0.838400i	$-0.683491\pi$
$929$	−940810.			−1.09011			−0.545055	+	0.838400i	$0.683491\pi$
$930$		0			0
$931$			200897.i			0.231779i
$932$	900719.	+	74181.1i	1.03695	+	0.0854007i
$933$		0			0
$934$	45804.7	−	1.11422e6i	0.0525069	−	1.27725i
$935$		−	665037.i		−	0.760717i
$936$		0			0
$937$	−634530.			−0.722725			−0.361362	−	0.932425i	$-0.617688\pi$
$937$	−634530.			−0.722725			−0.361362	+	0.932425i	$0.617688\pi$
$938$	−1.43519e6	−	58999.6i	−1.63119	−	0.0670569i
$939$		0			0
$940$	−102502.	+	1.24460e6i	−0.116005	+	1.40856i
$941$	68097.9			0.0769050			0.0384525	−	0.999260i	$-0.487757\pi$
$941$	68097.9			0.0769050			0.0384525	+	0.999260i	$0.487757\pi$
$942$		0			0
$943$			148239.i			0.166702i
$944$	−108839.	+	656287.i	−0.122135	+	0.736461i
$945$		0			0
$946$	−276279.	−	11357.6i	−0.308720	−	0.0126912i
$947$			532720.i			0.594017i	0.954875	+	0.297009i	$0.0959890\pi$
$947$			532720.i			0.594017i	−0.954875	+	0.297009i	$0.904011\pi$
$948$		0			0
$949$	−869232.			−0.965169
$950$	7264.52	−	176713.i	0.00804933	−	0.195803i
$951$		0			0
$952$	−46694.6	+	376915.i	−0.0515221	+	0.415882i
$953$	72542.5			0.0798742			0.0399371	−	0.999202i	$-0.487284\pi$
$953$	72542.5			0.0798742			0.0399371	+	0.999202i	$0.487284\pi$
$954$		0			0
$955$		−	315042.i		−	0.345432i
$956$	63026.0	−	765272.i	0.0689610	−	0.837336i
$957$		0			0
$958$	5256.15	−	127858.i	0.00572713	−	0.139315i
$959$			1.28224e6i			1.39422i
$960$		0			0
$961$	321592.			0.348224
$962$	418589.	+	17207.9i	0.452311	+	0.0185942i
$963$		0			0
$964$	−1.02294e6	−	84246.8i	−1.10077	−	0.0906566i
$965$	−1.16358e6			−1.24952
$966$		0			0
$967$			814951.i			0.871522i	0.900062	+	0.435761i	$0.143521\pi$
$967$			814951.i			0.871522i	−0.900062	+	0.435761i	$0.856479\pi$
$968$	−2.29946e6	−	284871.i	−2.45400	−	0.304017i
$969$		0			0
$970$	−1.73657e6	−	71389.0i	−1.84565	−	0.0758731i
$971$			939538.i			0.996496i	0.867034	+	0.498248i	$0.166023\pi$
$971$			939538.i			0.996496i	−0.867034	+	0.498248i	$0.833977\pi$
$972$		0			0
$973$	1.09168e6			1.15310
$974$	−56982.4	+	1.38612e6i	−0.0600652	+	1.46111i
$975$		0			0
$976$	−357956.	−	59363.4i	−0.375777	−	0.0623189i
$977$	1.74116e6			1.82410			0.912051	−	0.410077i	$-0.134498\pi$
$977$	1.74116e6			1.82410			0.912051	+	0.410077i	$0.134498\pi$
$978$		0			0
$979$			2.12785e6i			2.22012i
$980$	−563408.	−	46401.0i	−0.586639	−	0.0483142i
$981$		0			0
$982$	39428.5	−	959116.i	0.0408872	−	0.994599i
$983$			1.24396e6i			1.28735i	0.765298	+	0.643677i	$0.222592\pi$
$983$			1.24396e6i			1.28735i	−0.765298	+	0.643677i	$0.777408\pi$
$984$		0			0
$985$	−322106.			−0.331991
$986$	7140.15	+	293.526i	0.00734435	+	0.000301921i
$987$		0			0
$988$	38182.3	−	463616.i	0.0391155	−	0.474946i
$989$	110014.			0.112475
$990$		0			0
$991$			766088.i			0.780066i	0.920801	+	0.390033i	$0.127536\pi$
$991$			766088.i			0.780066i	−0.920801	+	0.390033i	$0.872464\pi$
$992$	162061.	−	777756.i	0.164685	−	0.790351i
$993$		0			0
$994$	−296714.	−	12197.7i	−0.300307	−	0.0123454i
$995$		−	24035.5i		−	0.0242777i
$996$		0			0
$997$	385359.			0.387682			0.193841	−	0.981033i	$-0.437905\pi$
$997$	385359.			0.387682			0.193841	+	0.981033i	$0.437905\pi$
$998$	56033.2	−	1.36303e6i	0.0562580	−	1.36850i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.5.d.f.163.22		22
3.2	odd	2		324.5.d.e.163.1		22
4.3	odd	2	inner	324.5.d.f.163.21		22
9.2	odd	6		108.5.f.a.91.14		44
9.4	even	3		36.5.f.a.7.8	✓	44
9.5	odd	6		108.5.f.a.19.15		44
9.7	even	3		36.5.f.a.31.9	yes	44
12.11	even	2		324.5.d.e.163.2		22
36.7	odd	6		36.5.f.a.31.8	yes	44
36.11	even	6		108.5.f.a.91.15		44
36.23	even	6		108.5.f.a.19.14		44
36.31	odd	6		36.5.f.a.7.9	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.5.f.a.7.8	✓	44	9.4	even	3
36.5.f.a.7.9	yes	44	36.31	odd	6
36.5.f.a.31.8	yes	44	36.7	odd	6
36.5.f.a.31.9	yes	44	9.7	even	3
108.5.f.a.19.14		44	36.23	even	6
108.5.f.a.19.15		44	9.5	odd	6
108.5.f.a.91.14		44	9.2	odd	6
108.5.f.a.91.15		44	36.11	even	6
324.5.d.e.163.1		22	3.2	odd	2
324.5.d.e.163.2		22	12.11	even	2
324.5.d.f.163.21		22	4.3	odd	2	inner
324.5.d.f.163.22		22	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	324.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(3.99662 + 0.164298i) q^{2} +(15.9460 + 1.31328i) q^{4} +29.7694 q^{5} -59.8988i q^{7} +(63.5145 + 7.86857i) q^{8} +O(q^{10})\)	\(q+(3.99662 + 0.164298i) q^{2} +(15.9460 + 1.31328i) q^{4} +29.7694 q^{5} -59.8988i q^{7} +(63.5145 + 7.86857i) q^{8} +(118.977 + 4.89106i) q^{10} +225.488i q^{11} +171.765 q^{13} +(9.84126 - 239.393i) q^{14} +(252.551 + 41.8830i) q^{16} -99.0725 q^{17} -169.267i q^{19} +(474.703 + 39.0954i) q^{20} +(-37.0472 + 901.189i) q^{22} -358.855i q^{23} +261.217 q^{25} +(686.480 + 28.2206i) q^{26} +(78.6636 - 955.147i) q^{28} -18.0327 q^{29} -775.841i q^{31} +(1002.47 + 208.884i) q^{32} +(-395.956 - 16.2774i) q^{34} -1783.15i q^{35} +609.762 q^{37} +(27.8102 - 676.496i) q^{38} +(1890.79 + 234.243i) q^{40} -413.091 q^{41} +306.571i q^{43} +(-296.127 + 3595.63i) q^{44} +(58.9591 - 1434.21i) q^{46} +2621.85i q^{47} -1186.86 q^{49} +(1043.99 + 42.9175i) q^{50} +(2738.96 + 225.575i) q^{52} +2034.30 q^{53} +6712.63i q^{55} +(471.318 - 3804.44i) q^{56} +(-72.0699 - 2.96274i) q^{58} +2598.63i q^{59} -1417.36 q^{61} +(127.469 - 3100.74i) q^{62} +(3972.17 + 999.536i) q^{64} +5113.34 q^{65} -5995.13i q^{67} +(-1579.81 - 130.110i) q^{68} +(292.968 - 7126.58i) q^{70} -1239.44i q^{71} -5060.60 q^{73} +(2436.99 + 100.183i) q^{74} +(222.294 - 2699.13i) q^{76} +13506.4 q^{77} +1889.08i q^{79} +(7518.28 + 1246.83i) q^{80} +(-1650.97 - 67.8700i) q^{82} -6733.68i q^{83} -2949.33 q^{85} +(-50.3691 + 1225.25i) q^{86} +(-1774.27 + 14321.7i) q^{88} +9436.67 q^{89} -10288.5i q^{91} +(471.275 - 5722.30i) q^{92} +(-430.765 + 10478.6i) q^{94} -5038.98i q^{95} -14595.8 q^{97} +(-4743.45 - 195.000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + q^{2} + q^{4} + 2 q^{5} + 61 q^{8}+O(q^{10}) \) 22 * q + q^2 + q^4 + 2 * q^5 + 61 * q^8	\( 22 q + q^{2} + q^{4} + 2 q^{5} + 61 q^{8} + 14 q^{10} + 2 q^{13} - 252 q^{14} + q^{16} - 28 q^{17} + 140 q^{20} + 33 q^{22} + 1752 q^{25} + 548 q^{26} - 258 q^{28} - 526 q^{29} + 121 q^{32} - 385 q^{34} - 4 q^{37} - 1395 q^{38} + 2276 q^{40} + 2762 q^{41} + 3357 q^{44} + 1788 q^{46} - 3428 q^{49} - 6375 q^{50} - 1438 q^{52} - 5044 q^{53} + 7506 q^{56} + 4064 q^{58} + 2 q^{61} - 9162 q^{62} + 4513 q^{64} + 2014 q^{65} + 11405 q^{68} - 3666 q^{70} - 1708 q^{73} - 14620 q^{74} - 1581 q^{76} + 3942 q^{77} + 22760 q^{80} - 4243 q^{82} + 1252 q^{85} - 22113 q^{86} - 1995 q^{88} + 6524 q^{89} + 30294 q^{92} - 7524 q^{94} - 5638 q^{97} - 46469 q^{98}+O(q^{100}) \) 22 * q + q^2 + q^4 + 2 * q^5 + 61 * q^8 + 14 * q^10 + 2 * q^13 - 252 * q^14 + q^16 - 28 * q^17 + 140 * q^20 + 33 * q^22 + 1752 * q^25 + 548 * q^26 - 258 * q^28 - 526 * q^29 + 121 * q^32 - 385 * q^34 - 4 * q^37 - 1395 * q^38 + 2276 * q^40 + 2762 * q^41 + 3357 * q^44 + 1788 * q^46 - 3428 * q^49 - 6375 * q^50 - 1438 * q^52 - 5044 * q^53 + 7506 * q^56 + 4064 * q^58 + 2 * q^61 - 9162 * q^62 + 4513 * q^64 + 2014 * q^65 + 11405 * q^68 - 3666 * q^70 - 1708 * q^73 - 14620 * q^74 - 1581 * q^76 + 3942 * q^77 + 22760 * q^80 - 4243 * q^82 + 1252 * q^85 - 22113 * q^86 - 1995 * q^88 + 6524 * q^89 + 30294 * q^92 - 7524 * q^94 - 5638 * q^97 - 46469 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more