LMFDB - Embedded newform 162.5.d.d.107.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,5,Mod(53,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5]))

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

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

chi := DirichletCharacter("162.53");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	162.d (of order $6$, degree $2$, 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:	$16.7459340196$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			107.3
Root			$-0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	162.107
Dual form			162.5.d.d.53.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.44949 + 1.41421i) q^{2} +(4.00000 + 6.92820i) q^{4} +(-39.7924 + 22.9742i) q^{5} +(40.2750 - 69.7583i) q^{7} +22.6274i q^{8} +O(q^{10})$	\(q+(2.44949 + 1.41421i) q^{2} +(4.00000 + 6.92820i) q^{4} +(-39.7924 + 22.9742i) q^{5} +(40.2750 - 69.7583i) q^{7} +22.6274i q^{8} -129.962 q^{10} +(-97.9560 - 56.5549i) q^{11} +(-35.1269 - 60.8416i) q^{13} +(197.306 - 113.915i) q^{14} +(-32.0000 + 55.4256i) q^{16} -256.030i q^{17} +192.435 q^{19} +(-318.339 - 183.793i) q^{20} +(-159.962 - 277.061i) q^{22} +(471.056 - 271.964i) q^{23} +(743.125 - 1287.13i) q^{25} -198.708i q^{26} +644.400 q^{28} +(-712.719 - 411.488i) q^{29} +(-307.704 - 532.959i) q^{31} +(-156.767 + 90.5097i) q^{32} +(362.081 - 627.142i) q^{34} +3701.14i q^{35} -2355.20 q^{37} +(471.366 + 272.144i) q^{38} +(-519.846 - 900.400i) q^{40} +(-434.893 + 251.085i) q^{41} +(82.3595 - 142.651i) q^{43} -904.879i q^{44} +1538.46 q^{46} +(-901.727 - 520.613i) q^{47} +(-2043.65 - 3539.71i) q^{49} +(3640.55 - 2101.87i) q^{50} +(281.015 - 486.733i) q^{52} +182.004i q^{53} +5197.21 q^{55} +(1578.45 + 911.319i) q^{56} +(-1163.86 - 2015.87i) q^{58} +(-1569.03 + 905.882i) q^{59} +(1429.92 - 2476.70i) q^{61} -1740.64i q^{62} -512.000 q^{64} +(2795.57 + 1614.02i) q^{65} +(4447.92 + 7704.03i) q^{67} +(1773.83 - 1024.12i) q^{68} +(-5234.20 + 9065.90i) q^{70} +3556.66i q^{71} -8008.40 q^{73} +(-5769.03 - 3330.75i) q^{74} +(769.738 + 1333.23i) q^{76} +(-7890.36 + 4555.50i) q^{77} +(2013.20 - 3486.96i) q^{79} -2940.69i q^{80} -1420.35 q^{82} +(-1599.54 - 923.492i) q^{83} +(5882.07 + 10188.0i) q^{85} +(403.477 - 232.948i) q^{86} +(1279.69 - 2216.49i) q^{88} -4204.70i q^{89} -5658.95 q^{91} +(3768.44 + 2175.71i) q^{92} +(-1472.51 - 2550.47i) q^{94} +(-7657.44 + 4421.02i) q^{95} +(-6593.40 + 11420.1i) q^{97} -11560.6i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 32 q^{4} + 52 q^{7}+O(q^{10}) $ 8 * q + 32 * q^4 + 52 * q^7	$ 8 q + 32 q^{4} + 52 q^{7} - 624 q^{10} - 572 q^{13} - 256 q^{16} - 248 q^{19} - 864 q^{22} + 1892 q^{25} + 832 q^{28} - 3584 q^{31} + 1608 q^{34} - 18800 q^{37} - 2496 q^{40} - 3020 q^{43} - 4320 q^{46} - 9324 q^{49} + 4576 q^{52} + 22248 q^{55} + 2952 q^{58} + 4144 q^{61} - 4096 q^{64} + 12076 q^{67} - 18096 q^{70} - 3584 q^{73} - 992 q^{76} + 15004 q^{79} + 10752 q^{82} + 24048 q^{85} + 6912 q^{88} + 24440 q^{91} + 12912 q^{94} - 46304 q^{97}+O(q^{100}) $ 8 * q + 32 * q^4 + 52 * q^7 - 624 * q^10 - 572 * q^13 - 256 * q^16 - 248 * q^19 - 864 * q^22 + 1892 * q^25 + 832 * q^28 - 3584 * q^31 + 1608 * q^34 - 18800 * q^37 - 2496 * q^40 - 3020 * q^43 - 4320 * q^46 - 9324 * q^49 + 4576 * q^52 + 22248 * q^55 + 2952 * q^58 + 4144 * q^61 - 4096 * q^64 + 12076 * q^67 - 18096 * q^70 - 3584 * q^73 - 992 * q^76 + 15004 * q^79 + 10752 * q^82 + 24048 * q^85 + 6912 * q^88 + 24440 * q^91 + 12912 * q^94 - 46304 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	2.44949	+	1.41421i	0.612372	+	0.353553i
$2$	2.44949	+	1.41421i	0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	4.00000	+	6.92820i	0.250000	+	0.433013i
$5$	−39.7924	+	22.9742i	−1.59170	+	0.918967i	−0.598681	+	0.800988i	$0.704308\pi$
$5$	−39.7924	+	22.9742i	−1.59170	+	0.918967i	−0.993016	+	0.117979i	$0.962358\pi$
$6$		0			0
$7$	40.2750	−	69.7583i	0.821939	−	1.42364i	−0.0822981	−	0.996608i	$-0.526226\pi$
$7$	40.2750	−	69.7583i	0.821939	−	1.42364i	0.904237	−	0.427032i	$-0.140441\pi$
$8$			22.6274i			0.353553i
$9$		0			0
$10$	−129.962			−1.29962
$11$	−97.9560	−	56.5549i	−0.809554	−	0.467396i	0.0372470	−	0.999306i	$-0.488141\pi$
$11$	−97.9560	−	56.5549i	−0.809554	−	0.467396i	−0.846801	+	0.531910i	$0.821475\pi$
$12$		0			0
$13$	−35.1269	−	60.8416i	−0.207852	−	0.360010i	0.743186	−	0.669085i	$-0.233314\pi$
$13$	−35.1269	−	60.8416i	−0.207852	−	0.360010i	−0.951038	+	0.309075i	$0.899980\pi$
$14$	197.306	−	113.915i	1.00667	−	0.581198i
$15$		0			0
$16$	−32.0000	+	55.4256i	−0.125000	+	0.216506i
$17$		−	256.030i		−	0.885916i	−0.896542	−	0.442958i	$-0.853929\pi$
$17$		−	256.030i		−	0.885916i	0.896542	−	0.442958i	$-0.146071\pi$
$18$		0			0
$19$	192.435			0.533060			0.266530	−	0.963827i	$-0.414123\pi$
$19$	192.435			0.533060			0.266530	+	0.963827i	$0.414123\pi$
$20$	−318.339	−	183.793i	−0.795849	−	0.459483i
$21$		0			0
$22$	−159.962	−	277.061i	−0.330499	−	0.572441i
$23$	471.056	−	271.964i	0.890464	−	0.514110i	0.0163699	−	0.999866i	$-0.494789\pi$
$23$	471.056	−	271.964i	0.890464	−	0.514110i	0.874094	+	0.485756i	$0.161456\pi$
$24$		0			0
$25$	743.125	−	1287.13i	1.18900	−	2.05941i
$26$		−	198.708i		−	0.293947i
$27$		0			0
$28$	644.400			0.821939
$29$	−712.719	−	411.488i	−0.847466	−	0.489285i	0.0123291	−	0.999924i	$-0.496075\pi$
$29$	−712.719	−	411.488i	−0.847466	−	0.489285i	−0.859795	+	0.510639i	$0.829409\pi$
$30$		0			0
$31$	−307.704	−	532.959i	−0.320191	−	0.554588i	0.660336	−	0.750970i	$-0.270414\pi$
$31$	−307.704	−	532.959i	−0.320191	−	0.554588i	−0.980527	+	0.196383i	$0.937081\pi$
$32$	−156.767	+	90.5097i	−0.153093	+	0.0883883i
$33$		0			0
$34$	362.081	−	627.142i	0.313219	−	0.542511i
$35$			3701.14i			3.02134i
$36$		0			0
$37$	−2355.20			−1.72038			−0.860189	−	0.509976i	$-0.829654\pi$
$37$	−2355.20			−1.72038			−0.860189	+	0.509976i	$0.829654\pi$
$38$	471.366	+	272.144i	0.326431	+	0.188465i
$39$		0			0
$40$	−519.846	−	900.400i	−0.324904	−	0.562750i
$41$	−434.893	+	251.085i	−0.258711	+	0.149367i	−0.623746	−	0.781627i	$-0.714390\pi$
$41$	−434.893	+	251.085i	−0.258711	+	0.149367i	0.365036	+	0.930994i	$0.381057\pi$
$42$		0			0
$43$	82.3595	−	142.651i	0.0445427	−	0.0771503i	−0.842894	−	0.538079i	$-0.819150\pi$
$43$	82.3595	−	142.651i	0.0445427	−	0.0771503i	0.887437	+	0.460929i	$0.152484\pi$
$44$		−	904.879i		−	0.467396i
$45$		0			0
$46$	1538.46			0.727061
$47$	−901.727	−	520.613i	−0.408206	−	0.235678i	0.281813	−	0.959469i	$-0.409064\pi$
$47$	−901.727	−	520.613i	−0.408206	−	0.235678i	−0.690019	+	0.723792i	$0.742398\pi$
$48$		0			0
$49$	−2043.65	−	3539.71i	−0.851166	−	1.47426i
$50$	3640.55	−	2101.87i	1.45622	−	0.840750i
$51$		0			0
$52$	281.015	−	486.733i	0.103926	−	0.180005i
$53$			182.004i			0.0647930i	0.999475	+	0.0323965i	$0.0103139\pi$
$53$			182.004i			0.0647930i	−0.999475	+	0.0323965i	$0.989686\pi$
$54$		0			0
$55$	5197.21			1.71809
$56$	1578.45	+	911.319i	0.503333	+	0.290599i
$57$		0			0
$58$	−1163.86	−	2015.87i	−0.345977	−	0.599249i
$59$	−1569.03	+	905.882i	−0.450742	+	0.260236i	−0.708144	−	0.706068i	$-0.750467\pi$
$59$	−1569.03	+	905.882i	−0.450742	+	0.260236i	0.257401	+	0.966305i	$0.417134\pi$
$60$		0			0
$61$	1429.92	−	2476.70i	0.384285	−	0.665601i	−0.607385	−	0.794408i	$-0.707781\pi$
$61$	1429.92	−	2476.70i	0.384285	−	0.665601i	0.991670	+	0.128807i	$0.0411146\pi$
$62$		−	1740.64i		−	0.452819i
$63$		0			0
$64$	−512.000			−0.125000
$65$	2795.57	+	1614.02i	0.661674	+	0.382018i
$66$		0			0
$67$	4447.92	+	7704.03i	0.990850	+	1.71620i	0.612312	+	0.790616i	$0.290240\pi$
$67$	4447.92	+	7704.03i	0.990850	+	1.71620i	0.378537	+	0.925586i	$0.376427\pi$
$68$	1773.83	−	1024.12i	0.383613	−	0.221479i
$69$		0			0
$70$	−5234.20	+	9065.90i	−1.06820	+	1.85018i
$71$			3556.66i			0.705547i	0.935709	+	0.352773i	$0.114761\pi$
$71$			3556.66i			0.705547i	−0.935709	+	0.352773i	$0.885239\pi$
$72$		0			0
$73$	−8008.40			−1.50280			−0.751398	−	0.659849i	$-0.770620\pi$
$73$	−8008.40			−1.50280			−0.751398	+	0.659849i	$0.770620\pi$
$74$	−5769.03	−	3330.75i	−1.05351	−	0.608245i
$75$		0			0
$76$	769.738	+	1333.23i	0.133265	+	0.230822i
$77$	−7890.36	+	4555.50i	−1.33081	+	0.768342i
$78$		0			0
$79$	2013.20	−	3486.96i	0.322576	−	0.558718i	−0.658443	−	0.752631i	$-0.728784\pi$
$79$	2013.20	−	3486.96i	0.322576	−	0.558718i	0.981019	+	0.193913i	$0.0621178\pi$
$80$		−	2940.69i		−	0.459483i
$81$		0			0
$82$	−1420.35			−0.211236
$83$	−1599.54	−	923.492i	−0.232187	−	0.134053i	0.379394	−	0.925235i	$-0.376133\pi$
$83$	−1599.54	−	923.492i	−0.232187	−	0.134053i	−0.611581	+	0.791182i	$0.709466\pi$
$84$		0			0
$85$	5882.07	+	10188.0i	0.814127	+	1.41011i
$86$	403.477	−	232.948i	0.0545535	−	0.0314965i
$87$		0			0
$88$	1279.69	−	2216.49i	0.165250	−	0.286221i
$89$		−	4204.70i		−	0.530830i	−0.964134	−	0.265415i	$-0.914491\pi$
$89$		−	4204.70i		−	0.530830i	0.964134	−	0.265415i	$-0.0855089\pi$
$90$		0			0
$91$	−5658.95			−0.683365
$92$	3768.44	+	2175.71i	0.445232	+	0.257055i
$93$		0			0
$94$	−1472.51	−	2550.47i	−0.166649	−	0.288645i
$95$	−7657.44	+	4421.02i	−0.848470	+	0.489864i
$96$		0			0
$97$	−6593.40	+	11420.1i	−0.700755	+	1.21374i	0.267447	+	0.963573i	$0.413820\pi$
$97$	−6593.40	+	11420.1i	−0.700755	+	1.21374i	−0.968202	+	0.250171i	$0.919513\pi$
$98$		−	11560.6i		−	1.20373i
$99$		0			0
$100$	11890.0			1.18900
$101$	8651.84	+	4995.14i	0.848136	+	0.489672i	0.860022	−	0.510258i	$-0.170450\pi$
$101$	8651.84	+	4995.14i	0.848136	+	0.489672i	−0.0118852	+	0.999929i	$0.503783\pi$
$102$		0			0
$103$	1639.49	+	2839.69i	0.154538	+	0.267668i	0.932891	−	0.360160i	$-0.117278\pi$
$103$	1639.49	+	2839.69i	0.154538	+	0.267668i	−0.778353	+	0.627827i	$0.783944\pi$
$104$	1376.69	−	794.832i	0.127283	−	0.0734867i
$105$		0			0
$106$	−257.392	+	445.816i	−0.0229078	+	0.0396775i
$107$		−	20923.5i		−	1.82754i	−0.406236	−	0.913768i	$-0.633159\pi$
$107$		−	20923.5i		−	1.82754i	0.406236	−	0.913768i	$-0.366841\pi$
$108$		0			0
$109$	3340.77			0.281186			0.140593	−	0.990067i	$-0.455099\pi$
$109$	3340.77			0.281186			0.140593	+	0.990067i	$0.455099\pi$
$110$	12730.5	+	7349.97i	1.05211	+	0.607435i
$111$		0			0
$112$	2577.60	+	4464.53i	0.205485	+	0.355910i
$113$	7683.71	−	4436.19i	0.601747	−	0.347419i	−0.167982	−	0.985790i	$-0.553725\pi$
$113$	7683.71	−	4436.19i	0.601747	−	0.347419i	0.769729	+	0.638371i	$0.220392\pi$
$114$		0			0
$115$	−12496.3	+	21644.2i	−0.944899	+	1.63661i
$116$		−	6583.81i		−	0.489285i
$117$		0			0
$118$	−5124.45			−0.368030
$119$	−17860.2	−	10311.6i	−1.26122	−	0.728169i
$120$		0			0
$121$	−923.578	−	1599.68i	−0.0630816	−	0.109261i
$122$	7005.17	−	4044.44i	0.470651	−	0.271731i
$123$		0			0
$124$	2461.63	−	4263.67i	0.160096	−	0.277294i
$125$			39573.0i			2.53267i
$126$		0			0
$127$	−15509.1			−0.961569			−0.480784	−	0.876839i	$-0.659648\pi$
$127$	−15509.1			−0.961569			−0.480784	+	0.876839i	$0.659648\pi$
$128$	−1254.14	−	724.077i	−0.0765466	−	0.0441942i
$129$		0			0
$130$	4565.15	+	7907.07i	0.270127	+	0.467874i
$131$	−11774.9	+	6798.24i	−0.686143	+	0.396145i	−0.802165	−	0.597102i	$-0.796319\pi$
$131$	−11774.9	+	6798.24i	−0.686143	+	0.396145i	0.116023	+	0.993247i	$0.462985\pi$
$132$		0			0
$133$	7750.30	−	13423.9i	0.438142	−	0.758885i
$134$			25161.3i			1.40127i
$135$		0			0
$136$	5793.29			0.313219
$137$	18762.2	+	10832.4i	0.999639	+	0.577142i	0.908141	−	0.418664i	$-0.137501\pi$
$137$	18762.2	+	10832.4i	0.999639	+	0.577142i	0.0914974	+	0.995805i	$0.470835\pi$
$138$		0			0
$139$	−7719.12	−	13369.9i	−0.399520	−	0.691989i	0.594147	−	0.804357i	$-0.297490\pi$
$139$	−7719.12	−	13369.9i	−0.399520	−	0.691989i	−0.993667	+	0.112368i	$0.964157\pi$
$140$	−25642.2	+	14804.6i	−1.30828	+	0.755334i
$141$		0			0
$142$	−5029.88	+	8712.00i	−0.249448	+	0.432057i
$143$			7946.41i			0.388596i
$144$		0			0
$145$	37814.4			1.79855
$146$	−19616.5	−	11325.6i	−0.920271	−	0.531319i
$147$		0			0
$148$	−9420.78	−	16317.3i	−0.430094	−	0.744945i
$149$	17729.3	−	10236.0i	0.798580	−	0.461060i	−0.0443947	−	0.999014i	$-0.514136\pi$
$149$	17729.3	−	10236.0i	0.798580	−	0.461060i	0.842974	+	0.537954i	$0.180803\pi$
$150$		0			0
$151$	16002.4	−	27716.9i	0.701827	−	1.21560i	−0.265997	−	0.963974i	$-0.585701\pi$
$151$	16002.4	−	27716.9i	0.701827	−	1.21560i	0.967824	−	0.251626i	$-0.0809654\pi$
$152$			4354.30i			0.188465i
$153$		0			0
$154$	−25769.8			−1.08660
$155$	24488.6	+	14138.5i	1.01930	+	0.588490i
$156$		0			0
$157$	12103.6	+	20964.0i	0.491037	+	0.850501i	0.999947	−	0.0103185i	$-0.00328455\pi$
$157$	12103.6	+	20964.0i	0.491037	+	0.850501i	−0.508910	+	0.860820i	$0.669951\pi$
$158$	9862.62	−	5694.18i	0.395074	−	0.228096i
$159$		0			0
$160$	4158.77	−	7203.20i	0.162452	−	0.281375i
$161$		−	43813.4i		−	1.69027i
$162$		0			0
$163$	21091.0			0.793821			0.396911	−	0.917857i	$-0.370082\pi$
$163$	21091.0			0.793821			0.396911	+	0.917857i	$0.370082\pi$
$164$	−3479.14	−	2008.68i	−0.129355	−	0.0746833i
$165$		0			0
$166$	−2612.03	−	4524.17i	−0.0947899	−	0.164181i
$167$	11230.1	−	6483.70i	0.402671	−	0.232482i	−0.284965	−	0.958538i	$-0.591982\pi$
$167$	11230.1	−	6483.70i	0.402671	−	0.232482i	0.687636	+	0.726056i	$0.258649\pi$
$168$		0			0
$169$	11812.7	−	20460.2i	0.413595	−	0.716368i
$170$			33274.0i			1.15135i
$171$		0			0
$172$	1317.75			0.0445427
$173$	−36181.3	−	20889.3i	−1.20891	−	0.697962i	−0.246386	−	0.969172i	$-0.579243\pi$
$173$	−36181.3	−	20889.3i	−1.20891	−	0.697962i	−0.962520	+	0.271210i	$0.912576\pi$
$174$		0			0
$175$	−59858.7	−	103678.i	−1.95457	−	3.38541i
$176$	6269.19	−	3619.52i	0.202388	−	0.116849i
$177$		0			0
$178$	5946.35	−	10299.4i	0.187677	−	0.325065i
$179$		−	13288.6i		−	0.414736i	−0.978263	−	0.207368i	$-0.933510\pi$
$179$		−	13288.6i		−	0.414736i	0.978263	−	0.207368i	$-0.0664897\pi$
$180$		0			0
$181$	−28910.7			−0.882475			−0.441237	−	0.897390i	$-0.645460\pi$
$181$	−28910.7			−0.882475			−0.441237	+	0.897390i	$0.645460\pi$
$182$	−13861.5	−	8002.96i	−0.418474	−	0.241606i
$183$		0			0
$184$	6153.84	+	10658.8i	0.181765	+	0.314827i
$185$	93719.0	−	54108.7i	2.73832	−	1.58097i
$186$		0			0
$187$	−14479.7	+	25079.7i	−0.414074	+	0.717197i
$188$		−	8329.80i		−	0.235678i
$189$		0			0
$190$	−25009.1			−0.692773
$191$	−43612.2	−	25179.5i	−1.19548	−	0.690209i	−0.235934	−	0.971769i	$-0.575815\pi$
$191$	−43612.2	−	25179.5i	−1.19548	−	0.690209i	−0.959544	+	0.281560i	$0.909148\pi$
$192$		0			0
$193$	1733.01	+	3001.66i	0.0465250	+	0.0805837i	0.888350	−	0.459167i	$-0.151852\pi$
$193$	1733.01	+	3001.66i	0.0465250	+	0.0805837i	−0.841825	+	0.539750i	$0.818519\pi$
$194$	−32300.9	+	18649.0i	−0.858246	+	0.495509i
$195$		0			0
$196$	16349.2	−	28317.6i	0.425583	−	0.737131i
$197$			7813.76i			0.201339i	0.994920	+	0.100669i	$0.0320984\pi$
$197$			7813.76i			0.201339i	−0.994920	+	0.100669i	$0.967902\pi$
$198$		0			0
$199$	29153.3			0.736176			0.368088	−	0.929791i	$-0.380013\pi$
$199$	29153.3			0.736176			0.368088	+	0.929791i	$0.380013\pi$
$200$	29124.4	+	16815.0i	0.728111	+	0.420375i
$201$		0			0
$202$	14128.4	+	24471.1i	0.346250	+	0.599723i
$203$	−57409.5	+	33145.4i	−1.39313	+	0.804324i
$204$		0			0
$205$	11537.0	−	19982.6i	0.274526	−	0.475493i
$206$			9274.37i			0.218550i
$207$		0			0
$208$	4496.25			0.103926
$209$	−18850.1	−	10883.1i	−0.431541	−	0.249150i
$210$		0			0
$211$	23579.0	+	40840.0i	0.529615	+	0.917321i	0.999403	+	0.0345415i	$0.0109971\pi$
$211$	23579.0	+	40840.0i	0.529615	+	0.917321i	−0.469788	+	0.882779i	$0.655670\pi$
$212$	−1260.96	+	728.014i	−0.0280562	+	0.0161983i
$213$		0			0
$214$	29590.2	−	51251.8i	0.646132	−	1.11913i
$215$			7568.56i			0.163733i
$216$		0			0
$217$	−49571.1			−1.05271
$218$	8183.19	+	4724.56i	0.172191	+	0.0994143i
$219$		0			0
$220$	20788.8	+	36007.3i	0.429522	+	0.743953i
$221$	−15577.3	+	8993.54i	−0.318938	+	0.184139i
$222$		0			0
$223$	−5026.64	+	8706.39i	−0.101081	+	0.175077i	−0.912130	−	0.409901i	$-0.865563\pi$
$223$	−5026.64	+	8706.39i	−0.101081	+	0.175077i	0.811050	+	0.584978i	$0.198897\pi$
$224$			14581.1i			0.290599i
$225$		0			0
$226$	25094.9			0.491324
$227$	−25939.0	−	14975.9i	−0.503386	−	0.290630i	0.226725	−	0.973959i	$-0.427198\pi$
$227$	−25939.0	−	14975.9i	−0.503386	−	0.290630i	−0.730111	+	0.683329i	$0.760532\pi$
$228$		0			0
$229$	10066.7	+	17436.1i	0.191963	+	0.332489i	0.945901	−	0.324456i	$-0.105181\pi$
$229$	10066.7	+	17436.1i	0.191963	+	0.332489i	−0.753938	+	0.656946i	$0.771848\pi$
$230$	−61219.1	+	35344.9i	−1.15726	+	0.668145i
$231$		0			0
$232$	9310.92	−	16127.0i	0.172988	−	0.299624i
$233$		−	19079.1i		−	0.351436i	−0.984441	−	0.175718i	$-0.943775\pi$
$233$		−	19079.1i		−	0.351436i	0.984441	−	0.175718i	$-0.0562246\pi$
$234$		0			0
$235$	47842.6			0.866321
$236$	−12552.3	−	7247.06i	−0.225371	−	0.130118i
$237$		0			0
$238$	−29165.6	−	50516.3i	−0.514893	−	0.891821i
$239$	78167.1	−	45129.8i	1.36845	−	0.790073i	0.377717	−	0.925921i	$-0.376709\pi$
$239$	78167.1	−	45129.8i	1.36845	−	0.790073i	0.990730	+	0.135848i	$0.0433757\pi$
$240$		0			0
$241$	−15080.5	+	26120.2i	−0.259646	+	0.449720i	−0.966147	−	0.257992i	$-0.916939\pi$
$241$	−15080.5	+	26120.2i	−0.259646	+	0.449720i	0.706501	+	0.707712i	$0.250272\pi$
$242$		−	5224.54i		−	0.0892109i
$243$		0			0
$244$	22878.8			0.384285
$245$	162644.	+	93902.3i	2.70960	+	1.56439i
$246$		0			0
$247$	−6759.64	−	11708.0i	−0.110797	−	0.191907i
$248$	12059.5	−	6962.54i	0.196076	−	0.113205i
$249$		0			0
$250$	−55964.7	+	96933.6i	−0.895435	+	1.55094i
$251$		−	16436.6i		−	0.260894i	−0.991455	−	0.130447i	$-0.958359\pi$
$251$		−	16436.6i		−	0.260894i	0.991455	−	0.130447i	$-0.0416412\pi$
$252$		0			0
$253$	−61523.6			−0.961172
$254$	−37989.5	−	21933.2i	−0.588838	−	0.339966i
$255$		0			0
$256$	−2048.00	−	3547.24i	−0.0312500	−	0.0541266i
$257$	20129.9	−	11622.0i	0.304772	−	0.175960i	−0.339813	−	0.940493i	$-0.610364\pi$
$257$	20129.9	−	11622.0i	0.304772	−	0.175960i	0.644585	+	0.764533i	$0.277030\pi$
$258$		0			0
$259$	−94855.5	+	164295.i	−1.41404	+	2.44920i
$260$			25824.4i			0.382018i
$261$		0			0
$262$	−38456.6			−0.560233
$263$	−26588.4	−	15350.8i	−0.384398	−	0.221932i	0.295332	−	0.955395i	$-0.404570\pi$
$263$	−26588.4	−	15350.8i	−0.384398	−	0.221932i	−0.679730	+	0.733462i	$0.737903\pi$
$264$		0			0
$265$	−4181.38	−	7242.36i	−0.0595426	−	0.103131i
$266$	37968.6	−	21921.2i	0.536613	−	0.309813i
$267$		0			0
$268$	−35583.4	+	61632.2i	−0.495425	+	0.858101i
$269$		−	98285.6i		−	1.35827i	−0.734014	−	0.679134i	$-0.762356\pi$
$269$		−	98285.6i		−	1.35827i	0.734014	−	0.679134i	$-0.237644\pi$
$270$		0			0
$271$	111736.			1.52144			0.760722	−	0.649078i	$-0.224845\pi$
$271$	111736.			1.52144			0.760722	+	0.649078i	$0.224845\pi$
$272$	14190.6	+	8192.95i	0.191806	+	0.110740i
$273$		0			0
$274$	30638.6	+	53067.6i	0.408101	+	0.706851i
$275$	−145587.	+	84054.8i	−1.92512	+	1.11147i
$276$		0			0
$277$	32204.3	−	55779.4i	0.419714	−	0.726967i	−0.576196	−	0.817311i	$-0.695464\pi$
$277$	32204.3	−	55779.4i	0.419714	−	0.726967i	0.995911	+	0.0903447i	$0.0287969\pi$
$278$		−	43666.0i		−	0.565007i
$279$		0			0
$280$	−83747.2			−1.06820
$281$	108135.	+	62431.6i	1.36947	+	0.790664i	0.990860	−	0.134893i	$-0.0430690\pi$
$281$	108135.	+	62431.6i	1.36947	+	0.790664i	0.378610	+	0.925556i	$0.376402\pi$
$282$		0			0
$283$	62898.9	+	108944.i	0.785362	+	1.36029i	0.928783	+	0.370625i	$0.120857\pi$
$283$	62898.9	+	108944.i	0.785362	+	1.36029i	−0.143421	+	0.989662i	$0.545810\pi$
$284$	−24641.3	+	14226.6i	−0.305511	+	0.176387i
$285$		0			0
$286$	−11237.9	+	19464.6i	−0.137390	+	0.237966i
$287$			40449.8i			0.491081i
$288$		0			0
$289$	17969.8			0.215153
$290$	92626.0	+	53477.7i	1.10138	+	0.635882i
$291$		0			0
$292$	−32033.6	−	55483.8i	−0.375699	−	0.650730i
$293$	−60944.4	+	35186.3i	−0.709902	+	0.409862i	−0.811025	−	0.585012i	$-0.801090\pi$
$293$	−60944.4	+	35186.3i	−0.709902	+	0.409862i	0.101123	+	0.994874i	$0.467757\pi$
$294$		0			0
$295$	41623.8	−	72094.5i	0.478297	−	0.828435i
$296$		−	53292.0i		−	0.608245i
$297$		0			0
$298$	57903.5			0.652037
$299$	−33093.5	−	19106.5i	−0.370169	−	0.213717i
$300$		0			0
$301$	−6634.06	−	11490.5i	−0.0732228	−	0.126826i
$302$	78395.2	−	45261.5i	0.859559	−	0.496267i
$303$		0			0
$304$	−6157.91	+	10665.8i	−0.0666325	+	0.115411i
$305$			131405.i			1.41258i
$306$		0			0
$307$	−26790.2			−0.284249			−0.142125	−	0.989849i	$-0.545393\pi$
$307$	−26790.2			−0.284249			−0.142125	+	0.989849i	$0.545393\pi$
$308$	−63122.9	−	36444.0i	−0.665404	−	0.384171i
$309$		0			0
$310$	39989.7	+	69264.1i	0.416126	+	0.720751i
$311$	−110747.	+	63939.7i	−1.14501	+	0.661074i	−0.947667	−	0.319260i	$-0.896566\pi$
$311$	−110747.	+	63939.7i	−1.14501	+	0.661074i	−0.197347	+	0.980334i	$0.563232\pi$
$312$		0			0
$313$	−4782.11	+	8282.85i	−0.0488125	+	0.0845457i	−0.889399	−	0.457131i	$-0.848877\pi$
$313$	−4782.11	+	8282.85i	−0.0488125	+	0.0845457i	0.840587	+	0.541677i	$0.182210\pi$
$314$			68468.2i			0.694432i
$315$		0			0
$316$	32211.2			0.322576
$317$	33769.7	+	19497.0i	0.336054	+	0.194021i	0.658526	−	0.752558i	$-0.271180\pi$
$317$	33769.7	+	19497.0i	0.336054	+	0.194021i	−0.322472	+	0.946579i	$0.604514\pi$
$318$		0			0
$319$	46543.4	+	80615.5i	0.457380	+	0.792205i
$320$	20373.7	−	11762.8i	0.198962	−	0.114871i
$321$		0			0
$322$	61961.5	−	107320.i	0.597599	−	1.03507i
$323$		−	49269.0i		−	0.472246i
$324$		0			0
$325$	−104415.			−0.988542
$326$	51662.3	+	29827.2i	0.486114	+	0.280658i
$327$		0			0
$328$	−5681.41	−	9840.49i	−0.0528091	−	0.0914680i
$329$	−72634.1	+	41935.3i	−0.671041	+	0.387426i
$330$		0			0
$331$	−25217.1	+	43677.3i	−0.230165	+	0.398658i	−0.957857	−	0.287247i	$-0.907260\pi$
$331$	−25217.1	+	43677.3i	−0.230165	+	0.398658i	0.727691	+	0.685905i	$0.240593\pi$
$332$		−	14775.9i		−	0.134053i
$333$		0			0
$334$	36677.3			0.328780
$335$	−353987.	−	204375.i	−3.15427	−	1.82112i
$336$		0			0
$337$	63687.0	+	110309.i	0.560778	+	0.971296i	0.997429	+	0.0716648i	$0.0228312\pi$
$337$	63687.0	+	110309.i	0.560778	+	0.971296i	−0.436651	+	0.899631i	$0.643835\pi$
$338$	57870.2	−	33411.4i	0.506549	−	0.292456i
$339$		0			0
$340$	−47056.6	+	81504.4i	−0.407064	+	0.705055i
$341$			69608.7i			0.598625i
$342$		0			0
$343$	−135831.			−1.15455
$344$	3227.82	+	1863.58i	0.0272767	+	0.0157482i
$345$		0			0
$346$	−59083.9	−	102336.i	−0.493534	−	0.854825i
$347$	167850.	−	96908.4i	1.39400	−	0.804827i	0.400246	−	0.916408i	$-0.368925\pi$
$347$	167850.	−	96908.4i	1.39400	−	0.804827i	0.993755	+	0.111581i	$0.0355914\pi$
$348$		0			0
$349$	−52034.4	+	90126.3i	−0.427209	+	0.739947i	−0.996624	−	0.0821031i	$-0.973836\pi$
$349$	−52034.4	+	90126.3i	−0.427209	+	0.739947i	0.569415	+	0.822050i	$0.307170\pi$
$350$		−	338612.i		−	2.76418i
$351$		0			0
$352$	20475.1			0.165250
$353$	139234.	+	80386.8i	1.11737	+	0.645112i	0.940727	−	0.339163i	$-0.110144\pi$
$353$	139234.	+	80386.8i	1.11737	+	0.645112i	0.176640	+	0.984276i	$0.443477\pi$
$354$		0			0
$355$	−81711.3	−	141528.i	−0.648374	−	1.12302i
$356$	29131.0	−	16818.8i	0.229856	−	0.132707i
$357$		0			0
$358$	18792.9	−	32550.2i	0.146631	−	0.253973i
$359$		−	21776.0i		−	0.168962i	−0.996425	−	0.0844811i	$-0.973077\pi$
$359$		−	21776.0i		−	0.168962i	0.996425	−	0.0844811i	$-0.0269233\pi$
$360$		0			0
$361$	−93289.9			−0.715847
$362$	−70816.6	−	40886.0i	−0.540403	−	0.312002i
$363$		0			0
$364$	−22635.8	−	39206.3i	−0.170841	−	0.295906i
$365$	318674.	−	183986.i	2.39200	−	1.38102i
$366$		0			0
$367$	125983.	−	218208.i	0.935360	−	1.62009i	0.161369	−	0.986894i	$-0.448409\pi$
$367$	125983.	−	218208.i	0.935360	−	1.62009i	0.773991	−	0.633196i	$-0.218257\pi$
$368$			34811.4i			0.257055i
$369$		0			0
$370$	306085.			2.23583
$371$	12696.3	+	7330.19i	0.0922419	+	0.0532559i
$372$		0			0
$373$	−64013.0	−	110874.i	−0.460098	−	0.796913i	0.538867	−	0.842391i	$-0.318852\pi$
$373$	−64013.0	−	110874.i	−0.460098	−	0.796913i	−0.998965	+	0.0454775i	$0.985519\pi$
$374$	−70936.0	+	40954.9i	−0.507135	+	0.292794i
$375$		0			0
$376$	11780.1	−	20403.8i	0.0833247	−	0.144323i
$377$			57817.3i			0.406795i
$378$		0			0
$379$	92997.5			0.647430			0.323715	−	0.946155i	$-0.395068\pi$
$379$	92997.5			0.647430			0.323715	+	0.946155i	$0.395068\pi$
$380$	−61259.5	−	35368.2i	−0.424235	−	0.244932i
$381$		0			0
$382$	−71218.5	−	123354.i	−0.488052	−	0.845330i
$383$	−241008.	+	139146.i	−1.64299	+	0.948580i	−0.663226	+	0.748419i	$0.730813\pi$
$383$	−241008.	+	139146.i	−1.64299	+	0.948580i	−0.979763	+	0.200161i	$0.935853\pi$
$384$		0			0
$385$	209318.	−	362549.i	1.41216	−	2.44594i
$386$			9803.38i			0.0657963i
$387$		0			0
$388$	−105494.			−0.700755
$389$	−120311.	−	69461.7i	−0.795073	−	0.459035i	0.0466728	−	0.998910i	$-0.485138\pi$
$389$	−120311.	−	69461.7i	−0.795073	−	0.459035i	−0.841745	+	0.539875i	$0.818472\pi$
$390$		0			0
$391$	−69630.9	−	120604.i	−0.455458	−	0.788876i
$392$	80094.4	−	46242.5i	0.521231	−	0.300933i
$393$		0			0
$394$	−11050.3	+	19139.7i	−0.0711840	+	0.123294i
$395$			185006.i			1.18575i
$396$		0			0
$397$	−1760.70			−0.0111713			−0.00558564	−	0.999984i	$-0.501778\pi$
$397$	−1760.70			−0.0111713			−0.00558564	+	0.999984i	$0.501778\pi$
$398$	71410.7	+	41229.0i	0.450814	+	0.260277i
$399$		0			0
$400$	47560.0	+	82376.3i	0.297250	+	0.514852i
$401$	−35557.2	+	20529.0i	−0.221126	+	0.127667i	−0.606471	−	0.795105i	$-0.707416\pi$
$401$	−35557.2	+	20529.0i	−0.221126	+	0.127667i	0.385346	+	0.922772i	$0.374082\pi$
$402$		0			0
$403$	−21617.4	+	37442.4i	−0.133105	+	0.230544i
$404$			79922.3i			0.489672i
$405$		0			0
$406$	−187499.			−1.13749
$407$	230706.	+	133198.i	1.39274	+	0.804098i
$408$		0			0
$409$	83356.8	+	144378.i	0.498304	+	0.863088i	0.999998	−	0.00195718i	$-0.000622989\pi$
$409$	83356.8	+	144378.i	0.498304	+	0.863088i	−0.501694	+	0.865045i	$0.667290\pi$
$410$	56519.3	−	32631.4i	0.336224	−	0.194119i
$411$		0			0
$412$	−13115.9	+	22717.5i	−0.0772690	+	0.133834i
$413$			145938.i			0.855593i
$414$		0			0
$415$	84865.9			0.492762
$416$	11013.5	+	6358.65i	0.0636413	+	0.0367433i
$417$		0			0
$418$	−30782.1	−	53316.2i	−0.176176	−	0.305145i
$419$	−287267.	+	165854.i	−1.63628	+	0.944708i	−0.654186	+	0.756334i	$0.726988\pi$
$419$	−287267.	+	165854.i	−1.63628	+	0.944708i	−0.982097	+	0.188374i	$0.939678\pi$
$420$		0			0
$421$	93913.4	−	162663.i	0.529863	−	0.917749i	−0.469530	−	0.882916i	$-0.655577\pi$
$421$	93913.4	−	162663.i	0.529863	−	0.917749i	0.999393	−	0.0348330i	$-0.0110899\pi$
$422$			133383.i			0.748989i
$423$		0			0
$424$	−4118.27			−0.0229078
$425$	−329544.	−	190262.i	−1.82446	−	1.05335i
$426$		0			0
$427$	−115180.	−	199498.i	−0.631717	−	1.09417i
$428$	144962.	−	83693.9i	0.791347	−	0.456884i
$429$		0			0
$430$	−10703.6	+	18539.1i	−0.0578884	+	0.100266i
$431$		−	6952.01i		−	0.0374245i	−0.999825	−	0.0187122i	$-0.994043\pi$
$431$		−	6952.01i		−	0.0374245i	0.999825	−	0.0187122i	$-0.00595664\pi$
$432$		0			0
$433$	−37941.0			−0.202364			−0.101182	−	0.994868i	$-0.532262\pi$
$433$	−37941.0			−0.202364			−0.101182	+	0.994868i	$0.532262\pi$
$434$	−121424.	−	70104.1i	−0.644651	−	0.372189i
$435$		0			0
$436$	13363.1	+	23145.5i	0.0702965	+	0.121757i
$437$	90647.4	−	52335.3i	0.474671	−	0.274051i
$438$		0			0
$439$	−124202.	+	215125.i	−0.644467	+	1.11625i	0.339957	+	0.940441i	$0.389587\pi$
$439$	−124202.	+	215125.i	−0.644467	+	1.11625i	−0.984424	+	0.175809i	$0.943746\pi$
$440$			117599.i			0.607435i
$441$		0			0
$442$	−50875.1			−0.260412
$443$	141031.	+	81424.3i	0.718633	+	0.414903i	0.814249	−	0.580515i	$-0.197149\pi$
$443$	141031.	+	81424.3i	0.718633	+	0.414903i	−0.0956163	+	0.995418i	$0.530482\pi$
$444$		0			0
$445$	96599.5	+	167315.i	0.487815	+	0.844920i
$446$	−24625.4	+	14217.5i	−0.123798	+	0.0714748i
$447$		0			0
$448$	−20620.8	+	35716.3i	−0.102742	+	0.177955i
$449$			139250.i			0.690723i	0.938470	+	0.345361i	$0.112244\pi$
$449$			139250.i			0.690723i	−0.938470	+	0.345361i	$0.887756\pi$
$450$		0			0
$451$	56800.5			0.279254
$452$	61469.7	+	35489.5i	0.300874	+	0.173709i
$453$		0			0
$454$	−42358.2	−	73366.5i	−0.205507	−	0.355948i
$455$	225183.	−	130010.i	1.08771	−	0.627990i
$456$		0			0
$457$	−125270.	+	216973.i	−0.599810	+	1.03890i	0.393039	+	0.919522i	$0.371424\pi$
$457$	−125270.	+	216973.i	−0.599810	+	1.03890i	−0.992849	+	0.119379i	$0.961910\pi$
$458$			56946.0i			0.271476i
$459$		0			0
$460$	−199941.			−0.944899
$461$	67711.5	+	39093.3i	0.318611	+	0.183950i	0.650773	−	0.759272i	$-0.274445\pi$
$461$	67711.5	+	39093.3i	0.318611	+	0.183950i	−0.332162	+	0.943222i	$0.607778\pi$
$462$		0			0
$463$	−176296.	−	305353.i	−0.822393	−	1.42443i	−0.903896	−	0.427753i	$-0.859305\pi$
$463$	−176296.	−	305353.i	−0.822393	−	1.42443i	0.0815028	−	0.996673i	$-0.474028\pi$
$464$	45614.0	−	26335.3i	0.211866	−	0.122321i
$465$		0			0
$466$	26981.9	−	46734.0i	0.124251	−	0.215209i
$467$			38384.6i			0.176005i	0.996120	+	0.0880023i	$0.0280483\pi$
$467$			38384.6i			0.176005i	−0.996120	+	0.0880023i	$0.971952\pi$
$468$		0			0
$469$	716560.			3.25767
$470$	117190.	+	67659.6i	0.530511	+	0.306291i
$471$		0			0
$472$	−20497.8	−	35503.2i	−0.0920074	−	0.159362i
$473$	−16135.2	+	9315.67i	−0.0721195	+	0.0416382i
$474$		0			0
$475$	143003.	−	247688.i	0.633808	−	1.09779i
$476$		−	164986.i		−	0.728169i
$477$		0			0
$478$	255293.			1.11733
$479$	45051.7	+	26010.6i	0.196354	+	0.113365i	0.594954	−	0.803760i	$-0.297170\pi$
$479$	45051.7	+	26010.6i	0.196354	+	0.113365i	−0.398600	+	0.917125i	$0.630504\pi$
$480$		0			0
$481$	82730.8	+	143294.i	0.357583	+	0.619352i
$482$	−73879.0	+	42654.0i	−0.318000	+	0.183597i
$483$		0			0
$484$	7388.62	−	12797.5i	0.0315408	−	0.0546303i
$485$		−	605912.i		−	2.57588i
$486$		0			0
$487$	−253420.			−1.06852			−0.534261	−	0.845320i	$-0.679410\pi$
$487$	−253420.			−1.06852			−0.534261	+	0.845320i	$0.679410\pi$
$488$	56041.4	+	32355.5i	0.235326	+	0.135865i
$489$		0			0
$490$	265596.	+	460025.i	1.10619	+	1.91597i
$491$	158096.	−	91276.7i	0.655779	−	0.378614i	−0.134888	−	0.990861i	$-0.543067\pi$
$491$	158096.	−	91276.7i	0.655779	−	0.378614i	0.790667	+	0.612247i	$0.209734\pi$
$492$		0			0
$493$	−105353.	+	182477.i	−0.433465	+	0.750784i
$494$		−	38238.3i		−	0.156691i
$495$		0			0
$496$	39386.1			0.160096
$497$	248107.	+	143244.i	1.00444	+	0.579916i
$498$		0			0
$499$	−17271.6	−	29915.3i	−0.0693636	−	0.120141i	0.829258	−	0.558866i	$-0.188764\pi$
$499$	−17271.6	−	29915.3i	−0.0693636	−	0.120141i	−0.898621	+	0.438725i	$0.855430\pi$
$500$	−274170.	+	158292.i	−1.09668	+	0.633168i
$501$		0			0
$502$	23244.8	−	40261.2i	0.0922400	−	0.159764i
$503$		−	466084.i		−	1.84216i	−0.389368	−	0.921082i	$-0.627307\pi$
$503$		−	466084.i		−	1.84216i	0.389368	−	0.921082i	$-0.372693\pi$
$504$		0			0
$505$	−459037.			−1.79997
$506$	−150702.	−	87007.6i	−0.588595	−	0.339826i
$507$		0			0
$508$	−62036.6	−	107450.i	−0.240392	−	0.416371i
$509$	136755.	−	78955.7i	0.527848	−	0.304753i	−0.212292	−	0.977206i	$-0.568093\pi$
$509$	136755.	−	78955.7i	0.527848	−	0.304753i	0.740139	+	0.672453i	$0.234759\pi$
$510$		0			0
$511$	−322538.	+	558653.i	−1.23521	+	2.13944i
$512$		−	11585.2i		−	0.0441942i
$513$		0			0
$514$	65743.9			0.248845
$515$	−130479.	−	75332.0i	−0.491955	−	0.284030i
$516$		0			0
$517$	58886.4	+	101994.i	0.220310	+	0.381588i
$518$	−464695.	+	268292.i	−1.73184	+	0.999880i
$519$		0			0
$520$	−36521.2	+	63256.6i	−0.135064	+	0.233937i
$521$			39855.1i			0.146828i	0.997302	+	0.0734139i	$0.0233894\pi$
$521$			39855.1i			0.146828i	−0.997302	+	0.0734139i	$0.976611\pi$
$522$		0			0
$523$	−250487.			−0.915762			−0.457881	−	0.889014i	$-0.651391\pi$
$523$	−250487.			−0.915762			−0.457881	+	0.889014i	$0.651391\pi$
$524$	−94199.1	−	54385.9i	−0.343071	−	0.198072i
$525$		0			0
$526$	−43418.7	−	75203.4i	−0.156930	−	0.271810i
$527$	−136453.	+	78781.3i	−0.491318	+	0.283663i
$528$		0			0
$529$	8008.38	−	13870.9i	0.0286176	−	0.0495672i
$530$		−	23653.5i		−	0.0842060i
$531$		0			0
$532$	124005.			0.438142
$533$	30552.9	+	17639.7i	0.107547	+	0.0620922i
$534$		0			0
$535$	480699.	+	832596.i	1.67945	+	2.90888i
$536$	−174322.	+	100645.i	−0.606769	+	0.350318i
$537$		0			0
$538$	138997.	−	240750.i	0.480220	−	0.831766i
$539$			462314.i			1.59133i
$540$		0			0
$541$	−324441.			−1.10852			−0.554258	−	0.832345i	$-0.686998\pi$
$541$	−324441.			−1.10852			−0.554258	+	0.832345i	$0.686998\pi$
$542$	273697.	+	158019.i	0.931690	+	0.537912i
$543$		0			0
$544$	23173.2	+	40137.1i	0.0783047	+	0.135628i
$545$	−132937.	+	76751.4i	−0.447563	+	0.258401i
$546$		0			0
$547$	−7037.20	+	12188.8i	−0.0235193	+	0.0407367i	−0.877546	−	0.479493i	$-0.840820\pi$
$547$	−7037.20	+	12188.8i	−0.0235193	+	0.0407367i	0.854026	+	0.520230i	$0.174154\pi$
$548$			173318.i			0.577142i
$549$		0			0
$550$	−475486.			−1.57185
$551$	−137152.	−	79184.6i	−0.451750	−	0.260818i
$552$		0			0
$553$	−162163.	−	280875.i	−0.530276	−	0.918464i
$554$	157768.	−	91087.4i	0.514043	−	0.296783i
$555$		0			0
$556$	61753.0	−	106959.i	0.199760	−	0.345994i
$557$		−	94500.4i		−	0.304595i	−0.988335	−	0.152298i	$-0.951333\pi$
$557$		−	94500.4i		−	0.304595i	0.988335	−	0.152298i	$-0.0486672\pi$
$558$		0			0
$559$	−11572.1			−0.0370331
$560$	−205138.	−	118436.i	−0.654139	−	0.377667i
$561$		0			0
$562$	176583.	+	305851.i	0.559084	+	0.968361i
$563$	92731.3	−	53538.5i	0.292556	−	0.168908i	−0.346538	−	0.938036i	$-0.612643\pi$
$563$	92731.3	−	53538.5i	0.292556	−	0.168908i	0.639094	+	0.769129i	$0.279309\pi$
$564$		0			0
$565$	−203836.	+	353054.i	−0.638533	+	1.10597i
$566$			355810.i			1.11067i
$567$		0			0
$568$	−80478.0			−0.249448
$569$	−205997.	−	118933.i	−0.636264	−	0.367347i	0.146910	−	0.989150i	$-0.453067\pi$
$569$	−205997.	−	118933.i	−0.636264	−	0.367347i	−0.783174	+	0.621803i	$0.786401\pi$
$570$		0			0
$571$	−122284.	−	211802.i	−0.375057	−	0.649618i	0.615278	−	0.788310i	$-0.289044\pi$
$571$	−122284.	−	211802.i	−0.375057	−	0.649618i	−0.990336	+	0.138692i	$0.955710\pi$
$572$	−55054.3	+	31785.6i	−0.168267	+	0.0971491i
$573$		0			0
$574$	−57204.7	+	99081.5i	−0.173623	+	0.300724i
$575$		−	808413.i		−	2.44511i
$576$		0			0
$577$	456171.			1.37018			0.685088	−	0.728461i	$-0.259764\pi$
$577$	456171.			1.37018			0.685088	+	0.728461i	$0.259764\pi$
$578$	44016.8	+	25413.1i	0.131754	+	0.0760680i
$579$		0			0
$580$	151258.	+	261986.i	0.449636	+	0.778793i
$581$	−128843.	+	74387.3i	−0.381687	+	0.220367i
$582$		0			0
$583$	10293.2	−	17828.3i	0.0302840	−	0.0524534i
$584$		−	181209.i		−	0.531319i
$585$		0			0
$586$	−199044.			−0.579633
$587$	517042.	+	298514.i	1.50055	+	0.866341i	1.00000		0.000630751i	$0.000200774\pi$
$587$	517042.	+	298514.i	1.50055	+	0.866341i	0.500546	+	0.865710i	$0.333133\pi$
$588$		0			0
$589$	−59212.9	−	102560.i	−0.170681	−	0.295628i
$590$	203914.	−	117730.i	0.585792	−	0.338207i
$591$		0			0
$592$	75366.3	−	130538.i	0.215047	−	0.372473i
$593$		−	597802.i		−	1.70000i	−0.526785	−	0.849999i	$-0.676603\pi$
$593$		−	597802.i		−	1.70000i	0.526785	−	0.849999i	$-0.323397\pi$
$594$		0			0
$595$	947601.			2.67665
$596$	141834.	+	81888.0i	0.399290	+	0.230530i
$597$		0			0
$598$	−54041.4	−	93602.5i	−0.151121	−	0.261749i
$599$	347165.	−	200436.i	0.967570	−	0.558627i	0.0690757	−	0.997611i	$-0.477995\pi$
$599$	347165.	−	200436.i	0.967570	−	0.558627i	0.898495	+	0.438984i	$0.144662\pi$
$600$		0			0
$601$	−38616.2	+	66885.2i	−0.106910	+	0.185174i	−0.914517	−	0.404547i	$-0.867429\pi$
$601$	−38616.2	+	66885.2i	−0.106910	+	0.185174i	0.807607	+	0.589722i	$0.200762\pi$
$602$		−	37527.9i		−	0.103553i
$603$		0			0
$604$	256038.			0.701827
$605$	73502.8	+	42436.9i	0.200814	+	0.115940i
$606$		0			0
$607$	300353.	+	520227.i	0.815182	+	1.41194i	0.909197	+	0.416366i	$0.136697\pi$
$607$	300353.	+	520227.i	0.815182	+	1.41194i	−0.0940146	+	0.995571i	$0.529970\pi$
$608$	−30167.5	+	17417.2i	−0.0816078	+	0.0471163i
$609$		0			0
$610$	−185835.	+	321876.i	−0.499423	+	0.865026i
$611$			73150.1i			0.195944i
$612$		0			0
$613$	211376.			0.562516			0.281258	−	0.959632i	$-0.409248\pi$
$613$	211376.			0.562516			0.281258	+	0.959632i	$0.409248\pi$
$614$	−65622.3	−	37887.1i	−0.174066	−	0.100497i
$615$		0			0
$616$	−103079.	−	178538.i	−0.271650	−	0.470511i
$617$	−327641.	+	189164.i	−0.860653	+	0.496898i	−0.864231	−	0.503095i	$-0.832194\pi$
$617$	−327641.	+	189164.i	−0.860653	+	0.496898i	0.00357801	+	0.999994i	$0.498861\pi$
$618$		0			0
$619$	245962.	−	426018.i	0.641927	−	1.11185i	−0.343075	−	0.939308i	$-0.611468\pi$
$619$	245962.	−	426018.i	0.641927	−	1.11185i	0.985002	−	0.172543i	$-0.0551983\pi$
$620$			226216.i			0.588490i
$621$		0			0
$622$	−361698.			−0.934900
$623$	−293313.	−	169344.i	−0.755710	−	0.436309i
$624$		0			0
$625$	−444704.	−	770249.i	−1.13844	−	1.97184i
$626$	−23427.5	+	13525.8i	−0.0597828	+	0.0345156i
$627$		0			0
$628$	−96828.6	+	167712.i	−0.245519	+	0.425251i
$629$			603000.i			1.52411i
$630$		0			0
$631$	−64515.4			−0.162033			−0.0810167	−	0.996713i	$-0.525817\pi$
$631$	−64515.4			−0.162033			−0.0810167	+	0.996713i	$0.525817\pi$
$632$	78900.9	+	45553.5i	0.197537	+	0.114048i
$633$		0			0
$634$	55145.7	+	95515.2i	0.137193	+	0.237626i
$635$	617146.	−	356310.i	1.53053	−	0.883650i
$636$		0			0
$637$	−143574.	+	248678.i	−0.353833	+	0.612856i
$638$			263289.i			0.646832i
$639$		0			0
$640$	66540.3			0.162452
$641$	372051.	+	214804.i	0.905495	+	0.522788i	0.878979	−	0.476861i	$-0.158225\pi$
$641$	372051.	+	214804.i	0.905495	+	0.522788i	0.0265161	+	0.999648i	$0.491559\pi$
$642$		0			0
$643$	−250475.	−	433835.i	−0.605818	−	1.04931i	−0.991922	−	0.126852i	$-0.959513\pi$
$643$	−250475.	−	433835.i	−0.605818	−	1.04931i	0.386103	−	0.922456i	$-0.373821\pi$
$644$	303548.	−	175254.i	0.731907	−	0.422567i
$645$		0			0
$646$	69676.8	−	120684.i	0.166964	−	0.289191i
$647$			175906.i			0.420216i	0.977678	+	0.210108i	$0.0673815\pi$
$647$			175906.i			0.420216i	−0.977678	+	0.210108i	$0.932618\pi$
$648$		0			0
$649$	204929.			0.486534
$650$	−255763.	−	147665.i	−0.605356	−	0.349503i
$651$		0			0
$652$	84364.1	+	146123.i	0.198455	+	0.343735i
$653$	−45516.4	+	26278.9i	−0.106744	+	0.0616284i	−0.552421	−	0.833565i	$-0.686296\pi$
$653$	−45516.4	+	26278.9i	−0.106744	+	0.0616284i	0.445678	+	0.895193i	$0.352963\pi$
$654$		0			0
$655$	312368.	−	541037.i	0.728087	−	1.26108i
$656$		−	32138.9i		−	0.0746833i
$657$		0			0
$658$	−237222.			−0.547902
$659$	−330751.	−	190959.i	−0.761607	−	0.439714i	0.0682654	−	0.997667i	$-0.478254\pi$
$659$	−330751.	−	190959.i	−0.761607	−	0.439714i	−0.829872	+	0.557953i	$0.811587\pi$
$660$		0			0
$661$	−355620.	−	615952.i	−0.813923	−	1.40976i	−0.910099	−	0.414392i	$-0.863994\pi$
$661$	−355620.	−	615952.i	−0.813923	−	1.40976i	0.0961753	−	0.995364i	$-0.469339\pi$
$662$	−123538.	+	71324.8i	−0.281893	+	0.162751i
$663$		0			0
$664$	20896.2	−	36193.4i	0.0473949	−	0.0820905i
$665$			712227.i			1.61055i
$666$		0			0
$667$	−447640.			−1.00618
$668$	89840.7	+	51869.6i	0.201336	+	0.116241i
$669$		0			0
$670$	−578059.	−	1.00123e6i	−1.28772	−	2.23040i
$671$	−280139.	+	161739.i	−0.622199	+	0.359227i
$672$		0			0
$673$	85387.1	−	147895.i	0.188522	−	0.326530i	−0.756236	−	0.654299i	$-0.772964\pi$
$673$	85387.1	−	147895.i	0.188522	−	0.326530i	0.944758	+	0.327770i	$0.106297\pi$
$674$			360268.i			0.793060i
$675$		0			0
$676$	189003.			0.413595
$677$	−223906.	−	129272.i	−0.488527	−	0.282051i	0.235436	−	0.971890i	$-0.424348\pi$
$677$	−223906.	−	129272.i	−0.488527	−	0.282051i	−0.723963	+	0.689839i	$0.757681\pi$
$678$		0			0
$679$	531099.	+	919890.i	1.15196	+	1.99524i
$680$	−230529.	+	133096.i	−0.498549	+	0.287837i
$681$		0			0
$682$	−98441.6	+	170506.i	−0.211646	+	0.366581i
$683$			402556.i			0.862948i	0.902125	+	0.431474i	$0.142006\pi$
$683$			402556.i			0.862948i	−0.902125	+	0.431474i	$0.857994\pi$
$684$		0			0
$685$	−995459.			−2.12150
$686$	−332718.	−	192095.i	−0.707013	−	0.408194i
$687$		0			0
$688$	5271.01	+	9129.65i	0.0111357	+	0.0192876i
$689$	11073.4	−	6393.23i	0.0233261	−	0.0134673i
$690$		0			0
$691$	−39761.5	+	68869.0i	−0.0832735	+	0.144234i	−0.904654	−	0.426146i	$-0.859871\pi$
$691$	−39761.5	+	68869.0i	−0.0832735	+	0.144234i	0.821381	+	0.570380i	$0.193204\pi$
$692$		−	334229.i		−	0.697962i
$693$		0			0
$694$	548197.			1.13820
$695$	614325.	+	354681.i	1.27183	+	0.734291i
$696$		0			0
$697$	64285.3	+	111345.i	0.132326	+	0.229196i
$698$	−254916.	+	147176.i	−0.523221	+	0.302082i
$699$		0			0
$700$	478870.	−	829426.i	0.977285	−	1.69271i
$701$			371798.i			0.756609i	0.925681	+	0.378305i	$0.123493\pi$
$701$			371798.i			0.756609i	−0.925681	+	0.378305i	$0.876507\pi$
$702$		0			0
$703$	−453221.			−0.917064
$704$	50153.5	+	28956.1i	0.101194	+	0.0584245i
$705$		0			0
$706$	227368.	+	393813.i	0.456163	+	0.790098i
$707$	696906.	−	402359.i	1.39423	−	0.804960i
$708$		0			0
$709$	466603.	−	808180.i	0.928228	−	1.60774i	0.141944	−	0.989875i	$-0.454665\pi$
$709$	466603.	−	808180.i	0.928228	−	1.60774i	0.786285	−	0.617864i	$-0.212002\pi$
$710$		−	462229.i		−	0.916939i
$711$		0			0
$712$	95141.6			0.187677
$713$	−289891.	−	167369.i	−0.570238	−	0.329227i
$714$		0			0
$715$	−182562.	−	316207.i	−0.357107	−	0.618528i
$716$	92065.8	−	53154.2i	0.179586	−	0.103684i
$717$		0			0
$718$	30796.0	−	53340.2i	0.0597372	−	0.103468i
$719$			180424.i			0.349010i	0.984656	+	0.174505i	$0.0558325\pi$
$719$			180424.i			0.349010i	−0.984656	+	0.174505i	$0.944168\pi$
$720$		0			0
$721$	264122.			0.508083
$722$	−228513.	−	131932.i	−0.438365	−	0.253090i
$723$		0			0
$724$	−115643.	−	200300.i	−0.220619	−	0.382123i
$725$	−1.05928e6	+	611575.i	−2.01527	+	1.16352i
$726$		0			0
$727$	227624.	−	394257.i	0.430675	−	0.745951i	−0.566256	−	0.824229i	$-0.691609\pi$
$727$	227624.	−	394257.i	0.430675	−	0.745951i	0.996932	+	0.0782779i	$0.0249421\pi$
$728$		−	128047.i		−	0.241606i
$729$		0			0
$730$	1.04078e6			1.95306
$731$	−36522.9	−	21086.5i	−0.0683486	−	0.0394611i
$732$		0			0
$733$	−275019.	−	476347.i	−0.511864	−	0.886575i	−0.999905	−	0.0137544i	$-0.995622\pi$
$733$	−275019.	−	476347.i	−0.511864	−	0.886575i	0.488041	−	0.872821i	$-0.337712\pi$
$734$	617187.	−	356333.i	1.14558	−	0.661399i
$735$		0			0
$736$	−49230.8	+	85270.2i	−0.0908826	+	0.157413i
$737$		−	1.00621e6i		−	1.85248i
$738$		0			0
$739$	663313.			1.21459			0.607295	−	0.794477i	$-0.292255\pi$
$739$	663313.			1.21459			0.607295	+	0.794477i	$0.292255\pi$
$740$	749752.	+	432869.i	1.36916	+	0.790485i
$741$		0			0
$742$	20732.9	+	35910.5i	0.0376576	+	0.0652249i
$743$	279153.	−	161169.i	0.505666	−	0.291947i	−0.225384	−	0.974270i	$-0.572364\pi$
$743$	279153.	−	161169.i	0.505666	−	0.291947i	0.731050	+	0.682323i	$0.239030\pi$
$744$		0			0
$745$	−470327.	+	814630.i	−0.847398	+	1.46774i
$746$		−	362112.i		−	0.650677i
$747$		0			0
$748$	−231676.			−0.414074
$749$	−1.45959e6	−	842692.i	−2.60175	−	1.50212i
$750$		0			0
$751$	−164336.	−	284638.i	−0.291375	−	0.504677i	0.682760	−	0.730643i	$-0.260780\pi$
$751$	−164336.	−	284638.i	−0.291375	−	0.504677i	−0.974135	+	0.225966i	$0.927446\pi$
$752$	57710.5	−	33319.2i	0.102052	−	0.0589195i
$753$		0			0
$754$	−81766.0	+	141623.i	−0.143824	+	0.249110i
$755$			1.47056e6i			2.57982i
$756$		0			0
$757$	530625.			0.925968			0.462984	−	0.886367i	$-0.346779\pi$
$757$	530625.			0.925968			0.462984	+	0.886367i	$0.346779\pi$
$758$	227797.	+	131518.i	0.396468	+	0.228901i
$759$		0			0
$760$	−100036.	−	173268.i	−0.173193	−	0.299979i
$761$	940741.	−	543137.i	1.62443	−	0.937864i	0.638713	−	0.769445i	$-0.279467\pi$
$761$	940741.	−	543137.i	1.62443	−	0.937864i	0.985715	−	0.168420i	$-0.0538664\pi$
$762$		0			0
$763$	134550.	−	233047.i	0.231118	−	0.400308i
$764$		−	402872.i		−	0.690209i
$765$		0			0
$766$	−787130.			−1.34150
$767$	110231.	+	63641.7i	0.187375	+	0.108181i
$768$		0			0
$769$	320037.	+	554320.i	0.541187	+	0.937364i	0.998836	+	0.0482307i	$0.0153583\pi$
$769$	320037.	+	554320.i	0.541187	+	0.937364i	−0.457649	+	0.889133i	$0.651308\pi$
$770$	1.02544e6	−	592040.i	1.72954	−	0.998549i
$771$		0			0
$772$	−13864.1	+	24013.3i	−0.0232625	+	0.0402918i
$773$		−	924647.i		−	1.54745i	−0.633521	−	0.773726i	$-0.718391\pi$
$773$		−	924647.i		−	1.54745i	0.633521	−	0.773726i	$-0.281609\pi$
$774$		0			0
$775$	−914650.			−1.52283
$776$	−258408.	−	149192.i	−0.429123	−	0.247754i
$777$		0			0
$778$	−196467.	−	340291.i	−0.324587	−	0.562201i
$779$	−83688.4	+	48317.5i	−0.137908	+	0.0796213i
$780$		0			0
$781$	201147.	−	348396.i	0.329770	−	0.571178i
$782$		−	393892.i		−	0.644115i
$783$		0			0
$784$	261587.			0.425583
$785$	−963261.	−	556139.i	−1.56317	−	0.902494i
$786$		0			0
$787$	−226727.	−	392703.i	−0.366062	−	0.634037i	0.622884	−	0.782314i	$-0.285961\pi$
$787$	−226727.	−	392703.i	−0.366062	−	0.634037i	−0.988946	+	0.148277i	$0.952627\pi$
$788$	−54135.3	+	31255.0i	−0.0871822	+	0.0503347i
$789$		0			0
$790$	−261638.	+	453171.i	−0.419225	+	0.726119i
$791$		−	714670.i		−	1.14223i
$792$		0			0
$793$	−200915.			−0.319497
$794$	−4312.80	−	2490.00i	−0.00684099	−	0.00394965i
$795$		0			0
$796$	116613.	+	201980.i	0.184044	+	0.318773i
$797$	−828944.	+	478591.i	−1.30499	+	0.753439i	−0.981256	−	0.192707i	$-0.938273\pi$
$797$	−828944.	+	478591.i	−1.30499	+	0.753439i	−0.323739	+	0.946147i	$0.604940\pi$
$798$		0			0
$799$	−133292.	+	230869.i	−0.208791	+	0.361636i
$800$			269040.i			0.420375i
$801$		0			0
$802$	−116129.			−0.180548
$803$	784471.	+	452915.i	1.21659	+	0.702401i
$804$		0			0
$805$	1.00658e6	+	1.74344e6i	1.55330	+	2.69039i
$806$	−105903.	+	61143.2i	−0.163019	+	0.0941192i
$807$		0			0
$808$	−113027.	+	195769.i	−0.173125	+	0.299862i
$809$			464039.i			0.709018i	0.935053	+	0.354509i	$0.115352\pi$
$809$			464039.i			0.709018i	−0.935053	+	0.354509i	$0.884648\pi$
$810$		0			0
$811$	−732128.			−1.11313			−0.556564	−	0.830804i	$-0.687881\pi$
$811$	−732128.			−1.11313			−0.556564	+	0.830804i	$0.687881\pi$
$812$	−459276.	−	265163.i	−0.696565	−	0.402162i
$813$		0			0
$814$	376741.	+	652534.i	0.568583	+	0.984815i
$815$	−839263.	+	484549.i	−1.26352	+	0.729495i
$816$		0			0
$817$	15848.8	−	27450.9i	0.0237439	−	0.0411257i
$818$			471537.i			0.704708i
$819$		0			0
$820$	184591.			0.274526
$821$	1.09670e6	+	633181.i	1.62705	+	0.939381i	0.984966	+	0.172751i	$0.0552655\pi$
$821$	1.09670e6	+	633181.i	1.62705	+	0.939381i	0.642089	+	0.766630i	$0.278068\pi$
$822$		0			0
$823$	86129.2	+	149180.i	0.127160	+	0.220248i	0.922575	−	0.385817i	$-0.126080\pi$
$823$	86129.2	+	149180.i	0.127160	+	0.220248i	−0.795415	+	0.606065i	$0.792747\pi$
$824$	−64254.7	+	37097.5i	−0.0946348	+	0.0546374i
$825$		0			0
$826$	−206387.	+	357473.i	−0.302498	+	0.523942i
$827$			135383.i			0.197949i	0.995090	+	0.0989746i	$0.0315563\pi$
$827$			135383.i			0.197949i	−0.995090	+	0.0989746i	$0.968444\pi$
$828$		0			0
$829$	290151.			0.422197			0.211099	−	0.977465i	$-0.432296\pi$
$829$	290151.			0.422197			0.211099	+	0.977465i	$0.432296\pi$
$830$	207878.	+	120018.i	0.301754	+	0.174218i
$831$		0			0
$832$	17985.0	+	31150.9i	0.0259815	+	0.0450012i
$833$	−906270.	+	523235.i	−1.30607	+	0.754062i
$834$		0			0
$835$	−297915.	+	516004.i	−0.427287	+	0.740083i
$836$		−	174130.i		−	0.249150i
$837$		0			0
$838$	−938212.			−1.33602
$839$	463122.	+	267383.i	0.657917	+	0.379849i	0.791483	−	0.611191i	$-0.209309\pi$
$839$	463122.	+	267383.i	0.657917	+	0.379849i	−0.133566	+	0.991040i	$0.542643\pi$
$840$		0			0
$841$	−14995.1	−	25972.3i	−0.0212010	−	0.0367213i
$842$	460080.	−	265627.i	0.648947	−	0.374670i
$843$		0			0
$844$	−188632.	+	326720.i	−0.264808	+	0.458660i
$845$			1.08555e6i			1.52032i
$846$		0			0
$847$	−148788.			−0.207397
$848$	−10087.7	−	5824.11i	−0.0140281	−	0.00809913i
$849$		0			0
$850$	−538142.	−	932090.i	−0.744834	−	1.29009i
$851$	−1.10943e6	+	640529.i	−1.53193	+	0.884463i
$852$		0			0
$853$	469672.	−	813495.i	0.645500	−	1.11804i	−0.338686	−	0.940900i	$-0.609982\pi$
$853$	469672.	−	813495.i	0.645500	−	1.11804i	0.984186	−	0.177139i	$-0.0566843\pi$
$854$		−	651559.i		−	0.893383i
$855$		0			0
$856$	473444.			0.646132
$857$	−581553.	−	335760.i	−0.791823	−	0.457159i	0.0487812	−	0.998809i	$-0.484466\pi$
$857$	−581553.	−	335760.i	−0.791823	−	0.457159i	−0.840604	+	0.541651i	$0.817800\pi$
$858$		0			0
$859$	571382.	+	989663.i	0.774356	+	1.34122i	0.935156	+	0.354236i	$0.115259\pi$
$859$	571382.	+	989663.i	0.774356	+	1.34122i	−0.160800	+	0.986987i	$0.551408\pi$
$860$	−52436.5	+	30274.3i	−0.0708985	+	0.0409333i
$861$		0			0
$862$	9831.62	−	17028.9i	0.0132316	−	0.0229177i
$863$		−	1.09963e6i		−	1.47647i	−0.674545	−	0.738234i	$-0.735660\pi$
$863$		−	1.09963e6i		−	1.47647i	0.674545	−	0.738234i	$-0.264340\pi$
$864$		0			0
$865$	1.91966e6			2.56562
$866$	−92936.1	−	53656.7i	−0.123922	−	0.0715464i
$867$		0			0
$868$	−198284.	−	343439.i	−0.263178	−	0.455837i
$869$	−394410.	+	227713.i	−0.522286	+	0.301542i
$870$		0			0
$871$	312484.	−	541238.i	0.411900	−	0.713431i
$872$			75593.0i			0.0994143i
$873$		0			0
$874$	296053.			0.387567
$875$	2.76055e6	+	1.59380e6i	3.60561	+	2.08170i
$876$		0			0
$877$	−389866.	−	675267.i	−0.506893	−	0.877964i	−0.999968	−	0.00797718i	$-0.997461\pi$
$877$	−389866.	−	675267.i	−0.506893	−	0.877964i	0.493076	−	0.869986i	$-0.335873\pi$
$878$	−608465.	+	351297.i	−0.789308	+	0.455707i
$879$		0			0
$880$	−166311.	+	288059.i	−0.214761	+	0.371977i
$881$		−	622180.i		−	0.801611i	−0.916163	−	0.400806i	$-0.868730\pi$
$881$		−	622180.i		−	0.801611i	0.916163	−	0.400806i	$-0.131270\pi$
$882$		0			0
$883$	−1.39076e6			−1.78373			−0.891865	−	0.452301i	$-0.850603\pi$
$883$	−1.39076e6			−1.78373			−0.891865	+	0.452301i	$0.850603\pi$
$884$	−124618.	−	71948.3i	−0.159469	−	0.0920696i
$885$		0			0
$886$	230303.	+	398896.i	0.293381	+	0.508150i
$887$	829234.	−	478758.i	1.05397	−	0.608512i	0.130214	−	0.991486i	$-0.458433\pi$
$887$	829234.	−	478758.i	1.05397	−	0.608512i	0.923759	+	0.382974i	$0.125100\pi$
$888$		0			0
$889$	−624631.	+	1.08189e6i	−0.790350	+	1.36893i
$890$			546450.i			0.689874i
$891$		0			0
$892$	−80426.2			−0.101081
$893$	−173523.	−	100184.i	−0.217598	−	0.125630i
$894$		0			0
$895$	305293.	+	528784.i	0.381129	+	0.660134i
$896$	−101021.	+	58324.4i	−0.125833	+	0.0726498i
$897$		0			0
$898$	−196930.	+	341092.i	−0.244207	+	0.422980i
$899$			506466.i			0.626659i
$900$		0			0
$901$	46598.3			0.0574012
$902$	139132.	+	80328.0i	0.171007	+	0.0987311i
$903$		0			0
$904$	100380.	+	173862.i	0.122831	+	0.212750i
$905$	1.15043e6	−	664200.i	1.40463	−	0.810965i
$906$		0			0
$907$	−109786.	+	190154.i	−0.133454	+	0.231149i	−0.925006	−	0.379953i	$-0.875940\pi$
$907$	−109786.	+	190154.i	−0.133454	+	0.231149i	0.791552	+	0.611102i	$0.209273\pi$
$908$		−	239614.i		−	0.290630i
$909$		0			0
$910$	735445.			0.888112
$911$	−1.31841e6	−	761186.i	−1.58860	−	0.917179i	−0.993538	−	0.113500i	$-0.963794\pi$
$911$	−1.31841e6	−	761186.i	−1.58860	−	0.917179i	−0.595063	−	0.803679i	$-0.702873\pi$
$912$		0			0
$913$	104456.	+	180923.i	0.125312	+	0.217047i
$914$	−613693.	+	354316.i	−0.734614	+	0.424129i
$915$		0			0
$916$	−80533.8	+	139489.i	−0.0959814	+	0.166245i
$917$			1.09520e6i			1.30243i
$918$		0			0
$919$	−239088.			−0.283091			−0.141546	−	0.989932i	$-0.545207\pi$
$919$	−239088.			−0.283091			−0.141546	+	0.989932i	$0.545207\pi$
$920$	−489753.	−	282759.i	−0.578630	−	0.334072i
$921$		0			0
$922$	110572.	+	191517.i	0.130072	+	0.225292i
$923$	216393.	−	124935.i	0.254004	−	0.146649i
$924$		0			0
$925$	−1.75020e6	+	3.03144e6i	−2.04553	+	3.54296i
$926$		−	997278.i		−	1.16304i
$927$		0			0
$928$	148975.			0.172988
$929$	−31813.2	−	18367.4i	−0.0368618	−	0.0212822i	0.481456	−	0.876470i	$-0.340108\pi$
$929$	−31813.2	−	18367.4i	−0.0368618	−	0.0212822i	−0.518318	+	0.855188i	$0.673442\pi$
$930$		0			0
$931$	−393269.	−	681162.i	−0.453722	−	0.785870i
$932$	132184.	−	76316.3i	0.152176	−	0.0878589i
$933$		0			0
$934$	−54284.1	+	94022.8i	−0.0622270	+	0.107780i
$935$		−	1.33064e6i		−	1.52208i
$936$		0			0
$937$	−849585.			−0.967671			−0.483835	−	0.875159i	$-0.660757\pi$
$937$	−849585.			−0.967671			−0.483835	+	0.875159i	$0.660757\pi$
$938$	1.75521e6	+	1.01337e6i	1.99491	+	1.15176i
$939$		0			0
$940$	191370.	+	331463.i	0.216580	+	0.375128i
$941$	99837.0	−	57640.9i	0.112749	−	0.0650956i	−0.442565	−	0.896736i	$-0.645931\pi$
$941$	99837.0	−	57640.9i	0.112749	−	0.0650956i	0.555314	+	0.831641i	$0.312598\pi$
$942$		0			0
$943$	−136572.	+	236550.i	−0.153582	+	0.266011i
$944$		−	115953.i		−	0.130118i
$945$		0			0
$946$	−52697.4			−0.0588853
$947$	44274.4	+	25561.8i	0.0493688	+	0.0285031i	0.524481	−	0.851422i	$-0.324259\pi$
$947$	44274.4	+	25561.8i	0.0493688	+	0.0285031i	−0.475112	+	0.879925i	$0.657593\pi$
$948$		0			0
$949$	281311.	+	487244.i	0.312359	+	0.541021i
$950$	700568.	−	404473.i	0.776253	−	0.448170i
$951$		0			0
$952$	233325.	−	404130.i	0.257446	−	0.445910i
$953$		−	407821.i		−	0.449038i	−0.974470	−	0.224519i	$-0.927919\pi$
$953$		−	407821.i		−	0.449038i	0.974470	−	0.224519i	$-0.0720812\pi$
$954$		0			0
$955$	2.31391e6			2.53712
$956$	625337.	+	361038.i	0.684224	+	0.395037i
$957$		0			0
$958$	73569.1	+	127425.i	0.0801612	+	0.138843i
$959$	1.51130e6	−	872547.i	1.64328	−	0.948750i
$960$		0			0
$961$	272397.	−	471806.i	0.294955	−	0.510877i
$962$			467996.i			0.505699i
$963$		0			0
$964$	−241288.			−0.259646
$965$	−137921.	−	79628.9i	−0.148107	−	0.0855099i
$966$		0			0
$967$	−639545.	−	1.10773e6i	−0.683941	−	1.18462i	−0.973768	−	0.227541i	$-0.926931\pi$
$967$	−639545.	−	1.10773e6i	−0.683941	−	1.18462i	0.289828	−	0.957079i	$-0.406402\pi$
$968$	36196.7	−	20898.2i	0.0386294	−	0.0223027i
$969$		0			0
$970$	856889.	−	1.48417e6i	0.910712	−	1.57740i
$971$			806048.i			0.854914i	0.904036	+	0.427457i	$0.140590\pi$
$971$			806048.i			0.854914i	−0.904036	+	0.427457i	$0.859410\pi$
$972$		0			0
$973$	−1.24355e6			−1.31352
$974$	−620750.	−	358390.i	−0.654333	−	0.377780i
$975$		0			0
$976$	91515.2	+	158509.i	0.0960713	+	0.166400i
$977$	−1.18399e6	+	683577.i	−1.24039	+	0.716141i	−0.969174	−	0.246377i	$-0.920760\pi$
$977$	−1.18399e6	+	683577.i	−1.24039	+	0.716141i	−0.271219	+	0.962518i	$0.587427\pi$
$978$		0			0
$979$	−237797.	+	411876.i	−0.248108	+	0.429735i
$980$			1.50244e6i			1.56439i
$981$		0			0
$982$	516339.			0.535441
$983$	−1.25036e6	−	721898.i	−1.29399	−	0.747083i	−0.314627	−	0.949215i	$-0.601879\pi$
$983$	−1.25036e6	−	721898.i	−1.29399	−	0.747083i	−0.979358	+	0.202133i	$0.935213\pi$
$984$		0			0
$985$	−179515.	−	310928.i	−0.185024	−	0.320470i
$986$	−516123.	+	297984.i	−0.530884	+	0.306506i
$987$		0			0
$988$	54077.1	−	93664.3i	0.0553987	−	0.0959533i
$989$		−	89595.3i		−	0.0915994i
$990$		0			0
$991$	−476821.			−0.485521			−0.242761	−	0.970086i	$-0.578053\pi$
$991$	−476821.			−0.485521			−0.242761	+	0.970086i	$0.578053\pi$
$992$	96475.8	+	55700.4i	0.0980382	+	0.0566024i
$993$		0			0
$994$	405157.	+	701752.i	0.410063	+	0.710249i
$995$	−1.16008e6	+	669773.i	−1.17177	+	0.676521i
$996$		0			0
$997$	512743.	−	888097.i	0.515834	−	0.893450i	−0.483998	−	0.875069i	$-0.660816\pi$
$997$	512743.	−	888097.i	0.515834	−	0.893450i	0.999831	−	0.0183805i	$-0.00585104\pi$
$998$		−	97702.9i		−	0.0980949i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.5.d.d.107.3		8
3.2	odd	2	inner	162.5.d.d.107.2		8
9.2	odd	6		162.5.b.a.161.4	yes	4
9.4	even	3	inner	162.5.d.d.53.2		8
9.5	odd	6	inner	162.5.d.d.53.3		8
9.7	even	3		162.5.b.a.161.1	✓	4
36.7	odd	6		1296.5.e.b.161.1		4
36.11	even	6		1296.5.e.b.161.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
162.5.b.a.161.1	✓	4	9.7	even	3
162.5.b.a.161.4	yes	4	9.2	odd	6
162.5.d.d.53.2		8	9.4	even	3	inner
162.5.d.d.53.3		8	9.5	odd	6	inner
162.5.d.d.107.2		8	3.2	odd	2	inner
162.5.d.d.107.3		8	1.1	even	1	trivial
1296.5.e.b.161.1		4	36.7	odd	6
1296.5.e.b.161.4		4	36.11	even	6

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:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	162.d (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.44949 + 1.41421i) q^{2} +(4.00000 + 6.92820i) q^{4} +(-39.7924 + 22.9742i) q^{5} +(40.2750 - 69.7583i) q^{7} +22.6274i q^{8} +O(q^{10})\)	\(q+(2.44949 + 1.41421i) q^{2} +(4.00000 + 6.92820i) q^{4} +(-39.7924 + 22.9742i) q^{5} +(40.2750 - 69.7583i) q^{7} +22.6274i q^{8} -129.962 q^{10} +(-97.9560 - 56.5549i) q^{11} +(-35.1269 - 60.8416i) q^{13} +(197.306 - 113.915i) q^{14} +(-32.0000 + 55.4256i) q^{16} -256.030i q^{17} +192.435 q^{19} +(-318.339 - 183.793i) q^{20} +(-159.962 - 277.061i) q^{22} +(471.056 - 271.964i) q^{23} +(743.125 - 1287.13i) q^{25} -198.708i q^{26} +644.400 q^{28} +(-712.719 - 411.488i) q^{29} +(-307.704 - 532.959i) q^{31} +(-156.767 + 90.5097i) q^{32} +(362.081 - 627.142i) q^{34} +3701.14i q^{35} -2355.20 q^{37} +(471.366 + 272.144i) q^{38} +(-519.846 - 900.400i) q^{40} +(-434.893 + 251.085i) q^{41} +(82.3595 - 142.651i) q^{43} -904.879i q^{44} +1538.46 q^{46} +(-901.727 - 520.613i) q^{47} +(-2043.65 - 3539.71i) q^{49} +(3640.55 - 2101.87i) q^{50} +(281.015 - 486.733i) q^{52} +182.004i q^{53} +5197.21 q^{55} +(1578.45 + 911.319i) q^{56} +(-1163.86 - 2015.87i) q^{58} +(-1569.03 + 905.882i) q^{59} +(1429.92 - 2476.70i) q^{61} -1740.64i q^{62} -512.000 q^{64} +(2795.57 + 1614.02i) q^{65} +(4447.92 + 7704.03i) q^{67} +(1773.83 - 1024.12i) q^{68} +(-5234.20 + 9065.90i) q^{70} +3556.66i q^{71} -8008.40 q^{73} +(-5769.03 - 3330.75i) q^{74} +(769.738 + 1333.23i) q^{76} +(-7890.36 + 4555.50i) q^{77} +(2013.20 - 3486.96i) q^{79} -2940.69i q^{80} -1420.35 q^{82} +(-1599.54 - 923.492i) q^{83} +(5882.07 + 10188.0i) q^{85} +(403.477 - 232.948i) q^{86} +(1279.69 - 2216.49i) q^{88} -4204.70i q^{89} -5658.95 q^{91} +(3768.44 + 2175.71i) q^{92} +(-1472.51 - 2550.47i) q^{94} +(-7657.44 + 4421.02i) q^{95} +(-6593.40 + 11420.1i) q^{97} -11560.6i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 32 q^{4} + 52 q^{7}+O(q^{10}) \) 8 * q + 32 * q^4 + 52 * q^7	\( 8 q + 32 q^{4} + 52 q^{7} - 624 q^{10} - 572 q^{13} - 256 q^{16} - 248 q^{19} - 864 q^{22} + 1892 q^{25} + 832 q^{28} - 3584 q^{31} + 1608 q^{34} - 18800 q^{37} - 2496 q^{40} - 3020 q^{43} - 4320 q^{46} - 9324 q^{49} + 4576 q^{52} + 22248 q^{55} + 2952 q^{58} + 4144 q^{61} - 4096 q^{64} + 12076 q^{67} - 18096 q^{70} - 3584 q^{73} - 992 q^{76} + 15004 q^{79} + 10752 q^{82} + 24048 q^{85} + 6912 q^{88} + 24440 q^{91} + 12912 q^{94} - 46304 q^{97}+O(q^{100}) \) 8 * q + 32 * q^4 + 52 * q^7 - 624 * q^10 - 572 * q^13 - 256 * q^16 - 248 * q^19 - 864 * q^22 + 1892 * q^25 + 832 * q^28 - 3584 * q^31 + 1608 * q^34 - 18800 * q^37 - 2496 * q^40 - 3020 * q^43 - 4320 * q^46 - 9324 * q^49 + 4576 * q^52 + 22248 * q^55 + 2952 * q^58 + 4144 * q^61 - 4096 * q^64 + 12076 * q^67 - 18096 * q^70 - 3584 * q^73 - 992 * q^76 + 15004 * q^79 + 10752 * q^82 + 24048 * q^85 + 6912 * q^88 + 24440 * q^91 + 12912 * q^94 - 46304 * q^97

Introduction

L-functions

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Database

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