LMFDB - Embedded newform 126.5.c.a.55.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [126,5,Mod(55,126)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("126.55"); S:= CuspForms(chi, 5); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(126, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 5, names="a")

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	126.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,0,32,0,0,-76] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$13.0246153486$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.0.1308672.3
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 72x^{2} + 1278 $ x^4 + 72*x^2 + 1278
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 14)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			55.4
Root			$-6.34371i$ of defining polynomial
Character	$\chi$	$=$	126.55
Dual form			126.5.c.a.55.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.82843 q^{2} +8.00000 q^{4} +23.1980i q^{5} +(6.45584 + 48.5729i) q^{7} +22.6274 q^{8} +65.6139i q^{10} -191.823 q^{11} -48.5729i q^{13} +(18.2599 + 137.385i) q^{14} +64.0000 q^{16} +181.977i q^{17} +599.915i q^{19} +185.584i q^{20} -542.558 q^{22} +469.529 q^{23} +86.8519 q^{25} -137.385i q^{26} +(51.6468 + 388.583i) q^{28} +338.881 q^{29} +267.556i q^{31} +181.019 q^{32} +514.710i q^{34} +(-1126.79 + 149.763i) q^{35} -668.530 q^{37} +1696.82i q^{38} +524.911i q^{40} -1323.85i q^{41} +1940.23 q^{43} -1534.59 q^{44} +1328.03 q^{46} -2936.89i q^{47} +(-2317.64 + 627.158i) q^{49} +245.654 q^{50} -388.583i q^{52} +1460.94 q^{53} -4449.92i q^{55} +(146.079 + 1099.08i) q^{56} +958.501 q^{58} +1730.83i q^{59} +246.343i q^{61} +756.763i q^{62} +512.000 q^{64} +1126.79 q^{65} -1076.59 q^{67} +1455.82i q^{68} +(-3187.05 + 423.593i) q^{70} +2276.39 q^{71} -7106.94i q^{73} -1890.89 q^{74} +4799.32i q^{76} +(-1238.38 - 9317.41i) q^{77} +7012.38 q^{79} +1484.67i q^{80} -3744.40i q^{82} +1448.36i q^{83} -4221.52 q^{85} +5487.81 q^{86} -4340.47 q^{88} +2133.73i q^{89} +(2359.32 - 313.579i) q^{91} +3756.23 q^{92} -8306.77i q^{94} -13916.8 q^{95} -5898.76i q^{97} +(-6555.29 + 1773.87i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 32 q^{4} - 76 q^{7} - 360 q^{11} + 288 q^{14} + 256 q^{16} - 1152 q^{22} + 792 q^{23} - 2300 q^{25} - 608 q^{28} - 1224 q^{29} - 4032 q^{35} - 3896 q^{37} + 3688 q^{43} - 2880 q^{44} + 3072 q^{46}+ \cdots - 21888 q^{98}+O(q^{100}) $ 4 * q + 32 * q^4 - 76 * q^7 - 360 * q^11 + 288 * q^14 + 256 * q^16 - 1152 * q^22 + 792 * q^23 - 2300 * q^25 - 608 * q^28 - 1224 * q^29 - 4032 * q^35 - 3896 * q^37 + 3688 * q^43 - 2880 * q^44 + 3072 * q^46 - 1532 * q^49 + 7488 * q^50 - 5832 * q^53 + 2304 * q^56 + 7296 * q^58 + 2048 * q^64 + 4032 * q^65 - 1048 * q^67 - 1344 * q^70 + 21528 * q^71 + 3456 * q^74 - 3528 * q^77 + 12776 * q^79 + 16512 * q^85 + 11520 * q^86 - 9216 * q^88 + 5568 * q^91 + 6336 * q^92 - 36864 * q^95 - 21888 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$1$	$-1$

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 $

$2$	2.82843			0.707107
$2$	2.82843			0.707107
$3$		0			0
$3$		0			0
$4$	8.00000			0.500000
$5$			23.1980i			0.927921i	0.885856	+	0.463960i	$0.153572\pi$
$5$			23.1980i			0.927921i	−0.885856	+	0.463960i	$0.846428\pi$
$6$		0			0
$7$	6.45584	+	48.5729i	0.131752	+	0.991283i
$7$	6.45584	+	48.5729i	0.131752	+	0.991283i
$8$	22.6274			0.353553
$9$		0			0
$10$			65.6139i			0.656139i
$11$	−191.823			−1.58532			−0.792659	−	0.609666i	$-0.791304\pi$
$11$	−191.823			−1.58532			−0.792659	+	0.609666i	$0.791304\pi$
$12$		0			0
$13$		−	48.5729i		−	0.287413i	−0.989620	−	0.143707i	$-0.954098\pi$
$13$		−	48.5729i		−	0.287413i	0.989620	−	0.143707i	$-0.0459022\pi$
$14$	18.2599	+	137.385i	0.0931627	+	0.700943i
$15$		0			0
$16$	64.0000			0.250000
$17$			181.977i			0.629680i	0.949145	+	0.314840i	$0.101951\pi$
$17$			181.977i			0.629680i	−0.949145	+	0.314840i	$0.898049\pi$
$18$		0			0
$19$			599.915i			1.66182i	0.556410	+	0.830908i	$0.312178\pi$
$19$			599.915i			1.66182i	−0.556410	+	0.830908i	$0.687822\pi$
$20$			185.584i			0.463960i
$21$		0			0
$22$	−542.558			−1.12099
$23$	469.529			0.887578			0.443789	−	0.896131i	$-0.353634\pi$
$23$	469.529			0.887578			0.443789	+	0.896131i	$0.353634\pi$
$24$		0			0
$25$	86.8519			0.138963
$26$		−	137.385i		−	0.203232i
$27$		0			0
$28$	51.6468	+	388.583i	0.0658760	+	0.495641i
$29$	338.881			0.402951			0.201475	−	0.979494i	$-0.435426\pi$
$29$	338.881			0.402951			0.201475	+	0.979494i	$0.435426\pi$
$30$		0			0
$31$			267.556i			0.278414i	0.990263	+	0.139207i	$0.0444554\pi$
$31$			267.556i			0.278414i	−0.990263	+	0.139207i	$0.955545\pi$
$32$	181.019			0.176777
$33$		0			0
$34$			514.710i			0.445251i
$35$	−1126.79	+	149.763i	−0.919832	+	0.122255i
$36$		0			0
$37$	−668.530			−0.488334			−0.244167	−	0.969733i	$-0.578515\pi$
$37$	−668.530			−0.488334			−0.244167	+	0.969733i	$0.578515\pi$
$38$			1696.82i			1.17508i
$39$		0			0
$40$			524.911i			0.328070i
$41$		−	1323.85i		−	0.787534i	−0.919210	−	0.393767i	$-0.871172\pi$
$41$		−	1323.85i		−	0.787534i	0.919210	−	0.393767i	$-0.128828\pi$
$42$		0			0
$43$	1940.23			1.04934			0.524671	−	0.851305i	$-0.324188\pi$
$43$	1940.23			1.04934			0.524671	+	0.851305i	$0.324188\pi$
$44$	−1534.59			−0.792659
$45$		0			0
$46$	1328.03			0.627613
$47$		−	2936.89i		−	1.32951i	−0.747062	−	0.664755i	$-0.768536\pi$
$47$		−	2936.89i		−	1.32951i	0.747062	−	0.664755i	$-0.231464\pi$
$48$		0			0
$49$	−2317.64	+	627.158i	−0.965283	+	0.261207i
$50$	245.654			0.0982618
$51$		0			0
$52$		−	388.583i		−	0.143707i
$53$	1460.94			0.520091			0.260046	−	0.965596i	$-0.416262\pi$
$53$	1460.94			0.520091			0.260046	+	0.965596i	$0.416262\pi$
$54$		0			0
$55$		−	4449.92i		−	1.47105i
$56$	146.079	+	1099.08i	0.0465813	+	0.350471i
$57$		0			0
$58$	958.501			0.284929
$59$			1730.83i			0.497223i	0.968603	+	0.248612i	$0.0799743\pi$
$59$			1730.83i			0.497223i	−0.968603	+	0.248612i	$0.920026\pi$
$60$		0			0
$61$			246.343i			0.0662034i	0.999452	+	0.0331017i	$0.0105385\pi$
$61$			246.343i			0.0662034i	−0.999452	+	0.0331017i	$0.989461\pi$
$62$			756.763i			0.196869i
$63$		0			0
$64$	512.000			0.125000
$65$	1126.79			0.266697
$66$		0			0
$67$	−1076.59			−0.239828			−0.119914	−	0.992784i	$-0.538262\pi$
$67$	−1076.59			−0.239828			−0.119914	+	0.992784i	$0.538262\pi$
$68$			1455.82i			0.314840i
$69$		0			0
$70$	−3187.05	+	423.593i	−0.650419	+	0.0864476i
$71$	2276.39			0.451574			0.225787	−	0.974177i	$-0.427505\pi$
$71$	2276.39			0.451574			0.225787	+	0.974177i	$0.427505\pi$
$72$		0			0
$73$		−	7106.94i		−	1.33363i	−0.745221	−	0.666817i	$-0.767656\pi$
$73$		−	7106.94i		−	1.33363i	0.745221	−	0.666817i	$-0.232344\pi$
$74$	−1890.89			−0.345305
$75$		0			0
$76$			4799.32i			0.830908i
$77$	−1238.38	−	9317.41i	−0.208869	−	1.57150i
$78$		0			0
$79$	7012.38			1.12360			0.561799	−	0.827274i	$-0.310109\pi$
$79$	7012.38			1.12360			0.561799	+	0.827274i	$0.310109\pi$
$80$			1484.67i			0.231980i
$81$		0			0
$82$		−	3744.40i		−	0.556871i
$83$			1448.36i			0.210243i	0.994459	+	0.105121i	$0.0335231\pi$
$83$			1448.36i			0.210243i	−0.994459	+	0.105121i	$0.966477\pi$
$84$		0			0
$85$	−4221.52			−0.584293
$86$	5487.81			0.741997
$87$		0			0
$88$	−4340.47			−0.560494
$89$			2133.73i			0.269376i	0.990888	+	0.134688i	$0.0430032\pi$
$89$			2133.73i			0.269376i	−0.990888	+	0.134688i	$0.956997\pi$
$90$		0			0
$91$	2359.32	−	313.579i	0.284908	−	0.0378673i
$92$	3756.23			0.443789
$93$		0			0
$94$		−	8306.77i		−	0.940105i
$95$	−13916.8			−1.54203
$96$		0			0
$97$		−	5898.76i		−	0.626928i	−0.949600	−	0.313464i	$-0.898511\pi$
$97$		−	5898.76i		−	0.626928i	0.949600	−	0.313464i	$-0.101489\pi$
$98$	−6555.29	+	1773.87i	−0.682558	+	0.184701i
$99$		0			0
$100$	694.816			0.0694816
$101$		−	9172.07i		−	0.899135i	−0.893246	−	0.449567i	$-0.851578\pi$
$101$		−	9172.07i		−	0.899135i	0.893246	−	0.449567i	$-0.148422\pi$
$102$		0			0
$103$			3906.46i			0.368222i	0.982905	+	0.184111i	$0.0589406\pi$
$103$			3906.46i			0.368222i	−0.982905	+	0.184111i	$0.941059\pi$
$104$		−	1099.08i		−	0.101616i
$105$		0			0
$106$	4132.15			0.367760
$107$	12141.3			1.06047			0.530233	−	0.847852i	$-0.322104\pi$
$107$	12141.3			1.06047			0.530233	+	0.847852i	$0.322104\pi$
$108$		0			0
$109$	6808.34			0.573044			0.286522	−	0.958074i	$-0.407501\pi$
$109$	6808.34			0.573044			0.286522	+	0.958074i	$0.407501\pi$
$110$		−	12586.3i		−	1.04019i
$111$		0			0
$112$	413.174	+	3108.66i	0.0329380	+	0.247821i
$113$	4764.20			0.373107			0.186553	−	0.982445i	$-0.440268\pi$
$113$	4764.20			0.373107			0.186553	+	0.982445i	$0.440268\pi$
$114$		0			0
$115$			10892.1i			0.823602i
$116$	2711.05			0.201475
$117$		0			0
$118$			4895.54i			0.351590i
$119$	−8839.17	+	1174.82i	−0.624191	+	0.0829615i
$120$		0			0
$121$	22155.2			1.51323
$122$			696.763i			0.0468129i
$123$		0			0
$124$			2140.45i			0.139207i
$125$			16513.6i			1.05687i
$126$		0			0
$127$	−27968.9			−1.73408			−0.867038	−	0.498242i	$-0.833979\pi$
$127$	−27968.9			−1.73408			−0.867038	+	0.498242i	$0.833979\pi$
$128$	1448.15			0.0883883
$129$		0			0
$130$	3187.05			0.188583
$131$			24016.5i			1.39948i	0.714397	+	0.699741i	$0.246701\pi$
$131$			24016.5i			1.39948i	−0.714397	+	0.699741i	$0.753299\pi$
$132$		0			0
$133$	−29139.6	+	3872.96i	−1.64733	+	0.218947i
$134$	−3045.05			−0.169584
$135$		0			0
$136$			4117.68i			0.222625i
$137$	4162.00			0.221748			0.110874	−	0.993834i	$-0.464635\pi$
$137$	4162.00			0.221748			0.110874	+	0.993834i	$0.464635\pi$
$138$		0			0
$139$			26365.8i			1.36462i	0.731064	+	0.682309i	$0.239024\pi$
$139$			26365.8i			1.36462i	−0.731064	+	0.682309i	$0.760976\pi$
$140$	−9014.35	+	1198.10i	−0.459916	+	0.0611277i
$141$		0			0
$142$	6438.59			0.319311
$143$			9317.41i			0.455641i
$144$		0			0
$145$			7861.38i			0.373906i
$146$		−	20101.5i		−	0.943022i
$147$		0			0
$148$	−5348.24			−0.244167
$149$	6576.57			0.296229			0.148114	−	0.988970i	$-0.452680\pi$
$149$	6576.57			0.296229			0.148114	+	0.988970i	$0.452680\pi$
$150$		0			0
$151$	−22930.4			−1.00568			−0.502839	−	0.864380i	$-0.667711\pi$
$151$	−22930.4			−1.00568			−0.502839	+	0.864380i	$0.667711\pi$
$152$			13574.5i			0.587540i
$153$		0			0
$154$	−3502.67	−	26353.6i	−0.147692	−	1.11122i
$155$	−6206.77			−0.258346
$156$		0			0
$157$			37292.9i			1.51296i	0.654017	+	0.756480i	$0.273082\pi$
$157$			37292.9i			1.51296i	−0.654017	+	0.756480i	$0.726918\pi$
$158$	19834.0			0.794504
$159$		0			0
$160$			4199.29i			0.164035i
$161$	3031.21	+	22806.4i	0.116940	+	0.879841i
$162$		0			0
$163$	40854.0			1.53766			0.768828	−	0.639455i	$-0.220840\pi$
$163$	40854.0			1.53766			0.768828	+	0.639455i	$0.220840\pi$
$164$		−	10590.8i		−	0.393767i
$165$		0			0
$166$			4096.58i			0.148664i
$167$			34774.9i			1.24690i	0.781862	+	0.623452i	$0.214270\pi$
$167$			34774.9i			1.24690i	−0.781862	+	0.623452i	$0.785730\pi$
$168$		0			0
$169$	26201.7			0.917394
$170$	−11940.3			−0.413158
$171$		0			0
$172$	15521.9			0.524671
$173$		−	31600.1i		−	1.05583i	−0.849296	−	0.527917i	$-0.822973\pi$
$173$		−	31600.1i		−	1.05583i	0.849296	−	0.527917i	$-0.177027\pi$
$174$		0			0
$175$	560.703	+	4218.65i	0.0183087	+	0.137752i
$176$	−12276.7			−0.396329
$177$		0			0
$178$			6035.09i			0.190478i
$179$	−22750.7			−0.710048			−0.355024	−	0.934857i	$-0.615527\pi$
$179$	−22750.7			−0.710048			−0.355024	+	0.934857i	$0.615527\pi$
$180$		0			0
$181$		−	55434.4i		−	1.69208i	−0.533116	−	0.846042i	$-0.678979\pi$
$181$		−	55434.4i		−	1.69208i	0.533116	−	0.846042i	$-0.321021\pi$
$182$	6673.17	−	886.935i	0.201460	−	0.0267762i
$183$		0			0
$184$	10624.2			0.313806
$185$		−	15508.6i		−	0.453136i
$186$		0			0
$187$		−	34907.5i		−	0.998242i
$188$		−	23495.1i		−	0.664755i
$189$		0			0
$190$	−39362.8			−1.09038
$191$	50817.6			1.39299			0.696494	−	0.717562i	$-0.254742\pi$
$191$	50817.6			1.39299			0.696494	+	0.717562i	$0.254742\pi$
$192$		0			0
$193$	−1248.34			−0.0335134			−0.0167567	−	0.999860i	$-0.505334\pi$
$193$	−1248.34			−0.0335134			−0.0167567	+	0.999860i	$0.505334\pi$
$194$		−	16684.2i		−	0.443305i
$195$		0			0
$196$	−18541.2	+	5017.26i	−0.482641	+	0.130603i
$197$	−64454.6			−1.66082			−0.830408	−	0.557155i	$-0.811893\pi$
$197$	−64454.6			−1.66082			−0.830408	+	0.557155i	$0.811893\pi$
$198$		0			0
$199$		−	2352.60i		−	0.0594076i	−0.999559	−	0.0297038i	$-0.990544\pi$
$199$		−	2352.60i		−	0.0594076i	0.999559	−	0.0297038i	$-0.00945641\pi$
$200$	1965.24			0.0491309
$201$		0			0
$202$		−	25942.5i		−	0.635784i
$203$	2187.77	+	16460.4i	0.0530895	+	0.399438i
$204$		0			0
$205$	30710.6			0.730769
$206$			11049.2i			0.260372i
$207$		0			0
$208$		−	3108.66i		−	0.0718533i
$209$		−	115078.i		−	2.63450i
$210$		0			0
$211$	−65056.4			−1.46125			−0.730626	−	0.682778i	$-0.760772\pi$
$211$	−65056.4			−1.46125			−0.730626	+	0.682778i	$0.760772\pi$
$212$	11687.5			0.260046
$213$		0			0
$214$	34340.7			0.749863
$215$			45009.6i			0.973706i
$216$		0			0
$217$	−12996.0	+	1727.30i	−0.275987	+	0.0366816i
$218$	19256.9			0.405203
$219$		0			0
$220$		−	35599.4i		−	0.735524i
$221$	8839.17			0.180978
$222$		0			0
$223$			30412.4i			0.611563i	0.952102	+	0.305781i	$0.0989177\pi$
$223$			30412.4i			0.611563i	−0.952102	+	0.305781i	$0.901082\pi$
$224$	1168.63	+	8792.63i	0.0232907	+	0.175236i
$225$		0			0
$226$	13475.2			0.263826
$227$		−	52125.5i		−	1.01158i	−0.862658	−	0.505788i	$-0.831202\pi$
$227$		−	52125.5i		−	1.01158i	0.862658	−	0.505788i	$-0.168798\pi$
$228$		0			0
$229$		−	81280.2i		−	1.54994i	−0.632000	−	0.774968i	$-0.717766\pi$
$229$		−	81280.2i		−	1.54994i	0.632000	−	0.774968i	$-0.282234\pi$
$230$			30807.6i			0.582375i
$231$		0			0
$232$	7668.01			0.142465
$233$	41718.9			0.768459			0.384229	−	0.923238i	$-0.374467\pi$
$233$	41718.9			0.768459			0.384229	+	0.923238i	$0.374467\pi$
$234$		0			0
$235$	68129.9			1.23368
$236$			13846.7i			0.248612i
$237$		0			0
$238$	−25000.9	+	3322.89i	−0.441370	+	0.0586627i
$239$	3936.55			0.0689160			0.0344580	−	0.999406i	$-0.489030\pi$
$239$	3936.55			0.0689160			0.0344580	+	0.999406i	$0.489030\pi$
$240$		0			0
$241$		−	70511.5i		−	1.21402i	−0.794694	−	0.607010i	$-0.792369\pi$
$241$		−	70511.5i		−	1.21402i	0.794694	−	0.607010i	$-0.207631\pi$
$242$	62664.4			1.07002
$243$		0			0
$244$			1970.74i			0.0331017i
$245$	−14548.8	−	53764.8i	−0.242379	−	0.895706i
$246$		0			0
$247$	29139.6			0.477628
$248$			6054.11i			0.0984343i
$249$		0			0
$250$			46707.4i			0.747318i
$251$			72042.3i			1.14351i	0.820424	+	0.571755i	$0.193737\pi$
$251$			72042.3i			1.14351i	−0.820424	+	0.571755i	$0.806263\pi$
$252$		0			0
$253$	−90066.6			−1.40709
$254$	−79108.1			−1.22618
$255$		0			0
$256$	4096.00			0.0625000
$257$		−	65615.5i		−	0.993436i	−0.867912	−	0.496718i	$-0.834538\pi$
$257$		−	65615.5i		−	0.993436i	0.867912	−	0.496718i	$-0.165462\pi$
$258$		0			0
$259$	−4315.92	−	32472.4i	−0.0643390	−	0.484078i
$260$	9014.35			0.133348
$261$		0			0
$262$			67929.0i			0.989583i
$263$	38706.1			0.559588			0.279794	−	0.960060i	$-0.409734\pi$
$263$	38706.1			0.559588			0.279794	+	0.960060i	$0.409734\pi$
$264$		0			0
$265$			33890.8i			0.482604i
$266$	−82419.2	+	10954.4i	−1.16484	+	0.154819i
$267$		0			0
$268$	−8612.70			−0.119914
$269$			87226.9i			1.20544i	0.797952	+	0.602721i	$0.205917\pi$
$269$			87226.9i			1.20544i	−0.797952	+	0.602721i	$0.794083\pi$
$270$		0			0
$271$			105362.i			1.43465i	0.696739	+	0.717324i	$0.254633\pi$
$271$			105362.i			1.43465i	−0.696739	+	0.717324i	$0.745367\pi$
$272$			11646.6i			0.157420i
$273$		0			0
$274$	11771.9			0.156800
$275$	−16660.2			−0.220301
$276$		0			0
$277$	36178.9			0.471515			0.235758	−	0.971812i	$-0.424243\pi$
$277$	36178.9			0.471515			0.235758	+	0.971812i	$0.424243\pi$
$278$			74573.7i			0.964931i
$279$		0			0
$280$	−25496.4	+	3388.75i	−0.325210	+	0.0432238i
$281$	−99142.2			−1.25558			−0.627792	−	0.778381i	$-0.716041\pi$
$281$	−99142.2			−1.25558			−0.627792	+	0.778381i	$0.716041\pi$
$282$		0			0
$283$		−	4153.27i		−	0.0518581i	−0.999664	−	0.0259291i	$-0.991746\pi$
$283$		−	4153.27i		−	0.0518581i	0.999664	−	0.0259291i	$-0.00825441\pi$
$284$	18211.1			0.225787
$285$		0			0
$286$			26353.6i			0.322187i
$287$	64302.9	−	8546.54i	0.780669	−	0.103759i
$288$		0			0
$289$	50405.2			0.603503
$290$			22235.3i			0.264392i
$291$		0			0
$292$		−	56855.5i		−	0.666817i
$293$			20239.4i			0.235756i	0.993028	+	0.117878i	$0.0376092\pi$
$293$			20239.4i			0.235756i	−0.993028	+	0.117878i	$0.962391\pi$
$294$		0			0
$295$	−40151.9			−0.461384
$296$	−15127.1			−0.172652
$297$		0			0
$298$	18601.3			0.209465
$299$		−	22806.4i		−	0.255102i
$300$		0			0
$301$	12525.8	+	94242.7i	0.138253	+	1.04019i
$302$	−64857.1			−0.711121
$303$		0			0
$304$			38394.6i			0.415454i
$305$	−5714.66			−0.0614315
$306$		0			0
$307$			63269.8i			0.671305i	0.941986	+	0.335652i	$0.108957\pi$
$307$			63269.8i			0.671305i	−0.941986	+	0.335652i	$0.891043\pi$
$308$	−9907.05	−	74539.3i	−0.104434	−	0.785749i
$309$		0			0
$310$	−17555.4			−0.182679
$311$			14375.4i			0.148627i	0.997235	+	0.0743137i	$0.0236766\pi$
$311$			14375.4i			0.148627i	−0.997235	+	0.0743137i	$0.976323\pi$
$312$		0			0
$313$			36763.0i			0.375252i	0.982241	+	0.187626i	$0.0600792\pi$
$313$			36763.0i			0.375252i	−0.982241	+	0.187626i	$0.939921\pi$
$314$			105480.i			1.06982i
$315$		0			0
$316$	56099.0			0.561799
$317$	125556.			1.24945			0.624726	−	0.780844i	$-0.285211\pi$
$317$	125556.			1.24945			0.624726	+	0.780844i	$0.285211\pi$
$318$		0			0
$319$	−65005.4			−0.638804
$320$			11877.4i			0.115990i
$321$		0			0
$322$	8573.55	+	64506.1i	0.0826892	+	0.622142i
$323$	−109171.			−1.04641
$324$		0			0
$325$		−	4218.65i		−	0.0399399i
$326$	115553.			1.08729
$327$		0			0
$328$		−	29955.2i		−	0.278435i
$329$	142653.	−	18960.1i	1.31792	−	0.175165i
$330$		0			0
$331$	5376.54			0.0490735			0.0245367	−	0.999699i	$-0.492189\pi$
$331$	5376.54			0.0490735			0.0245367	+	0.999699i	$0.492189\pi$
$332$			11586.9i			0.105121i
$333$		0			0
$334$			98358.3i			0.881694i
$335$		−	24974.7i		−	0.222541i
$336$		0			0
$337$	2202.27			0.0193914			0.00969572	−	0.999953i	$-0.496914\pi$
$337$	2202.27			0.0193914			0.00969572	+	0.999953i	$0.496914\pi$
$338$	74109.5			0.648695
$339$		0			0
$340$	−33772.1			−0.292146
$341$		−	51323.5i		−	0.441375i
$342$		0			0
$343$	−45425.2	−	108526.i	−0.386108	−	0.922454i
$344$	43902.5			0.370998
$345$		0			0
$346$		−	89378.5i		−	0.746587i
$347$	−222201.			−1.84538			−0.922691	−	0.385541i	$-0.874015\pi$
$347$	−222201.			−1.84538			−0.922691	+	0.385541i	$0.874015\pi$
$348$		0			0
$349$		−	102679.i		−	0.843006i	−0.906827	−	0.421503i	$-0.861503\pi$
$349$		−	102679.i		−	0.843006i	0.906827	−	0.421503i	$-0.138497\pi$
$350$	1585.91	+	11932.1i	0.0129462	+	0.0974052i
$351$		0			0
$352$	−34723.7			−0.280247
$353$		−	62595.6i		−	0.502336i	−0.967943	−	0.251168i	$-0.919185\pi$
$353$		−	62595.6i		−	0.502336i	0.967943	−	0.251168i	$-0.0808147\pi$
$354$		0			0
$355$			52807.7i			0.419025i
$356$			17069.8i			0.134688i
$357$		0			0
$358$	−64348.6			−0.502080
$359$	−95505.9			−0.741040			−0.370520	−	0.928825i	$-0.620820\pi$
$359$	−95505.9			−0.741040			−0.370520	+	0.928825i	$0.620820\pi$
$360$		0			0
$361$	−229577.			−1.76163
$362$		−	156792.i		−	1.19648i
$363$		0			0
$364$	18874.6	−	2508.63i	0.142454	−	0.0189336i
$365$	164867.			1.23751
$366$		0			0
$367$		−	82330.9i		−	0.611267i	−0.952149	−	0.305633i	$-0.901132\pi$
$367$		−	82330.9i		−	0.611267i	0.952149	−	0.305633i	$-0.0988682\pi$
$368$	30049.9			0.221895
$369$		0			0
$370$		−	43864.9i		−	0.320415i
$371$	9431.58	+	70961.9i	0.0685230	+	0.515558i
$372$		0			0
$373$	130223.			0.935991			0.467995	−	0.883731i	$-0.344976\pi$
$373$	130223.			0.935991			0.467995	+	0.883731i	$0.344976\pi$
$374$		−	98733.4i		−	0.705864i
$375$		0			0
$376$		−	66454.2i		−	0.470053i
$377$		−	16460.4i		−	0.115813i
$378$		0			0
$379$	192349.			1.33909			0.669546	−	0.742770i	$-0.266489\pi$
$379$	192349.			1.33909			0.669546	+	0.742770i	$0.266489\pi$
$380$	−111335.			−0.771016
$381$		0			0
$382$	143734.			0.984992
$383$			101933.i			0.694891i	0.937700	+	0.347446i	$0.112951\pi$
$383$			101933.i			0.694891i	−0.937700	+	0.347446i	$0.887049\pi$
$384$		0			0
$385$	216145.	−	28728.0i	1.45823	−	0.193813i
$386$	−3530.84			−0.0236975
$387$		0			0
$388$		−	47190.1i		−	0.313464i
$389$	−191074.			−1.26271			−0.631353	−	0.775495i	$-0.717500\pi$
$389$	−191074.			−1.26271			−0.631353	+	0.775495i	$0.717500\pi$
$390$		0			0
$391$			85443.7i			0.558890i
$392$	−52442.3	+	14191.0i	−0.341279	+	0.0923506i
$393$		0			0
$394$	−182305.			−1.17437
$395$			162673.i			1.04261i
$396$		0			0
$397$			201143.i			1.27622i	0.769947	+	0.638108i	$0.220283\pi$
$397$			201143.i			1.27622i	−0.769947	+	0.638108i	$0.779717\pi$
$398$		−	6654.16i		−	0.0420076i
$399$		0			0
$400$	5558.52			0.0347408
$401$	39978.4			0.248621			0.124310	−	0.992243i	$-0.460328\pi$
$401$	39978.4			0.248621			0.124310	+	0.992243i	$0.460328\pi$
$402$		0			0
$403$	12996.0			0.0800200
$404$		−	73376.6i		−	0.449567i
$405$		0			0
$406$	6187.93	+	46557.1i	0.0375399	+	0.282445i
$407$	128240.			0.774165
$408$		0			0
$409$		−	80655.7i		−	0.482157i	−0.970506	−	0.241078i	$-0.922499\pi$
$409$		−	80655.7i		−	0.482157i	0.970506	−	0.241078i	$-0.0775011\pi$
$410$	86862.6			0.516732
$411$		0			0
$412$			31251.7i			0.184111i
$413$	−84071.6	+	11174.0i	−0.492889	+	0.0655101i
$414$		0			0
$415$	−33599.1			−0.195088
$416$		−	8792.63i		−	0.0508080i
$417$		0			0
$418$		−	325489.i		−	1.86288i
$419$		−	252034.i		−	1.43559i	−0.696254	−	0.717795i	$-0.745151\pi$
$419$		−	252034.i		−	1.43559i	0.696254	−	0.717795i	$-0.254849\pi$
$420$		0			0
$421$	−84439.3			−0.476410			−0.238205	−	0.971215i	$-0.576559\pi$
$421$	−84439.3			−0.476410			−0.238205	+	0.971215i	$0.576559\pi$
$422$	−184007.			−1.03326
$423$		0			0
$424$	33057.2			0.183880
$425$			15805.1i			0.0875023i
$426$		0			0
$427$	−11965.6	+	1590.35i	−0.0656263	+	0.00872242i
$428$	97130.2			0.530233
$429$		0			0
$430$			127306.i			0.688514i
$431$	127512.			0.686431			0.343215	−	0.939257i	$-0.388484\pi$
$431$	127512.			0.686431			0.343215	+	0.939257i	$0.388484\pi$
$432$		0			0
$433$		−	233539.i		−	1.24562i	−0.782375	−	0.622808i	$-0.785992\pi$
$433$		−	233539.i		−	1.24562i	0.782375	−	0.622808i	$-0.214008\pi$
$434$	−36758.2	+	4885.55i	−0.195153	+	0.0259378i
$435$		0			0
$436$	54466.7			0.286522
$437$			281678.i			1.47499i
$438$		0			0
$439$		−	304238.i		−	1.57864i	−0.613980	−	0.789322i	$-0.710432\pi$
$439$		−	304238.i		−	1.57864i	0.613980	−	0.789322i	$-0.289568\pi$
$440$		−	100690.i		−	0.520094i
$441$		0			0
$442$	25000.9			0.127971
$443$	87061.0			0.443625			0.221813	−	0.975089i	$-0.428803\pi$
$443$	87061.0			0.443625			0.221813	+	0.975089i	$0.428803\pi$
$444$		0			0
$445$	−49498.2			−0.249960
$446$			86019.3i			0.432440i
$447$		0			0
$448$	3305.39	+	24869.3i	0.0164690	+	0.123910i
$449$	91141.4			0.452088			0.226044	−	0.974117i	$-0.427421\pi$
$449$	91141.4			0.452088			0.226044	+	0.974117i	$0.427421\pi$
$450$		0			0
$451$			253944.i			1.24849i
$452$	38113.6			0.186553
$453$		0			0
$454$		−	147433.i		−	0.715292i
$455$	7274.41	+	54731.6i	0.0351378	+	0.264372i
$456$		0			0
$457$	−411928.			−1.97237			−0.986187	−	0.165634i	$-0.947033\pi$
$457$	−411928.			−1.97237			−0.986187	+	0.165634i	$0.947033\pi$
$458$		−	229895.i		−	1.09597i
$459$		0			0
$460$			87137.1i			0.411801i
$461$			157397.i			0.740617i	0.928909	+	0.370309i	$0.120748\pi$
$461$			157397.i			0.740617i	−0.928909	+	0.370309i	$0.879252\pi$
$462$		0			0
$463$	245557.			1.14549			0.572745	−	0.819734i	$-0.305879\pi$
$463$	245557.			1.14549			0.572745	+	0.819734i	$0.305879\pi$
$464$	21688.4			0.100738
$465$		0			0
$466$	117999.			0.543383
$467$			33069.2i			0.151632i	0.997122	+	0.0758158i	$0.0241561\pi$
$467$			33069.2i			0.151632i	−0.997122	+	0.0758158i	$0.975844\pi$
$468$		0			0
$469$	−6950.28	−	52292.9i	−0.0315978	−	0.237737i
$470$	192701.			0.872343
$471$		0			0
$472$			39164.3i			0.175795i
$473$	−372182.			−1.66354
$474$		0			0
$475$			52103.8i			0.230931i
$476$	−70713.3	+	9398.55i	−0.312095	+	0.0414808i
$477$		0			0
$478$	11134.2			0.0487309
$479$		−	384277.i		−	1.67484i	−0.546559	−	0.837421i	$-0.684063\pi$
$479$		−	384277.i		−	1.67484i	0.546559	−	0.837421i	$-0.315937\pi$
$480$		0			0
$481$			32472.4i			0.140354i
$482$		−	199437.i		−	0.858442i
$483$		0			0
$484$	177242.			0.756615
$485$	136840.			0.581739
$486$		0			0
$487$	−173526.			−0.731657			−0.365829	−	0.930682i	$-0.619214\pi$
$487$	−173526.			−0.731657			−0.365829	+	0.930682i	$0.619214\pi$
$488$			5574.10i			0.0234064i
$489$		0			0
$490$	−41150.3	−	152070.i	−0.171388	−	0.633360i
$491$	20006.3			0.0829858			0.0414929	−	0.999139i	$-0.486789\pi$
$491$	20006.3			0.0829858			0.0414929	+	0.999139i	$0.486789\pi$
$492$		0			0
$493$			61668.8i			0.253730i
$494$	82419.2			0.337734
$495$		0			0
$496$			17123.6i			0.0696036i
$497$	14696.0	+	110571.i	0.0594958	+	0.447638i
$498$		0			0
$499$	−428368.			−1.72035			−0.860174	−	0.510000i	$-0.829645\pi$
$499$	−428368.			−1.72035			−0.860174	+	0.510000i	$0.829645\pi$
$500$			132108.i			0.528434i
$501$		0			0
$502$			203766.i			0.808584i
$503$		−	36793.4i		−	0.145423i	−0.997353	−	0.0727116i	$-0.976835\pi$
$503$		−	36793.4i		−	0.145423i	0.997353	−	0.0727116i	$-0.0231653\pi$
$504$		0			0
$505$	212774.			0.834326
$506$	−254747.			−0.994965
$507$		0			0
$508$	−223751.			−0.867038
$509$			137334.i			0.530080i	0.964237	+	0.265040i	$0.0853852\pi$
$509$			137334.i			0.530080i	−0.964237	+	0.265040i	$0.914615\pi$
$510$		0			0
$511$	345204.	−	45881.3i	1.32201	−	0.175709i
$512$	11585.2			0.0441942
$513$		0			0
$514$		−	185589.i		−	0.702466i
$515$	−90622.2			−0.341681
$516$		0			0
$517$			563363.i			2.10769i
$518$	−12207.3	−	91845.8i	−0.0454945	−	0.342294i
$519$		0			0
$520$	25496.4			0.0942916
$521$		−	102775.i		−	0.378629i	−0.981916	−	0.189315i	$-0.939373\pi$
$521$		−	102775.i		−	0.378629i	0.981916	−	0.189315i	$-0.0606266\pi$
$522$		0			0
$523$		−	314194.i		−	1.14867i	−0.818621	−	0.574334i	$-0.805261\pi$
$523$		−	314194.i		−	1.14867i	0.818621	−	0.574334i	$-0.194739\pi$
$524$			192132.i			0.699741i
$525$		0			0
$526$	109478.			0.395689
$527$	−48689.2			−0.175312
$528$		0			0
$529$	−59383.5			−0.212204
$530$			95857.8i			0.341252i
$531$		0			0
$532$	−233117.	+	30983.7i	−0.823664	+	0.109474i
$533$	−64302.9			−0.226348
$534$		0			0
$535$			281654.i			0.984029i
$536$	−24360.4			−0.0847919
$537$		0			0
$538$			246715.i			0.852376i
$539$	444578.	−	120303.i	1.53028	−	0.414096i
$540$		0			0
$541$	298384.			1.01948			0.509742	−	0.860327i	$-0.329741\pi$
$541$	298384.			1.01948			0.509742	+	0.860327i	$0.329741\pi$
$542$			298009.i			1.01445i
$543$		0			0
$544$			32941.4i			0.111313i
$545$			157940.i			0.531740i
$546$		0			0
$547$	361462.			1.20806			0.604029	−	0.796963i	$-0.293561\pi$
$547$	361462.			1.20806			0.604029	+	0.796963i	$0.293561\pi$
$548$	33296.0			0.110874
$549$		0			0
$550$	−47122.3			−0.155776
$551$			203300.i			0.669629i
$552$		0			0
$553$	45270.8	+	340611.i	0.148036	+	1.11380i
$554$	102329.			0.333412
$555$		0			0
$556$			210926.i			0.682309i
$557$	−112424.			−0.362367			−0.181183	−	0.983449i	$-0.557993\pi$
$557$	−112424.			−0.362367			−0.181183	+	0.983449i	$0.557993\pi$
$558$		0			0
$559$		−	94242.7i		−	0.301595i
$560$	−72114.8	+	9584.82i	−0.229958	+	0.0305638i
$561$		0			0
$562$	−280416.			−0.887832
$563$		−	441530.i		−	1.39298i	−0.717569	−	0.696488i	$-0.754745\pi$
$563$		−	441530.i		−	1.39298i	0.717569	−	0.696488i	$-0.245255\pi$
$564$		0			0
$565$			110520.i			0.346214i
$566$		−	11747.2i		−	0.0366692i
$567$		0			0
$568$	51508.8			0.159656
$569$	−397273.			−1.22706			−0.613529	−	0.789673i	$-0.710250\pi$
$569$	−397273.			−1.22706			−0.613529	+	0.789673i	$0.710250\pi$
$570$		0			0
$571$	−67235.8			−0.206219			−0.103109	−	0.994670i	$-0.532879\pi$
$571$	−67235.8			−0.206219			−0.103109	+	0.994670i	$0.532879\pi$
$572$			74539.3i			0.227821i
$573$		0			0
$574$	181876.	−	24173.3i	0.552016	−	0.0733688i
$575$	40779.5			0.123341
$576$		0			0
$577$		−	64756.1i		−	0.194504i	−0.995260	−	0.0972521i	$-0.968995\pi$
$577$		−	64756.1i		−	0.194504i	0.995260	−	0.0972521i	$-0.0310053\pi$
$578$	142567.			0.426741
$579$		0			0
$580$			62891.0i			0.186953i
$581$	−70351.0	+	9350.39i	−0.208410	+	0.0276999i
$582$		0			0
$583$	−280242.			−0.824510
$584$		−	160812.i		−	0.471511i
$585$		0			0
$586$			57245.8i			0.166705i
$587$			338967.i			0.983741i	0.870668	+	0.491870i	$0.163687\pi$
$587$			338967.i			0.983741i	−0.870668	+	0.491870i	$0.836313\pi$
$588$		0			0
$589$	−160511.			−0.462673
$590$	−113567.			−0.326248
$591$		0			0
$592$	−42785.9			−0.122084
$593$		−	255668.i		−	0.727054i	−0.931584	−	0.363527i	$-0.881572\pi$
$593$		−	255668.i		−	0.727054i	0.931584	−	0.363527i	$-0.118428\pi$
$594$		0			0
$595$	−27253.5	−	205051.i	−0.0769817	−	0.579200i
$596$	52612.6			0.148114
$597$		0			0
$598$		−	64506.1i		−	0.180384i
$599$	−129521.			−0.360982			−0.180491	−	0.983577i	$-0.557769\pi$
$599$	−129521.			−0.360982			−0.180491	+	0.983577i	$0.557769\pi$
$600$		0			0
$601$		−	377277.i		−	1.04451i	−0.852790	−	0.522254i	$-0.825091\pi$
$601$		−	377277.i		−	1.04451i	0.852790	−	0.522254i	$-0.174909\pi$
$602$	35428.4	+	266559.i	0.0977595	+	0.735529i
$603$		0			0
$604$	−183444.			−0.502839
$605$			513957.i			1.40416i
$606$		0			0
$607$			421091.i			1.14287i	0.820646	+	0.571437i	$0.193614\pi$
$607$			421091.i			1.14287i	−0.820646	+	0.571437i	$0.806386\pi$
$608$			108596.i			0.293770i
$609$		0			0
$610$	−16163.5			−0.0434386
$611$	−142653.			−0.382119
$612$		0			0
$613$	412173.			1.09688			0.548440	−	0.836190i	$-0.315222\pi$
$613$	412173.			1.09688			0.548440	+	0.836190i	$0.315222\pi$
$614$			178954.i			0.474684i
$615$		0			0
$616$	−28021.4	−	210829.i	−0.0738462	−	0.555608i
$617$	262676.			0.690002			0.345001	−	0.938602i	$-0.387879\pi$
$617$	262676.			0.690002			0.345001	+	0.938602i	$0.387879\pi$
$618$		0			0
$619$		−	373975.i		−	0.976026i	−0.872836	−	0.488013i	$-0.837722\pi$
$619$		−	373975.i		−	0.976026i	0.872836	−	0.488013i	$-0.162278\pi$
$620$	−49654.2			−0.129173
$621$		0			0
$622$			40659.7i			0.105095i
$623$	−103641.	+	13775.0i	−0.267028	+	0.0354908i
$624$		0			0
$625$	−328799.			−0.841726
$626$			103982.i			0.265343i
$627$		0			0
$628$			298344.i			0.756480i
$629$		−	121657.i		−	0.307494i
$630$		0			0
$631$	−408746.			−1.02659			−0.513293	−	0.858214i	$-0.671574\pi$
$631$	−408746.			−1.02659			−0.513293	+	0.858214i	$0.671574\pi$
$632$	158672.			0.397252
$633$		0			0
$634$	355126.			0.883495
$635$		−	648824.i		−	1.60909i
$636$		0			0
$637$	30462.8	+	112575.i	0.0750743	+	0.277435i
$638$	−183863.			−0.451703
$639$		0			0
$640$			33594.3i			0.0820174i
$641$	528074.			1.28522			0.642612	−	0.766192i	$-0.277851\pi$
$641$	528074.			1.28522			0.642612	+	0.766192i	$0.277851\pi$
$642$		0			0
$643$		−	323445.i		−	0.782310i	−0.920325	−	0.391155i	$-0.872076\pi$
$643$		−	323445.i		−	0.782310i	0.920325	−	0.391155i	$-0.127924\pi$
$644$	24249.6	+	182451.i	0.0584701	+	0.439921i
$645$		0			0
$646$	−308782.			−0.739925
$647$		−	592372.i		−	1.41510i	−0.706665	−	0.707548i	$-0.749801\pi$
$647$		−	592372.i		−	1.41510i	0.706665	−	0.707548i	$-0.250199\pi$
$648$		0			0
$649$		−	332015.i		−	0.788257i
$650$		−	11932.1i		−	0.0282417i
$651$		0			0
$652$	326832.			0.768828
$653$	329810.			0.773459			0.386730	−	0.922193i	$-0.373605\pi$
$653$	329810.			0.773459			0.386730	+	0.922193i	$0.373605\pi$
$654$		0			0
$655$	−557135.			−1.29861
$656$		−	84726.1i		−	0.196884i
$657$		0			0
$658$	403483.	−	53627.2i	0.931910	−	0.123861i
$659$	526737.			1.21290			0.606448	−	0.795123i	$-0.292594\pi$
$659$	526737.			1.21290			0.606448	+	0.795123i	$0.292594\pi$
$660$		0			0
$661$		−	144047.i		−	0.329686i	−0.986320	−	0.164843i	$-0.947288\pi$
$661$		−	144047.i		−	0.329686i	0.986320	−	0.164843i	$-0.0527117\pi$
$662$	15207.2			0.0347002
$663$		0			0
$664$			32772.7i			0.0743320i
$665$	−89845.0	−	675981.i	−0.203166	−	1.52859i
$666$		0			0
$667$	159115.			0.357650
$668$			278199.i			0.623452i
$669$		0			0
$670$		−	70639.1i		−	0.157360i
$671$		−	47254.3i		−	0.104953i
$672$		0			0
$673$	620117.			1.36913			0.684563	−	0.728953i	$-0.259993\pi$
$673$	620117.			1.36913			0.684563	+	0.728953i	$0.259993\pi$
$674$	6228.95			0.0137118
$675$		0			0
$676$	209613.			0.458697
$677$			626172.i			1.36621i	0.730322	+	0.683103i	$0.239370\pi$
$677$			626172.i			1.36621i	−0.730322	+	0.683103i	$0.760630\pi$
$678$		0			0
$679$	286520.	−	38081.5i	0.621463	−	0.0825989i
$680$	−95522.0			−0.206579
$681$		0			0
$682$		−	145165.i		−	0.312099i
$683$	−185558.			−0.397775			−0.198888	−	0.980022i	$-0.563733\pi$
$683$	−185558.			−0.397775			−0.198888	+	0.980022i	$0.563733\pi$
$684$		0			0
$685$			96550.1i			0.205765i
$686$	−128482.	−	306957.i	−0.273019	−	0.652273i
$687$		0			0
$688$	124175.			0.262336
$689$		−	70961.9i		−	0.149481i
$690$		0			0
$691$		−	548881.i		−	1.14953i	−0.818317	−	0.574767i	$-0.805093\pi$
$691$		−	548881.i		−	1.14953i	0.818317	−	0.574767i	$-0.194907\pi$
$692$		−	252800.i		−	0.527917i
$693$		0			0
$694$	−628478.			−1.30488
$695$	−611634.			−1.26626
$696$		0			0
$697$	240910.			0.495894
$698$		−	290420.i		−	0.596095i
$699$		0			0
$700$	4485.62	+	33749.2i	0.00915433	+	0.0688759i
$701$	−517501.			−1.05311			−0.526556	−	0.850140i	$-0.676517\pi$
$701$	−517501.			−1.05311			−0.526556	+	0.850140i	$0.676517\pi$
$702$		0			0
$703$		−	401061.i		−	0.811522i
$704$	−98213.6			−0.198165
$705$		0			0
$706$		−	177047.i		−	0.355205i
$707$	445514.	−	59213.5i	0.891297	−	0.118463i
$708$		0			0
$709$	6035.96			0.0120075			0.00600377	−	0.999982i	$-0.498089\pi$
$709$	6035.96			0.0120075			0.00600377	+	0.999982i	$0.498089\pi$
$710$			149363.i			0.296296i
$711$		0			0
$712$			48280.7i			0.0952388i
$713$			125625.i			0.247115i
$714$		0			0
$715$	−216145.			−0.422799
$716$	−182005.			−0.355024
$717$		0			0
$718$	−270132.			−0.523994
$719$		−	748658.i		−	1.44819i	−0.689700	−	0.724095i	$-0.742258\pi$
$719$		−	748658.i		−	1.44819i	0.689700	−	0.724095i	$-0.257742\pi$
$720$		0			0
$721$	−189748.	+	25219.5i	−0.365012	+	0.0485139i
$722$	−649343.			−1.24566
$723$		0			0
$724$		−	443475.i		−	0.846042i
$725$	29432.5			0.0559953
$726$		0			0
$727$		−	370335.i		−	0.700691i	−0.936621	−	0.350345i	$-0.886064\pi$
$727$		−	370335.i		−	0.700691i	0.936621	−	0.350345i	$-0.113936\pi$
$728$	53385.4	−	7095.48i	0.100730	−	0.0133881i
$729$		0			0
$730$	466314.			0.875050
$731$			353079.i			0.660750i
$732$		0			0
$733$			144545.i			0.269027i	0.990912	+	0.134513i	$0.0429471\pi$
$733$			144545.i			0.269027i	−0.990912	+	0.134513i	$0.957053\pi$
$734$		−	232867.i		−	0.432231i
$735$		0			0
$736$	84993.8			0.156903
$737$	206515.			0.380203
$738$		0			0
$739$	4650.26			0.00851506			0.00425753	−	0.999991i	$-0.498645\pi$
$739$	4650.26			0.00851506			0.00425753	+	0.999991i	$0.498645\pi$
$740$		−	124069.i		−	0.226568i
$741$		0			0
$742$	26676.5	+	200710.i	0.0484531	+	0.364554i
$743$	−500204.			−0.906087			−0.453043	−	0.891489i	$-0.649662\pi$
$743$	−500204.			−0.906087			−0.453043	+	0.891489i	$0.649662\pi$
$744$		0			0
$745$			152563.i			0.274877i
$746$	368327.			0.661845
$747$		0			0
$748$		−	279260.i		−	0.499121i
$749$	78382.2	+	589737.i	0.139718	+	1.05122i
$750$		0			0
$751$	944576.			1.67478			0.837389	−	0.546608i	$-0.184081\pi$
$751$	944576.			1.67478			0.837389	+	0.546608i	$0.184081\pi$
$752$		−	187961.i		−	0.332377i
$753$		0			0
$754$		−	46557.1i		−	0.0818924i
$755$		−	531941.i		−	0.933189i
$756$		0			0
$757$	−654028.			−1.14131			−0.570656	−	0.821189i	$-0.693311\pi$
$757$	−654028.			−1.14131			−0.570656	+	0.821189i	$0.693311\pi$
$758$	544044.			0.946881
$759$		0			0
$760$	−314902.			−0.545191
$761$		−	643673.i		−	1.11147i	−0.831361	−	0.555733i	$-0.812438\pi$
$761$		−	643673.i		−	1.11147i	0.831361	−	0.555733i	$-0.187562\pi$
$762$		0			0
$763$	43953.6	+	330700.i	0.0754997	+	0.568049i
$764$	406541.			0.696494
$765$		0			0
$766$			288310.i			0.491362i
$767$	84071.6			0.142909
$768$		0			0
$769$		−	103697.i		−	0.175354i	−0.996149	−	0.0876768i	$-0.972056\pi$
$769$		−	103697.i		−	0.175354i	0.996149	−	0.0876768i	$-0.0279443\pi$
$770$	611352.	−	81255.1i	1.03112	−	0.137047i
$771$		0			0
$772$	−9986.72			−0.0167567
$773$			796380.i			1.33279i	0.745599	+	0.666394i	$0.232163\pi$
$773$			796380.i			1.33279i	−0.745599	+	0.666394i	$0.767837\pi$
$774$		0			0
$775$			23237.8i			0.0386893i
$776$		−	133474.i		−	0.221652i
$777$		0			0
$778$	−540439.			−0.892868
$779$	794195.			1.30874
$780$		0			0
$781$	−436664.			−0.715889
$782$			241671.i			0.395195i
$783$		0			0
$784$	−148329.	+	40138.1i	−0.241321	+	0.0653017i
$785$	−865122.			−1.40391
$786$		0			0
$787$			1.16895e6i			1.88733i	0.330905	+	0.943664i	$0.392646\pi$
$787$			1.16895e6i			1.88733i	−0.330905	+	0.943664i	$0.607354\pi$
$788$	−515637.			−0.830408
$789$		0			0
$790$			460109.i			0.737237i
$791$	30756.9	+	231411.i	0.0491575	+	0.369854i
$792$		0			0
$793$	11965.6			0.0190277
$794$			568919.i			0.902421i
$795$		0			0
$796$		−	18820.8i		−	0.0297038i
$797$			808048.i			1.27210i	0.771649	+	0.636049i	$0.219432\pi$
$797$			808048.i			1.27210i	−0.771649	+	0.636049i	$0.780568\pi$
$798$		0			0
$799$	534447.			0.837165
$800$	15721.9			0.0245654
$801$		0			0
$802$	113076.			0.175801
$803$			1.36328e6i			2.11423i
$804$		0			0
$805$	−529062.	+	70318.0i	−0.816423	+	0.108511i
$806$	36758.2			0.0565827
$807$		0			0
$808$		−	207540.i		−	0.317892i
$809$	692708.			1.05841			0.529204	−	0.848495i	$-0.322491\pi$
$809$	692708.			1.05841			0.529204	+	0.848495i	$0.322491\pi$
$810$		0			0
$811$			382267.i			0.581200i	0.956845	+	0.290600i	$0.0938548\pi$
$811$			382267.i			0.581200i	−0.956845	+	0.290600i	$0.906145\pi$
$812$	17502.1	+	131683.i	0.0265448	+	0.199719i
$813$		0			0
$814$	362717.			0.547417
$815$			947732.i			1.42682i
$816$		0			0
$817$			1.16398e6i			1.74381i
$818$		−	228129.i		−	0.340936i
$819$		0			0
$820$	245685.			0.365385
$821$	−116392.			−0.172678			−0.0863392	−	0.996266i	$-0.527517\pi$
$821$	−116392.			−0.172678			−0.0863392	+	0.996266i	$0.527517\pi$
$822$		0			0
$823$	640526.			0.945665			0.472832	−	0.881152i	$-0.343232\pi$
$823$	640526.			0.945665			0.472832	+	0.881152i	$0.343232\pi$
$824$			88393.2i			0.130186i
$825$		0			0
$826$	−237790.	+	31604.8i	−0.348525	+	0.0463227i
$827$	158299.			0.231455			0.115727	−	0.993281i	$-0.463080\pi$
$827$	158299.			0.231455			0.115727	+	0.993281i	$0.463080\pi$
$828$		0			0
$829$		−	680501.i		−	0.990192i	−0.868838	−	0.495096i	$-0.835133\pi$
$829$		−	680501.i		−	0.990192i	0.868838	−	0.495096i	$-0.164867\pi$
$830$	−95032.6			−0.137948
$831$		0			0
$832$		−	24869.3i		−	0.0359267i
$833$	−114129.	−	421759.i	−0.164477	−	0.607819i
$834$		0			0
$835$	−806709.			−1.15703
$836$		−	920622.i		−	1.31725i
$837$		0			0
$838$		−	712859.i		−	1.01512i
$839$		−	622397.i		−	0.884186i	−0.896969	−	0.442093i	$-0.854236\pi$
$839$		−	622397.i		−	0.884186i	0.896969	−	0.442093i	$-0.145764\pi$
$840$		0			0
$841$	−592440.			−0.837631
$842$	−238831.			−0.336873
$843$		0			0
$844$	−520451.			−0.730626
$845$			607827.i			0.851269i
$846$		0			0
$847$	143031.	+	1.07614e6i	0.199371	+	1.50004i
$848$	93500.0			0.130023
$849$		0			0
$850$			44703.6i			0.0618735i
$851$	−313894.			−0.433435
$852$		0			0
$853$			826596.i			1.13604i	0.823013	+	0.568022i	$0.192291\pi$
$853$			826596.i			1.13604i	−0.823013	+	0.568022i	$0.807709\pi$
$854$	−33843.7	+	4498.19i	−0.0464048	+	0.00616768i
$855$		0			0
$856$	274726.			0.374931
$857$		−	539076.i		−	0.733987i	−0.930223	−	0.366994i	$-0.880387\pi$
$857$		−	539076.i		−	0.733987i	0.930223	−	0.366994i	$-0.119613\pi$
$858$		0			0
$859$			499964.i			0.677567i	0.940864	+	0.338783i	$0.110015\pi$
$859$			499964.i			0.677567i	−0.940864	+	0.338783i	$0.889985\pi$
$860$			360077.i			0.486853i
$861$		0			0
$862$	360659.			0.485380
$863$	−1.16944e6			−1.57021			−0.785103	−	0.619365i	$-0.787390\pi$
$863$	−1.16944e6			−1.57021			−0.785103	+	0.619365i	$0.787390\pi$
$864$		0			0
$865$	733059.			0.979730
$866$		−	660548.i		−	0.880783i
$867$		0			0
$868$	−103968.	+	13818.4i	−0.137994	+	0.0183408i
$869$	−1.34514e6			−1.78126
$870$		0			0
$871$			52292.9i			0.0689297i
$872$	154055.			0.202602
$873$		0			0
$874$			796705.i			1.04298i
$875$	−802110.	+	106609.i	−1.04765	+	0.139244i
$876$		0			0
$877$	187496.			0.243777			0.121888	−	0.992544i	$-0.461105\pi$
$877$	187496.			0.243777			0.121888	+	0.992544i	$0.461105\pi$
$878$		−	860515.i		−	1.11627i
$879$		0			0
$880$		−	284795.i		−	0.367762i
$881$			179673.i			0.231489i	0.993279	+	0.115745i	$0.0369254\pi$
$881$			179673.i			0.231489i	−0.993279	+	0.115745i	$0.963075\pi$
$882$		0			0
$883$	−1.04658e6			−1.34231			−0.671155	−	0.741317i	$-0.734201\pi$
$883$	−1.04658e6			−1.34231			−0.671155	+	0.741317i	$0.734201\pi$
$884$	70713.3			0.0904892
$885$		0			0
$886$	246246.			0.313691
$887$			1.30029e6i			1.65270i	0.563158	+	0.826349i	$0.309586\pi$
$887$			1.30029e6i			1.65270i	−0.563158	+	0.826349i	$0.690414\pi$
$888$		0			0
$889$	−180563.	−	1.35853e6i	−0.228468	−	1.71896i
$890$	−140002.			−0.176748
$891$		0			0
$892$			243299.i			0.305781i
$893$	1.76188e6			2.20940
$894$		0			0
$895$		−	527770.i		−	0.658868i
$896$	9349.06	+	70341.0i	0.0116453	+	0.0876178i
$897$		0			0
$898$	257787.			0.319675
$899$			90669.8i			0.112187i
$900$		0			0
$901$			265858.i			0.327491i
$902$			718263.i			0.882817i
$903$		0			0
$904$	107802.			0.131913
$905$	1.28597e6			1.57012
$906$		0			0
$907$	1.18388e6			1.43911			0.719556	−	0.694435i	$-0.244346\pi$
$907$	1.18388e6			1.43911			0.719556	+	0.694435i	$0.244346\pi$
$908$		−	417004.i		−	0.505788i
$909$		0			0
$910$	20575.1	+	154804.i	0.0248462	+	0.186939i
$911$	1.30731e6			1.57522			0.787612	−	0.616172i	$-0.211317\pi$
$911$	1.30731e6			1.57522			0.787612	+	0.616172i	$0.211317\pi$
$912$		0			0
$913$		−	277830.i		−	0.333301i
$914$	−1.16511e6			−1.39468
$915$		0			0
$916$		−	650242.i		−	0.774968i
$917$	−1.16655e6	+	155047.i	−1.38728	+	0.184384i
$918$		0			0
$919$	698775.			0.827382			0.413691	−	0.910417i	$-0.364239\pi$
$919$	698775.			0.827382			0.413691	+	0.910417i	$0.364239\pi$
$920$			246461.i			0.291187i
$921$		0			0
$922$			445185.i			0.523696i
$923$		−	110571.i		−	0.129789i
$924$		0			0
$925$	−58063.1			−0.0678605
$926$	694541.			0.809984
$927$		0			0
$928$	61344.1			0.0712323
$929$		−	1.39460e6i		−	1.61591i	−0.589244	−	0.807955i	$-0.700574\pi$
$929$		−	1.39460e6i		−	1.61591i	0.589244	−	0.807955i	$-0.299426\pi$
$930$		0			0
$931$	−376241.	−	1.39039e6i	−0.434077	−	1.60412i
$932$	333751.			0.384229
$933$		0			0
$934$			93533.8i			0.107220i
$935$	809786.			0.926290
$936$		0			0
$937$			509380.i			0.580180i	0.956999	+	0.290090i	$0.0936852\pi$
$937$			509380.i			0.580180i	−0.956999	+	0.290090i	$0.906315\pi$
$938$	−19658.4	−	147907.i	−0.0223430	−	0.168106i
$939$		0			0
$940$	545040.			0.616840
$941$		−	1.62505e6i		−	1.83522i	−0.397486	−	0.917608i	$-0.630117\pi$
$941$		−	1.62505e6i		−	1.83522i	0.397486	−	0.917608i	$-0.369883\pi$
$942$		0			0
$943$		−	621584.i		−	0.698998i
$944$			110773.i			0.124306i
$945$		0			0
$946$	−1.05269e6			−1.17630
$947$	−1.22462e6			−1.36553			−0.682763	−	0.730640i	$-0.739222\pi$
$947$	−1.22462e6			−1.36553			−0.682763	+	0.730640i	$0.739222\pi$
$948$		0			0
$949$	−345204.			−0.383304
$950$			147372.i			0.163293i
$951$		0			0
$952$	−200007.	+	26583.1i	−0.220685	+	0.0293313i
$953$	1.14847e6			1.26454			0.632269	−	0.774749i	$-0.282124\pi$
$953$	1.14847e6			1.26454			0.632269	+	0.774749i	$0.282124\pi$
$954$		0			0
$955$			1.17887e6i			1.29258i
$956$	31492.4			0.0344580
$957$		0			0
$958$		−	1.08690e6i		−	1.18429i
$959$	26869.2	+	202160.i	0.0292158	+	0.219815i
$960$		0			0
$961$	851935.			0.922485
$962$			91845.8i			0.0992451i
$963$		0			0
$964$		−	564092.i		−	0.607010i
$965$		−	28959.0i		−	0.0310978i
$966$		0			0
$967$	−733668.			−0.784597			−0.392298	−	0.919838i	$-0.628320\pi$
$967$	−733668.			−0.784597			−0.392298	+	0.919838i	$0.628320\pi$
$968$	501315.			0.535008
$969$		0			0
$970$	387041.			0.411352
$971$		−	786749.i		−	0.834445i	−0.908804	−	0.417223i	$-0.863004\pi$
$971$		−	786749.i		−	0.834445i	0.908804	−	0.417223i	$-0.136996\pi$
$972$		0			0
$973$	−1.28066e6	+	170213.i	−1.35272	+	0.179791i
$974$	−490807.			−0.517360
$975$		0			0
$976$			15765.9i			0.0165508i
$977$	−837039.			−0.876913			−0.438457	−	0.898752i	$-0.644475\pi$
$977$	−837039.			−0.876913			−0.438457	+	0.898752i	$0.644475\pi$
$978$		0			0
$979$		−	409299.i		−	0.427046i
$980$	−116390.	−	430118.i	−0.121190	−	0.447853i
$981$		0			0
$982$	56586.3			0.0586798
$983$		−	644129.i		−	0.666600i	−0.942821	−	0.333300i	$-0.891838\pi$
$983$		−	644129.i		−	0.666600i	0.942821	−	0.333300i	$-0.108162\pi$
$984$		0			0
$985$		−	1.49522e6i		−	1.54111i
$986$			174426.i			0.179414i
$987$		0			0
$988$	233117.			0.238814
$989$	910996.			0.931374
$990$		0			0
$991$	92517.5			0.0942056			0.0471028	−	0.998890i	$-0.485001\pi$
$991$	92517.5			0.0942056			0.0471028	+	0.998890i	$0.485001\pi$
$992$			48432.8i			0.0492172i
$993$		0			0
$994$	41566.6	+	312741.i	0.0420699	+	0.316528i
$995$	54575.7			0.0551256
$996$		0			0
$997$			366383.i			0.368591i	0.982871	+	0.184295i	$0.0590003\pi$
$997$			366383.i			0.368591i	−0.982871	+	0.184295i	$0.941000\pi$
$998$	−1.21161e6			−1.21647
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.5.c.a.55.4		4
3.2	odd	2		14.5.b.a.13.1	✓	4
4.3	odd	2		1008.5.f.h.433.3		4
7.6	odd	2	inner	126.5.c.a.55.3		4
12.11	even	2		112.5.c.c.97.4		4
15.2	even	4		350.5.d.a.349.1		8
15.8	even	4		350.5.d.a.349.8		8
15.14	odd	2		350.5.b.a.251.4		4
21.2	odd	6		98.5.d.d.31.4		8
21.5	even	6		98.5.d.d.31.3		8
21.11	odd	6		98.5.d.d.19.3		8
21.17	even	6		98.5.d.d.19.4		8
21.20	even	2		14.5.b.a.13.2	yes	4
24.5	odd	2		448.5.c.e.321.4		4
24.11	even	2		448.5.c.f.321.1		4
28.27	even	2		1008.5.f.h.433.2		4
84.83	odd	2		112.5.c.c.97.1		4
105.62	odd	4		350.5.d.a.349.4		8
105.83	odd	4		350.5.d.a.349.5		8
105.104	even	2		350.5.b.a.251.3		4
168.83	odd	2		448.5.c.f.321.4		4
168.125	even	2		448.5.c.e.321.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.5.b.a.13.1	✓	4	3.2	odd	2
14.5.b.a.13.2	yes	4	21.20	even	2
98.5.d.d.19.3		8	21.11	odd	6
98.5.d.d.19.4		8	21.17	even	6
98.5.d.d.31.3		8	21.5	even	6
98.5.d.d.31.4		8	21.2	odd	6
112.5.c.c.97.1		4	84.83	odd	2
112.5.c.c.97.4		4	12.11	even	2
126.5.c.a.55.3		4	7.6	odd	2	inner
126.5.c.a.55.4		4	1.1	even	1	trivial
350.5.b.a.251.3		4	105.104	even	2
350.5.b.a.251.4		4	15.14	odd	2
350.5.d.a.349.1		8	15.2	even	4
350.5.d.a.349.4		8	105.62	odd	4
350.5.d.a.349.5		8	105.83	odd	4
350.5.d.a.349.8		8	15.8	even	4
448.5.c.e.321.1		4	168.125	even	2
448.5.c.e.321.4		4	24.5	odd	2
448.5.c.f.321.1		4	24.11	even	2
448.5.c.f.321.4		4	168.83	odd	2
1008.5.f.h.433.2		4	28.27	even	2
1008.5.f.h.433.3		4	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	126.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.82843 q^{2} +8.00000 q^{4} +23.1980i q^{5} +(6.45584 + 48.5729i) q^{7} +22.6274 q^{8} +65.6139i q^{10} -191.823 q^{11} -48.5729i q^{13} +(18.2599 + 137.385i) q^{14} +64.0000 q^{16} +181.977i q^{17} +599.915i q^{19} +185.584i q^{20} -542.558 q^{22} +469.529 q^{23} +86.8519 q^{25} -137.385i q^{26} +(51.6468 + 388.583i) q^{28} +338.881 q^{29} +267.556i q^{31} +181.019 q^{32} +514.710i q^{34} +(-1126.79 + 149.763i) q^{35} -668.530 q^{37} +1696.82i q^{38} +524.911i q^{40} -1323.85i q^{41} +1940.23 q^{43} -1534.59 q^{44} +1328.03 q^{46} -2936.89i q^{47} +(-2317.64 + 627.158i) q^{49} +245.654 q^{50} -388.583i q^{52} +1460.94 q^{53} -4449.92i q^{55} +(146.079 + 1099.08i) q^{56} +958.501 q^{58} +1730.83i q^{59} +246.343i q^{61} +756.763i q^{62} +512.000 q^{64} +1126.79 q^{65} -1076.59 q^{67} +1455.82i q^{68} +(-3187.05 + 423.593i) q^{70} +2276.39 q^{71} -7106.94i q^{73} -1890.89 q^{74} +4799.32i q^{76} +(-1238.38 - 9317.41i) q^{77} +7012.38 q^{79} +1484.67i q^{80} -3744.40i q^{82} +1448.36i q^{83} -4221.52 q^{85} +5487.81 q^{86} -4340.47 q^{88} +2133.73i q^{89} +(2359.32 - 313.579i) q^{91} +3756.23 q^{92} -8306.77i q^{94} -13916.8 q^{95} -5898.76i q^{97} +(-6555.29 + 1773.87i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 32 q^{4} - 76 q^{7} - 360 q^{11} + 288 q^{14} + 256 q^{16} - 1152 q^{22} + 792 q^{23} - 2300 q^{25} - 608 q^{28} - 1224 q^{29} - 4032 q^{35} - 3896 q^{37} + 3688 q^{43} - 2880 q^{44} + 3072 q^{46}+ \cdots - 21888 q^{98}+O(q^{100}) \) 4 * q + 32 * q^4 - 76 * q^7 - 360 * q^11 + 288 * q^14 + 256 * q^16 - 1152 * q^22 + 792 * q^23 - 2300 * q^25 - 608 * q^28 - 1224 * q^29 - 4032 * q^35 - 3896 * q^37 + 3688 * q^43 - 2880 * q^44 + 3072 * q^46 - 1532 * q^49 + 7488 * q^50 - 5832 * q^53 + 2304 * q^56 + 7296 * q^58 + 2048 * q^64 + 4032 * q^65 - 1048 * q^67 - 1344 * q^70 + 21528 * q^71 + 3456 * q^74 - 3528 * q^77 + 12776 * q^79 + 16512 * q^85 + 11520 * q^86 - 9216 * q^88 + 5568 * q^91 + 6336 * q^92 - 36864 * q^95 - 21888 * q^98

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