LMFDB - Embedded newform 1008.4.bt.a.593.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1008,4,Mod(17,1008)] 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("1008.17"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1008, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 3, 1])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1008.bt (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,0,0,0,-56] 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:	$59.4739252858$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 48 x^{14} + 1647 x^{12} - 27620 x^{10} + 336765 x^{8} - 1200006 x^{6} + 3242464 x^{4} + \cdots + 810000 $ x^16 - 48x^14 + 1647x^12 - 27620x^10 + 336765x^8 - 1200006x^6 + 3242464x^4 - 1762200*x^2 + 810000
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{8} $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			593.7
Root			$-4.21355 + 2.43270i$ of defining polynomial
Character	$\chi$	$=$	1008.593
Dual form			1008.4.bt.a.17.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(6.38217 - 11.0542i) q^{5} +(-2.53897 + 18.3454i) q^{7} +(46.8633 - 27.0565i) q^{11} -8.85528i q^{13} +(-34.4587 - 59.6841i) q^{17} +(141.898 + 81.9246i) q^{19} +(-81.3807 - 46.9852i) q^{23} +(-18.9642 - 32.8469i) q^{25} -119.620i q^{29} +(-85.6311 + 49.4391i) q^{31} +(186.590 + 145.150i) q^{35} +(-47.0949 + 81.5708i) q^{37} +259.347 q^{41} -5.01418 q^{43} +(-28.6747 + 49.6660i) q^{47} +(-330.107 - 93.1568i) q^{49} +(407.058 - 235.015i) q^{53} -690.718i q^{55} +(112.979 + 195.685i) q^{59} +(370.650 + 213.995i) q^{61} +(-97.8884 - 56.5159i) q^{65} +(81.9267 + 141.901i) q^{67} +79.8529i q^{71} +(666.447 - 384.774i) q^{73} +(377.379 + 928.422i) q^{77} +(267.408 - 463.165i) q^{79} -438.520 q^{83} -879.684 q^{85} +(12.8242 - 22.2121i) q^{89} +(162.454 + 22.4833i) q^{91} +(1811.23 - 1045.71i) q^{95} -1381.00i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 56 q^{7} + 612 q^{19} - 20 q^{25} - 1128 q^{31} - 1196 q^{37} - 328 q^{43} + 784 q^{49} - 1632 q^{61} - 308 q^{67} + 4068 q^{73} + 2176 q^{79} - 4608 q^{85} - 924 q^{91}+O(q^{100}) $ 16 * q - 56 * q^7 + 612 * q^19 - 20 * q^25 - 1128 * q^31 - 1196 * q^37 - 328 * q^43 + 784 * q^49 - 1632 * q^61 - 308 * q^67 + 4068 * q^73 + 2176 * q^79 - 4608 * q^85 - 924 * q^91

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

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 $

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	6.38217	−	11.0542i	0.570839	−	0.988721i	−0.425642	−	0.904892i	$-0.639952\pi$
$5$	6.38217	−	11.0542i	0.570839	−	0.988721i	0.996480	−	0.0838295i	$-0.0267151\pi$
$6$		0			0
$7$	−2.53897	+	18.3454i	−0.137091	+	0.990558i
$7$	−2.53897	+	18.3454i	−0.137091	+	0.990558i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	46.8633	−	27.0565i	1.28453	−	0.741623i	0.306856	−	0.951756i	$-0.400723\pi$
$11$	46.8633	−	27.0565i	1.28453	−	0.741623i	0.977673	+	0.210133i	$0.0673897\pi$
$12$		0			0
$13$		−	8.85528i		−	0.188924i	−0.995528	−	0.0944620i	$-0.969887\pi$
$13$		−	8.85528i		−	0.188924i	0.995528	−	0.0944620i	$-0.0301131\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−34.4587	−	59.6841i	−0.491615	−	0.851502i	0.508339	−	0.861157i	$-0.330260\pi$
$17$	−34.4587	−	59.6841i	−0.491615	−	0.851502i	−0.999953	+	0.00965543i	$0.996927\pi$
$18$		0			0
$19$	141.898	+	81.9246i	1.71334	+	0.989199i	0.929960	+	0.367660i	$0.119841\pi$
$19$	141.898	+	81.9246i	1.71334	+	0.989199i	0.783383	+	0.621540i	$0.213492\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−81.3807	−	46.9852i	−0.737785	−	0.425960i	0.0834783	−	0.996510i	$-0.473397\pi$
$23$	−81.3807	−	46.9852i	−0.737785	−	0.425960i	−0.821263	+	0.570549i	$0.806730\pi$
$24$		0			0
$25$	−18.9642	−	32.8469i	−0.151713	−	0.262775i
$26$		0			0
$27$		0			0
$28$		0			0
$29$		−	119.620i		−	0.765961i	−0.923756	−	0.382981i	$-0.874898\pi$
$29$		−	119.620i		−	0.765961i	0.923756	−	0.382981i	$-0.125102\pi$
$30$		0			0
$31$	−85.6311	+	49.4391i	−0.496123	+	0.286437i	−0.727111	−	0.686520i	$-0.759137\pi$
$31$	−85.6311	+	49.4391i	−0.496123	+	0.286437i	0.230988	+	0.972957i	$0.425804\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	186.590	+	145.150i	0.901129	+	0.700994i
$36$		0			0
$37$	−47.0949	+	81.5708i	−0.209253	+	0.362437i	−0.951479	−	0.307712i	$-0.900437\pi$
$37$	−47.0949	+	81.5708i	−0.209253	+	0.362437i	0.742227	+	0.670149i	$0.233770\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	259.347			0.987883			0.493941	−	0.869495i	$-0.335556\pi$
$41$	259.347			0.987883			0.493941	+	0.869495i	$0.335556\pi$
$42$		0			0
$43$	−5.01418			−0.0177827			−0.00889133	−	0.999960i	$-0.502830\pi$
$43$	−5.01418			−0.0177827			−0.00889133	+	0.999960i	$0.502830\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−28.6747	+	49.6660i	−0.0889921	+	0.154139i	−0.907085	−	0.420947i	$-0.861698\pi$
$47$	−28.6747	+	49.6660i	−0.0889921	+	0.154139i	0.818093	+	0.575086i	$0.195031\pi$
$48$		0			0
$49$	−330.107	−	93.1568i	−0.962412	−	0.271594i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	407.058	−	235.015i	1.05497	−	0.609090i	0.130937	−	0.991391i	$-0.458202\pi$
$53$	407.058	−	235.015i	1.05497	−	0.609090i	0.924038	+	0.382301i	$0.124868\pi$
$54$		0			0
$55$		−	690.718i		−	1.69339i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	112.979	+	195.685i	0.249299	+	0.431798i	0.963331	−	0.268314i	$-0.0864666\pi$
$59$	112.979	+	195.685i	0.249299	+	0.431798i	−0.714033	+	0.700112i	$0.753133\pi$
$60$		0			0
$61$	370.650	+	213.995i	0.777982	+	0.449168i	0.835715	−	0.549164i	$-0.185054\pi$
$61$	370.650	+	213.995i	0.777982	+	0.449168i	−0.0577325	+	0.998332i	$0.518387\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−97.8884	−	56.5159i	−0.186793	−	0.107845i
$66$		0			0
$67$	81.9267	+	141.901i	0.149387	+	0.258746i	0.931001	−	0.365016i	$-0.118937\pi$
$67$	81.9267	+	141.901i	0.149387	+	0.258746i	−0.781614	+	0.623762i	$0.785603\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			79.8529i			0.133476i	0.997771	+	0.0667380i	$0.0212592\pi$
$71$			79.8529i			0.133476i	−0.997771	+	0.0667380i	$0.978741\pi$
$72$		0			0
$73$	666.447	−	384.774i	1.06852	−	0.616909i	0.140741	−	0.990046i	$-0.455051\pi$
$73$	666.447	−	384.774i	1.06852	−	0.616909i	0.927776	+	0.373138i	$0.121718\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	377.379	+	928.422i	0.558523	+	1.37407i
$78$		0			0
$79$	267.408	−	463.165i	0.380833	−	0.659622i	−0.610349	−	0.792133i	$-0.708971\pi$
$79$	267.408	−	463.165i	0.380833	−	0.659622i	0.991182	+	0.132511i	$0.0423040\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−438.520			−0.579926			−0.289963	−	0.957038i	$-0.593643\pi$
$83$	−438.520			−0.579926			−0.289963	+	0.957038i	$0.593643\pi$
$84$		0			0
$85$	−879.684			−1.12253
$86$		0			0
$87$		0			0
$88$		0			0
$89$	12.8242	−	22.2121i	0.0152737	−	0.0264548i	−0.858288	−	0.513169i	$-0.828471\pi$
$89$	12.8242	−	22.2121i	0.0152737	−	0.0264548i	0.873561	+	0.486714i	$0.161805\pi$
$90$		0			0
$91$	162.454	+	22.4833i	0.187140	+	0.0258999i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	1811.23	−	1045.71i	1.95608	−	1.12935i
$96$		0			0
$97$		−	1381.00i		−	1.44555i	−0.691081	−	0.722777i	$-0.742865\pi$
$97$		−	1381.00i		−	1.44555i	0.691081	−	0.722777i	$-0.257135\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−356.808	−	618.009i	−0.351522	−	0.608854i	0.634994	−	0.772517i	$-0.281002\pi$
$101$	−356.808	−	618.009i	−0.351522	−	0.608854i	−0.986516	+	0.163663i	$0.947669\pi$
$102$		0			0
$103$	−1552.42	−	896.288i	−1.48509	−	0.857416i	−0.485232	−	0.874385i	$-0.661265\pi$
$103$	−1552.42	−	896.288i	−1.48509	−	0.857416i	−0.999856	+	0.0169695i	$0.994598\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	19.5366	+	11.2794i	0.0176511	+	0.0101909i	0.508800	−	0.860885i	$-0.330089\pi$
$107$	19.5366	+	11.2794i	0.0176511	+	0.0101909i	−0.491148	+	0.871076i	$0.663423\pi$
$108$		0			0
$109$	−476.210	−	824.820i	−0.418465	−	0.724802i	0.577320	−	0.816518i	$-0.304098\pi$
$109$	−476.210	−	824.820i	−0.418465	−	0.724802i	−0.995785	+	0.0917154i	$0.970765\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$			120.145i			0.100020i	0.998749	+	0.0500102i	$0.0159254\pi$
$113$			120.145i			0.100020i	−0.998749	+	0.0500102i	$0.984075\pi$
$114$		0			0
$115$	−1038.77	+	599.735i	−0.842312	+	0.486309i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	1182.42	−	480.622i	0.910859	−	0.370240i
$120$		0			0
$121$	798.612	−	1383.24i	0.600009	−	1.03925i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	1111.41			0.795262
$126$		0			0
$127$	−884.302			−0.617867			−0.308934	−	0.951084i	$-0.599972\pi$
$127$	−884.302			−0.617867			−0.308934	+	0.951084i	$0.599972\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	803.439	−	1391.60i	0.535853	−	0.928125i	−0.463268	−	0.886218i	$-0.653323\pi$
$131$	803.439	−	1391.60i	0.535853	−	0.928125i	0.999122	−	0.0419070i	$-0.0133433\pi$
$132$		0			0
$133$	−1863.21	+	2395.16i	−1.21474	+	1.56156i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−615.297	+	355.242i	−0.383711	+	0.221535i	−0.679431	−	0.733739i	$-0.737773\pi$
$137$	−615.297	+	355.242i	−0.383711	+	0.221535i	0.295721	+	0.955274i	$0.404440\pi$
$138$		0			0
$139$		−	1531.91i		−	0.934782i	−0.884051	−	0.467391i	$-0.845194\pi$
$139$		−	1531.91i		−	0.934782i	0.884051	−	0.467391i	$-0.154806\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−239.593	−	414.987i	−0.140110	−	0.242678i
$144$		0			0
$145$	−1322.31	−	763.435i	−0.757322	−	0.437240i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	2079.39	+	1200.54i	1.14329	+	0.660079i	0.947243	−	0.320516i	$-0.103856\pi$
$149$	2079.39	+	1200.54i	1.14329	+	0.660079i	0.196046	+	0.980595i	$0.437190\pi$
$150$		0			0
$151$	1233.99	+	2137.33i	0.665035	+	1.15188i	0.979276	+	0.202532i	$0.0649169\pi$
$151$	1233.99	+	2137.33i	0.665035	+	1.15188i	−0.314240	+	0.949343i	$0.601750\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$			1262.12i			0.654036i
$156$		0			0
$157$	2109.74	−	1218.06i	1.07246	−	0.619184i	0.143606	−	0.989635i	$-0.454130\pi$
$157$	2109.74	−	1218.06i	1.07246	−	0.619184i	0.928852	+	0.370451i	$0.120797\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	1068.59	−	1373.67i	0.523083	−	0.672424i
$162$		0			0
$163$	1638.50	−	2837.97i	0.787347	−	1.36372i	−0.140240	−	0.990118i	$-0.544787\pi$
$163$	1638.50	−	2837.97i	0.787347	−	1.36372i	0.927587	−	0.373607i	$-0.121879\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	365.585			0.169400			0.0847000	−	0.996406i	$-0.473007\pi$
$167$	365.585			0.169400			0.0847000	+	0.996406i	$0.473007\pi$
$168$		0			0
$169$	2118.58			0.964308
$170$		0			0
$171$		0			0
$172$		0			0
$173$	1046.47	−	1812.53i	0.459892	−	0.796557i	−0.539062	−	0.842266i	$-0.681221\pi$
$173$	1046.47	−	1812.53i	0.459892	−	0.796557i	0.998955	+	0.0457089i	$0.0145547\pi$
$174$		0			0
$175$	650.739	−	264.508i	0.281093	−	0.114257i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	1524.01	−	879.890i	0.636370	−	0.367408i	−0.146845	−	0.989160i	$-0.546912\pi$
$179$	1524.01	−	879.890i	0.636370	−	0.367408i	0.783215	+	0.621751i	$0.213578\pi$
$180$		0			0
$181$			3197.54i			1.31310i	0.754282	+	0.656551i	$0.227985\pi$
$181$			3197.54i			1.31310i	−0.754282	+	0.656551i	$0.772015\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	601.135	+	1041.20i	0.238899	+	0.413786i
$186$		0			0
$187$	−3229.69	−	1864.66i	−1.26299	−	0.729186i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	475.772	+	274.687i	0.180239	+	0.104061i	0.587405	−	0.809293i	$-0.300150\pi$
$191$	475.772	+	274.687i	0.180239	+	0.104061i	−0.407166	+	0.913354i	$0.633483\pi$
$192$		0			0
$193$	352.238	+	610.094i	0.131371	+	0.227542i	0.924205	−	0.381896i	$-0.124729\pi$
$193$	352.238	+	610.094i	0.131371	+	0.227542i	−0.792834	+	0.609437i	$0.791395\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	5317.81i		−	1.92324i	−0.274384	−	0.961620i	$-0.588474\pi$
$197$		−	5317.81i		−	1.92324i	0.274384	−	0.961620i	$-0.411526\pi$
$198$		0			0
$199$	2155.80	−	1244.65i	0.767942	−	0.443371i	−0.0641982	−	0.997937i	$-0.520449\pi$
$199$	2155.80	−	1244.65i	0.767942	−	0.443371i	0.832140	+	0.554566i	$0.187116\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	2194.48	+	303.711i	0.758729	+	0.105007i
$204$		0			0
$205$	1655.20	−	2866.88i	0.563922	−	0.976741i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	8866.38			2.93445
$210$		0			0
$211$	3454.31			1.12704			0.563519	−	0.826103i	$-0.309447\pi$
$211$	3454.31			1.12704			0.563519	+	0.826103i	$0.309447\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−32.0013	+	55.4279i	−0.0101510	+	0.0175821i
$216$		0			0
$217$	−689.566	−	1696.46i	−0.215718	−	0.530706i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−528.520	+	305.141i	−0.160869	+	0.0928778i
$222$		0			0
$223$			3896.38i			1.17005i	0.811016	+	0.585024i	$0.198915\pi$
$223$			3896.38i			1.17005i	−0.811016	+	0.585024i	$0.801085\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	302.747	+	524.374i	0.0885201	+	0.153321i	0.906886	−	0.421377i	$-0.138453\pi$
$227$	302.747	+	524.374i	0.0885201	+	0.153321i	−0.818366	+	0.574698i	$0.805120\pi$
$228$		0			0
$229$	−1912.98	−	1104.46i	−0.552023	−	0.318711i	0.197914	−	0.980219i	$-0.436583\pi$
$229$	−1912.98	−	1104.46i	−0.552023	−	0.318711i	−0.749938	+	0.661509i	$0.769917\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−2065.77	−	1192.67i	−0.580829	−	0.335342i	0.180634	−	0.983550i	$-0.442185\pi$
$233$	−2065.77	−	1192.67i	−0.580829	−	0.335342i	−0.761463	+	0.648209i	$0.775518\pi$
$234$		0			0
$235$	366.013	+	633.953i	0.101600	+	0.175977i
$236$		0			0
$237$		0			0
$238$		0			0
$239$			3017.95i			0.816798i	0.912803	+	0.408399i	$0.133913\pi$
$239$			3017.95i			0.816798i	−0.912803	+	0.408399i	$0.866087\pi$
$240$		0			0
$241$	−2178.48	+	1257.75i	−0.582275	+	0.336176i	−0.762037	−	0.647534i	$-0.775800\pi$
$241$	−2178.48	+	1257.75i	−0.582275	+	0.336176i	0.179762	+	0.983710i	$0.442467\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−3136.58	+	3054.54i	−0.817913	+	0.796521i
$246$		0			0
$247$	725.465	−	1256.54i	0.186883	−	0.323692i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	1306.11			0.328451			0.164226	−	0.986423i	$-0.447488\pi$
$251$	1306.11			0.328451			0.164226	+	0.986423i	$0.447488\pi$
$252$		0			0
$253$	−5085.03			−1.26361
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−3735.91	+	6470.79i	−0.906770	+	1.57057i	−0.0882460	+	0.996099i	$0.528126\pi$
$257$	−3735.91	+	6470.79i	−0.906770	+	1.57057i	−0.818524	+	0.574473i	$0.805207\pi$
$258$		0			0
$259$	−1376.88	−	1071.08i	−0.330328	−	0.256964i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−1330.77	+	768.318i	−0.312010	+	0.180139i	−0.647825	−	0.761789i	$-0.724321\pi$
$263$	−1330.77	+	768.318i	−0.312010	+	0.180139i	0.335816	+	0.941928i	$0.390988\pi$
$264$		0			0
$265$		−	5999.62i		−	1.39077i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−1958.09	−	3391.52i	−0.443818	−	0.768715i	0.554151	−	0.832416i	$-0.313043\pi$
$269$	−1958.09	−	3391.52i	−0.443818	−	0.768715i	−0.997969	+	0.0637010i	$0.979710\pi$
$270$		0			0
$271$	−3117.42	−	1799.84i	−0.698780	−	0.403441i	0.108113	−	0.994139i	$-0.465519\pi$
$271$	−3117.42	−	1799.84i	−0.698780	−	0.403441i	−0.806893	+	0.590698i	$0.798853\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−1777.45	−	1026.21i	−0.389760	−	0.225028i
$276$		0			0
$277$	−142.040	−	246.021i	−0.0308100	−	0.0533645i	0.850209	−	0.526445i	$-0.176475\pi$
$277$	−142.040	−	246.021i	−0.0308100	−	0.0533645i	−0.881019	+	0.473080i	$0.843142\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$			321.256i			0.0682011i	0.999418	+	0.0341006i	$0.0108566\pi$
$281$			321.256i			0.0682011i	−0.999418	+	0.0341006i	$0.989143\pi$
$282$		0			0
$283$	−5891.40	+	3401.40i	−1.23748	+	0.714460i	−0.968579	−	0.248707i	$-0.919994\pi$
$283$	−5891.40	+	3401.40i	−1.23748	+	0.714460i	−0.268903	+	0.963167i	$0.586661\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−658.474	+	4757.82i	−0.135430	+	0.978556i
$288$		0			0
$289$	81.7017	−	141.511i	0.0166297	−	0.0288035i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−3180.05			−0.634063			−0.317031	−	0.948415i	$-0.602686\pi$
$293$	−3180.05			−0.634063			−0.317031	+	0.948415i	$0.602686\pi$
$294$		0			0
$295$	2884.20			0.569237
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−416.067	+	720.649i	−0.0804741	+	0.139385i
$300$		0			0
$301$	12.7308	−	91.9871i	0.00243785	−	0.0176148i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	4731.11	−	2731.51i	0.888204	−	0.512805i
$306$		0			0
$307$			2976.39i			0.553328i	0.960967	+	0.276664i	$0.0892289\pi$
$307$			2976.39i			0.553328i	−0.960967	+	0.276664i	$0.910771\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−2340.89	−	4054.55i	−0.426817	−	0.739268i	0.569772	−	0.821803i	$-0.307032\pi$
$311$	−2340.89	−	4054.55i	−0.426817	−	0.739268i	−0.996588	+	0.0825352i	$0.973698\pi$
$312$		0			0
$313$	−850.477	−	491.023i	−0.153584	−	0.0886718i	0.421238	−	0.906950i	$-0.361596\pi$
$313$	−850.477	−	491.023i	−0.153584	−	0.0886718i	−0.574823	+	0.818278i	$0.694929\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−4269.80	−	2465.17i	−0.756516	−	0.436775i	0.0715272	−	0.997439i	$-0.477213\pi$
$317$	−4269.80	−	2465.17i	−0.756516	−	0.436775i	−0.828044	+	0.560664i	$0.810546\pi$
$318$		0			0
$319$	−3236.50	−	5605.79i	−0.568055	−	0.983899i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	11292.0i		−	1.94522i
$324$		0			0
$325$	−290.868	+	167.933i	−0.0496445	+	0.0286623i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−838.338	−	652.148i	−0.140483	−	0.109283i
$330$		0			0
$331$	−2017.25	+	3493.99i	−0.334980	+	0.580202i	−0.983481	−	0.181012i	$-0.942063\pi$
$331$	−2017.25	+	3493.99i	−0.334980	+	0.580202i	0.648501	+	0.761214i	$0.275396\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	2091.48			0.341104
$336$		0			0
$337$	2771.62			0.448011			0.224006	−	0.974588i	$-0.428087\pi$
$337$	2771.62			0.448011			0.224006	+	0.974588i	$0.428087\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−2675.30	+	4633.76i	−0.424856	+	0.735872i
$342$		0			0
$343$	2547.13	−	5819.43i	0.400968	−	0.916092i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−3743.15	+	2161.11i	−0.579085	+	0.334335i	−0.760770	−	0.649022i	$-0.775178\pi$
$347$	−3743.15	+	2161.11i	−0.579085	+	0.334335i	0.181685	+	0.983357i	$0.441845\pi$
$348$		0			0
$349$			1331.65i			0.204245i	0.994772	+	0.102122i	$0.0325634\pi$
$349$			1331.65i			0.204245i	−0.994772	+	0.102122i	$0.967437\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	5674.26	+	9828.10i	0.855553	+	1.48186i	0.876131	+	0.482073i	$0.160116\pi$
$353$	5674.26	+	9828.10i	0.855553	+	1.48186i	−0.0205782	+	0.999788i	$0.506551\pi$
$354$		0			0
$355$	882.713	+	509.634i	0.131970	+	0.0761932i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−7247.49	−	4184.34i	−1.06548	−	0.615156i	−0.138538	−	0.990357i	$-0.544240\pi$
$359$	−7247.49	−	4184.34i	−1.06548	−	0.615156i	−0.926943	+	0.375201i	$0.877574\pi$
$360$		0			0
$361$	9993.77	+	17309.7i	1.45703	+	2.52365i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		−	9822.76i		−	1.40862i
$366$		0			0
$367$	−2351.31	+	1357.53i	−0.334434	+	0.193086i	−0.657808	−	0.753186i	$-0.728516\pi$
$367$	−2351.31	+	1357.53i	−0.334434	+	0.193086i	0.323374	+	0.946271i	$0.395183\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	3277.93	+	8064.33i	0.458711	+	1.12851i
$372$		0			0
$373$	−3048.56	+	5280.25i	−0.423186	+	0.732979i	−0.996249	−	0.0865320i	$-0.972422\pi$
$373$	−3048.56	+	5280.25i	−0.423186	+	0.732979i	0.573063	+	0.819511i	$0.305755\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−1059.27			−0.144708
$378$		0			0
$379$	9922.24			1.34478			0.672389	−	0.740198i	$-0.265268\pi$
$379$	9922.24			1.34478			0.672389	+	0.740198i	$0.265268\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−609.532	+	1055.74i	−0.0813202	+	0.140851i	−0.903817	−	0.427919i	$-0.859247\pi$
$383$	−609.532	+	1055.74i	−0.0813202	+	0.140851i	0.822497	+	0.568769i	$0.192580\pi$
$384$		0			0
$385$	12671.5	+	1753.71i	1.67740	+	0.232149i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−11374.6	+	6567.15i	−1.48256	+	0.855958i	−0.999804	−	0.0197949i	$-0.993699\pi$
$389$	−11374.6	+	6567.15i	−1.48256	+	0.855958i	−0.482759	+	0.875753i	$0.660365\pi$
$390$		0			0
$391$			6476.19i			0.837634i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−3413.29	−	5911.99i	−0.434788	−	0.753075i
$396$		0			0
$397$	2697.68	+	1557.51i	0.341040	+	0.196900i	0.660732	−	0.750622i	$-0.270246\pi$
$397$	2697.68	+	1557.51i	0.341040	+	0.196900i	−0.319692	+	0.947522i	$0.603579\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	9724.47	+	5614.42i	1.21101	+	0.699179i	0.962980	−	0.269572i	$-0.0868822\pi$
$401$	9724.47	+	5614.42i	1.21101	+	0.699179i	0.248034	+	0.968751i	$0.420216\pi$
$402$		0			0
$403$	437.797	+	758.287i	0.0541147	+	0.0937295i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			5096.90i			0.620747i
$408$		0			0
$409$	−10739.4	+	6200.41i	−1.29836	+	0.749610i	−0.980121	−	0.198399i	$-0.936426\pi$
$409$	−10739.4	+	6200.41i	−1.29836	+	0.749610i	−0.318242	+	0.948010i	$0.603092\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−3876.78	+	1575.81i	−0.461898	+	0.187749i
$414$		0			0
$415$	−2798.71	+	4847.51i	−0.331044	+	0.573385i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−8260.19			−0.963095			−0.481547	−	0.876420i	$-0.659925\pi$
$419$	−8260.19			−0.963095			−0.481547	+	0.876420i	$0.659925\pi$
$420$		0			0
$421$	5571.81			0.645020			0.322510	−	0.946566i	$-0.395473\pi$
$421$	5571.81			0.645020			0.322510	+	0.946566i	$0.395473\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−1306.96	+	2263.72i	−0.149169	+	0.258368i
$426$		0			0
$427$	−4866.89	+	6256.40i	−0.551582	+	0.709060i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−6094.88	+	3518.88i	−0.681160	+	0.393268i	−0.800292	−	0.599611i	$-0.795322\pi$
$431$	−6094.88	+	3518.88i	−0.681160	+	0.393268i	0.119132	+	0.992878i	$0.461989\pi$
$432$		0			0
$433$		−	9212.26i		−	1.02243i	−0.859452	−	0.511216i	$-0.829195\pi$
$433$		−	9212.26i		−	1.02243i	0.859452	−	0.511216i	$-0.170805\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−7698.48	−	13334.2i	−0.842719	−	1.45963i
$438$		0			0
$439$	7345.30	+	4240.81i	0.798570	+	0.461054i	0.842971	−	0.537959i	$-0.180805\pi$
$439$	7345.30	+	4240.81i	0.798570	+	0.461054i	−0.0444012	+	0.999014i	$0.514138\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	11305.9	+	6527.49i	1.21255	+	0.700068i	0.963315	−	0.268374i	$-0.0864863\pi$
$443$	11305.9	+	6527.49i	1.21255	+	0.700068i	0.249239	+	0.968442i	$0.419820\pi$
$444$		0			0
$445$	−163.692	−	283.523i	−0.0174376	−	0.0302029i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			14114.0i			1.48348i	0.670689	+	0.741738i	$0.265998\pi$
$449$			14114.0i			1.48348i	−0.670689	+	0.741738i	$0.734002\pi$
$450$		0			0
$451$	12153.9	−	7017.03i	1.26896	−	0.732637i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	1285.34	−	1652.31i	0.132435	−	0.170245i
$456$		0			0
$457$	4486.87	−	7771.49i	0.459271	−	0.795481i	−0.539651	−	0.841889i	$-0.681444\pi$
$457$	4486.87	−	7771.49i	0.459271	−	0.795481i	0.998923	+	0.0464073i	$0.0147772\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−955.010			−0.0964842			−0.0482421	−	0.998836i	$-0.515362\pi$
$461$	−955.010			−0.0964842			−0.0482421	+	0.998836i	$0.515362\pi$
$462$		0			0
$463$	−12004.5			−1.20496			−0.602479	−	0.798135i	$-0.705820\pi$
$463$	−12004.5			−1.20496			−0.602479	+	0.798135i	$0.705820\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	2532.46	−	4386.34i	0.250938	−	0.434638i	−0.712846	−	0.701320i	$-0.752594\pi$
$467$	2532.46	−	4386.34i	0.250938	−	0.434638i	0.963784	+	0.266683i	$0.0859276\pi$
$468$		0			0
$469$	−2811.24	+	1142.69i	−0.276783	+	0.112505i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−234.981	+	135.666i	−0.0228423	+	0.0131880i
$474$		0			0
$475$		−	6214.52i		−	0.600299i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−7606.85	−	13175.5i	−0.725607	−	1.25679i	−0.958724	−	0.284340i	$-0.908226\pi$
$479$	−7606.85	−	13175.5i	−0.725607	−	1.25679i	0.233116	−	0.972449i	$-0.425108\pi$
$480$		0			0
$481$	722.332	+	417.038i	0.0684730	+	0.0395329i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−15265.9	−	8813.75i	−1.42925	−	0.825179i
$486$		0			0
$487$	7905.92	+	13693.5i	0.735629	+	1.27415i	0.954447	+	0.298382i	$0.0964468\pi$
$487$	7905.92	+	13693.5i	0.735629	+	1.27415i	−0.218817	+	0.975766i	$0.570220\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$			18064.2i			1.66034i	0.557512	+	0.830169i	$0.311756\pi$
$491$			18064.2i			1.66034i	−0.557512	+	0.830169i	$0.688244\pi$
$492$		0			0
$493$	−7139.42	+	4121.94i	−0.652217	+	0.376558i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−1464.93	−	202.744i	−0.132216	−	0.0182984i
$498$		0			0
$499$	−5262.33	+	9114.62i	−0.472092	+	0.817688i	−0.999490	−	0.0319305i	$-0.989834\pi$
$499$	−5262.33	+	9114.62i	−0.472092	+	0.817688i	0.527398	+	0.849619i	$0.323168\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	7790.82			0.690607			0.345304	−	0.938491i	$-0.387776\pi$
$503$	7790.82			0.690607			0.345304	+	0.938491i	$0.387776\pi$
$504$		0			0
$505$	−9108.83			−0.802649
$506$		0			0
$507$		0			0
$508$		0			0
$509$	5098.24	−	8830.41i	0.443960	−	0.768961i	−0.554019	−	0.832504i	$-0.686907\pi$
$509$	5098.24	−	8830.41i	0.443960	−	0.768961i	0.997979	+	0.0635430i	$0.0202400\pi$
$510$		0			0
$511$	5366.74	+	13203.2i	0.464600	+	1.14300i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−19815.6	+	11440.5i	−1.69549	+	0.978892i
$516$		0			0
$517$			3103.35i			0.263994i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	963.789	+	1669.33i	0.0810449	+	0.140374i	0.903699	−	0.428168i	$-0.140841\pi$
$521$	963.789	+	1669.33i	0.0810449	+	0.140374i	−0.822654	+	0.568542i	$0.807508\pi$
$522$		0			0
$523$	6716.70	+	3877.89i	0.561569	+	0.324222i	0.753775	−	0.657133i	$-0.228231\pi$
$523$	6716.70	+	3877.89i	0.561569	+	0.324222i	−0.192206	+	0.981355i	$0.561564\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	5901.47	+	3407.21i	0.487803	+	0.281633i
$528$		0			0
$529$	−1668.28	−	2889.55i	−0.137115	−	0.237491i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		−	2296.59i		−	0.186635i
$534$		0			0
$535$	249.371	−	143.975i	0.0201519	−	0.0116347i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−17990.4	+	4565.93i	−1.43767	+	0.364876i
$540$		0			0
$541$	−8380.42	+	14515.3i	−0.665993	+	1.15353i	0.313022	+	0.949746i	$0.398659\pi$
$541$	−8380.42	+	14515.3i	−0.665993	+	1.15353i	−0.979015	+	0.203788i	$0.934675\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−12157.0			−0.955503
$546$		0			0
$547$	−5869.79			−0.458819			−0.229410	−	0.973330i	$-0.573680\pi$
$547$	−5869.79			−0.458819			−0.229410	+	0.973330i	$0.573680\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	9799.82	−	16973.8i	0.757688	−	1.31235i
$552$		0			0
$553$	7818.00	+	6081.67i	0.601185	+	0.467666i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−18756.5	+	10829.1i	−1.42682	+	0.823774i	−0.996868	−	0.0790779i	$-0.974802\pi$
$557$	−18756.5	+	10829.1i	−1.42682	+	0.823774i	−0.429951	+	0.902852i	$0.641469\pi$
$558$		0			0
$559$			44.4019i			0.00335957i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−4795.36	−	8305.80i	−0.358970	−	0.621755i	0.628819	−	0.777552i	$-0.283539\pi$
$563$	−4795.36	−	8305.80i	−0.358970	−	0.621755i	−0.987789	+	0.155797i	$0.950205\pi$
$564$		0			0
$565$	1328.11	+	766.787i	0.0988923	+	0.0570955i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	14405.5	+	8317.01i	1.06135	+	0.612772i	0.925806	−	0.377999i	$-0.123388\pi$
$569$	14405.5	+	8317.01i	1.06135	+	0.612772i	0.135546	+	0.990771i	$0.456721\pi$
$570$		0			0
$571$	3165.51	+	5482.83i	0.232001	+	0.401838i	0.958397	−	0.285439i	$-0.0921394\pi$
$571$	3165.51	+	5482.83i	0.232001	+	0.401838i	−0.726396	+	0.687277i	$0.758806\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			3564.14i			0.258495i
$576$		0			0
$577$	8431.94	−	4868.18i	0.608364	−	0.351239i	−0.163961	−	0.986467i	$-0.552427\pi$
$577$	8431.94	−	4868.18i	0.608364	−	0.351239i	0.772325	+	0.635228i	$0.219094\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	1113.39	−	8044.83i	0.0795028	−	0.574450i
$582$		0			0
$583$	12717.4	−	22027.1i	0.903430	−	1.56479i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−10940.3			−0.769255			−0.384628	−	0.923072i	$-0.625670\pi$
$587$	−10940.3			−0.769255			−0.384628	+	0.923072i	$0.625670\pi$
$588$		0			0
$589$	−16201.1			−1.13337
$590$		0			0
$591$		0			0
$592$		0			0
$593$	12430.4	−	21530.0i	0.860799	−	1.49095i	−0.0103608	−	0.999946i	$-0.503298\pi$
$593$	12430.4	−	21530.0i	0.860799	−	1.49095i	0.871159	−	0.491000i	$-0.163369\pi$
$594$		0			0
$595$	2233.49	−	16138.2i	0.153889	−	1.11193i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−20207.8	+	11667.0i	−1.37841	+	0.795825i	−0.991968	−	0.126488i	$-0.959629\pi$
$599$	−20207.8	+	11667.0i	−1.37841	+	0.795825i	−0.386442	+	0.922314i	$0.626296\pi$
$600$		0			0
$601$		−	13012.4i		−	0.883175i	−0.897218	−	0.441587i	$-0.854416\pi$
$601$		−	13012.4i		−	0.883175i	0.897218	−	0.441587i	$-0.145584\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−10193.8	−	17656.1i	−0.685017	−	1.18648i
$606$		0			0
$607$	−7355.69	−	4246.81i	−0.491859	−	0.283975i	0.233486	−	0.972360i	$-0.424987\pi$
$607$	−7355.69	−	4246.81i	−0.491859	−	0.283975i	−0.725345	+	0.688385i	$0.758320\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	439.806	+	253.922i	0.0291205	+	0.0168127i
$612$		0			0
$613$	4569.79	+	7915.11i	0.301097	+	0.521514i	0.976385	−	0.216040i	$-0.0693140\pi$
$613$	4569.79	+	7915.11i	0.301097	+	0.521514i	−0.675288	+	0.737554i	$0.735981\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$			7360.91i			0.480290i	0.970737	+	0.240145i	$0.0771950\pi$
$617$			7360.91i			0.480290i	−0.970737	+	0.240145i	$0.922805\pi$
$618$		0			0
$619$	−19878.5	+	11476.9i	−1.29077	+	0.745225i	−0.978790	−	0.204864i	$-0.934325\pi$
$619$	−19878.5	+	11476.9i	−1.29077	+	0.745225i	−0.311978	+	0.950089i	$0.600991\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	374.930	+	291.660i	0.0241112	+	0.0187562i
$624$		0			0
$625$	9463.74	−	16391.7i	0.605679	−	1.04907i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	6491.31			0.411487
$630$		0			0
$631$	−21126.0			−1.33282			−0.666412	−	0.745584i	$-0.732171\pi$
$631$	−21126.0			−1.33282			−0.666412	+	0.745584i	$0.732171\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−5643.77	+	9775.29i	−0.352703	+	0.610899i
$636$		0			0
$637$	−824.929	+	2923.19i	−0.0513106	+	0.181823i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−15447.5	+	8918.61i	−0.951855	+	0.549554i	−0.893657	−	0.448751i	$-0.851869\pi$
$641$	−15447.5	+	8918.61i	−0.951855	+	0.549554i	−0.0581985	+	0.998305i	$0.518536\pi$
$642$		0			0
$643$		−	25449.0i		−	1.56082i	−0.625266	−	0.780412i	$-0.715009\pi$
$643$		−	25449.0i		−	1.56082i	0.625266	−	0.780412i	$-0.284991\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	13149.2	+	22775.1i	0.798993	+	1.38390i	0.920273	+	0.391277i	$0.127967\pi$
$647$	13149.2	+	22775.1i	0.798993	+	1.38390i	−0.121280	+	0.992618i	$0.538700\pi$
$648$		0			0
$649$	10589.1	+	6113.64i	0.640462	+	0.369771i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	8203.79	+	4736.46i	0.491637	+	0.283847i	0.725253	−	0.688482i	$-0.241723\pi$
$653$	8203.79	+	4736.46i	0.491637	+	0.283847i	−0.233616	+	0.972329i	$0.575056\pi$
$654$		0			0
$655$	−10255.4	−	17762.8i	−0.611771	−	1.05962i
$656$		0			0
$657$		0			0
$658$		0			0
$659$		−	22384.5i		−	1.32318i	−0.749865	−	0.661591i	$-0.769882\pi$
$659$		−	22384.5i		−	1.32318i	0.749865	−	0.661591i	$-0.230118\pi$
$660$		0			0
$661$	−19857.3	+	11464.6i	−1.16847	+	0.674618i	−0.953320	−	0.301962i	$-0.902359\pi$
$661$	−19857.3	+	11464.6i	−1.16847	+	0.674618i	−0.215153	+	0.976580i	$0.569025\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	14585.4	+	35882.7i	0.850521	+	2.09244i
$666$		0			0
$667$	−5620.37	+	9734.77i	−0.326269	+	0.565115i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	23159.9			1.33245
$672$		0			0
$673$	−4873.86			−0.279158			−0.139579	−	0.990211i	$-0.544575\pi$
$673$	−4873.86			−0.279158			−0.139579	+	0.990211i	$0.544575\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	8123.71	−	14070.7i	0.461181	−	0.798789i	−0.537839	−	0.843048i	$-0.680759\pi$
$677$	8123.71	−	14070.7i	0.461181	−	0.798789i	0.999020	+	0.0442583i	$0.0140925\pi$
$678$		0			0
$679$	25334.9	+	3506.30i	1.43191	+	0.198173i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	18786.2	−	10846.2i	1.05247	−	0.607641i	0.129127	−	0.991628i	$-0.458783\pi$
$683$	18786.2	−	10846.2i	1.05247	−	0.607641i	0.923339	+	0.383987i	$0.125449\pi$
$684$		0			0
$685$			9068.85i			0.505844i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−2081.12	−	3604.61i	−0.115072	−	0.199310i
$690$		0			0
$691$	19499.9	+	11258.3i	1.07353	+	0.619803i	0.929144	−	0.369718i	$-0.120546\pi$
$691$	19499.9	+	11258.3i	1.07353	+	0.619803i	0.144387	+	0.989521i	$0.453879\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−16934.1	−	9776.90i	−0.924239	−	0.533610i
$696$		0			0
$697$	−8936.75	−	15478.9i	−0.485658	−	0.841184i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			33929.0i			1.82807i	0.405631	+	0.914037i	$0.367052\pi$
$701$			33929.0i			1.82807i	−0.405631	+	0.914037i	$0.632948\pi$
$702$		0			0
$703$	−13365.3	+	7716.46i	−0.717044	+	0.413986i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	12243.6	−	4976.68i	0.651296	−	0.264734i
$708$		0			0
$709$	−9593.62	+	16616.6i	−0.508175	+	0.880185i	0.491780	+	0.870719i	$0.336346\pi$
$709$	−9593.62	+	16616.6i	−0.508175	+	0.880185i	−0.999955	+	0.00946553i	$0.996987\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	9291.63			0.488043
$714$		0			0
$715$	−6116.49			−0.319922
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−6883.43	+	11922.4i	−0.357036	+	0.618404i	−0.987464	−	0.157844i	$-0.949546\pi$
$719$	−6883.43	+	11922.4i	−0.357036	+	0.618404i	0.630429	+	0.776247i	$0.282879\pi$
$720$		0			0
$721$	20384.3	−	26204.0i	1.05291	−	1.35352i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−3929.15	+	2268.49i	−0.201276	+	0.116207i
$726$		0			0
$727$		−	12226.1i		−	0.623717i	−0.950129	−	0.311858i	$-0.899049\pi$
$727$		−	12226.1i		−	0.623717i	0.950129	−	0.311858i	$-0.100951\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	172.782	+	299.267i	0.00874222	+	0.0151420i
$732$		0			0
$733$	2256.76	+	1302.94i	0.113718	+	0.0656553i	0.555780	−	0.831329i	$-0.312420\pi$
$733$	2256.76	+	1302.94i	0.113718	+	0.0656553i	−0.442062	+	0.896984i	$0.645753\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	7678.71	+	4433.30i	0.383784	+	0.221578i
$738$		0			0
$739$	16871.7	+	29222.7i	0.839833	+	1.45463i	0.890034	+	0.455894i	$0.150680\pi$
$739$	16871.7	+	29222.7i	0.839833	+	1.45463i	−0.0502016	+	0.998739i	$0.515986\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		−	14586.9i		−	0.720244i	−0.932905	−	0.360122i	$-0.882735\pi$
$743$		−	14586.9i		−	0.720244i	0.932905	−	0.360122i	$-0.117265\pi$
$744$		0			0
$745$	26542.0	−	15324.0i	1.30527	−	0.753597i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−256.528	+	329.768i	−0.0125145	+	0.0160874i
$750$		0			0
$751$	−3757.62	+	6508.39i	−0.182580	+	0.316238i	−0.942758	−	0.333477i	$-0.891778\pi$
$751$	−3757.62	+	6508.39i	−0.182580	+	0.316238i	0.760178	+	0.649714i	$0.225111\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	31502.0			1.51851
$756$		0			0
$757$	23917.4			1.14834			0.574169	−	0.818737i	$-0.305325\pi$
$757$	23917.4			1.14834			0.574169	+	0.818737i	$0.305325\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−6099.27	+	10564.2i	−0.290537	+	0.503224i	−0.973937	−	0.226820i	$-0.927167\pi$
$761$	−6099.27	+	10564.2i	−0.290537	+	0.503224i	0.683400	+	0.730044i	$0.260500\pi$
$762$		0			0
$763$	16340.7	−	6642.07i	0.775327	−	0.315150i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	1732.85	−	1000.46i	0.0815769	−	0.0470985i
$768$		0			0
$769$			2013.08i			0.0943999i	0.998885	+	0.0471999i	$0.0150298\pi$
$769$			2013.08i			0.0943999i	−0.998885	+	0.0471999i	$0.984970\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−15139.1	−	26221.7i	−0.704418	−	1.22009i	−0.966901	−	0.255152i	$-0.917875\pi$
$773$	−15139.1	−	26221.7i	−0.704418	−	1.22009i	0.262483	−	0.964937i	$-0.415459\pi$
$774$		0			0
$775$	3247.85	+	1875.14i	0.150537	+	0.0869125i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	36800.7	+	21246.9i	1.69258	+	0.977213i
$780$		0			0
$781$	2160.54	+	3742.17i	0.0989888	+	0.171454i
$782$		0			0
$783$		0			0
$784$		0			0
$785$		−	31095.5i		−	1.41382i
$786$		0			0
$787$	−24839.3	+	14341.0i	−1.12507	+	0.649557i	−0.942689	−	0.333671i	$-0.891712\pi$
$787$	−24839.3	+	14341.0i	−1.12507	+	0.649557i	−0.182377	+	0.983229i	$0.558379\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−2204.11	−	305.045i	−0.0990761	−	0.0137119i
$792$		0			0
$793$	1894.99	−	3282.21i	0.0848586	−	0.146979i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	27108.9			1.20483			0.602413	−	0.798184i	$-0.294206\pi$
$797$	27108.9			1.20483			0.602413	+	0.798184i	$0.294206\pi$
$798$		0			0
$799$	3952.36			0.174999
$800$		0			0
$801$		0			0
$802$		0			0
$803$	20821.3	−	36063.5i	0.915028	−	1.58487i
$804$		0			0
$805$	−8364.97	−	20579.4i	−0.366244	−	0.901029i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	17128.3	−	9889.03i	0.744375	−	0.429765i	−0.0792832	−	0.996852i	$-0.525263\pi$
$809$	17128.3	−	9889.03i	0.744375	−	0.429765i	0.823658	+	0.567087i	$0.191930\pi$
$810$		0			0
$811$		−	44456.6i		−	1.92488i	−0.271487	−	0.962442i	$-0.587516\pi$
$811$		−	44456.6i		−	1.92488i	0.271487	−	0.962442i	$-0.412484\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−20914.4	−	36224.8i	−0.898896	−	1.55693i
$816$		0			0
$817$	−711.499	−	410.784i	−0.0304678	−	0.0175906i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−9958.57	−	5749.58i	−0.423333	−	0.244411i	0.273169	−	0.961966i	$-0.411928\pi$
$821$	−9958.57	−	5749.58i	−0.423333	−	0.244411i	−0.696502	+	0.717555i	$0.745261\pi$
$822$		0			0
$823$	596.549	+	1033.25i	0.0252666	+	0.0437630i	0.878382	−	0.477959i	$-0.158623\pi$
$823$	596.549	+	1033.25i	0.0252666	+	0.0437630i	−0.853116	+	0.521722i	$0.825290\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	29552.9i		−	1.24263i	−0.783561	−	0.621315i	$-0.786599\pi$
$827$		−	29552.9i		−	1.24263i	0.783561	−	0.621315i	$-0.213401\pi$
$828$		0			0
$829$	−11762.7	+	6791.21i	−0.492806	+	0.284521i	−0.725738	−	0.687972i	$-0.758501\pi$
$829$	−11762.7	+	6791.21i	−0.492806	+	0.284521i	0.232932	+	0.972493i	$0.425168\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	5815.07	+	22912.2i	0.241873	+	0.953015i
$834$		0			0
$835$	2333.22	−	4041.26i	0.0967000	−	0.167489i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	11623.6			0.478297			0.239149	−	0.970983i	$-0.423132\pi$
$839$	11623.6			0.478297			0.239149	+	0.970983i	$0.423132\pi$
$840$		0			0
$841$	10080.1			0.413303
$842$		0			0
$843$		0			0
$844$		0			0
$845$	13521.2	−	23419.3i	0.550464	−	0.953432i
$846$		0			0
$847$	23348.4	+	18162.9i	0.947178	+	0.736816i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	7665.24	−	4425.53i	0.308767	−	0.178267i
$852$		0			0
$853$		−	1019.82i		−	0.0409354i	−0.999791	−	0.0204677i	$-0.993484\pi$
$853$		−	1019.82i		−	0.0409354i	0.999791	−	0.0204677i	$-0.00651553\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−4299.43	−	7446.83i	−0.171372	−	0.296825i	0.767528	−	0.641016i	$-0.221487\pi$
$857$	−4299.43	−	7446.83i	−0.171372	−	0.296825i	−0.938900	+	0.344191i	$0.888153\pi$
$858$		0			0
$859$	−32182.1	−	18580.4i	−1.27828	−	0.738013i	−0.301745	−	0.953389i	$-0.597569\pi$
$859$	−32182.1	−	18580.4i	−1.27828	−	0.738013i	−0.976531	+	0.215375i	$0.930903\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	10634.2	+	6139.68i	0.419459	+	0.242175i	0.694846	−	0.719159i	$-0.255473\pi$
$863$	10634.2	+	6139.68i	0.419459	+	0.242175i	−0.275387	+	0.961334i	$0.588806\pi$
$864$		0			0
$865$	−13357.5	−	23135.8i	−0.525049	−	0.909411i
$866$		0			0
$867$		0			0
$868$		0			0
$869$		−	28940.6i		−	1.12974i
$870$		0			0
$871$	1256.57	−	725.483i	0.0488833	−	0.0282228i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−2821.84	+	20389.3i	−0.109024	+	0.787753i
$876$		0			0
$877$	−15935.8	+	27601.6i	−0.613583	+	1.06276i	0.377048	+	0.926194i	$0.376939\pi$
$877$	−15935.8	+	27601.6i	−0.613583	+	1.06276i	−0.990631	+	0.136564i	$0.956394\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	29427.6			1.12536			0.562679	−	0.826676i	$-0.309771\pi$
$881$	29427.6			1.12536			0.562679	+	0.826676i	$0.309771\pi$
$882$		0			0
$883$	−846.860			−0.0322753			−0.0161377	−	0.999870i	$-0.505137\pi$
$883$	−846.860			−0.0322753			−0.0161377	+	0.999870i	$0.505137\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−3940.07	+	6824.39i	−0.149148	+	0.258332i	−0.930913	−	0.365241i	$-0.880986\pi$
$887$	−3940.07	+	6824.39i	−0.149148	+	0.258332i	0.781765	+	0.623574i	$0.214320\pi$
$888$		0			0
$889$	2245.22	−	16222.9i	0.0847043	−	0.612034i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−8137.73	+	4698.32i	−0.304948	+	0.176062i
$894$		0			0
$895$		−	22462.4i		−	0.838923i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	5913.91	+	10243.2i	0.219399	+	0.380011i
$900$		0			0
$901$	−28053.3	−	16196.6i	−1.03728	−	0.598875i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	35346.4	+	20407.2i	1.29829	+	0.749569i
$906$		0			0
$907$	10646.6	+	18440.4i	0.389762	+	0.675088i	0.992417	−	0.122914i	$-0.0392239\pi$
$907$	10646.6	+	18440.4i	0.389762	+	0.675088i	−0.602655	+	0.798002i	$0.705891\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$			14634.3i			0.532225i	0.963942	+	0.266112i	$0.0857393\pi$
$911$			14634.3i			0.532225i	−0.963942	+	0.266112i	$0.914261\pi$
$912$		0			0
$913$	−20550.5	+	11864.8i	−0.744931	+	0.430086i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	23489.5	+	18272.6i	0.845901	+	0.658032i
$918$		0			0
$919$	6098.61	−	10563.1i	0.218906	−	0.379156i	−0.735568	−	0.677451i	$-0.763085\pi$
$919$	6098.61	−	10563.1i	0.218906	−	0.379156i	0.954474	+	0.298295i	$0.0964179\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	707.119			0.0252168
$924$		0			0
$925$	3572.46			0.126986
$926$		0			0
$927$		0			0
$928$		0			0
$929$	12348.1	−	21387.5i	0.436091	−	0.755331i	−0.561293	−	0.827617i	$-0.689696\pi$
$929$	12348.1	−	21387.5i	0.436091	−	0.755331i	0.997384	+	0.0722858i	$0.0230294\pi$
$930$		0			0
$931$	−39209.6	−	40262.6i	−1.38028	−	1.41735i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−41224.9	+	23801.2i	−1.44192	+	0.832495i
$936$		0			0
$937$			14448.0i			0.503730i	0.967762	+	0.251865i	$0.0810439\pi$
$937$			14448.0i			0.503730i	−0.967762	+	0.251865i	$0.918956\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−15580.4	−	26986.0i	−0.539752	−	0.934878i	−0.998917	−	0.0465268i	$-0.985185\pi$
$941$	−15580.4	−	26986.0i	−0.539752	−	0.934878i	0.459165	−	0.888351i	$-0.348149\pi$
$942$		0			0
$943$	−21105.9	−	12185.5i	−0.728845	−	0.420799i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−8887.48	−	5131.19i	−0.304968	−	0.176073i	0.339705	−	0.940532i	$-0.389673\pi$
$947$	−8887.48	−	5131.19i	−0.304968	−	0.176073i	−0.644672	+	0.764459i	$0.723006\pi$
$948$		0			0
$949$	−3407.28	−	5901.58i	−0.116549	−	0.201869i
$950$		0			0
$951$		0			0
$952$		0			0
$953$			12686.9i			0.431236i	0.976478	+	0.215618i	$0.0691766\pi$
$953$			12686.9i			0.431236i	−0.976478	+	0.215618i	$0.930823\pi$
$954$		0			0
$955$	6072.91	−	3506.20i	0.205775	−	0.118804i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−4954.83	−	12189.8i	−0.166840	−	0.410458i
$960$		0			0
$961$	−10007.0	+	17332.7i	−0.335908	+	0.581810i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	8992.17			0.299967
$966$		0			0
$967$	−16129.8			−0.536401			−0.268200	−	0.963363i	$-0.586429\pi$
$967$	−16129.8			−0.536401			−0.268200	+	0.963363i	$0.586429\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−26382.4	+	45695.6i	−0.871937	+	1.51024i	−0.0119472	+	0.999929i	$0.503803\pi$
$971$	−26382.4	+	45695.6i	−0.871937	+	1.51024i	−0.859990	+	0.510311i	$0.829530\pi$
$972$		0			0
$973$	28103.5	+	3889.47i	0.925956	+	0.128151i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−46759.5	+	26996.6i	−1.53118	+	0.884030i	−0.531877	+	0.846821i	$0.678513\pi$
$977$	−46759.5	+	26996.6i	−1.53118	+	0.884030i	−0.999308	+	0.0372085i	$0.988153\pi$
$978$		0			0
$979$		−	1387.91i		−	0.0453093i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	26119.2	+	45239.8i	0.847480	+	1.46788i	0.883450	+	0.468526i	$0.155215\pi$
$983$	26119.2	+	45239.8i	0.847480	+	1.46788i	−0.0359696	+	0.999353i	$0.511452\pi$
$984$		0			0
$985$	−58784.4	−	33939.2i	−1.90155	−	1.09786i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	408.057	+	235.592i	0.0131198	+	0.00757471i
$990$		0			0
$991$	−4812.21	−	8334.99i	−0.154253	−	0.267174i	0.778534	−	0.627603i	$-0.215964\pi$
$991$	−4812.21	−	8334.99i	−0.154253	−	0.267174i	−0.932787	+	0.360429i	$0.882630\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		−	31774.3i		−	1.01237i
$996$		0			0
$997$	−25023.0	+	14447.0i	−0.794871	+	0.458919i	−0.841675	−	0.539985i	$-0.818430\pi$
$997$	−25023.0	+	14447.0i	−0.794871	+	0.458919i	0.0468034	+	0.998904i	$0.485097\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.4.bt.a.593.7		16
3.2	odd	2	inner	1008.4.bt.a.593.2		16
4.3	odd	2		63.4.p.a.26.1	yes	16
7.3	odd	6	inner	1008.4.bt.a.17.2		16
12.11	even	2		63.4.p.a.26.8	yes	16
21.17	even	6	inner	1008.4.bt.a.17.7		16
28.3	even	6		63.4.p.a.17.8	yes	16
28.11	odd	6		441.4.p.c.80.8		16
28.19	even	6		441.4.c.a.440.16		16
28.23	odd	6		441.4.c.a.440.15		16
28.27	even	2		441.4.p.c.215.1		16
84.11	even	6		441.4.p.c.80.1		16
84.23	even	6		441.4.c.a.440.2		16
84.47	odd	6		441.4.c.a.440.1		16
84.59	odd	6		63.4.p.a.17.1	✓	16
84.83	odd	2		441.4.p.c.215.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.p.a.17.1	✓	16	84.59	odd	6
63.4.p.a.17.8	yes	16	28.3	even	6
63.4.p.a.26.1	yes	16	4.3	odd	2
63.4.p.a.26.8	yes	16	12.11	even	2
441.4.c.a.440.1		16	84.47	odd	6
441.4.c.a.440.2		16	84.23	even	6
441.4.c.a.440.15		16	28.23	odd	6
441.4.c.a.440.16		16	28.19	even	6
441.4.p.c.80.1		16	84.11	even	6
441.4.p.c.80.8		16	28.11	odd	6
441.4.p.c.215.1		16	28.27	even	2
441.4.p.c.215.8		16	84.83	odd	2
1008.4.bt.a.17.2		16	7.3	odd	6	inner
1008.4.bt.a.17.7		16	21.17	even	6	inner
1008.4.bt.a.593.2		16	3.2	odd	2	inner
1008.4.bt.a.593.7		16	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1008.bt (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(6.38217 - 11.0542i) q^{5} +(-2.53897 + 18.3454i) q^{7} +(46.8633 - 27.0565i) q^{11} -8.85528i q^{13} +(-34.4587 - 59.6841i) q^{17} +(141.898 + 81.9246i) q^{19} +(-81.3807 - 46.9852i) q^{23} +(-18.9642 - 32.8469i) q^{25} -119.620i q^{29} +(-85.6311 + 49.4391i) q^{31} +(186.590 + 145.150i) q^{35} +(-47.0949 + 81.5708i) q^{37} +259.347 q^{41} -5.01418 q^{43} +(-28.6747 + 49.6660i) q^{47} +(-330.107 - 93.1568i) q^{49} +(407.058 - 235.015i) q^{53} -690.718i q^{55} +(112.979 + 195.685i) q^{59} +(370.650 + 213.995i) q^{61} +(-97.8884 - 56.5159i) q^{65} +(81.9267 + 141.901i) q^{67} +79.8529i q^{71} +(666.447 - 384.774i) q^{73} +(377.379 + 928.422i) q^{77} +(267.408 - 463.165i) q^{79} -438.520 q^{83} -879.684 q^{85} +(12.8242 - 22.2121i) q^{89} +(162.454 + 22.4833i) q^{91} +(1811.23 - 1045.71i) q^{95} -1381.00i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 56 q^{7} + 612 q^{19} - 20 q^{25} - 1128 q^{31} - 1196 q^{37} - 328 q^{43} + 784 q^{49} - 1632 q^{61} - 308 q^{67} + 4068 q^{73} + 2176 q^{79} - 4608 q^{85} - 924 q^{91}+O(q^{100}) \) 16 * q - 56 * q^7 + 612 * q^19 - 20 * q^25 - 1128 * q^31 - 1196 * q^37 - 328 * q^43 + 784 * q^49 - 1632 * q^61 - 308 * q^67 + 4068 * q^73 + 2176 * q^79 - 4608 * q^85 - 924 * q^91

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