LMFDB - Embedded newform 1008.4.bt.a.17.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,4,Mod(17,1008)]

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

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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			17.2
Root			$4.21355 + 2.43270i$ of defining polynomial
Character	$\chi$	$=$	1008.17
Dual form			1008.4.bt.a.593.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-6.38217 - 11.0542i) q^{5} +(-2.53897 - 18.3454i) q^{7} +O(q^{10})$	$q+(-6.38217 - 11.0542i) q^{5} +(-2.53897 - 18.3454i) q^{7} +(-46.8633 - 27.0565i) q^{11} +8.85528i q^{13} +(34.4587 - 59.6841i) q^{17} +(141.898 - 81.9246i) q^{19} +(81.3807 - 46.9852i) q^{23} +(-18.9642 + 32.8469i) q^{25} -119.620i q^{29} +(-85.6311 - 49.4391i) q^{31} +(-186.590 + 145.150i) q^{35} +(-47.0949 - 81.5708i) q^{37} -259.347 q^{41} -5.01418 q^{43} +(28.6747 + 49.6660i) q^{47} +(-330.107 + 93.1568i) q^{49} +(-407.058 - 235.015i) q^{53} +690.718i q^{55} +(-112.979 + 195.685i) q^{59} +(370.650 - 213.995i) q^{61} +(97.8884 - 56.5159i) q^{65} +(81.9267 - 141.901i) q^{67} +79.8529i q^{71} +(666.447 + 384.774i) q^{73} +(-377.379 + 928.422i) q^{77} +(267.408 + 463.165i) q^{79} +438.520 q^{83} -879.684 q^{85} +(-12.8242 - 22.2121i) q^{89} +(162.454 - 22.4833i) q^{91} +(-1811.23 - 1045.71i) q^{95} +1381.00i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 56 q^{7}+O(q^{10}) $ 16 * q - 56 * q^7	$ 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

Display 100 coefficients 10 coefficients

Character values

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

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

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	−0.996480	−	0.0838295i	$-0.973285\pi$
$5$	−6.38217	−	11.0542i	−0.570839	−	0.988721i	0.425642	−	0.904892i	$-0.360048\pi$
$6$		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	$-0.599277\pi$
$11$	−46.8633	−	27.0565i	−1.28453	−	0.741623i	−0.977673	+	0.210133i	$0.932610\pi$
$12$		0			0
$13$			8.85528i			0.188924i	0.995528	+	0.0944620i	$0.0301131\pi$
$13$			8.85528i			0.188924i	−0.995528	+	0.0944620i	$0.969887\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	34.4587	−	59.6841i	0.491615	−	0.851502i	−0.508339	−	0.861157i	$-0.669740\pi$
$17$	34.4587	−	59.6841i	0.491615	−	0.851502i	0.999953	+	0.00965543i	$0.00307347\pi$
$18$		0			0
$19$	141.898	−	81.9246i	1.71334	−	0.989199i	0.783383	−	0.621540i	$-0.213492\pi$
$19$	141.898	−	81.9246i	1.71334	−	0.989199i	0.929960	−	0.367660i	$-0.119841\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	81.3807	−	46.9852i	0.737785	−	0.425960i	−0.0834783	−	0.996510i	$-0.526603\pi$
$23$	81.3807	−	46.9852i	0.737785	−	0.425960i	0.821263	+	0.570549i	$0.193270\pi$
$24$		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	0.230988	−	0.972957i	$-0.425804\pi$
$31$	−85.6311	−	49.4391i	−0.496123	−	0.286437i	−0.727111	+	0.686520i	$0.759137\pi$
$32$		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	0.742227	−	0.670149i	$-0.233770\pi$
$37$	−47.0949	−	81.5708i	−0.209253	−	0.362437i	−0.951479	+	0.307712i	$0.900437\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−259.347			−0.987883			−0.493941	−	0.869495i	$-0.664444\pi$
$41$	−259.347			−0.987883			−0.493941	+	0.869495i	$0.664444\pi$
$42$		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	$-0.138302\pi$
$47$	28.6747	+	49.6660i	0.0889921	+	0.154139i	−0.818093	+	0.575086i	$0.804969\pi$
$48$		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	$-0.541798\pi$
$53$	−407.058	−	235.015i	−1.05497	−	0.609090i	−0.924038	+	0.382301i	$0.875132\pi$
$54$		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	$-0.913533\pi$
$59$	−112.979	+	195.685i	−0.249299	+	0.431798i	0.714033	+	0.700112i	$0.246867\pi$
$60$		0			0
$61$	370.650	−	213.995i	0.777982	−	0.449168i	−0.0577325	−	0.998332i	$-0.518387\pi$
$61$	370.650	−	213.995i	0.777982	−	0.449168i	0.835715	+	0.549164i	$0.185054\pi$
$62$		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	−0.781614	−	0.623762i	$-0.785603\pi$
$67$	81.9267	−	141.901i	0.149387	−	0.258746i	0.931001	+	0.365016i	$0.118937\pi$
$68$		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	0.927776	−	0.373138i	$-0.121718\pi$
$73$	666.447	+	384.774i	1.06852	+	0.616909i	0.140741	+	0.990046i	$0.455051\pi$
$74$		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	0.991182	−	0.132511i	$-0.0423040\pi$
$79$	267.408	+	463.165i	0.380833	+	0.659622i	−0.610349	+	0.792133i	$0.708971\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	438.520			0.579926			0.289963	−	0.957038i	$-0.406357\pi$
$83$	438.520			0.579926			0.289963	+	0.957038i	$0.406357\pi$
$84$		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	$-0.171529\pi$
$89$	−12.8242	−	22.2121i	−0.0152737	−	0.0264548i	−0.873561	+	0.486714i	$0.838195\pi$
$90$		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	$0.257135\pi$
$97$			1381.00i			1.44555i	−0.691081	+	0.722777i	$0.742865\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	356.808	−	618.009i	0.351522	−	0.608854i	−0.634994	−	0.772517i	$-0.718998\pi$
$101$	356.808	−	618.009i	0.351522	−	0.608854i	0.986516	+	0.163663i	$0.0523309\pi$
$102$		0			0
$103$	−1552.42	+	896.288i	−1.48509	+	0.857416i	−0.999856	−	0.0169695i	$-0.994598\pi$
$103$	−1552.42	+	896.288i	−1.48509	+	0.857416i	−0.485232	+	0.874385i	$0.661265\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−19.5366	+	11.2794i	−0.0176511	+	0.0101909i	−0.508800	−	0.860885i	$-0.669911\pi$
$107$	−19.5366	+	11.2794i	−0.0176511	+	0.0101909i	0.491148	+	0.871076i	$0.336577\pi$
$108$		0			0
$109$	−476.210	+	824.820i	−0.418465	+	0.724802i	−0.995785	−	0.0917154i	$-0.970765\pi$
$109$	−476.210	+	824.820i	−0.418465	+	0.724802i	0.577320	+	0.816518i	$0.304098\pi$
$110$		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	−0.999122	−	0.0419070i	$-0.986657\pi$
$131$	−803.439	−	1391.60i	−0.535853	−	0.928125i	0.463268	−	0.886218i	$-0.346677\pi$
$132$		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	$-0.262227\pi$
$137$	615.297	+	355.242i	0.383711	+	0.221535i	−0.295721	+	0.955274i	$0.595560\pi$
$138$		0			0
$139$			1531.91i			0.934782i	0.884051	+	0.467391i	$0.154806\pi$
$139$			1531.91i			0.934782i	−0.884051	+	0.467391i	$0.845194\pi$
$140$		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	$-0.896144\pi$
$149$	−2079.39	+	1200.54i	−1.14329	+	0.660079i	−0.196046	+	0.980595i	$0.562810\pi$
$150$		0			0
$151$	1233.99	−	2137.33i	0.665035	−	1.15188i	−0.314240	−	0.949343i	$-0.601750\pi$
$151$	1233.99	−	2137.33i	0.665035	−	1.15188i	0.979276	−	0.202532i	$-0.0649169\pi$
$152$		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	0.928852	−	0.370451i	$-0.120797\pi$
$157$	2109.74	+	1218.06i	1.07246	+	0.619184i	0.143606	+	0.989635i	$0.454130\pi$
$158$		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	0.927587	+	0.373607i	$0.121879\pi$
$163$	1638.50	+	2837.97i	0.787347	+	1.36372i	−0.140240	+	0.990118i	$0.544787\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−365.585			−0.169400			−0.0847000	−	0.996406i	$-0.526993\pi$
$167$	−365.585			−0.169400			−0.0847000	+	0.996406i	$0.526993\pi$
$168$		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	$-0.318779\pi$
$173$	−1046.47	−	1812.53i	−0.459892	−	0.796557i	−0.998955	+	0.0457089i	$0.985445\pi$
$174$		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	$-0.453088\pi$
$179$	−1524.01	−	879.890i	−0.636370	−	0.367408i	−0.783215	+	0.621751i	$0.786422\pi$
$180$		0			0
$181$		−	3197.54i		−	1.31310i	−0.754282	−	0.656551i	$-0.772015\pi$
$181$		−	3197.54i		−	1.31310i	0.754282	−	0.656551i	$-0.227985\pi$
$182$		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	$-0.699850\pi$
$191$	−475.772	+	274.687i	−0.180239	+	0.104061i	0.407166	+	0.913354i	$0.366517\pi$
$192$		0			0
$193$	352.238	−	610.094i	0.131371	−	0.227542i	−0.792834	−	0.609437i	$-0.791395\pi$
$193$	352.238	−	610.094i	0.131371	−	0.227542i	0.924205	+	0.381896i	$0.124729\pi$
$194$		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	0.832140	−	0.554566i	$-0.187116\pi$
$199$	2155.80	+	1244.65i	0.767942	+	0.443371i	−0.0641982	+	0.997937i	$0.520449\pi$
$200$		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	$-0.801085\pi$
$223$		−	3896.38i		−	1.17005i	0.811016	−	0.585024i	$-0.198915\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−302.747	+	524.374i	−0.0885201	+	0.153321i	−0.906886	−	0.421377i	$-0.861547\pi$
$227$	−302.747	+	524.374i	−0.0885201	+	0.153321i	0.818366	+	0.574698i	$0.194880\pi$
$228$		0			0
$229$	−1912.98	+	1104.46i	−0.552023	+	0.318711i	−0.749938	−	0.661509i	$-0.769917\pi$
$229$	−1912.98	+	1104.46i	−0.552023	+	0.318711i	0.197914	+	0.980219i	$0.436583\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	2065.77	−	1192.67i	0.580829	−	0.335342i	−0.180634	−	0.983550i	$-0.557815\pi$
$233$	2065.77	−	1192.67i	0.580829	−	0.335342i	0.761463	+	0.648209i	$0.224482\pi$
$234$		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	0.179762	−	0.983710i	$-0.442467\pi$
$241$	−2178.48	−	1257.75i	−0.582275	−	0.336176i	−0.762037	+	0.647534i	$0.775800\pi$
$242$		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	$-0.552512\pi$
$251$	−1306.11			−0.328451			−0.164226	+	0.986423i	$0.552512\pi$
$252$		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	0.818524	+	0.574473i	$0.194793\pi$
$257$	3735.91	+	6470.79i	0.906770	+	1.57057i	0.0882460	+	0.996099i	$0.471874\pi$
$258$		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	$-0.275679\pi$
$263$	1330.77	+	768.318i	0.312010	+	0.180139i	−0.335816	+	0.941928i	$0.609012\pi$
$264$		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	$-0.686957\pi$
$269$	1958.09	−	3391.52i	0.443818	−	0.768715i	0.997969	+	0.0637010i	$0.0202904\pi$
$270$		0			0
$271$	−3117.42	+	1799.84i	−0.698780	+	0.403441i	−0.806893	−	0.590698i	$-0.798853\pi$
$271$	−3117.42	+	1799.84i	−0.698780	+	0.403441i	0.108113	+	0.994139i	$0.465519\pi$
$272$		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	−0.881019	−	0.473080i	$-0.843142\pi$
$277$	−142.040	+	246.021i	−0.0308100	+	0.0533645i	0.850209	+	0.526445i	$0.176475\pi$
$278$		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	−0.268903	−	0.963167i	$-0.586661\pi$
$283$	−5891.40	−	3401.40i	−1.23748	−	0.714460i	−0.968579	+	0.248707i	$0.919994\pi$
$284$		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	$-0.397314\pi$
$293$	3180.05			0.634063			0.317031	+	0.948415i	$0.397314\pi$
$294$		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	$-0.910771\pi$
$307$		−	2976.39i		−	0.553328i	0.960967	−	0.276664i	$-0.0892289\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	2340.89	−	4054.55i	0.426817	−	0.739268i	−0.569772	−	0.821803i	$-0.692968\pi$
$311$	2340.89	−	4054.55i	0.426817	−	0.739268i	0.996588	+	0.0825352i	$0.0263017\pi$
$312$		0			0
$313$	−850.477	+	491.023i	−0.153584	+	0.0886718i	−0.574823	−	0.818278i	$-0.694929\pi$
$313$	−850.477	+	491.023i	−0.153584	+	0.0886718i	0.421238	+	0.906950i	$0.361596\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	4269.80	−	2465.17i	0.756516	−	0.436775i	−0.0715272	−	0.997439i	$-0.522787\pi$
$317$	4269.80	−	2465.17i	0.756516	−	0.436775i	0.828044	+	0.560664i	$0.189454\pi$
$318$		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	0.648501	−	0.761214i	$-0.275396\pi$
$331$	−2017.25	−	3493.99i	−0.334980	−	0.580202i	−0.983481	+	0.181012i	$0.942063\pi$
$332$		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	$-0.224822\pi$
$347$	3743.15	+	2161.11i	0.579085	+	0.334335i	−0.181685	+	0.983357i	$0.558155\pi$
$348$		0			0
$349$		−	1331.65i		−	0.204245i	−0.994772	−	0.102122i	$-0.967437\pi$
$349$		−	1331.65i		−	0.204245i	0.994772	−	0.102122i	$-0.0325634\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−5674.26	+	9828.10i	−0.855553	+	1.48186i	0.0205782	+	0.999788i	$0.493449\pi$
$353$	−5674.26	+	9828.10i	−0.855553	+	1.48186i	−0.876131	+	0.482073i	$0.839884\pi$
$354$		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	$-0.455760\pi$
$359$	7247.49	−	4184.34i	1.06548	−	0.615156i	0.926943	+	0.375201i	$0.122426\pi$
$360$		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	0.323374	−	0.946271i	$-0.395183\pi$
$367$	−2351.31	−	1357.53i	−0.334434	−	0.193086i	−0.657808	+	0.753186i	$0.728516\pi$
$368$		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	0.573063	−	0.819511i	$-0.305755\pi$
$373$	−3048.56	−	5280.25i	−0.423186	−	0.732979i	−0.996249	+	0.0865320i	$0.972422\pi$
$374$		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	$-0.140753\pi$
$383$	609.532	+	1055.74i	0.0813202	+	0.140851i	−0.822497	+	0.568769i	$0.807420\pi$
$384$		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	$-0.00630133\pi$
$389$	11374.6	+	6567.15i	1.48256	+	0.855958i	0.482759	+	0.875753i	$0.339635\pi$
$390$		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	−0.319692	−	0.947522i	$-0.603579\pi$
$397$	2697.68	−	1557.51i	0.341040	−	0.196900i	0.660732	+	0.750622i	$0.270246\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−9724.47	+	5614.42i	−1.21101	+	0.699179i	−0.962980	−	0.269572i	$-0.913118\pi$
$401$	−9724.47	+	5614.42i	−1.21101	+	0.699179i	−0.248034	+	0.968751i	$0.579784\pi$
$402$		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	−0.318242	−	0.948010i	$-0.603092\pi$
$409$	−10739.4	−	6200.41i	−1.29836	−	0.749610i	−0.980121	+	0.198399i	$0.936426\pi$
$410$		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	$-0.340075\pi$
$419$	8260.19			0.963095			0.481547	+	0.876420i	$0.340075\pi$
$420$		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	$-0.204678\pi$
$431$	6094.88	+	3518.88i	0.681160	+	0.393268i	−0.119132	+	0.992878i	$0.538011\pi$
$432$		0			0
$433$			9212.26i			1.02243i	0.859452	+	0.511216i	$0.170805\pi$
$433$			9212.26i			1.02243i	−0.859452	+	0.511216i	$0.829195\pi$
$434$		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	−0.0444012	−	0.999014i	$-0.514138\pi$
$439$	7345.30	−	4240.81i	0.798570	−	0.461054i	0.842971	+	0.537959i	$0.180805\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−11305.9	+	6527.49i	−1.21255	+	0.700068i	−0.963315	−	0.268374i	$-0.913514\pi$
$443$	−11305.9	+	6527.49i	−1.21255	+	0.700068i	−0.249239	+	0.968442i	$0.580180\pi$
$444$		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	0.998923	−	0.0464073i	$-0.0147772\pi$
$457$	4486.87	+	7771.49i	0.459271	+	0.795481i	−0.539651	+	0.841889i	$0.681444\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	955.010			0.0964842			0.0482421	−	0.998836i	$-0.484638\pi$
$461$	955.010			0.0964842			0.0482421	+	0.998836i	$0.484638\pi$
$462$		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	$-0.247406\pi$
$467$	−2532.46	−	4386.34i	−0.250938	−	0.434638i	−0.963784	+	0.266683i	$0.914072\pi$
$468$		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	−0.233116	−	0.972449i	$-0.574892\pi$
$479$	7606.85	−	13175.5i	0.725607	−	1.25679i	0.958724	−	0.284340i	$-0.0917744\pi$
$480$		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	−0.218817	−	0.975766i	$-0.570220\pi$
$487$	7905.92	−	13693.5i	0.735629	−	1.27415i	0.954447	−	0.298382i	$-0.0964468\pi$
$488$		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	0.527398	−	0.849619i	$-0.323168\pi$
$499$	−5262.33	−	9114.62i	−0.472092	−	0.817688i	−0.999490	+	0.0319305i	$0.989834\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−7790.82			−0.690607			−0.345304	−	0.938491i	$-0.612224\pi$
$503$	−7790.82			−0.690607			−0.345304	+	0.938491i	$0.612224\pi$
$504$		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	$-0.313093\pi$
$509$	−5098.24	−	8830.41i	−0.443960	−	0.768961i	−0.997979	+	0.0635430i	$0.979760\pi$
$510$		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	$-0.859159\pi$
$521$	−963.789	+	1669.33i	−0.0810449	+	0.140374i	0.822654	+	0.568542i	$0.192492\pi$
$522$		0			0
$523$	6716.70	−	3877.89i	0.561569	−	0.324222i	−0.192206	−	0.981355i	$-0.561564\pi$
$523$	6716.70	−	3877.89i	0.561569	−	0.324222i	0.753775	+	0.657133i	$0.228231\pi$
$524$		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	−0.979015	−	0.203788i	$-0.934675\pi$
$541$	−8380.42	−	14515.3i	−0.665993	−	1.15353i	0.313022	−	0.949746i	$-0.398659\pi$
$542$		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	$-0.0251976\pi$
$557$	18756.5	+	10829.1i	1.42682	+	0.823774i	0.429951	+	0.902852i	$0.358531\pi$
$558$		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	$-0.716461\pi$
$563$	4795.36	−	8305.80i	0.358970	−	0.621755i	0.987789	+	0.155797i	$0.0497946\pi$
$564$		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	$-0.876612\pi$
$569$	−14405.5	+	8317.01i	−1.06135	+	0.612772i	−0.135546	+	0.990771i	$0.543279\pi$
$570$		0			0
$571$	3165.51	−	5482.83i	0.232001	−	0.401838i	−0.726396	−	0.687277i	$-0.758806\pi$
$571$	3165.51	−	5482.83i	0.232001	−	0.401838i	0.958397	+	0.285439i	$0.0921394\pi$
$572$		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	0.772325	−	0.635228i	$-0.219094\pi$
$577$	8431.94	+	4868.18i	0.608364	+	0.351239i	−0.163961	+	0.986467i	$0.552427\pi$
$578$		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	$-0.374330\pi$
$587$	10940.3			0.769255			0.384628	+	0.923072i	$0.374330\pi$
$588$		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	−0.871159	−	0.491000i	$-0.836631\pi$
$593$	−12430.4	−	21530.0i	−0.860799	−	1.49095i	0.0103608	−	0.999946i	$-0.496702\pi$
$594$		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	$-0.0403706\pi$
$599$	20207.8	+	11667.0i	1.37841	+	0.795825i	0.386442	+	0.922314i	$0.373704\pi$
$600$		0			0
$601$			13012.4i			0.883175i	0.897218	+	0.441587i	$0.145584\pi$
$601$			13012.4i			0.883175i	−0.897218	+	0.441587i	$0.854416\pi$
$602$		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	−0.725345	−	0.688385i	$-0.758320\pi$
$607$	−7355.69	+	4246.81i	−0.491859	+	0.283975i	0.233486	+	0.972360i	$0.424987\pi$
$608$		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	−0.675288	−	0.737554i	$-0.735981\pi$
$613$	4569.79	−	7915.11i	0.301097	−	0.521514i	0.976385	+	0.216040i	$0.0693140\pi$
$614$		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	−0.311978	−	0.950089i	$-0.600991\pi$
$619$	−19878.5	−	11476.9i	−1.29077	−	0.745225i	−0.978790	+	0.204864i	$0.934325\pi$
$620$		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	$-0.148131\pi$
$641$	15447.5	+	8918.61i	0.951855	+	0.549554i	0.0581985	+	0.998305i	$0.481464\pi$
$642$		0			0
$643$			25449.0i			1.56082i	0.625266	+	0.780412i	$0.284991\pi$
$643$			25449.0i			1.56082i	−0.625266	+	0.780412i	$0.715009\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−13149.2	+	22775.1i	−0.798993	+	1.38390i	0.121280	+	0.992618i	$0.461300\pi$
$647$	−13149.2	+	22775.1i	−0.798993	+	1.38390i	−0.920273	+	0.391277i	$0.872033\pi$
$648$		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	$-0.758277\pi$
$653$	−8203.79	+	4736.46i	−0.491637	+	0.283847i	0.233616	+	0.972329i	$0.424944\pi$
$654$		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	−0.215153	−	0.976580i	$-0.569025\pi$
$661$	−19857.3	−	11464.6i	−1.16847	−	0.674618i	−0.953320	+	0.301962i	$0.902359\pi$
$662$		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	$-0.319241\pi$
$677$	−8123.71	−	14070.7i	−0.461181	−	0.798789i	−0.999020	+	0.0442583i	$0.985908\pi$
$678$		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	$-0.541217\pi$
$683$	−18786.2	−	10846.2i	−1.05247	−	0.607641i	−0.923339	+	0.383987i	$0.874551\pi$
$684$		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	0.144387	−	0.989521i	$-0.453879\pi$
$691$	19499.9	−	11258.3i	1.07353	−	0.619803i	0.929144	+	0.369718i	$0.120546\pi$
$692$		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	−0.999955	−	0.00946553i	$-0.996987\pi$
$709$	−9593.62	−	16616.6i	−0.508175	−	0.880185i	0.491780	−	0.870719i	$-0.336346\pi$
$710$		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	$-0.0504542\pi$
$719$	6883.43	+	11922.4i	0.357036	+	0.618404i	−0.630429	+	0.776247i	$0.717121\pi$
$720$		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	$0.100951\pi$
$727$			12226.1i			0.623717i	−0.950129	+	0.311858i	$0.899049\pi$
$728$		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	−0.442062	−	0.896984i	$-0.645753\pi$
$733$	2256.76	−	1302.94i	0.113718	−	0.0656553i	0.555780	+	0.831329i	$0.312420\pi$
$734$		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	−0.0502016	−	0.998739i	$-0.515986\pi$
$739$	16871.7	−	29222.7i	0.839833	−	1.45463i	0.890034	−	0.455894i	$-0.150680\pi$
$740$		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	0.760178	−	0.649714i	$-0.225111\pi$
$751$	−3757.62	−	6508.39i	−0.182580	−	0.316238i	−0.942758	+	0.333477i	$0.891778\pi$
$752$		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	$-0.0728328\pi$
$761$	6099.27	+	10564.2i	0.290537	+	0.503224i	−0.683400	+	0.730044i	$0.739500\pi$
$762$		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	$-0.984970\pi$
$769$		−	2013.08i		−	0.0943999i	0.998885	−	0.0471999i	$-0.0150298\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	15139.1	−	26221.7i	0.704418	−	1.22009i	−0.262483	−	0.964937i	$-0.584541\pi$
$773$	15139.1	−	26221.7i	0.704418	−	1.22009i	0.966901	−	0.255152i	$-0.0821254\pi$
$774$		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	−0.182377	−	0.983229i	$-0.558379\pi$
$787$	−24839.3	−	14341.0i	−1.12507	−	0.649557i	−0.942689	+	0.333671i	$0.891712\pi$
$788$		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	$-0.705794\pi$
$797$	−27108.9			−1.20483			−0.602413	+	0.798184i	$0.705794\pi$
$798$		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	$-0.474737\pi$
$809$	−17128.3	−	9889.03i	−0.744375	−	0.429765i	−0.823658	+	0.567087i	$0.808070\pi$
$810$		0			0
$811$			44456.6i			1.92488i	0.271487	+	0.962442i	$0.412484\pi$
$811$			44456.6i			1.92488i	−0.271487	+	0.962442i	$0.587516\pi$
$812$		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	$-0.588072\pi$
$821$	9958.57	−	5749.58i	0.423333	−	0.244411i	0.696502	+	0.717555i	$0.254739\pi$
$822$		0			0
$823$	596.549	−	1033.25i	0.0252666	−	0.0437630i	−0.853116	−	0.521722i	$-0.825290\pi$
$823$	596.549	−	1033.25i	0.0252666	−	0.0437630i	0.878382	+	0.477959i	$0.158623\pi$
$824$		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	0.232932	−	0.972493i	$-0.425168\pi$
$829$	−11762.7	−	6791.21i	−0.492806	−	0.284521i	−0.725738	+	0.687972i	$0.758501\pi$
$830$		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	$-0.576868\pi$
$839$	−11623.6			−0.478297			−0.239149	+	0.970983i	$0.576868\pi$
$840$		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	$0.00651553\pi$
$853$			1019.82i			0.0409354i	−0.999791	+	0.0204677i	$0.993484\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	4299.43	−	7446.83i	0.171372	−	0.296825i	−0.767528	−	0.641016i	$-0.778513\pi$
$857$	4299.43	−	7446.83i	0.171372	−	0.296825i	0.938900	+	0.344191i	$0.111847\pi$
$858$		0			0
$859$	−32182.1	+	18580.4i	−1.27828	+	0.738013i	−0.976531	−	0.215375i	$-0.930903\pi$
$859$	−32182.1	+	18580.4i	−1.27828	+	0.738013i	−0.301745	+	0.953389i	$0.597569\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−10634.2	+	6139.68i	−0.419459	+	0.242175i	−0.694846	−	0.719159i	$-0.744527\pi$
$863$	−10634.2	+	6139.68i	−0.419459	+	0.242175i	0.275387	+	0.961334i	$0.411194\pi$
$864$		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	−0.990631	−	0.136564i	$-0.956394\pi$
$877$	−15935.8	−	27601.6i	−0.613583	−	1.06276i	0.377048	−	0.926194i	$-0.376939\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−29427.6			−1.12536			−0.562679	−	0.826676i	$-0.690229\pi$
$881$	−29427.6			−1.12536			−0.562679	+	0.826676i	$0.690229\pi$
$882$		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	$-0.119014\pi$
$887$	3940.07	+	6824.39i	0.149148	+	0.258332i	−0.781765	+	0.623574i	$0.785680\pi$
$888$		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	−0.602655	−	0.798002i	$-0.705891\pi$
$907$	10646.6	−	18440.4i	0.389762	−	0.675088i	0.992417	+	0.122914i	$0.0392239\pi$
$908$		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	0.954474	−	0.298295i	$-0.0964179\pi$
$919$	6098.61	+	10563.1i	0.218906	+	0.379156i	−0.735568	+	0.677451i	$0.763085\pi$
$920$		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	$-0.310304\pi$
$929$	−12348.1	−	21387.5i	−0.436091	−	0.755331i	−0.997384	+	0.0722858i	$0.976971\pi$
$930$		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	$-0.918956\pi$
$937$		−	14448.0i		−	0.503730i	0.967762	−	0.251865i	$-0.0810439\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	15580.4	−	26986.0i	0.539752	−	0.934878i	−0.459165	−	0.888351i	$-0.651851\pi$
$941$	15580.4	−	26986.0i	0.539752	−	0.934878i	0.998917	−	0.0465268i	$-0.0148153\pi$
$942$		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	$-0.610327\pi$
$947$	8887.48	−	5131.19i	0.304968	−	0.176073i	0.644672	+	0.764459i	$0.276994\pi$
$948$		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	0.859990	+	0.510311i	$0.170470\pi$
$971$	26382.4	+	45695.6i	0.871937	+	1.51024i	0.0119472	+	0.999929i	$0.496197\pi$
$972$		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	0.999308	+	0.0372085i	$0.0118466\pi$
$977$	46759.5	+	26996.6i	1.53118	+	0.884030i	0.531877	+	0.846821i	$0.321487\pi$
$978$		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	0.0359696	+	0.999353i	$0.488548\pi$
$983$	−26119.2	+	45239.8i	−0.847480	+	1.46788i	−0.883450	+	0.468526i	$0.844785\pi$
$984$		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	−0.932787	−	0.360429i	$-0.882630\pi$
$991$	−4812.21	+	8334.99i	−0.154253	+	0.267174i	0.778534	+	0.627603i	$0.215964\pi$
$992$		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	0.0468034	−	0.998904i	$-0.485097\pi$
$997$	−25023.0	−	14447.0i	−0.794871	−	0.458919i	−0.841675	+	0.539985i	$0.818430\pi$
$998$		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.17.2		16
3.2	odd	2	inner	1008.4.bt.a.17.7		16
4.3	odd	2		63.4.p.a.17.8	yes	16
7.5	odd	6	inner	1008.4.bt.a.593.7		16
12.11	even	2		63.4.p.a.17.1	✓	16
21.5	even	6	inner	1008.4.bt.a.593.2		16
28.3	even	6		441.4.c.a.440.15		16
28.11	odd	6		441.4.c.a.440.16		16
28.19	even	6		63.4.p.a.26.1	yes	16
28.23	odd	6		441.4.p.c.215.1		16
28.27	even	2		441.4.p.c.80.8		16
84.11	even	6		441.4.c.a.440.1		16
84.23	even	6		441.4.p.c.215.8		16
84.47	odd	6		63.4.p.a.26.8	yes	16
84.59	odd	6		441.4.c.a.440.2		16
84.83	odd	2		441.4.p.c.80.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.p.a.17.1	✓	16	12.11	even	2
63.4.p.a.17.8	yes	16	4.3	odd	2
63.4.p.a.26.1	yes	16	28.19	even	6
63.4.p.a.26.8	yes	16	84.47	odd	6
441.4.c.a.440.1		16	84.11	even	6
441.4.c.a.440.2		16	84.59	odd	6
441.4.c.a.440.15		16	28.3	even	6
441.4.c.a.440.16		16	28.11	odd	6
441.4.p.c.80.1		16	84.83	odd	2
441.4.p.c.80.8		16	28.27	even	2
441.4.p.c.215.1		16	28.23	odd	6
441.4.p.c.215.8		16	84.23	even	6
1008.4.bt.a.17.2		16	1.1	even	1	trivial
1008.4.bt.a.17.7		16	3.2	odd	2	inner
1008.4.bt.a.593.2		16	21.5	even	6	inner
1008.4.bt.a.593.7		16	7.5	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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)

\(f(q)\)	\(=\)	\(q+(-6.38217 - 11.0542i) q^{5} +(-2.53897 - 18.3454i) q^{7} +O(q^{10})\)	\(q+(-6.38217 - 11.0542i) q^{5} +(-2.53897 - 18.3454i) q^{7} +(-46.8633 - 27.0565i) q^{11} +8.85528i q^{13} +(34.4587 - 59.6841i) q^{17} +(141.898 - 81.9246i) q^{19} +(81.3807 - 46.9852i) q^{23} +(-18.9642 + 32.8469i) q^{25} -119.620i q^{29} +(-85.6311 - 49.4391i) q^{31} +(-186.590 + 145.150i) q^{35} +(-47.0949 - 81.5708i) q^{37} -259.347 q^{41} -5.01418 q^{43} +(28.6747 + 49.6660i) q^{47} +(-330.107 + 93.1568i) q^{49} +(-407.058 - 235.015i) q^{53} +690.718i q^{55} +(-112.979 + 195.685i) q^{59} +(370.650 - 213.995i) q^{61} +(97.8884 - 56.5159i) q^{65} +(81.9267 - 141.901i) q^{67} +79.8529i q^{71} +(666.447 + 384.774i) q^{73} +(-377.379 + 928.422i) q^{77} +(267.408 + 463.165i) q^{79} +438.520 q^{83} -879.684 q^{85} +(-12.8242 - 22.2121i) q^{89} +(162.454 - 22.4833i) q^{91} +(-1811.23 - 1045.71i) q^{95} +1381.00i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 56 q^{7}+O(q^{10}) \) 16 * q - 56 * q^7	\( 16 q - 56 q^{7} + 612 q^{19} - 20 q^{25} - 1128 q^{31} - 1196 q^{37} - 328 q^{43} + 784 q^{49} - 1632 q^{61} - 308 q^{67} + 4068 q^{73} + 2176 q^{79} - 4608 q^{85} - 924 q^{91}+O(q^{100}) \) 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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