LMFDB - Embedded newform 1008.4.bt.a.17.6

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			17.6
Root			$0.648633 + 0.374489i$ of defining polynomial
Character	$\chi$	$=$	1008.17
Dual form			1008.4.bt.a.593.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(5.42768 + 9.40102i) q^{5} +(18.2341 - 3.24321i) q^{7} +O(q^{10})$	$q+(5.42768 + 9.40102i) q^{5} +(18.2341 - 3.24321i) q^{7} +(-44.9131 - 25.9306i) q^{11} +32.1880i q^{13} +(40.7324 - 70.5506i) q^{17} +(0.0420661 - 0.0242869i) q^{19} +(77.3322 - 44.6478i) q^{23} +(3.58060 - 6.20178i) q^{25} -175.246i q^{29} +(-186.238 - 107.524i) q^{31} +(129.458 + 153.816i) q^{35} +(-32.2729 - 55.8983i) q^{37} +411.485 q^{41} +234.771 q^{43} +(-316.076 - 547.460i) q^{47} +(321.963 - 118.274i) q^{49} +(230.049 + 132.819i) q^{53} -562.971i q^{55} +(-175.530 + 304.026i) q^{59} +(-673.827 + 389.034i) q^{61} +(-302.600 + 174.706i) q^{65} +(-98.0043 + 169.748i) q^{67} -142.632i q^{71} +(676.261 + 390.439i) q^{73} +(-903.046 - 327.157i) q^{77} +(644.525 + 1116.35i) q^{79} +235.123 q^{83} +884.330 q^{85} +(-335.390 - 580.913i) q^{89} +(104.392 + 586.919i) q^{91} +(0.456642 + 0.263642i) q^{95} -655.891i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	5.42768	+	9.40102i	0.485466	+	0.840852i	0.999861	−	0.0167014i	$-0.00531648\pi$
$5$	5.42768	+	9.40102i	0.485466	+	0.840852i	−0.514394	+	0.857554i	$0.671983\pi$
$6$		0			0
$7$	18.2341	−	3.24321i	0.984548	−	0.175117i
$7$	18.2341	−	3.24321i	0.984548	−	0.175117i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−44.9131	−	25.9306i	−1.23107	−	0.710760i	−0.263819	−	0.964572i	$-0.584982\pi$
$11$	−44.9131	−	25.9306i	−1.23107	−	0.710760i	−0.967254	+	0.253812i	$0.918315\pi$
$12$		0			0
$13$			32.1880i			0.686719i	0.939204	+	0.343360i	$0.111565\pi$
$13$			32.1880i			0.686719i	−0.939204	+	0.343360i	$0.888435\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	40.7324	−	70.5506i	0.581121	−	1.00653i	−0.414225	−	0.910174i	$-0.635947\pi$
$17$	40.7324	−	70.5506i	0.581121	−	1.00653i	0.995347	−	0.0963575i	$-0.0307192\pi$
$18$		0			0
$19$	0.0420661	−	0.0242869i	0.000507927	−	0.000293252i	−0.499746	−	0.866172i	$-0.666573\pi$
$19$	0.0420661	−	0.0242869i	0.000507927	−	0.000293252i	0.500254	+	0.865879i	$0.333240\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	77.3322	−	44.6478i	0.701082	−	0.404770i	−0.106668	−	0.994295i	$-0.534018\pi$
$23$	77.3322	−	44.6478i	0.701082	−	0.404770i	0.807750	+	0.589525i	$0.200685\pi$
$24$		0			0
$25$	3.58060	−	6.20178i	0.0286448	−	0.0496142i
$26$		0			0
$27$		0			0
$28$		0			0
$29$		−	175.246i		−	1.12215i	−0.827766	−	0.561074i	$-0.810388\pi$
$29$		−	175.246i		−	1.12215i	0.827766	−	0.561074i	$-0.189612\pi$
$30$		0			0
$31$	−186.238	−	107.524i	−1.07901	−	0.622966i	−0.148380	−	0.988930i	$-0.547406\pi$
$31$	−186.238	−	107.524i	−1.07901	−	0.622966i	−0.930629	+	0.365964i	$0.880739\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	129.458	+	153.816i	0.625212	+	0.742846i
$36$		0			0
$37$	−32.2729	−	55.8983i	−0.143395	−	0.248368i	0.785378	−	0.619017i	$-0.212469\pi$
$37$	−32.2729	−	55.8983i	−0.143395	−	0.248368i	−0.928773	+	0.370649i	$0.879135\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	411.485			1.56740			0.783698	−	0.621142i	$-0.213331\pi$
$41$	411.485			1.56740			0.783698	+	0.621142i	$0.213331\pi$
$42$		0			0
$43$	234.771			0.832611			0.416305	−	0.909225i	$-0.363325\pi$
$43$	234.771			0.832611			0.416305	+	0.909225i	$0.363325\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−316.076	−	547.460i	−0.980946	−	1.69905i	−0.658726	−	0.752382i	$-0.728905\pi$
$47$	−316.076	−	547.460i	−0.980946	−	1.69905i	−0.322219	−	0.946665i	$-0.604429\pi$
$48$		0			0
$49$	321.963	−	118.274i	0.938668	−	0.344822i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	230.049	+	132.819i	0.596220	+	0.344228i	0.767553	−	0.640985i	$-0.221474\pi$
$53$	230.049	+	132.819i	0.596220	+	0.344228i	−0.171333	+	0.985213i	$0.554807\pi$
$54$		0			0
$55$		−	562.971i		−	1.38020i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−175.530	+	304.026i	−0.387322	+	0.670862i	−0.992088	−	0.125541i	$-0.959933\pi$
$59$	−175.530	+	304.026i	−0.387322	+	0.670862i	0.604766	+	0.796403i	$0.293267\pi$
$60$		0			0
$61$	−673.827	+	389.034i	−1.41434	+	0.816569i	−0.995793	−	0.0916261i	$-0.970794\pi$
$61$	−673.827	+	389.034i	−1.41434	+	0.816569i	−0.418546	+	0.908196i	$0.637460\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−302.600	+	174.706i	−0.577430	+	0.333379i
$66$		0			0
$67$	−98.0043	+	169.748i	−0.178703	+	0.309523i	−0.941437	−	0.337190i	$-0.890524\pi$
$67$	−98.0043	+	169.748i	−0.178703	+	0.309523i	0.762733	+	0.646713i	$0.223857\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	142.632i		−	0.238412i	−0.992870	−	0.119206i	$-0.961965\pi$
$71$		−	142.632i		−	0.238412i	0.992870	−	0.119206i	$-0.0380349\pi$
$72$		0			0
$73$	676.261	+	390.439i	1.08425	+	0.625993i	0.932040	−	0.362355i	$-0.118027\pi$
$73$	676.261	+	390.439i	1.08425	+	0.625993i	0.152211	+	0.988348i	$0.451361\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−903.046	−	327.157i	−1.33652	−	0.484196i
$78$		0			0
$79$	644.525	+	1116.35i	0.917908	+	1.58986i	0.802588	+	0.596534i	$0.203456\pi$
$79$	644.525	+	1116.35i	0.917908	+	1.58986i	0.115320	+	0.993328i	$0.463211\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	235.123			0.310940			0.155470	−	0.987841i	$-0.450311\pi$
$83$	235.123			0.310940			0.155470	+	0.987841i	$0.450311\pi$
$84$		0			0
$85$	884.330			1.12846
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−335.390	−	580.913i	−0.399453	−	0.691872i	0.594206	−	0.804313i	$-0.297466\pi$
$89$	−335.390	−	580.913i	−0.399453	−	0.691872i	−0.993658	+	0.112441i	$0.964133\pi$
$90$		0			0
$91$	104.392	+	586.919i	0.120256	+	0.676108i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	0.456642	+	0.263642i	0.000493163	+	0.000284728i
$96$		0			0
$97$		−	655.891i		−	0.686553i	−0.939234	−	0.343276i	$-0.888463\pi$
$97$		−	655.891i		−	0.686553i	0.939234	−	0.343276i	$-0.111537\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	581.618	−	1007.39i	0.573002	−	0.992468i	−0.423254	−	0.906011i	$-0.639112\pi$
$101$	581.618	−	1007.39i	0.573002	−	0.992468i	0.996256	−	0.0864572i	$-0.0275546\pi$
$102$		0			0
$103$	−22.8802	+	13.2099i	−0.0218879	+	0.0126370i	−0.510904	−	0.859638i	$-0.670689\pi$
$103$	−22.8802	+	13.2099i	−0.0218879	+	0.0126370i	0.489016	+	0.872275i	$0.337356\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1270.53	−	733.538i	1.14791	−	0.662746i	0.199532	−	0.979891i	$-0.436058\pi$
$107$	1270.53	−	733.538i	1.14791	−	0.662746i	0.948377	+	0.317145i	$0.102724\pi$
$108$		0			0
$109$	67.5343	−	116.973i	0.0593450	−	0.102789i	−0.834827	−	0.550513i	$-0.814432\pi$
$109$	67.5343	−	116.973i	0.0593450	−	0.102789i	0.894172	+	0.447724i	$0.147765\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$			288.471i			0.240151i	0.992765	+	0.120076i	$0.0383137\pi$
$113$			288.471i			0.240151i	−0.992765	+	0.120076i	$0.961686\pi$
$114$		0			0
$115$	839.469	+	484.668i	0.680703	+	0.393004i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	513.908	−	1418.53i	0.395881	−	1.09274i
$120$		0			0
$121$	679.288	+	1176.56i	0.510359	+	0.883969i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	1434.66			1.02656
$126$		0			0
$127$	2269.80			1.58592			0.792961	−	0.609273i	$-0.208539\pi$
$127$	2269.80			1.58592			0.792961	+	0.609273i	$0.208539\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−194.846	−	337.483i	−0.129952	−	0.225084i	0.793706	−	0.608302i	$-0.208149\pi$
$131$	−194.846	−	337.483i	−0.129952	−	0.225084i	−0.923658	+	0.383218i	$0.874816\pi$
$132$		0			0
$133$	0.688269	−	0.579277i	0.000448725	−	0.000377667i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−1271.93	−	734.347i	−0.793197	−	0.457953i	0.0478898	−	0.998853i	$-0.484750\pi$
$137$	−1271.93	−	734.347i	−0.793197	−	0.457953i	−0.841087	+	0.540900i	$0.818084\pi$
$138$		0			0
$139$		−	624.712i		−	0.381204i	−0.981667	−	0.190602i	$-0.938956\pi$
$139$		−	624.712i		−	0.381204i	0.981667	−	0.190602i	$-0.0610440\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	834.654	−	1445.66i	0.488093	−	0.845401i
$144$		0			0
$145$	1647.49	−	951.177i	0.943561	−	0.544765i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	1387.25	−	800.930i	0.762739	−	0.440367i	−0.0675396	−	0.997717i	$-0.521515\pi$
$149$	1387.25	−	800.930i	0.762739	−	0.440367i	0.830278	+	0.557349i	$0.188182\pi$
$150$		0			0
$151$	202.188	−	350.200i	0.108966	−	0.188734i	−0.806386	−	0.591390i	$-0.798579\pi$
$151$	202.188	−	350.200i	0.108966	−	0.188734i	0.915351	+	0.402656i	$0.131913\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		−	2334.43i		−	1.20972i
$156$		0			0
$157$	−2088.91	−	1206.04i	−1.06187	−	0.613071i	−0.135921	−	0.990720i	$-0.543399\pi$
$157$	−2088.91	−	1206.04i	−1.06187	−	0.613071i	−0.925949	+	0.377649i	$0.876733\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	1265.28	−	1064.92i	0.619367	−	0.521287i
$162$		0			0
$163$	−472.684	−	818.712i	−0.227138	−	0.393414i	0.729821	−	0.683638i	$-0.239603\pi$
$163$	−472.684	−	818.712i	−0.227138	−	0.393414i	−0.956959	+	0.290224i	$0.906270\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	1271.18			0.589022			0.294511	−	0.955648i	$-0.404843\pi$
$167$	1271.18			0.589022			0.294511	+	0.955648i	$0.404843\pi$
$168$		0			0
$169$	1160.93			0.528417
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−2217.49	−	3840.81i	−0.974525	−	1.68793i	−0.681493	−	0.731825i	$-0.738669\pi$
$173$	−2217.49	−	3840.81i	−0.974525	−	1.68793i	−0.293032	−	0.956103i	$-0.594664\pi$
$174$		0			0
$175$	45.1752	−	124.696i	0.0195139	−	0.0538637i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	941.835	+	543.769i	0.393274	+	0.227057i	0.683578	−	0.729878i	$-0.260423\pi$
$179$	941.835	+	543.769i	0.393274	+	0.227057i	−0.290304	+	0.956935i	$0.593756\pi$
$180$		0			0
$181$			2916.08i			1.19752i	0.800930	+	0.598758i	$0.204339\pi$
$181$			2916.08i			1.19752i	−0.800930	+	0.598758i	$0.795661\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	350.334	−	606.796i	0.139227	−	0.241149i
$186$		0			0
$187$	−3658.84	+	2112.43i	−1.43081	+	0.826076i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−3948.97	+	2279.94i	−1.49601	+	0.863719i	−0.999989	−	0.00459364i	$-0.998538\pi$
$191$	−3948.97	+	2279.94i	−1.49601	+	0.863719i	−0.496017	+	0.868313i	$0.665204\pi$
$192$		0			0
$193$	1878.60	−	3253.83i	0.700645	−	1.21355i	−0.267595	−	0.963531i	$-0.586229\pi$
$193$	1878.60	−	3253.83i	0.700645	−	1.21355i	0.968240	−	0.250022i	$-0.0804378\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			2014.34i			0.728507i	0.931300	+	0.364253i	$0.118676\pi$
$197$			2014.34i			0.728507i	−0.931300	+	0.364253i	$0.881324\pi$
$198$		0			0
$199$	−10.8355	−	6.25590i	−0.00385986	−	0.00222849i	0.498069	−	0.867137i	$-0.334043\pi$
$199$	−10.8355	−	6.25590i	−0.00385986	−	0.00222849i	−0.501929	+	0.864909i	$0.667376\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−568.358	−	3195.44i	−0.196507	−	1.10481i
$204$		0			0
$205$	2233.41	+	3868.38i	0.760918	+	1.31795i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−2.51909			−0.000833727
$210$		0			0
$211$	2915.84			0.951349			0.475675	−	0.879621i	$-0.342204\pi$
$211$	2915.84			0.951349			0.475675	+	0.879621i	$0.342204\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	1274.26	+	2207.09i	0.404205	+	0.700103i
$216$		0			0
$217$	−3744.60	−	1356.60i	−1.17143	−	0.424387i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	2270.88	+	1311.10i	0.691205	+	0.399067i
$222$		0			0
$223$			1097.87i			0.329681i	0.986320	+	0.164841i	$0.0527110\pi$
$223$			1097.87i			0.329681i	−0.986320	+	0.164841i	$0.947289\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	250.297	−	433.527i	0.0731841	−	0.126759i	−0.827111	−	0.562039i	$-0.810017\pi$
$227$	250.297	−	433.527i	0.0731841	−	0.126759i	0.900295	+	0.435280i	$0.143351\pi$
$228$		0			0
$229$	−981.664	+	566.764i	−0.283276	+	0.163549i	−0.634906	−	0.772590i	$-0.718961\pi$
$229$	−981.664	+	566.764i	−0.283276	+	0.163549i	0.351630	+	0.936139i	$0.385628\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	2975.12	−	1717.68i	0.836508	−	0.482958i	−0.0195676	−	0.999809i	$-0.506229\pi$
$233$	2975.12	−	1717.68i	0.836508	−	0.482958i	0.856076	+	0.516850i	$0.172896\pi$
$234$		0			0
$235$	3431.12	−	5942.87i	0.952432	−	1.64966i
$236$		0			0
$237$		0			0
$238$		0			0
$239$		−	2213.97i		−	0.599203i	−0.954064	−	0.299602i	$-0.903146\pi$
$239$		−	2213.97i		−	0.599203i	0.954064	−	0.299602i	$-0.0968537\pi$
$240$		0			0
$241$	5154.55	+	2975.98i	1.37773	+	0.795435i	0.991886	−	0.127128i	$-0.0405760\pi$
$241$	5154.55	+	2975.98i	1.37773	+	0.795435i	0.385847	+	0.922563i	$0.373909\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	2859.41	+	2384.83i	0.745636	+	0.621882i
$246$		0			0
$247$	0.781746	+	1.35402i	0.000201382	+	0.000348803i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−4889.86			−1.22966			−0.614831	−	0.788659i	$-0.710776\pi$
$251$	−4889.86			−1.22966			−0.614831	+	0.788659i	$0.710776\pi$
$252$		0			0
$253$	−4630.97			−1.15078
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−1598.21	−	2768.18i	−0.387913	−	0.671884i	0.604256	−	0.796790i	$-0.293470\pi$
$257$	−1598.21	−	2768.18i	−0.387913	−	0.671884i	−0.992169	+	0.124906i	$0.960137\pi$
$258$		0			0
$259$	−769.756	−	914.586i	−0.184673	−	0.219419i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−648.189	−	374.232i	−0.151973	−	0.0877419i	0.422085	−	0.906556i	$-0.361298\pi$
$263$	−648.189	−	374.232i	−0.151973	−	0.0877419i	−0.574058	+	0.818814i	$0.694632\pi$
$264$		0			0
$265$			2883.59i			0.668444i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−649.628	+	1125.19i	−0.147244	+	0.255033i	−0.930208	−	0.367033i	$-0.880373\pi$
$269$	−649.628	+	1125.19i	−0.147244	+	0.255033i	0.782964	+	0.622067i	$0.213707\pi$
$270$		0			0
$271$	−72.3660	+	41.7806i	−0.0162211	+	0.00936527i	−0.508089	−	0.861305i	$-0.669648\pi$
$271$	−72.3660	+	41.7806i	−0.0162211	+	0.00936527i	0.491868	+	0.870670i	$0.336314\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−321.631	+	185.694i	−0.0705276	+	0.0407191i
$276$		0			0
$277$	2320.93	−	4019.97i	0.503434	−	0.871973i	−0.496558	−	0.868003i	$-0.665403\pi$
$277$	2320.93	−	4019.97i	0.503434	−	0.871973i	0.999992	−	0.00396948i	$-0.00126353\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$		−	179.289i		−	0.0380622i	−0.999819	−	0.0190311i	$-0.993942\pi$
$281$		−	179.289i		−	0.0380622i	0.999819	−	0.0190311i	$-0.00605816\pi$
$282$		0			0
$283$	3506.14	+	2024.27i	0.736461	+	0.425196i	0.820781	−	0.571243i	$-0.193539\pi$
$283$	3506.14	+	2024.27i	0.736461	+	0.425196i	−0.0843205	+	0.996439i	$0.526872\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	7503.06	−	1334.53i	1.54318	−	0.274477i
$288$		0			0
$289$	−861.761	−	1492.61i	−0.175404	−	0.303809i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	3389.52			0.675828			0.337914	−	0.941177i	$-0.390279\pi$
$293$	3389.52			0.675828			0.337914	+	0.941177i	$0.390279\pi$
$294$		0			0
$295$	−3810.88			−0.752128
$296$		0			0
$297$		0			0
$298$		0			0
$299$	1437.12	+	2489.17i	0.277963	+	0.481446i
$300$		0			0
$301$	4280.84	−	761.412i	0.819745	−	0.145804i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−7314.63	−	4223.11i	−1.37323	−	0.792834i
$306$		0			0
$307$			2014.64i			0.374534i	0.982309	+	0.187267i	$0.0599629\pi$
$307$			2014.64i			0.374534i	−0.982309	+	0.187267i	$0.940037\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−2922.01	+	5061.07i	−0.532772	+	0.922788i	0.466496	+	0.884524i	$0.345516\pi$
$311$	−2922.01	+	5061.07i	−0.532772	+	0.922788i	−0.999268	+	0.0382648i	$0.987817\pi$
$312$		0			0
$313$	2121.29	−	1224.73i	0.383074	−	0.221168i	−0.296081	−	0.955163i	$-0.595680\pi$
$313$	2121.29	−	1224.73i	0.383074	−	0.221168i	0.679155	+	0.733995i	$0.262346\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−5303.24	+	3061.83i	−0.939621	+	0.542490i	−0.889842	−	0.456270i	$-0.849185\pi$
$317$	−5303.24	+	3061.83i	−0.939621	+	0.542490i	−0.0497796	+	0.998760i	$0.515852\pi$
$318$		0			0
$319$	−4544.22	+	7870.82i	−0.797578	+	1.38145i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	3.95705i		−	0.000681660i
$324$		0			0
$325$	199.623	+	115.252i	0.0340710	+	0.0196709i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−7538.88	−	8957.33i	−1.26332	−	1.50101i
$330$		0			0
$331$	3798.52	+	6579.23i	0.630772	+	1.09253i	0.987394	+	0.158280i	$0.0505949\pi$
$331$	3798.52	+	6579.23i	0.630772	+	1.09253i	−0.356622	+	0.934249i	$0.616072\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−2127.74			−0.347018
$336$		0			0
$337$	−3863.22			−0.624460			−0.312230	−	0.950007i	$-0.601076\pi$
$337$	−3863.22			−0.624460			−0.312230	+	0.950007i	$0.601076\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	5576.34	+	9658.50i	0.885559	+	1.53383i
$342$		0			0
$343$	5487.11	−	3200.81i	0.863779	−	0.503870i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−1579.98	−	912.204i	−0.244432	−	0.141123i	0.372780	−	0.927920i	$-0.378405\pi$
$347$	−1579.98	−	912.204i	−0.244432	−	0.141123i	−0.617212	+	0.786797i	$0.711738\pi$
$348$		0			0
$349$			1537.52i			0.235822i	0.993024	+	0.117911i	$0.0376197\pi$
$349$			1537.52i			0.235822i	−0.993024	+	0.117911i	$0.962380\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−2963.66	+	5133.22i	−0.446855	+	0.773976i	−0.998179	−	0.0603149i	$-0.980789\pi$
$353$	−2963.66	+	5133.22i	−0.446855	+	0.773976i	0.551324	+	0.834291i	$0.314123\pi$
$354$		0			0
$355$	1340.88	−	774.159i	0.200469	−	0.115741i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	4191.12	−	2419.74i	0.616153	−	0.355736i	−0.159217	−	0.987244i	$-0.550897\pi$
$359$	4191.12	−	2419.74i	0.616153	−	0.355736i	0.775370	+	0.631508i	$0.217564\pi$
$360$		0			0
$361$	−3429.50	+	5940.07i	−0.500000	+	0.866025i
$362$		0			0
$363$		0			0
$364$		0			0
$365$			8476.72i			1.21559i
$366$		0			0
$367$	−9967.21	−	5754.57i	−1.41767	−	0.818491i	−0.421575	−	0.906794i	$-0.638522\pi$
$367$	−9967.21	−	5754.57i	−1.41767	−	0.818491i	−0.996094	+	0.0883026i	$0.971856\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	4625.49	+	1675.73i	0.647287	+	0.234501i
$372$		0			0
$373$	−93.7487	−	162.378i	−0.0130137	−	0.0225405i	0.859445	−	0.511228i	$-0.170809\pi$
$373$	−93.7487	−	162.378i	−0.0130137	−	0.0225405i	−0.872459	+	0.488687i	$0.837476\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	5640.81			0.770601
$378$		0			0
$379$	−3515.82			−0.476506			−0.238253	−	0.971203i	$-0.576575\pi$
$379$	−3515.82			−0.476506			−0.238253	+	0.971203i	$0.576575\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−1014.69	−	1757.49i	−0.135374	−	0.234474i	0.790366	−	0.612634i	$-0.209890\pi$
$383$	−1014.69	−	1757.49i	−0.135374	−	0.234474i	−0.925740	+	0.378160i	$0.876557\pi$
$384$		0			0
$385$	−1825.83	−	10265.3i	−0.241696	−	1.35887i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	5577.15	+	3219.97i	0.726923	+	0.419689i	0.817295	−	0.576219i	$-0.195472\pi$
$389$	5577.15	+	3219.97i	0.726923	+	0.419689i	−0.0903727	+	0.995908i	$0.528806\pi$
$390$		0			0
$391$		−	7274.45i		−	0.940882i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−6996.55	+	12118.4i	−0.891227	+	1.54365i
$396$		0			0
$397$	−8369.80	+	4832.31i	−1.05811	+	0.610898i	−0.924908	−	0.380191i	$-0.875858\pi$
$397$	−8369.80	+	4832.31i	−1.05811	+	0.610898i	−0.133199	+	0.991089i	$0.542525\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−10186.9	+	5881.40i	−1.26860	+	0.732426i	−0.974723	−	0.223417i	$-0.928279\pi$
$401$	−10186.9	+	5881.40i	−1.26860	+	0.732426i	−0.293876	+	0.955843i	$0.594945\pi$
$402$		0			0
$403$	3461.00	−	5994.62i	0.427803	−	0.740976i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			3347.42i			0.407679i
$408$		0			0
$409$	−4565.71	−	2636.01i	−0.551980	−	0.318686i	0.197940	−	0.980214i	$-0.436575\pi$
$409$	−4565.71	−	2636.01i	−0.551980	−	0.318686i	−0.749920	+	0.661528i	$0.769908\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−2214.60	+	6112.92i	−0.263858	+	0.728322i
$414$		0			0
$415$	1276.17	+	2210.39i	0.150951	+	0.261455i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	5103.18			0.595003			0.297502	−	0.954721i	$-0.403847\pi$
$419$	5103.18			0.595003			0.297502	+	0.954721i	$0.403847\pi$
$420$		0			0
$421$	−8395.31			−0.971882			−0.485941	−	0.873992i	$-0.661523\pi$
$421$	−8395.31			−0.971882			−0.485941	+	0.873992i	$0.661523\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−291.693	−	505.227i	−0.0332922	−	0.0576638i
$426$		0			0
$427$	−11024.9	+	9279.04i	−1.24949	+	1.05163i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−1808.68	−	1044.24i	−0.202137	−	0.116704i	0.395515	−	0.918460i	$-0.370566\pi$
$431$	−1808.68	−	1044.24i	−0.202137	−	0.116704i	−0.597652	+	0.801756i	$0.703900\pi$
$432$		0			0
$433$		−	11495.3i		−	1.27582i	−0.770111	−	0.637910i	$-0.779799\pi$
$433$		−	11495.3i		−	1.27582i	0.770111	−	0.637910i	$-0.220201\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	2.16871	−	3.75631i	0.000237399	−	0.000411187i
$438$		0			0
$439$	−3682.95	+	2126.35i	−0.400404	+	0.231173i	−0.686658	−	0.726980i	$-0.740923\pi$
$439$	−3682.95	+	2126.35i	−0.400404	+	0.231173i	0.286254	+	0.958154i	$0.407590\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	2862.03	−	1652.40i	0.306951	−	0.177218i	−0.338610	−	0.940927i	$-0.609957\pi$
$443$	2862.03	−	1652.40i	0.306951	−	0.177218i	0.645561	+	0.763708i	$0.276623\pi$
$444$		0			0
$445$	3640.78	−	6306.02i	0.387842	−	0.671761i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	6952.63i		−	0.730768i	−0.930857	−	0.365384i	$-0.880938\pi$
$449$		−	6952.63i		−	0.730768i	0.930857	−	0.365384i	$-0.119062\pi$
$450$		0			0
$451$	−18481.1	−	10670.0i	−1.92958	−	1.11404i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−4951.02	+	4167.00i	−0.510127	+	0.429345i
$456$		0			0
$457$	−4870.57	−	8436.08i	−0.498546	−	0.863508i	0.501452	−	0.865185i	$-0.332799\pi$
$457$	−4870.57	−	8436.08i	−0.498546	−	0.863508i	−0.999999	+	0.00167767i	$0.999466\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	5563.15			0.562043			0.281021	−	0.959702i	$-0.409327\pi$
$461$	5563.15			0.562043			0.281021	+	0.959702i	$0.409327\pi$
$462$		0			0
$463$	−4114.02			−0.412948			−0.206474	−	0.978452i	$-0.566199\pi$
$463$	−4114.02			−0.412948			−0.206474	+	0.978452i	$0.566199\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	3030.79	+	5249.49i	0.300318	+	0.520166i	0.976208	−	0.216837i	$-0.0695739\pi$
$467$	3030.79	+	5249.49i	0.300318	+	0.520166i	−0.675890	+	0.737002i	$0.736241\pi$
$468$		0			0
$469$	−1236.49	+	3413.05i	−0.121739	+	0.336034i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−10544.3	−	6087.75i	−1.02500	−	0.591787i
$474$		0			0
$475$		−	0.347846i		−	3.36005e-5i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−4123.33	+	7141.82i	−0.393319	+	0.681248i	−0.992885	−	0.119077i	$-0.962006\pi$
$479$	−4123.33	+	7141.82i	−0.393319	+	0.681248i	0.599566	+	0.800325i	$0.295340\pi$
$480$		0			0
$481$	1799.25	−	1038.80i	0.170559	−	0.0984724i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	6166.04	−	3559.96i	0.577290	−	0.333298i
$486$		0			0
$487$	5872.08	−	10170.7i	0.546385	−	0.946366i	−0.452134	−	0.891950i	$-0.649337\pi$
$487$	5872.08	−	10170.7i	0.546385	−	0.946366i	0.998518	−	0.0544159i	$-0.0173297\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$			6008.34i			0.552246i	0.961122	+	0.276123i	$0.0890497\pi$
$491$			6008.34i			0.552246i	−0.961122	+	0.276123i	$0.910950\pi$
$492$		0			0
$493$	−12363.7	−	7138.18i	−1.12948	−	0.652104i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−462.584	−	2600.76i	−0.0417500	−	0.234728i
$498$		0			0
$499$	−6824.93	−	11821.1i	−0.612276	−	1.06049i	−0.990856	−	0.134925i	$-0.956921\pi$
$499$	−6824.93	−	11821.1i	−0.612276	−	1.06049i	0.378580	−	0.925569i	$-0.376413\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	4862.69			0.431047			0.215524	−	0.976499i	$-0.430854\pi$
$503$	4862.69			0.431047			0.215524	+	0.976499i	$0.430854\pi$
$504$		0			0
$505$	12627.4			1.11269
$506$		0			0
$507$		0			0
$508$		0			0
$509$	8861.33	+	15348.3i	0.771653	+	1.33654i	0.936656	+	0.350250i	$0.113903\pi$
$509$	8861.33	+	15348.3i	0.771653	+	1.33654i	−0.165003	+	0.986293i	$0.552763\pi$
$510$		0			0
$511$	13597.3	+	4926.05i	1.17712	+	0.426449i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−248.373	−	143.398i	−0.0212517	−	0.0122697i
$516$		0			0
$517$			32784.1i			2.78887i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−6877.95	+	11913.0i	−0.578366	+	1.00176i	0.417301	+	0.908768i	$0.362976\pi$
$521$	−6877.95	+	11913.0i	−0.578366	+	1.00176i	−0.995667	+	0.0929909i	$0.970357\pi$
$522$		0			0
$523$	−1136.17	+	655.971i	−0.0949932	+	0.0548443i	−0.546744	−	0.837300i	$-0.684133\pi$
$523$	−1136.17	+	655.971i	−0.0949932	+	0.0548443i	0.451751	+	0.892144i	$0.350800\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−15171.8	+	8759.46i	−1.25407	+	0.724038i
$528$		0			0
$529$	−2096.65	+	3631.50i	−0.172323	+	0.298472i
$530$		0			0
$531$		0			0
$532$		0			0
$533$			13244.9i			1.07636i
$534$		0			0
$535$	13792.0	+	7962.82i	1.11454	+	0.643482i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−17527.3	−	3036.65i	−1.40065	−	0.242667i
$540$		0			0
$541$	−597.954	−	1035.69i	−0.0475195	−	0.0823061i	0.841287	−	0.540588i	$-0.181798\pi$
$541$	−597.954	−	1035.69i	−0.0475195	−	0.0823061i	−0.888807	+	0.458282i	$0.848465\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	1466.22			0.115240
$546$		0			0
$547$	6178.59			0.482957			0.241478	−	0.970406i	$-0.422368\pi$
$547$	6178.59			0.482957			0.241478	+	0.970406i	$0.422368\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−4.25617	−	7.37189i	−0.000329072	−	0.000569970i
$552$		0			0
$553$	15372.9	+	18265.3i	1.18214	+	1.40455i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	2906.56	+	1678.10i	0.221104	+	0.127654i	0.606461	−	0.795113i	$-0.292589\pi$
$557$	2906.56	+	1678.10i	0.221104	+	0.127654i	−0.385357	+	0.922767i	$0.625922\pi$
$558$		0			0
$559$			7556.82i			0.571770i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	1792.64	−	3104.94i	0.134193	−	0.232429i	−0.791096	−	0.611692i	$-0.790489\pi$
$563$	1792.64	−	3104.94i	0.134193	−	0.232429i	0.925289	+	0.379263i	$0.123822\pi$
$564$		0			0
$565$	−2711.92	+	1565.73i	−0.201932	+	0.116585i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	15835.9	−	9142.84i	1.16674	−	0.673617i	0.213829	−	0.976871i	$-0.431407\pi$
$569$	15835.9	−	9142.84i	1.16674	−	0.673617i	0.952910	+	0.303254i	$0.0980732\pi$
$570$		0			0
$571$	−8181.51	+	14170.8i	−0.599624	+	1.03858i	0.393252	+	0.919431i	$0.371350\pi$
$571$	−8181.51	+	14170.8i	−0.599624	+	1.03858i	−0.992876	+	0.119149i	$0.961983\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	639.463i		−	0.0463782i
$576$		0			0
$577$	−6678.26	−	3855.69i	−0.481836	−	0.278188i	0.239345	−	0.970935i	$-0.423067\pi$
$577$	−6678.26	−	3855.69i	−0.481836	−	0.278188i	−0.721181	+	0.692746i	$0.756401\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	4287.24	−	762.552i	0.306136	−	0.0544509i
$582$		0			0
$583$	−6888.14	−	11930.6i	−0.489327	−	0.847539i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−4182.21			−0.294069			−0.147034	−	0.989131i	$-0.546973\pi$
$587$	−4182.21			−0.294069			−0.147034	+	0.989131i	$0.546973\pi$
$588$		0			0
$589$	−10.4457			−0.000730744
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−8094.65	−	14020.4i	−0.560552	−	0.970905i	−0.997448	−	0.0713932i	$-0.977256\pi$
$593$	−8094.65	−	14020.4i	−0.560552	−	0.970905i	0.436896	−	0.899512i	$-0.356078\pi$
$594$		0			0
$595$	16124.9	−	2868.07i	1.11102	−	0.197612i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−11065.5	−	6388.67i	−0.754798	−	0.435783i	0.0726267	−	0.997359i	$-0.476862\pi$
$599$	−11065.5	−	6388.67i	−0.754798	−	0.435783i	−0.827425	+	0.561576i	$0.810195\pi$
$600$		0			0
$601$		−	24022.7i		−	1.63046i	−0.579137	−	0.815231i	$-0.696610\pi$
$601$		−	24022.7i		−	1.63046i	0.579137	−	0.815231i	$-0.303390\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−7373.92	+	12772.0i	−0.495525	+	0.858274i
$606$		0			0
$607$	−8371.72	+	4833.42i	−0.559798	+	0.323200i	−0.753065	−	0.657947i	$-0.771425\pi$
$607$	−8371.72	+	4833.42i	−0.559798	+	0.323200i	0.193266	+	0.981146i	$0.438092\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	17621.7	−	10173.9i	1.16677	−	0.673634i
$612$		0			0
$613$	−7192.73	+	12458.2i	−0.473918	+	0.820850i	−0.999554	−	0.0298593i	$-0.990494\pi$
$613$	−7192.73	+	12458.2i	−0.473918	+	0.820850i	0.525636	+	0.850710i	$0.323827\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$			7712.69i			0.503244i	0.967826	+	0.251622i	$0.0809639\pi$
$617$			7712.69i			0.503244i	−0.967826	+	0.251622i	$0.919036\pi$
$618$		0			0
$619$	−12398.9	−	7158.52i	−0.805096	−	0.464822i	0.0401539	−	0.999194i	$-0.487215\pi$
$619$	−12398.9	−	7158.52i	−0.805096	−	0.464822i	−0.845250	+	0.534371i	$0.820549\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−7999.55	−	9504.67i	−0.514439	−	0.611230i
$624$		0			0
$625$	7339.28	+	12712.0i	0.469714	+	0.813569i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−5258.21			−0.333320
$630$		0			0
$631$	−4971.96			−0.313678			−0.156839	−	0.987624i	$-0.550130\pi$
$631$	−4971.96			−0.313678			−0.156839	+	0.987624i	$0.550130\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	12319.7	+	21338.4i	0.769911	+	1.33353i
$636$		0			0
$637$	3807.00	+	10363.4i	0.236796	+	0.644601i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−25481.7	−	14711.9i	−1.57015	−	0.906529i	−0.996149	−	0.0876763i	$-0.972056\pi$
$641$	−25481.7	−	14711.9i	−1.57015	−	0.906529i	−0.574004	−	0.818852i	$-0.694611\pi$
$642$		0			0
$643$			31273.9i			1.91807i	0.283283	+	0.959036i	$0.408576\pi$
$643$			31273.9i			1.91807i	−0.283283	+	0.959036i	$0.591424\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−4005.82	+	6938.29i	−0.243408	+	0.421595i	−0.961683	−	0.274164i	$-0.911599\pi$
$647$	−4005.82	+	6938.29i	−0.243408	+	0.421595i	0.718275	+	0.695760i	$0.244932\pi$
$648$		0			0
$649$	15767.2	−	9103.17i	0.953644	−	0.550586i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	13372.0	−	7720.32i	0.801357	−	0.462664i	−0.0425886	−	0.999093i	$-0.513560\pi$
$653$	13372.0	−	7720.32i	0.801357	−	0.462664i	0.843945	+	0.536429i	$0.180227\pi$
$654$		0			0
$655$	2115.12	−	3663.50i	0.126175	−	0.218542i
$656$		0			0
$657$		0			0
$658$		0			0
$659$			31288.9i			1.84953i	0.380537	+	0.924766i	$0.375739\pi$
$659$			31288.9i			1.84953i	−0.380537	+	0.924766i	$0.624261\pi$
$660$		0			0
$661$	−26263.2	−	15163.1i	−1.54541	−	0.892246i	−0.998483	−	0.0550690i	$-0.982462\pi$
$661$	−26263.2	−	15163.1i	−1.54541	−	0.892246i	−0.546932	−	0.837177i	$-0.684205\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	9.18150	+	3.32629i	0.000535403	+	0.000193967i
$666$		0			0
$667$	−7824.33	−	13552.1i	−0.454212	−	0.786718i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	40351.5			2.32154
$672$		0			0
$673$	12067.9			0.691207			0.345604	−	0.938381i	$-0.387674\pi$
$673$	12067.9			0.691207			0.345604	+	0.938381i	$0.387674\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	3272.41	+	5667.98i	0.185774	+	0.321770i	0.943837	−	0.330411i	$-0.107187\pi$
$677$	3272.41	+	5667.98i	0.185774	+	0.321770i	−0.758063	+	0.652181i	$0.773854\pi$
$678$		0			0
$679$	−2127.19	−	11959.6i	−0.120227	−	0.675944i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−27267.1	−	15742.7i	−1.52759	−	0.881956i	−0.999462	−	0.0327927i	$-0.989560\pi$
$683$	−27267.1	−	15742.7i	−1.52759	−	0.881956i	−0.528130	−	0.849163i	$-0.677107\pi$
$684$		0			0
$685$		−	15943.2i		−	0.889282i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−4275.18	+	7404.82i	−0.236388	+	0.409436i
$690$		0			0
$691$	8690.83	−	5017.66i	0.478459	−	0.276238i	−0.241315	−	0.970447i	$-0.577579\pi$
$691$	8690.83	−	5017.66i	0.478459	−	0.276238i	0.719774	+	0.694209i	$0.244245\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	5872.93	−	3390.74i	0.320537	−	0.185062i
$696$		0			0
$697$	16760.8	−	29030.6i	0.910847	−	1.57763i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	768.196i		−	0.0413900i	−0.999786	−	0.0206950i	$-0.993412\pi$
$701$		−	768.196i		−	0.0413900i	0.999786	−	0.0206950i	$-0.00658789\pi$
$702$		0			0
$703$	−2.71519	−	1.56761i	−0.000145669	−	8.41019e-5i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	7338.09	−	20255.2i	0.390350	−	1.07747i
$708$		0			0
$709$	−6984.30	−	12097.2i	−0.369959	−	0.640787i	0.619600	−	0.784918i	$-0.287295\pi$
$709$	−6984.30	−	12097.2i	−0.369959	−	0.640787i	−0.989559	+	0.144130i	$0.953962\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−19202.9			−1.00863
$714$		0			0
$715$	18120.9			0.947810
$716$		0			0
$717$		0			0
$718$		0			0
$719$	5984.78	+	10365.9i	0.310424	+	0.537669i	0.978454	−	0.206465i	$-0.0661958\pi$
$719$	5984.78	+	10365.9i	0.310424	+	0.537669i	−0.668031	+	0.744134i	$0.732862\pi$
$720$		0			0
$721$	−374.357	+	315.075i	−0.0193367	+	0.0162746i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−1086.83	−	627.484i	−0.0556745	−	0.0321437i
$726$		0			0
$727$		−	12223.3i		−	0.623575i	−0.950152	−	0.311787i	$-0.899072\pi$
$727$		−	12223.3i		−	0.623575i	0.950152	−	0.311787i	$-0.100928\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	9562.80	−	16563.3i	0.483848	−	0.838049i
$732$		0			0
$733$	−20598.5	+	11892.5i	−1.03796	+	0.599264i	−0.919253	−	0.393666i	$-0.871207\pi$
$733$	−20598.5	+	11892.5i	−1.03796	+	0.599264i	−0.118702	+	0.992930i	$0.537873\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	8803.34	−	5082.61i	0.439994	−	0.254030i
$738$		0			0
$739$	5739.04	−	9940.31i	0.285675	−	0.494804i	−0.687097	−	0.726565i	$-0.741115\pi$
$739$	5739.04	−	9940.31i	0.285675	−	0.494804i	0.972773	+	0.231761i	$0.0744488\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		−	18604.0i		−	0.918593i	−0.888283	−	0.459297i	$-0.848101\pi$
$743$		−	18604.0i		−	0.918593i	0.888283	−	0.459297i	$-0.151899\pi$
$744$		0			0
$745$	15059.1	+	8694.38i	0.740568	+	0.427567i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	20787.8	−	17496.0i	1.01411	−	0.853523i
$750$		0			0
$751$	15506.2	+	26857.6i	0.753436	+	1.30499i	0.946148	+	0.323734i	$0.104938\pi$
$751$	15506.2	+	26857.6i	0.753436	+	1.30499i	−0.192713	+	0.981255i	$0.561728\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	4389.64			0.211597
$756$		0			0
$757$	−19065.9			−0.915407			−0.457703	−	0.889105i	$-0.651328\pi$
$757$	−19065.9			−0.915407			−0.457703	+	0.889105i	$0.651328\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	7339.58	+	12712.5i	0.349618	+	0.605556i	0.986182	−	0.165668i	$-0.0529780\pi$
$761$	7339.58	+	12712.5i	0.349618	+	0.605556i	−0.636563	+	0.771224i	$0.719645\pi$
$762$		0			0
$763$	852.058	−	2351.92i	0.0404280	−	0.111593i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−9786.01	−	5649.95i	−0.460694	−	0.265982i
$768$		0			0
$769$			29972.5i			1.40551i	0.711434	+	0.702753i	$0.248046\pi$
$769$			29972.5i			1.40551i	−0.711434	+	0.702753i	$0.751954\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−11343.9	+	19648.2i	−0.527828	+	0.914225i	0.471646	+	0.881788i	$0.343660\pi$
$773$	−11343.9	+	19648.2i	−0.527828	+	0.914225i	−0.999474	+	0.0324367i	$0.989673\pi$
$774$		0			0
$775$	−1333.68	+	770.003i	−0.0618159	+	0.0356894i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	17.3096	−	9.99369i	0.000796123	−	0.000459642i
$780$		0			0
$781$	−3698.52	+	6406.02i	−0.169454	+	0.293503i
$782$		0			0
$783$		0			0
$784$		0			0
$785$		−	26183.9i		−	1.19050i
$786$		0			0
$787$	18132.8	+	10469.0i	0.821301	+	0.474178i	0.850865	−	0.525385i	$-0.176079\pi$
$787$	18132.8	+	10469.0i	0.821301	+	0.474178i	−0.0295639	+	0.999563i	$0.509412\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	935.573	+	5260.01i	0.0420545	+	0.236440i
$792$		0			0
$793$	−12522.2	−	21689.2i	−0.560754	−	0.971254i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	27393.4			1.21747			0.608735	−	0.793373i	$-0.291677\pi$
$797$	27393.4			1.21747			0.608735	+	0.793373i	$0.291677\pi$
$798$		0			0
$799$	−51498.2			−2.28019
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−20248.6	−	35071.7i	−0.889861	−	1.54128i
$804$		0			0
$805$	16878.8	+	6114.89i	0.739007	+	0.267729i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−23214.2	−	13402.7i	−1.00886	−	0.582465i	−0.0980012	−	0.995186i	$-0.531245\pi$
$809$	−23214.2	−	13402.7i	−1.00886	−	0.582465i	−0.910857	+	0.412722i	$0.864578\pi$
$810$		0			0
$811$			17139.6i			0.742113i	0.928610	+	0.371056i	$0.121004\pi$
$811$			17139.6i			0.742113i	−0.928610	+	0.371056i	$0.878996\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	5131.15	−	8887.41i	0.220535	−	0.381979i
$816$		0			0
$817$	9.87590	−	5.70185i	0.000422906	−	0.000244165i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−7473.17	+	4314.64i	−0.317680	+	0.183413i	−0.650358	−	0.759628i	$-0.725381\pi$
$821$	−7473.17	+	4314.64i	−0.317680	+	0.183413i	0.332678	+	0.943041i	$0.392048\pi$
$822$		0			0
$823$	−2642.48	+	4576.91i	−0.111921	+	0.193853i	−0.916545	−	0.399932i	$-0.869034\pi$
$823$	−2642.48	+	4576.91i	−0.111921	+	0.193853i	0.804624	+	0.593785i	$0.202367\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	1845.35i		−	0.0775926i	−0.999247	−	0.0387963i	$-0.987648\pi$
$827$		−	1845.35i		−	0.0775926i	0.999247	−	0.0387963i	$-0.0123523\pi$
$828$		0			0
$829$	16881.6	+	9746.58i	0.707263	+	0.408339i	0.810047	−	0.586365i	$-0.199442\pi$
$829$	16881.6	+	9746.58i	0.707263	+	0.408339i	−0.102784	+	0.994704i	$0.532775\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	4770.05	−	27532.3i	0.198406	−	1.14518i
$834$		0			0
$835$	6899.54	+	11950.4i	0.285950	+	0.495281i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	27816.7			1.14462			0.572312	−	0.820036i	$-0.306047\pi$
$839$	27816.7			1.14462			0.572312	+	0.820036i	$0.306047\pi$
$840$		0			0
$841$	−6322.03			−0.259217
$842$		0			0
$843$		0			0
$844$		0			0
$845$	6301.16	+	10913.9i	0.256529	+	0.444320i
$846$		0			0
$847$	16202.0	+	19250.5i	0.657271	+	0.780937i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−4991.47	−	2881.83i	−0.201064	−	0.116084i
$852$		0			0
$853$			9210.41i			0.369705i	0.982766	+	0.184852i	$0.0591807\pi$
$853$			9210.41i			0.369705i	−0.982766	+	0.184852i	$0.940819\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	17250.5	−	29878.7i	0.687589	−	1.19094i	−0.285026	−	0.958520i	$-0.592002\pi$
$857$	17250.5	−	29878.7i	0.687589	−	1.19094i	0.972615	−	0.232420i	$-0.0746644\pi$
$858$		0			0
$859$	37843.6	−	21849.0i	1.50315	−	0.867845i	0.503158	−	0.864195i	$-0.332171\pi$
$859$	37843.6	−	21849.0i	1.50315	−	0.867845i	0.999993	−	0.00365004i	$-0.00116185\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	24537.6	−	14166.8i	0.967869	−	0.558800i	0.0692834	−	0.997597i	$-0.477929\pi$
$863$	24537.6	−	14166.8i	0.967869	−	0.558800i	0.898586	+	0.438797i	$0.144595\pi$
$864$		0			0
$865$	24071.7	−	41693.4i	0.946199	−	1.63886i
$866$		0			0
$867$		0			0
$868$		0			0
$869$		−	66851.6i		−	2.60965i
$870$		0			0
$871$	−5463.86	−	3154.56i	−0.212556	−	0.122719i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	26159.6	−	4652.89i	1.01069	−	0.179767i
$876$		0			0
$877$	22562.9	+	39080.1i	0.868751	+	1.50472i	0.863274	+	0.504736i	$0.168410\pi$
$877$	22562.9	+	39080.1i	0.868751	+	1.50472i	0.00547715	+	0.999985i	$0.498257\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	4244.09			0.162301			0.0811504	−	0.996702i	$-0.474141\pi$
$881$	4244.09			0.162301			0.0811504	+	0.996702i	$0.474141\pi$
$882$		0			0
$883$	21.9077			0.000834939			0.000417470	−	1.00000i	$-0.499867\pi$
$883$	21.9077			0.000834939			0.000417470		1.00000i	$0.499867\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	3750.82	+	6496.61i	0.141984	+	0.245924i	0.928244	−	0.371972i	$-0.121318\pi$
$887$	3750.82	+	6496.61i	0.141984	+	0.245924i	−0.786259	+	0.617896i	$0.787985\pi$
$888$		0			0
$889$	41387.7	−	7361.43i	1.56142	−	0.277722i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−26.5922	−	15.3530i	−0.000996498	−	0.000575328i
$894$		0			0
$895$			11805.6i			0.440914i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−18843.2	+	32637.3i	−0.699060	+	1.21081i
$900$		0			0
$901$	18740.9	−	10820.1i	0.692952	−	0.400076i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−27414.1	+	15827.5i	−1.00693	+	0.581354i
$906$		0			0
$907$	20568.7	−	35626.0i	0.753001	−	1.30424i	−0.193362	−	0.981128i	$-0.561939\pi$
$907$	20568.7	−	35626.0i	0.753001	−	1.30424i	0.946362	−	0.323108i	$-0.104728\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$		−	14080.6i		−	0.512086i	−0.966665	−	0.256043i	$-0.917581\pi$
$911$		−	14080.6i		−	0.512086i	0.966665	−	0.256043i	$-0.0824189\pi$
$912$		0			0
$913$	−10560.1	−	6096.86i	−0.382790	−	0.221004i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−4647.36	−	5521.76i	−0.167360	−	0.198849i
$918$		0			0
$919$	6311.58	+	10932.0i	0.226550	+	0.392397i	0.956783	−	0.290801i	$-0.0939219\pi$
$919$	6311.58	+	10932.0i	0.226550	+	0.392397i	−0.730233	+	0.683198i	$0.760589\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	4591.03			0.163722
$924$		0			0
$925$	−462.225			−0.0164301
$926$		0			0
$927$		0			0
$928$		0			0
$929$	16736.8	+	28989.1i	0.591085	+	1.02379i	0.994087	+	0.108590i	$0.0346336\pi$
$929$	16736.8	+	28989.1i	0.591085	+	1.02379i	−0.403002	+	0.915199i	$0.632033\pi$
$930$		0			0
$931$	10.6712	−	12.7948i	0.000375655	−	0.000450411i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−39718.0	−	22931.2i	−1.38922	−	0.802064i
$936$		0			0
$937$			25652.3i			0.894371i	0.894441	+	0.447185i	$0.147574\pi$
$937$			25652.3i			0.894371i	−0.894441	+	0.447185i	$0.852426\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−1301.48	+	2254.23i	−0.0450872	+	0.0780933i	−0.887688	−	0.460445i	$-0.847690\pi$
$941$	−1301.48	+	2254.23i	−0.0450872	+	0.0780933i	0.842601	+	0.538538i	$0.181023\pi$
$942$		0			0
$943$	31821.1	−	18371.9i	1.09887	−	0.634435i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	32577.1	−	18808.4i	1.11786	−	0.645397i	0.177006	−	0.984210i	$-0.443359\pi$
$947$	32577.1	−	18808.4i	1.11786	−	0.645397i	0.940854	+	0.338813i	$0.110025\pi$
$948$		0			0
$949$	−12567.5	+	21767.5i	−0.429881	+	0.744576i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	23444.5i		−	0.796896i	−0.917191	−	0.398448i	$-0.869549\pi$
$953$		−	23444.5i		−	0.796896i	0.917191	−	0.398448i	$-0.130451\pi$
$954$		0			0
$955$	−42867.4	−	24749.5i	−1.45252	−	0.838614i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−25574.0	−	9265.02i	−0.861135	−	0.311974i
$960$		0			0
$961$	8227.49	+	14250.4i	0.276174	+	0.478347i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	40785.7			1.36056
$966$		0			0
$967$	−4312.24			−0.143405			−0.0717023	−	0.997426i	$-0.522843\pi$
$967$	−4312.24			−0.143405			−0.0717023	+	0.997426i	$0.522843\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−23526.3	−	40748.8i	−0.777545	−	1.34675i	−0.933353	−	0.358960i	$-0.883131\pi$
$971$	−23526.3	−	40748.8i	−0.777545	−	1.34675i	0.155808	−	0.987787i	$-0.450202\pi$
$972$		0			0
$973$	−2026.07	−	11391.1i	−0.0667553	−	0.375314i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	17721.5	+	10231.5i	0.580308	+	0.335041i	0.761256	−	0.648452i	$-0.224583\pi$
$977$	17721.5	+	10231.5i	0.580308	+	0.335041i	−0.180948	+	0.983493i	$0.557916\pi$
$978$		0			0
$979$			34787.4i			1.13566i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−22314.5	+	38649.9i	−0.724031	+	1.25406i	0.235340	+	0.971913i	$0.424380\pi$
$983$	−22314.5	+	38649.9i	−0.724031	+	1.25406i	−0.959372	+	0.282146i	$0.908954\pi$
$984$		0			0
$985$	−18936.9	+	10933.2i	−0.612567	+	0.353666i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	18155.4	−	10482.0i	0.583729	−	0.337016i
$990$		0			0
$991$	21565.5	−	37352.5i	0.691272	−	1.19732i	−0.280149	−	0.959957i	$-0.590384\pi$
$991$	21565.5	−	37352.5i	0.691272	−	1.19732i	0.971421	−	0.237362i	$-0.0762828\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		−	135.820i		−	0.00432743i
$996$		0			0
$997$	3136.96	+	1811.13i	0.0996475	+	0.0575315i	0.548996	−	0.835825i	$-0.315010\pi$
$997$	3136.96	+	1811.13i	0.0996475	+	0.0575315i	−0.449348	+	0.893357i	$0.648344\pi$
$998$		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.17.6		16
3.2	odd	2	inner	1008.4.bt.a.17.3		16
4.3	odd	2		63.4.p.a.17.5	yes	16
7.5	odd	6	inner	1008.4.bt.a.593.3		16
12.11	even	2		63.4.p.a.17.4	✓	16
21.5	even	6	inner	1008.4.bt.a.593.6		16
28.3	even	6		441.4.c.a.440.10		16
28.11	odd	6		441.4.c.a.440.9		16
28.19	even	6		63.4.p.a.26.4	yes	16
28.23	odd	6		441.4.p.c.215.4		16
28.27	even	2		441.4.p.c.80.5		16
84.11	even	6		441.4.c.a.440.8		16
84.23	even	6		441.4.p.c.215.5		16
84.47	odd	6		63.4.p.a.26.5	yes	16
84.59	odd	6		441.4.c.a.440.7		16
84.83	odd	2		441.4.p.c.80.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.p.a.17.4	✓	16	12.11	even	2
63.4.p.a.17.5	yes	16	4.3	odd	2
63.4.p.a.26.4	yes	16	28.19	even	6
63.4.p.a.26.5	yes	16	84.47	odd	6
441.4.c.a.440.7		16	84.59	odd	6
441.4.c.a.440.8		16	84.11	even	6
441.4.c.a.440.9		16	28.11	odd	6
441.4.c.a.440.10		16	28.3	even	6
441.4.p.c.80.4		16	84.83	odd	2
441.4.p.c.80.5		16	28.27	even	2
441.4.p.c.215.4		16	28.23	odd	6
441.4.p.c.215.5		16	84.23	even	6
1008.4.bt.a.17.3		16	3.2	odd	2	inner
1008.4.bt.a.17.6		16	1.1	even	1	trivial
1008.4.bt.a.593.3		16	7.5	odd	6	inner
1008.4.bt.a.593.6		16	21.5	even	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)

\(f(q)\)	\(=\)	\(q+(5.42768 + 9.40102i) q^{5} +(18.2341 - 3.24321i) q^{7} +O(q^{10})\)	\(q+(5.42768 + 9.40102i) q^{5} +(18.2341 - 3.24321i) q^{7} +(-44.9131 - 25.9306i) q^{11} +32.1880i q^{13} +(40.7324 - 70.5506i) q^{17} +(0.0420661 - 0.0242869i) q^{19} +(77.3322 - 44.6478i) q^{23} +(3.58060 - 6.20178i) q^{25} -175.246i q^{29} +(-186.238 - 107.524i) q^{31} +(129.458 + 153.816i) q^{35} +(-32.2729 - 55.8983i) q^{37} +411.485 q^{41} +234.771 q^{43} +(-316.076 - 547.460i) q^{47} +(321.963 - 118.274i) q^{49} +(230.049 + 132.819i) q^{53} -562.971i q^{55} +(-175.530 + 304.026i) q^{59} +(-673.827 + 389.034i) q^{61} +(-302.600 + 174.706i) q^{65} +(-98.0043 + 169.748i) q^{67} -142.632i q^{71} +(676.261 + 390.439i) q^{73} +(-903.046 - 327.157i) q^{77} +(644.525 + 1116.35i) q^{79} +235.123 q^{83} +884.330 q^{85} +(-335.390 - 580.913i) q^{89} +(104.392 + 586.919i) q^{91} +(0.456642 + 0.263642i) q^{95} -655.891i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 56 q^{7}+O(q^{10}) \) 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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