LMFDB - Embedded newform 1008.4.bt.a.593.1

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			593.1
Root			$-1.57646 + 0.910170i$ of defining polynomial
Character	$\chi$	$=$	1008.593
Dual form			1008.4.bt.a.17.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.54372 + 13.0661i) q^{5} +(-16.2919 - 8.80760i) q^{7} +O(q^{10})$	$q+(-7.54372 + 13.0661i) q^{5} +(-16.2919 - 8.80760i) q^{7} +(8.56529 - 4.94517i) q^{11} +67.8891i q^{13} +(35.0687 + 60.7407i) q^{17} +(53.2242 + 30.7290i) q^{19} +(113.895 + 65.7575i) q^{23} +(-51.3154 - 88.8809i) q^{25} -158.738i q^{29} +(66.2349 - 38.2407i) q^{31} +(237.983 - 146.430i) q^{35} +(-174.341 + 301.967i) q^{37} +138.909 q^{41} -539.651 q^{43} +(-111.821 + 193.680i) q^{47} +(187.852 + 286.985i) q^{49} +(-459.003 + 265.005i) q^{53} +149.220i q^{55} +(-271.438 - 470.145i) q^{59} +(-116.218 - 67.0983i) q^{61} +(-887.046 - 512.136i) q^{65} +(160.290 + 277.630i) q^{67} -416.958i q^{71} +(472.510 - 272.804i) q^{73} +(-183.100 + 5.12660i) q^{77} +(-161.369 + 279.499i) q^{79} -885.170 q^{83} -1058.19 q^{85} +(812.312 - 1406.97i) q^{89} +(597.940 - 1106.04i) q^{91} +(-803.017 + 463.622i) q^{95} -739.155i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−7.54372	+	13.0661i	−0.674731	+	1.16867i	0.301817	+	0.953366i	$0.402407\pi$
$5$	−7.54372	+	13.0661i	−0.674731	+	1.16867i	−0.976547	+	0.215302i	$0.930926\pi$
$6$		0			0
$7$	−16.2919	−	8.80760i	−0.879680	−	0.475566i
$7$	−16.2919	−	8.80760i	−0.879680	−	0.475566i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	8.56529	−	4.94517i	0.234776	−	0.135548i	−0.377998	−	0.925807i	$-0.623387\pi$
$11$	8.56529	−	4.94517i	0.234776	−	0.135548i	0.612773	+	0.790259i	$0.290054\pi$
$12$		0			0
$13$			67.8891i			1.44839i	0.689596	+	0.724194i	$0.257788\pi$
$13$			67.8891i			1.44839i	−0.689596	+	0.724194i	$0.742212\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	35.0687	+	60.7407i	0.500318	+	0.866575i	1.00000		0.000366661i	$0.000116712\pi$
$17$	35.0687	+	60.7407i	0.500318	+	0.866575i	−0.499682	+	0.866209i	$0.666550\pi$
$18$		0			0
$19$	53.2242	+	30.7290i	0.642656	+	0.371038i	0.785637	−	0.618688i	$-0.212335\pi$
$19$	53.2242	+	30.7290i	0.642656	+	0.371038i	−0.142981	+	0.989725i	$0.545669\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	113.895	+	65.7575i	1.03256	+	0.596147i	0.917716	−	0.397236i	$-0.130031\pi$
$23$	113.895	+	65.7575i	1.03256	+	0.596147i	0.114841	+	0.993384i	$0.463364\pi$
$24$		0			0
$25$	−51.3154	−	88.8809i	−0.410523	−	0.711047i
$26$		0			0
$27$		0			0
$28$		0			0
$29$		−	158.738i		−	1.01645i	−0.861225	−	0.508223i	$-0.830302\pi$
$29$		−	158.738i		−	1.01645i	0.861225	−	0.508223i	$-0.169698\pi$
$30$		0			0
$31$	66.2349	−	38.2407i	0.383746	−	0.221556i	−0.295701	−	0.955281i	$-0.595553\pi$
$31$	66.2349	−	38.2407i	0.383746	−	0.221556i	0.679447	+	0.733725i	$0.262220\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	237.983	−	146.430i	1.14933	−	0.707175i
$36$		0			0
$37$	−174.341	+	301.967i	−0.774634	+	1.34171i	0.160366	+	0.987058i	$0.448733\pi$
$37$	−174.341	+	301.967i	−0.774634	+	1.34171i	−0.935000	+	0.354648i	$0.884601\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	138.909			0.529120			0.264560	−	0.964369i	$-0.414773\pi$
$41$	138.909			0.529120			0.264560	+	0.964369i	$0.414773\pi$
$42$		0			0
$43$	−539.651			−1.91386			−0.956931	−	0.290316i	$-0.906240\pi$
$43$	−539.651			−1.91386			−0.956931	+	0.290316i	$0.906240\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−111.821	+	193.680i	−0.347039	+	0.601089i	−0.985722	−	0.168381i	$-0.946146\pi$
$47$	−111.821	+	193.680i	−0.347039	+	0.601089i	0.638683	+	0.769470i	$0.279480\pi$
$48$		0			0
$49$	187.852	+	286.985i	0.547674	+	0.836692i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−459.003	+	265.005i	−1.18960	+	0.686817i	−0.958216	−	0.286045i	$-0.907659\pi$
$53$	−459.003	+	265.005i	−1.18960	+	0.686817i	−0.231386	+	0.972862i	$0.574326\pi$
$54$		0			0
$55$			149.220i			0.365833i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−271.438	−	470.145i	−0.598953	−	1.03742i	−0.992976	−	0.118317i	$-0.962250\pi$
$59$	−271.438	−	470.145i	−0.598953	−	1.03742i	0.394023	−	0.919101i	$-0.371083\pi$
$60$		0			0
$61$	−116.218	−	67.0983i	−0.243937	−	0.140837i	0.373048	−	0.927812i	$-0.378313\pi$
$61$	−116.218	−	67.0983i	−0.243937	−	0.140837i	−0.616985	+	0.786975i	$0.711646\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−887.046	−	512.136i	−1.69269	−	0.977272i
$66$		0			0
$67$	160.290	+	277.630i	0.292276	+	0.506238i	0.974348	−	0.225048i	$-0.0722539\pi$
$67$	160.290	+	277.630i	0.292276	+	0.506238i	−0.682071	+	0.731286i	$0.738921\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	416.958i		−	0.696955i	−0.937317	−	0.348478i	$-0.886699\pi$
$71$		−	416.958i		−	0.696955i	0.937317	−	0.348478i	$-0.113301\pi$
$72$		0			0
$73$	472.510	−	272.804i	0.757577	−	0.437387i	−0.0708484	−	0.997487i	$-0.522571\pi$
$73$	472.510	−	272.804i	0.757577	−	0.437387i	0.828425	+	0.560100i	$0.189237\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−183.100	+	5.12660i	−0.270989	+	0.00758740i
$78$		0			0
$79$	−161.369	+	279.499i	−0.229815	+	0.398052i	−0.957753	−	0.287591i	$-0.907146\pi$
$79$	−161.369	+	279.499i	−0.229815	+	0.398052i	0.727938	+	0.685643i	$0.240479\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−885.170			−1.17060			−0.585301	−	0.810816i	$-0.699024\pi$
$83$	−885.170			−1.17060			−0.585301	+	0.810816i	$0.699024\pi$
$84$		0			0
$85$	−1058.19			−1.35032
$86$		0			0
$87$		0			0
$88$		0			0
$89$	812.312	−	1406.97i	0.967471	−	1.67571i	0.264645	−	0.964346i	$-0.414745\pi$
$89$	812.312	−	1406.97i	0.967471	−	1.67571i	0.702826	−	0.711362i	$-0.251921\pi$
$90$		0			0
$91$	597.940	−	1106.04i	0.688804	−	1.27412i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−803.017	+	463.622i	−0.867240	+	0.500701i
$96$		0			0
$97$		−	739.155i		−	0.773710i	−0.922141	−	0.386855i	$-0.873561\pi$
$97$		−	739.155i		−	0.773710i	0.922141	−	0.386855i	$-0.126439\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	119.758	+	207.427i	0.117984	+	0.204354i	0.918969	−	0.394331i	$-0.129024\pi$
$101$	119.758	+	207.427i	0.117984	+	0.204354i	−0.800985	+	0.598685i	$0.795690\pi$
$102$		0			0
$103$	44.2852	+	25.5681i	0.0423645	+	0.0244592i	0.521033	−	0.853537i	$-0.325547\pi$
$103$	44.2852	+	25.5681i	0.0423645	+	0.0244592i	−0.478668	+	0.877996i	$0.658880\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−1031.43	−	595.495i	−0.931886	−	0.538025i	−0.0444785	−	0.999010i	$-0.514163\pi$
$107$	−1031.43	−	595.495i	−0.931886	−	0.538025i	−0.887408	+	0.460986i	$0.847496\pi$
$108$		0			0
$109$	−194.585	−	337.031i	−0.170989	−	0.296162i	0.767777	−	0.640718i	$-0.221363\pi$
$109$	−194.585	−	337.031i	−0.170989	−	0.296162i	−0.938766	+	0.344555i	$0.888030\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$		−	718.545i		−	0.598186i	−0.954224	−	0.299093i	$-0.903316\pi$
$113$		−	718.545i		−	0.598186i	0.954224	−	0.299093i	$-0.0966841\pi$
$114$		0			0
$115$	−1718.39	+	992.113i	−1.39340	+	0.804478i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−36.3552	−	1298.45i	−0.0280057	−	1.00024i
$120$		0			0
$121$	−616.591	+	1067.97i	−0.463254	+	0.802379i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−337.493			−0.241490
$126$		0			0
$127$	179.456			0.125387			0.0626934	−	0.998033i	$-0.480031\pi$
$127$	179.456			0.125387			0.0626934	+	0.998033i	$0.480031\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	1223.43	−	2119.05i	0.815968	−	1.41330i	−0.0926619	−	0.995698i	$-0.529538\pi$
$131$	1223.43	−	2119.05i	0.815968	−	1.41330i	0.908630	−	0.417601i	$-0.137129\pi$
$132$		0			0
$133$	−596.474	−	969.411i	−0.388879	−	0.632020i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−443.021	+	255.778i	−0.276276	+	0.159508i	−0.631736	−	0.775183i	$-0.717658\pi$
$137$	−443.021	+	255.778i	−0.276276	+	0.159508i	0.355460	+	0.934691i	$0.384324\pi$
$138$		0			0
$139$			599.427i			0.365775i	0.983134	+	0.182888i	$0.0585444\pi$
$139$			599.427i			0.365775i	−0.983134	+	0.182888i	$0.941456\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	335.723	+	581.490i	0.196326	+	0.340046i
$144$		0			0
$145$	2074.09	+	1197.48i	1.18789	+	0.685828i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	1899.63	+	1096.75i	1.04445	+	0.603016i	0.921092	−	0.389346i	$-0.127299\pi$
$149$	1899.63	+	1096.75i	1.04445	+	0.603016i	0.123362	+	0.992362i	$0.460632\pi$
$150$		0			0
$151$	−358.683	−	621.257i	−0.193306	−	0.334816i	0.753038	−	0.657977i	$-0.228588\pi$
$151$	−358.683	−	621.257i	−0.193306	−	0.334816i	−0.946344	+	0.323161i	$0.895254\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$			1153.91i			0.597963i
$156$		0			0
$157$	−1561.39	+	901.471i	−0.793712	+	0.458250i	−0.841268	−	0.540619i	$-0.818190\pi$
$157$	−1561.39	+	901.471i	−0.793712	+	0.458250i	0.0475556	+	0.998869i	$0.484857\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−1276.41	−	2074.46i	−0.624813	−	1.01547i
$162$		0			0
$163$	−1453.90	+	2518.24i	−0.698642	+	1.21008i	0.270296	+	0.962777i	$0.412878\pi$
$163$	−1453.90	+	2518.24i	−0.698642	+	1.21008i	−0.968938	+	0.247305i	$0.920455\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−3491.37			−1.61779			−0.808893	−	0.587956i	$-0.799933\pi$
$167$	−3491.37			−1.61779			−0.808893	+	0.587956i	$0.799933\pi$
$168$		0			0
$169$	−2411.93			−1.09783
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−877.377	+	1519.66i	−0.385583	+	0.667848i	−0.991850	−	0.127412i	$-0.959333\pi$
$173$	−877.377	+	1519.66i	−0.385583	+	0.667848i	0.606267	+	0.795261i	$0.292666\pi$
$174$		0			0
$175$	53.1981	+	1900.01i	0.0229794	+	0.820725i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	685.639	−	395.854i	0.286296	−	0.165293i	−0.349974	−	0.936759i	$-0.613810\pi$
$179$	685.639	−	395.854i	0.286296	−	0.165293i	0.636270	+	0.771466i	$0.280476\pi$
$180$		0			0
$181$			2522.19i			1.03576i	0.855452	+	0.517882i	$0.173279\pi$
$181$			2522.19i			1.03576i	−0.855452	+	0.517882i	$0.826721\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−2630.36	−	4555.91i	−1.04534	−	1.81058i
$186$		0			0
$187$	600.746	+	346.841i	0.234925	+	0.135634i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	782.266	+	451.642i	0.296350	+	0.171098i	0.640802	−	0.767706i	$-0.278602\pi$
$191$	782.266	+	451.642i	0.296350	+	0.171098i	−0.344452	+	0.938804i	$0.611935\pi$
$192$		0			0
$193$	99.4374	+	172.231i	0.0370863	+	0.0642354i	0.883973	−	0.467538i	$-0.154859\pi$
$193$	99.4374	+	172.231i	0.0370863	+	0.0642354i	−0.846886	+	0.531774i	$0.821526\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	3220.69i		−	1.16480i	−0.812904	−	0.582398i	$-0.802114\pi$
$197$		−	3220.69i		−	1.16480i	0.812904	−	0.582398i	$-0.197886\pi$
$198$		0			0
$199$	−2468.10	+	1424.96i	−0.879191	+	0.507601i	−0.870392	−	0.492360i	$-0.836134\pi$
$199$	−2468.10	+	1424.96i	−0.879191	+	0.507601i	−0.00879944	+	0.999961i	$0.502801\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−1398.10	+	2586.15i	−0.483387	+	0.894148i
$204$		0			0
$205$	−1047.89	+	1815.00i	−0.357014	+	0.618366i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	607.841			0.201173
$210$		0			0
$211$	−1204.50			−0.392993			−0.196496	−	0.980505i	$-0.562956\pi$
$211$	−1204.50			−0.392993			−0.196496	+	0.980505i	$0.562956\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	4070.98	−	7051.14i	1.29134	−	2.23667i
$216$		0			0
$217$	−1415.90	+	39.6437i	−0.442938	+	0.0124018i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−4123.63	+	2380.78i	−1.25514	+	0.724654i
$222$		0			0
$223$		−	3377.73i		−	1.01430i	−0.861857	−	0.507151i	$-0.830699\pi$
$223$		−	3377.73i		−	1.01430i	0.861857	−	0.507151i	$-0.169301\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−2261.98	−	3917.86i	−0.661378	−	1.14554i	−0.980254	−	0.197744i	$-0.936638\pi$
$227$	−2261.98	−	3917.86i	−0.661378	−	1.14554i	0.318875	−	0.947797i	$-0.396695\pi$
$228$		0			0
$229$	3389.61	+	1956.99i	0.978131	+	0.564724i	0.901705	−	0.432351i	$-0.142316\pi$
$229$	3389.61	+	1956.99i	0.978131	+	0.564724i	0.0764258	+	0.997075i	$0.475649\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	3783.80	+	2184.58i	1.06388	+	0.614234i	0.926504	−	0.376284i	$-0.122798\pi$
$233$	3783.80	+	2184.58i	1.06388	+	0.614234i	0.137381	+	0.990518i	$0.456132\pi$
$234$		0			0
$235$	−1687.10	−	2922.14i	−0.468316	−	0.811147i
$236$		0			0
$237$		0			0
$238$		0			0
$239$			1945.23i			0.526471i	0.964732	+	0.263235i	$0.0847896\pi$
$239$			1945.23i			0.526471i	−0.964732	+	0.263235i	$0.915210\pi$
$240$		0			0
$241$	−3499.81	+	2020.61i	−0.935446	+	0.540080i	−0.888530	−	0.458819i	$-0.848273\pi$
$241$	−3499.81	+	2020.61i	−0.935446	+	0.540080i	−0.0469158	+	0.998899i	$0.514939\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−5166.88	+	289.561i	−1.34735	+	0.0755077i
$246$		0			0
$247$	−2086.16	+	3613.34i	−0.537407	+	0.930816i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	4415.70			1.11042			0.555212	−	0.831709i	$-0.312637\pi$
$251$	4415.70			1.11042			0.555212	+	0.831709i	$0.312637\pi$
$252$		0			0
$253$	1300.73			0.323226
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−348.800	+	604.139i	−0.0846597	+	0.146635i	−0.905246	−	0.424888i	$-0.860314\pi$
$257$	−348.800	+	604.139i	−0.0846597	+	0.146635i	0.820586	+	0.571522i	$0.193647\pi$
$258$		0			0
$259$	5499.95	−	3384.10i	1.31950	−	0.811882i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−690.664	+	398.755i	−0.161932	+	0.0934915i	−0.578776	−	0.815487i	$-0.696469\pi$
$263$	−690.664	+	398.755i	−0.161932	+	0.0934915i	0.416844	+	0.908978i	$0.363136\pi$
$264$		0			0
$265$		−	7996.51i		−	1.85367i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	205.351	+	355.679i	0.0465446	+	0.0806176i	0.888359	−	0.459149i	$-0.151846\pi$
$269$	205.351	+	355.679i	0.0465446	+	0.0806176i	−0.841815	+	0.539767i	$0.818512\pi$
$270$		0			0
$271$	−3283.42	−	1895.69i	−0.735992	−	0.424925i	0.0846182	−	0.996413i	$-0.473033\pi$
$271$	−3283.42	−	1895.69i	−0.735992	−	0.424925i	−0.820610	+	0.571488i	$0.806366\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−879.063	−	507.527i	−0.192762	−	0.111291i
$276$		0			0
$277$	−1623.31	−	2811.66i	−0.352113	−	0.609877i	0.634507	−	0.772917i	$-0.281203\pi$
$277$	−1623.31	−	2811.66i	−0.352113	−	0.609877i	−0.986619	+	0.163040i	$0.947870\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$		−	1599.58i		−	0.339583i	−0.985480	−	0.169791i	$-0.945691\pi$
$281$		−	1599.58i		−	0.339583i	0.985480	−	0.169791i	$-0.0543094\pi$
$282$		0			0
$283$	3694.70	−	2133.13i	0.776067	−	0.448062i	−0.0589678	−	0.998260i	$-0.518781\pi$
$283$	3694.70	−	2133.13i	0.776067	−	0.448062i	0.835034	+	0.550198i	$0.185448\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−2263.09	−	1223.45i	−0.465456	−	0.251631i
$288$		0			0
$289$	−3.12079	+	5.40536i	−0.000635210	+	0.00110022i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	2926.77			0.583562			0.291781	−	0.956485i	$-0.405752\pi$
$293$	2926.77			0.583562			0.291781	+	0.956485i	$0.405752\pi$
$294$		0			0
$295$	8190.62			1.61653
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−4464.22	+	7732.25i	−0.863453	+	1.49554i
$300$		0			0
$301$	8791.95	+	4753.03i	1.68359	+	0.910167i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	1753.43	−	1012.34i	0.329183	−	0.190054i
$306$		0			0
$307$			3571.36i			0.663935i	0.943291	+	0.331968i	$0.107712\pi$
$307$			3571.36i			0.663935i	−0.943291	+	0.331968i	$0.892288\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−1286.71	−	2228.64i	−0.234606	−	0.406349i	0.724552	−	0.689220i	$-0.242047\pi$
$311$	−1286.71	−	2228.64i	−0.234606	−	0.406349i	−0.959158	+	0.282871i	$0.908713\pi$
$312$		0			0
$313$	−1278.56	−	738.176i	−0.230889	−	0.133304i	0.380093	−	0.924948i	$-0.375892\pi$
$313$	−1278.56	−	738.176i	−0.230889	−	0.133304i	−0.610982	+	0.791644i	$0.709225\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−2188.36	−	1263.45i	−0.387730	−	0.223856i	0.293446	−	0.955976i	$-0.405198\pi$
$317$	−2188.36	−	1263.45i	−0.387730	−	0.223856i	−0.681176	+	0.732120i	$0.738531\pi$
$318$		0			0
$319$	−784.988	−	1359.64i	−0.137777	−	0.238637i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			4310.50i			0.742546i
$324$		0			0
$325$	6034.05	−	3483.76i	1.02987	−	0.594597i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	3527.64	−	2170.54i	0.591141	−	0.363726i
$330$		0			0
$331$	737.778	−	1277.87i	0.122513	−	0.212200i	−0.798245	−	0.602333i	$-0.794238\pi$
$331$	737.778	−	1277.87i	0.122513	−	0.212200i	0.920758	+	0.390134i	$0.127571\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−4836.73			−0.788832
$336$		0			0
$337$	−6727.28			−1.08741			−0.543706	−	0.839275i	$-0.682979\pi$
$337$	−6727.28			−1.08741			−0.543706	+	0.839275i	$0.682979\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	378.214	−	655.086i	0.0600629	−	0.104032i
$342$		0			0
$343$	−532.819	−	6330.06i	−0.0838761	−	0.996476i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−466.060	+	269.080i	−0.0721021	+	0.0416281i	−0.535618	−	0.844461i	$-0.679921\pi$
$347$	−466.060	+	269.080i	−0.0721021	+	0.0416281i	0.463516	+	0.886089i	$0.346588\pi$
$348$		0			0
$349$		−	6975.93i		−	1.06995i	−0.844867	−	0.534976i	$-0.820321\pi$
$349$		−	6975.93i		−	1.06995i	0.844867	−	0.534976i	$-0.179679\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	4438.40	+	7687.53i	0.669213	+	1.15911i	0.978125	+	0.208020i	$0.0667019\pi$
$353$	4438.40	+	7687.53i	0.669213	+	1.15911i	−0.308912	+	0.951091i	$0.599965\pi$
$354$		0			0
$355$	5448.02	+	3145.42i	0.814509	+	0.470257i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	9565.96	+	5522.91i	1.40633	+	0.811944i	0.995032	−	0.0995575i	$-0.0317427\pi$
$359$	9565.96	+	5522.91i	1.40633	+	0.811944i	0.411297	+	0.911502i	$0.365076\pi$
$360$		0			0
$361$	−1540.96	−	2669.02i	−0.224662	−	0.389126i
$362$		0			0
$363$		0			0
$364$		0			0
$365$			8231.82i			1.18047i
$366$		0			0
$367$	−7210.59	+	4163.04i	−1.02559	+	0.592122i	−0.915717	−	0.401824i	$-0.868376\pi$
$367$	−7210.59	+	4163.04i	−1.02559	+	0.592122i	−0.109868	+	0.993946i	$0.535043\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	9812.09	−	274.728i	1.37310	−	0.0384452i
$372$		0			0
$373$	2272.66	−	3936.36i	0.315479	−	0.546426i	−0.664060	−	0.747679i	$-0.731168\pi$
$373$	2272.66	−	3936.36i	0.315479	−	0.546426i	0.979539	+	0.201253i	$0.0645014\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	10776.6			1.47221
$378$		0			0
$379$	−11527.2			−1.56230			−0.781151	−	0.624343i	$-0.785367\pi$
$379$	−11527.2			−1.56230			−0.781151	+	0.624343i	$0.785367\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	1960.23	−	3395.22i	0.261522	−	0.452970i	−0.705124	−	0.709084i	$-0.749109\pi$
$383$	1960.23	−	3395.22i	0.261522	−	0.452970i	0.966647	+	0.256114i	$0.0824422\pi$
$384$		0			0
$385$	1314.27	−	2431.08i	0.173978	−	0.321816i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−689.734	+	398.218i	−0.0898995	+	0.0519035i	−0.544276	−	0.838906i	$-0.683195\pi$
$389$	−689.734	+	398.218i	−0.0898995	+	0.0519035i	0.454376	+	0.890810i	$0.349862\pi$
$390$		0			0
$391$			9224.11i			1.19305i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−2434.64	−	4216.92i	−0.310127	−	0.537155i
$396$		0			0
$397$	3338.59	+	1927.54i	0.422063	+	0.243678i	0.695960	−	0.718081i	$-0.254979\pi$
$397$	3338.59	+	1927.54i	0.422063	+	0.243678i	−0.273896	+	0.961759i	$0.588313\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−4031.65	−	2327.68i	−0.502073	−	0.289872i	0.227496	−	0.973779i	$-0.426946\pi$
$401$	−4031.65	−	2327.68i	−0.502073	−	0.289872i	−0.729569	+	0.683907i	$0.760279\pi$
$402$		0			0
$403$	2596.13	+	4496.63i	0.320899	+	0.555814i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			3448.58i			0.420000i
$408$		0			0
$409$	−8478.82	+	4895.25i	−1.02506	+	0.591821i	−0.915566	−	0.402167i	$-0.868257\pi$
$409$	−8478.82	+	4895.25i	−1.02506	+	0.591821i	−0.109497	+	0.993987i	$0.534924\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	281.397	+	10050.3i	0.0335269	+	1.19744i
$414$		0			0
$415$	6677.47	−	11565.7i	0.789842	−	1.36805i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	3007.46			0.350654			0.175327	−	0.984510i	$-0.443902\pi$
$419$	3007.46			0.350654			0.175327	+	0.984510i	$0.443902\pi$
$420$		0			0
$421$	7646.06			0.885145			0.442573	−	0.896733i	$-0.354066\pi$
$421$	7646.06			0.885145			0.442573	+	0.896733i	$0.354066\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	3599.13	−	6233.87i	0.410784	−	0.711499i
$426$		0			0
$427$	1302.43	+	2116.76i	0.147609	+	0.239899i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−12983.1	+	7495.81i	−1.45099	+	0.837727i	−0.998537	−	0.0540641i	$-0.982782\pi$
$431$	−12983.1	+	7495.81i	−1.45099	+	0.837727i	−0.452448	+	0.891791i	$0.649449\pi$
$432$		0			0
$433$			5666.63i			0.628916i	0.949271	+	0.314458i	$0.101823\pi$
$433$			5666.63i			0.628916i	−0.949271	+	0.314458i	$0.898177\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	4041.32	+	6999.78i	0.442386	+	0.766235i
$438$		0			0
$439$	4790.07	+	2765.55i	0.520769	+	0.300666i	0.737249	−	0.675621i	$-0.236124\pi$
$439$	4790.07	+	2765.55i	0.520769	+	0.300666i	−0.216480	+	0.976287i	$0.569458\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−349.200	−	201.611i	−0.0374515	−	0.0216226i	0.481157	−	0.876634i	$-0.340217\pi$
$443$	−349.200	−	201.611i	−0.0374515	−	0.0216226i	−0.518609	+	0.855012i	$0.673550\pi$
$444$		0			0
$445$	12255.7	+	21227.5i	1.30556	+	2.26130i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	8429.03i		−	0.885948i	−0.896534	−	0.442974i	$-0.853923\pi$
$449$		−	8429.03i		−	0.885948i	0.896534	−	0.442974i	$-0.146077\pi$
$450$		0			0
$451$	1189.79	−	686.928i	0.124224	−	0.0717210i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	9940.98	+	16156.4i	1.02426	+	1.66467i
$456$		0			0
$457$	−342.830	+	593.799i	−0.0350917	+	0.0607807i	−0.883038	−	0.469302i	$-0.844506\pi$
$457$	−342.830	+	593.799i	−0.0350917	+	0.0607807i	0.847946	+	0.530082i	$0.177839\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	4864.48			0.491456			0.245728	−	0.969339i	$-0.420973\pi$
$461$	4864.48			0.491456			0.245728	+	0.969339i	$0.420973\pi$
$462$		0			0
$463$	8354.23			0.838562			0.419281	−	0.907857i	$-0.362282\pi$
$463$	8354.23			0.838562			0.419281	+	0.907857i	$0.362282\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−501.469	+	868.570i	−0.0496900	+	0.0860656i	−0.889801	−	0.456350i	$-0.849157\pi$
$467$	−501.469	+	868.570i	−0.0496900	+	0.0860656i	0.840111	+	0.542415i	$0.182490\pi$
$468$		0			0
$469$	−166.170	−	5934.89i	−0.0163604	−	0.584324i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−4622.27	+	2668.67i	−0.449328	+	0.259420i
$474$		0			0
$475$		−	6307.49i		−	0.609279i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	3026.38	+	5241.84i	0.288682	+	0.500012i	0.973495	−	0.228706i	$-0.0734496\pi$
$479$	3026.38	+	5241.84i	0.288682	+	0.500012i	−0.684813	+	0.728719i	$0.740116\pi$
$480$		0			0
$481$	−20500.3	−	11835.8i	−1.94331	−	1.12197i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	9657.88	+	5575.98i	0.904210	+	0.522046i
$486$		0			0
$487$	7654.72	+	13258.4i	0.712255	+	1.23366i	0.964009	+	0.265871i	$0.0856596\pi$
$487$	7654.72	+	13258.4i	0.712255	+	1.23366i	−0.251753	+	0.967791i	$0.581007\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$		−	4291.01i		−	0.394400i	−0.980363	−	0.197200i	$-0.936815\pi$
$491$		−	4291.01i		−	0.394400i	0.980363	−	0.197200i	$-0.0631848\pi$
$492$		0			0
$493$	9641.87	−	5566.74i	0.880828	−	0.508546i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−3672.40	+	6793.04i	−0.331448	+	0.613098i
$498$		0			0
$499$	3445.77	−	5968.24i	0.309126	−	0.535421i	−0.669046	−	0.743221i	$-0.733297\pi$
$499$	3445.77	−	5968.24i	0.309126	−	0.535421i	0.978171	+	0.207800i	$0.0666303\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	13534.6			1.19975			0.599877	−	0.800092i	$-0.295216\pi$
$503$	13534.6			1.19975			0.599877	+	0.800092i	$0.295216\pi$
$504$		0			0
$505$	−3613.68			−0.318429
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−6043.91	+	10468.4i	−0.526310	+	0.911595i	0.473221	+	0.880944i	$0.343091\pi$
$509$	−6043.91	+	10468.4i	−0.526310	+	0.911595i	−0.999530	+	0.0306510i	$0.990242\pi$
$510$		0			0
$511$	−10100.8	+	282.812i	−0.874431	+	0.0244831i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−668.150	+	385.757i	−0.0571693	+	0.0330067i
$516$		0			0
$517$			2211.91i			0.188161i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−3812.94	−	6604.20i	−0.320629	−	0.555346i	0.659989	−	0.751275i	$-0.270561\pi$
$521$	−3812.94	−	6604.20i	−0.320629	−	0.555346i	−0.980618	+	0.195930i	$0.937228\pi$
$522$		0			0
$523$	−13328.7	−	7695.34i	−1.11439	−	0.643392i	−0.174425	−	0.984670i	$-0.555807\pi$
$523$	−13328.7	−	7695.34i	−1.11439	−	0.643392i	−0.939962	+	0.341279i	$0.889140\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	4645.54	+	2682.10i	0.383990	+	0.221697i
$528$		0			0
$529$	2564.60	+	4442.02i	0.210783	+	0.365088i
$530$		0			0
$531$		0			0
$532$		0			0
$533$			9430.40i			0.766371i
$534$		0			0
$535$	15561.6	−	8984.49i	1.25754	−	0.726044i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	3028.20	+	1529.15i	0.241992	+	0.122199i
$540$		0			0
$541$	6850.44	−	11865.3i	0.544406	−	0.942939i	−0.454238	−	0.890880i	$-0.650088\pi$
$541$	6850.44	−	11865.3i	0.544406	−	0.942939i	0.998644	−	0.0520584i	$-0.0165782\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	5871.58			0.461487
$546$		0			0
$547$	6139.00			0.479863			0.239931	−	0.970790i	$-0.422875\pi$
$547$	6139.00			0.479863			0.239931	+	0.970790i	$0.422875\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	4877.87	−	8448.71i	0.377140	−	0.653226i
$552$		0			0
$553$	5090.72	−	3132.30i	0.391464	−	0.240866i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−19687.1	+	11366.4i	−1.49761	+	0.864646i	−0.999996	−	0.00275234i	$-0.999124\pi$
$557$	−19687.1	+	11366.4i	−1.49761	+	0.864646i	−0.497615	+	0.867398i	$0.665791\pi$
$558$		0			0
$559$		−	36636.4i		−	2.77202i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	4958.81	+	8588.90i	0.371206	+	0.642947i	0.989751	−	0.142802i	$-0.0456112\pi$
$563$	4958.81	+	8588.90i	0.371206	+	0.642947i	−0.618546	+	0.785749i	$0.712278\pi$
$564$		0			0
$565$	9388.59	+	5420.51i	0.699081	+	0.403615i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	4448.79	+	2568.51i	0.327773	+	0.189240i	0.654852	−	0.755757i	$-0.272731\pi$
$569$	4448.79	+	2568.51i	0.327773	+	0.189240i	−0.327079	+	0.944997i	$0.606064\pi$
$570$		0			0
$571$	−9093.02	−	15749.6i	−0.666429	−	1.15429i	−0.978896	−	0.204360i	$-0.934489\pi$
$571$	−9093.02	−	15749.6i	−0.666429	−	1.15429i	0.312467	−	0.949929i	$-0.398845\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	13497.5i		−	0.978930i
$576$		0			0
$577$	10737.5	−	6199.32i	0.774713	−	0.447281i	−0.0598401	−	0.998208i	$-0.519059\pi$
$577$	10737.5	−	6199.32i	0.774713	−	0.447281i	0.834553	+	0.550927i	$0.185726\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	14421.1	+	7796.23i	1.02976	+	0.556699i
$582$		0			0
$583$	−2621.00	+	4539.70i	−0.186193	+	0.322496i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	18977.6			1.33439			0.667195	−	0.744883i	$-0.267495\pi$
$587$	18977.6			1.33439			0.667195	+	0.744883i	$0.267495\pi$
$588$		0			0
$589$	4700.40			0.328822
$590$		0			0
$591$		0			0
$592$		0			0
$593$	5364.44	−	9291.48i	0.371486	−	0.643432i	−0.618308	−	0.785936i	$-0.712182\pi$
$593$	5364.44	−	9291.48i	0.371486	−	0.643432i	0.989794	+	0.142503i	$0.0455151\pi$
$594$		0			0
$595$	17240.0	+	9320.14i	1.18785	+	0.642165i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	1577.36	−	910.687i	0.107594	−	0.0621196i	−0.445237	−	0.895413i	$-0.646881\pi$
$599$	1577.36	−	910.687i	0.107594	−	0.0621196i	0.552832	+	0.833293i	$0.313547\pi$
$600$		0			0
$601$		−	18933.3i		−	1.28503i	−0.766273	−	0.642516i	$-0.777891\pi$
$601$		−	18933.3i		−	1.28503i	0.766273	−	0.642516i	$-0.222109\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−9302.77	−	16112.9i	−0.625143	−	1.08278i
$606$		0			0
$607$	−13323.3	−	7692.20i	−0.890898	−	0.514360i	−0.0166621	−	0.999861i	$-0.505304\pi$
$607$	−13323.3	−	7692.20i	−0.890898	−	0.514360i	−0.874236	+	0.485501i	$0.838637\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−13148.8	−	7591.46i	−0.870611	−	0.502647i
$612$		0			0
$613$	2753.60	+	4769.38i	0.181431	+	0.314247i	0.942368	−	0.334578i	$-0.108594\pi$
$613$	2753.60	+	4769.38i	0.181431	+	0.314247i	−0.760937	+	0.648825i	$0.775261\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	18134.0i		−	1.18322i	−0.806224	−	0.591610i	$-0.798493\pi$
$617$		−	18134.0i		−	1.18322i	0.806224	−	0.591610i	$-0.201507\pi$
$618$		0			0
$619$	−3148.73	+	1817.92i	−0.204456	+	0.118043i	−0.598732	−	0.800949i	$-0.704329\pi$
$619$	−3148.73	+	1817.92i	−0.204456	+	0.118043i	0.394276	+	0.918992i	$0.370995\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−25626.1	+	15767.6i	−1.64797	+	1.01399i
$624$		0			0
$625$	8960.38	−	15519.8i	0.573464	−	0.993270i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−24455.6			−1.55025
$630$		0			0
$631$	5912.59			0.373021			0.186511	−	0.982453i	$-0.440282\pi$
$631$	5912.59			0.373021			0.186511	+	0.982453i	$0.440282\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−1353.76	+	2344.79i	−0.0846024	+	0.146536i
$636$		0			0
$637$	−19483.2	+	12753.1i	−1.21185	+	0.793245i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	23786.7	−	13733.3i	1.46571	−	0.846227i	0.466443	−	0.884551i	$-0.345535\pi$
$641$	23786.7	−	13733.3i	1.46571	−	0.846227i	0.999265	+	0.0383236i	$0.0122018\pi$
$642$		0			0
$643$			28474.0i			1.74635i	0.487403	+	0.873177i	$0.337944\pi$
$643$			28474.0i			1.74635i	−0.487403	+	0.873177i	$0.662056\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−661.681	−	1146.06i	−0.0402061	−	0.0696390i	0.845222	−	0.534415i	$-0.179468\pi$
$647$	−661.681	−	1146.06i	−0.0402061	−	0.0696390i	−0.885428	+	0.464776i	$0.846135\pi$
$648$		0			0
$649$	−4649.89	−	2684.62i	−0.281239	−	0.162374i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−3331.38	−	1923.37i	−0.199643	−	0.115264i	0.396846	−	0.917885i	$-0.370105\pi$
$653$	−3331.38	−	1923.37i	−0.199643	−	0.115264i	−0.596489	+	0.802621i	$0.703438\pi$
$654$		0			0
$655$	18458.5	+	31971.0i	1.10112	+	1.90719i
$656$		0			0
$657$		0			0
$658$		0			0
$659$			6796.84i			0.401771i	0.979615	+	0.200886i	$0.0643819\pi$
$659$			6796.84i			0.401771i	−0.979615	+	0.200886i	$0.935618\pi$
$660$		0			0
$661$	−26902.5	+	15532.2i	−1.58304	+	0.913966i	−0.588623	+	0.808408i	$0.700330\pi$
$661$	−26902.5	+	15532.2i	−1.58304	+	0.913966i	−0.994413	+	0.105559i	$0.966337\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	17166.1	−	480.631i	1.00101	−	0.0280272i
$666$		0			0
$667$	10438.2	−	18079.5i	0.605952	−	1.04954i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−1327.25			−0.0763605
$672$		0			0
$673$	15508.2			0.888259			0.444129	−	0.895963i	$-0.353513\pi$
$673$	15508.2			0.888259			0.444129	+	0.895963i	$0.353513\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−15337.4	+	26565.2i	−0.870701	+	1.50810i	−0.00942744	+	0.999956i	$0.503001\pi$
$677$	−15337.4	+	26565.2i	−0.870701	+	1.50810i	−0.861273	+	0.508142i	$0.830332\pi$
$678$		0			0
$679$	−6510.19	+	12042.2i	−0.367950	+	0.680617i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−15292.8	+	8829.33i	−0.856756	+	0.494648i	−0.862925	−	0.505333i	$-0.831370\pi$
$683$	−15292.8	+	8829.33i	−0.856756	+	0.494648i	0.00616869	+	0.999981i	$0.498036\pi$
$684$		0			0
$685$		−	7718.08i		−	0.430500i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−17991.0	−	31161.3i	−0.994778	−	1.72301i
$690$		0			0
$691$	−11402.3	−	6583.11i	−0.627733	−	0.362422i	0.152141	−	0.988359i	$-0.451383\pi$
$691$	−11402.3	−	6583.11i	−0.627733	−	0.362422i	−0.779874	+	0.625937i	$0.784717\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−7832.18	−	4521.91i	−0.427470	−	0.246800i
$696$		0			0
$697$	4871.35	+	8437.42i	0.264728	+	0.458522i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			25910.0i			1.39602i	0.716090	+	0.698008i	$0.245930\pi$
$701$			25910.0i			1.39602i	−0.716090	+	0.698008i	$0.754070\pi$
$702$		0			0
$703$	−18558.3	+	10714.6i	−0.995646	+	0.574837i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−124.152	−	4434.16i	−0.00660424	−	0.235875i
$708$		0			0
$709$	−3104.25	+	5376.71i	−0.164432	+	0.284805i	−0.936454	−	0.350792i	$-0.885913\pi$
$709$	−3104.25	+	5376.71i	−0.164432	+	0.284805i	0.772021	+	0.635597i	$0.219246\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	10058.5			0.528320
$714$		0			0
$715$	−10130.4			−0.529868
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−14379.4	+	24905.9i	−0.745843	+	1.29184i	0.203957	+	0.978980i	$0.434620\pi$
$719$	−14379.4	+	24905.9i	−0.745843	+	1.29184i	−0.949800	+	0.312858i	$0.898713\pi$
$720$		0			0
$721$	−496.296	−	806.599i	−0.0256353	−	0.0416634i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−14108.8	+	8145.72i	−0.722742	+	0.417275i
$726$		0			0
$727$		−	35275.7i		−	1.79959i	−0.436312	−	0.899795i	$-0.643716\pi$
$727$		−	35275.7i		−	1.79959i	0.436312	−	0.899795i	$-0.356284\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−18924.8	−	32778.8i	−0.957539	−	1.65851i
$732$		0			0
$733$	−6885.15	−	3975.14i	−0.346942	−	0.200307i	0.316395	−	0.948627i	$-0.397527\pi$
$733$	−6885.15	−	3975.14i	−0.346942	−	0.200307i	−0.663338	+	0.748320i	$0.730861\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	2745.86	+	1585.32i	0.137239	+	0.0792348i
$738$		0			0
$739$	16676.8	+	28885.1i	0.830130	+	1.43783i	0.897935	+	0.440129i	$0.145067\pi$
$739$	16676.8	+	28885.1i	0.830130	+	1.43783i	−0.0678046	+	0.997699i	$0.521599\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		−	32933.6i		−	1.62613i	−0.582171	−	0.813066i	$-0.697797\pi$
$743$		−	32933.6i		−	1.62613i	0.582171	−	0.813066i	$-0.302203\pi$
$744$		0			0
$745$	−28660.5	+	16547.2i	−1.40945	+	0.813747i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	11559.0	+	18786.1i	0.563895	+	0.916463i
$750$		0			0
$751$	−19818.3	+	34326.3i	−0.962956	+	1.66789i	−0.247945	+	0.968774i	$0.579755\pi$
$751$	−19818.3	+	34326.3i	−0.962956	+	1.66789i	−0.715010	+	0.699114i	$0.753578\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	10823.2			0.521718
$756$		0			0
$757$	−3996.51			−0.191883			−0.0959417	−	0.995387i	$-0.530586\pi$
$757$	−3996.51			−0.191883			−0.0959417	+	0.995387i	$0.530586\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	13117.8	−	22720.8i	0.624863	−	1.08230i	−0.363704	−	0.931515i	$-0.618488\pi$
$761$	13117.8	−	22720.8i	0.624863	−	1.08230i	0.988567	−	0.150781i	$-0.0481787\pi$
$762$		0			0
$763$	201.724	+	7204.70i	0.00957128	+	0.341845i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	31917.7	−	18427.7i	1.50258	−	0.867517i
$768$		0			0
$769$			36456.9i			1.70958i	0.518971	+	0.854792i	$0.326315\pi$
$769$			36456.9i			1.70958i	−0.518971	+	0.854792i	$0.673685\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−4732.74	−	8197.34i	−0.220213	−	0.381420i	0.734660	−	0.678436i	$-0.237342\pi$
$773$	−4732.74	−	8197.34i	−0.220213	−	0.381420i	−0.954873	+	0.297016i	$0.904009\pi$
$774$		0			0
$775$	−6797.74	−	3924.68i	−0.315074	−	0.181908i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	7393.31	+	4268.53i	0.340042	+	0.196323i
$780$		0			0
$781$	−2061.93	−	3571.37i	−0.0944707	−	0.163628i
$782$		0			0
$783$		0			0
$784$		0			0
$785$		−	27201.8i		−	1.23678i
$786$		0			0
$787$	−21665.9	+	12508.8i	−0.981330	+	0.566571i	−0.902671	−	0.430331i	$-0.858397\pi$
$787$	−21665.9	+	12508.8i	−0.981330	+	0.566571i	−0.0786582	+	0.996902i	$0.525064\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−6328.66	+	11706.5i	−0.284477	+	0.526213i
$792$		0			0
$793$	4555.24	−	7889.91i	0.203987	−	0.353315i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	38893.5			1.72858			0.864290	−	0.502994i	$-0.167768\pi$
$797$	38893.5			1.72858			0.864290	+	0.502994i	$0.167768\pi$
$798$		0			0
$799$	−15685.7			−0.694519
$800$		0			0
$801$		0			0
$802$		0			0
$803$	2698.12	−	4673.28i	0.118574	−	0.205376i
$804$		0			0
$805$	36734.0	−	1028.51i	1.60833	−	0.0450314i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−6072.26	+	3505.82i	−0.263893	+	0.152359i	−0.626109	−	0.779735i	$-0.715354\pi$
$809$	−6072.26	+	3505.82i	−0.263893	+	0.152359i	0.362216	+	0.932094i	$0.382020\pi$
$810$		0			0
$811$			5013.82i			0.217089i	0.994092	+	0.108544i	$0.0346189\pi$
$811$			5013.82i			0.217089i	−0.994092	+	0.108544i	$0.965381\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−21935.7	−	37993.7i	−0.942790	−	1.63296i
$816$		0			0
$817$	−28722.5	−	16582.9i	−1.22995	−	0.710115i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−603.281	−	348.304i	−0.0256451	−	0.0148062i	0.487123	−	0.873334i	$-0.338046\pi$
$821$	−603.281	−	348.304i	−0.0256451	−	0.0148062i	−0.512768	+	0.858527i	$0.671380\pi$
$822$		0			0
$823$	3206.57	+	5553.95i	0.135813	+	0.235235i	0.925908	−	0.377750i	$-0.123302\pi$
$823$	3206.57	+	5553.95i	0.135813	+	0.235235i	−0.790095	+	0.612985i	$0.789969\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			16718.9i			0.702989i	0.936190	+	0.351494i	$0.114326\pi$
$827$			16718.9i			0.702989i	−0.936190	+	0.351494i	$0.885674\pi$
$828$		0			0
$829$	−12606.9	+	7278.59i	−0.528173	+	0.304941i	−0.740272	−	0.672307i	$-0.765303\pi$
$829$	−12606.9	+	7278.59i	−0.528173	+	0.304941i	0.212099	+	0.977248i	$0.431970\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−10844.0	+	21474.5i	−0.451045	+	0.893212i
$834$		0			0
$835$	26337.9	−	45618.6i	1.09157	−	1.89065i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	19467.0			0.801045			0.400523	−	0.916287i	$-0.368829\pi$
$839$	19467.0			0.801045			0.400523	+	0.916287i	$0.368829\pi$
$840$		0			0
$841$	−808.829			−0.0331637
$842$		0			0
$843$		0			0
$844$		0			0
$845$	18194.9	−	31514.6i	0.740740	−	1.28300i
$846$		0			0
$847$	19451.7	−	11968.5i	0.789099	−	0.485529i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−39713.2	+	22928.4i	−1.59971	+	0.923592i
$852$		0			0
$853$			22345.3i			0.896938i	0.893798	+	0.448469i	$0.148031\pi$
$853$			22345.3i			0.896938i	−0.893798	+	0.448469i	$0.851969\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−24039.8	−	41638.2i	−0.958209	−	1.65967i	−0.726847	−	0.686800i	$-0.759015\pi$
$857$	−24039.8	−	41638.2i	−0.958209	−	1.65967i	−0.231363	−	0.972868i	$-0.574318\pi$
$858$		0			0
$859$	22612.6	+	13055.4i	0.898173	+	0.518560i	0.876607	−	0.481207i	$-0.159801\pi$
$859$	22612.6	+	13055.4i	0.898173	+	0.518560i	0.0215659	+	0.999767i	$0.493135\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−2536.20	−	1464.27i	−0.100038	−	0.0577572i	0.449146	−	0.893458i	$-0.351728\pi$
$863$	−2536.20	−	1464.27i	−0.100038	−	0.0577572i	−0.549185	+	0.835701i	$0.685062\pi$
$864$		0			0
$865$	−13237.4	−	22927.8i	−0.520329	−	0.901236i
$866$		0			0
$867$		0			0
$868$		0			0
$869$			3191.98i			0.124604i
$870$		0			0
$871$	−18848.1	+	10881.9i	−0.733229	+	0.423330i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	5498.40	+	2972.50i	0.212434	+	0.114845i
$876$		0			0
$877$	−6545.28	+	11336.8i	−0.252016	+	0.436505i	−0.964081	−	0.265609i	$-0.914427\pi$
$877$	−6545.28	+	11336.8i	−0.252016	+	0.436505i	0.712064	+	0.702114i	$0.247760\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−7888.79			−0.301680			−0.150840	−	0.988558i	$-0.548198\pi$
$881$	−7888.79			−0.301680			−0.150840	+	0.988558i	$0.548198\pi$
$882$		0			0
$883$	−45061.9			−1.71739			−0.858694	−	0.512489i	$-0.828724\pi$
$883$	−45061.9			−1.71739			−0.858694	+	0.512489i	$0.828724\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−1773.29	+	3071.43i	−0.0671266	+	0.116267i	−0.897635	−	0.440739i	$-0.854716\pi$
$887$	−1773.29	+	3071.43i	−0.0671266	+	0.116267i	0.830509	+	0.557006i	$0.188050\pi$
$888$		0			0
$889$	−2923.68	−	1580.58i	−0.110300	−	0.0596297i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−11903.2	+	6872.32i	−0.446053	+	0.257529i
$894$		0			0
$895$			11944.8i			0.446114i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−6070.26	−	10514.0i	−0.225200	−	0.390058i
$900$		0			0
$901$	−32193.2	−	18586.8i	−1.19036	−	0.687253i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−32955.2	−	19026.7i	−1.21046	−	0.698861i
$906$		0			0
$907$	−7339.77	−	12712.9i	−0.268703	−	0.465406i	0.699825	−	0.714315i	$-0.253262\pi$
$907$	−7339.77	−	12712.9i	−0.268703	−	0.465406i	−0.968527	+	0.248908i	$0.919928\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$		−	12355.2i		−	0.449336i	−0.974435	−	0.224668i	$-0.927870\pi$
$911$		−	12355.2i		−	0.449336i	0.974435	−	0.224668i	$-0.0721297\pi$
$912$		0			0
$913$	−7581.74	+	4377.32i	−0.274829	+	0.158673i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−38595.8	+	23747.8i	−1.38991	+	0.855204i
$918$		0			0
$919$	−1535.18	+	2659.01i	−0.0551044	+	0.0954437i	−0.892262	−	0.451518i	$-0.850883\pi$
$919$	−1535.18	+	2659.01i	−0.0551044	+	0.0954437i	0.837157	+	0.546962i	$0.184216\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	28306.9			1.00946
$924$		0			0
$925$	35785.5			1.27202
$926$		0			0
$927$		0			0
$928$		0			0
$929$	15264.3	−	26438.6i	0.539082	−	0.933717i	−0.459872	−	0.887985i	$-0.652105\pi$
$929$	15264.3	−	26438.6i	0.539082	−	0.933717i	0.998954	−	0.0457316i	$-0.0145619\pi$
$930$		0			0
$931$	1179.51	+	21047.1i	0.0415220	+	0.740913i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−9063.72	+	5232.94i	−0.317022	+	0.183033i
$936$		0			0
$937$		−	18235.1i		−	0.635769i	−0.948129	−	0.317885i	$-0.897028\pi$
$937$		−	18235.1i		−	0.635769i	0.948129	−	0.317885i	$-0.102972\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	6686.17	+	11580.8i	0.231629	+	0.401193i	0.958288	−	0.285806i	$-0.0922611\pi$
$941$	6686.17	+	11580.8i	0.231629	+	0.401193i	−0.726659	+	0.686999i	$0.758928\pi$
$942$		0			0
$943$	15821.1	+	9134.30i	0.546347	+	0.315433i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	4431.54	+	2558.55i	0.152065	+	0.0877948i	0.574102	−	0.818784i	$-0.305351\pi$
$947$	4431.54	+	2558.55i	0.152065	+	0.0877948i	−0.422037	+	0.906579i	$0.638685\pi$
$948$		0			0
$949$	18520.4	+	32078.3i	0.633506	+	1.09727i
$950$		0			0
$951$		0			0
$952$		0			0
$953$			35456.7i			1.20520i	0.798044	+	0.602599i	$0.205868\pi$
$953$			35456.7i			1.20520i	−0.798044	+	0.602599i	$0.794132\pi$
$954$		0			0
$955$	−11802.4	+	6814.12i	−0.399913	+	0.230890i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	9470.45	−	265.162i	0.318891	−	0.00892861i
$960$		0			0
$961$	−11970.8	+	20734.0i	−0.401826	+	0.695983i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−3000.51			−0.100093
$966$		0			0
$967$	2804.92			0.0932784			0.0466392	−	0.998912i	$-0.485149\pi$
$967$	2804.92			0.0932784			0.0466392	+	0.998912i	$0.485149\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	13683.8	−	23701.0i	0.452248	−	0.783316i	−0.546278	−	0.837604i	$-0.683956\pi$
$971$	13683.8	−	23701.0i	0.452248	−	0.783316i	0.998525	+	0.0542881i	$0.0172889\pi$
$972$		0			0
$973$	5279.52	−	9765.81i	0.173950	−	0.321765i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−20868.5	+	12048.4i	−0.683359	+	0.394537i	−0.801119	−	0.598505i	$-0.795762\pi$
$977$	−20868.5	+	12048.4i	−0.683359	+	0.394537i	0.117761	+	0.993042i	$0.462428\pi$
$978$		0			0
$979$		−	16068.1i		−	0.524554i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−4655.36	−	8063.32i	−0.151051	−	0.261628i	0.780563	−	0.625077i	$-0.214932\pi$
$983$	−4655.36	−	8063.32i	−0.151051	−	0.261628i	−0.931614	+	0.363449i	$0.881599\pi$
$984$		0			0
$985$	42081.9	+	24296.0i	1.36126	+	0.785924i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−61463.8	−	35486.1i	−1.97617	−	1.14094i
$990$		0			0
$991$	−12095.2	−	20949.6i	−0.387707	−	0.671528i	0.604434	−	0.796655i	$-0.293399\pi$
$991$	−12095.2	−	20949.6i	−0.387707	−	0.671528i	−0.992141	+	0.125127i	$0.960066\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		−	42998.0i		−	1.36998i
$996$		0			0
$997$	42319.8	−	24433.4i	1.34431	−	0.776140i	0.356877	−	0.934151i	$-0.383841\pi$
$997$	42319.8	−	24433.4i	1.34431	−	0.776140i	0.987437	+	0.158011i	$0.0505081\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.4.bt.a.593.1		16
3.2	odd	2	inner	1008.4.bt.a.593.8		16
4.3	odd	2		63.4.p.a.26.3	yes	16
7.3	odd	6	inner	1008.4.bt.a.17.8		16
12.11	even	2		63.4.p.a.26.6	yes	16
21.17	even	6	inner	1008.4.bt.a.17.1		16
28.3	even	6		63.4.p.a.17.6	yes	16
28.11	odd	6		441.4.p.c.80.6		16
28.19	even	6		441.4.c.a.440.11		16
28.23	odd	6		441.4.c.a.440.12		16
28.27	even	2		441.4.p.c.215.3		16
84.11	even	6		441.4.p.c.80.3		16
84.23	even	6		441.4.c.a.440.5		16
84.47	odd	6		441.4.c.a.440.6		16
84.59	odd	6		63.4.p.a.17.3	✓	16
84.83	odd	2		441.4.p.c.215.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.p.a.17.3	✓	16	84.59	odd	6
63.4.p.a.17.6	yes	16	28.3	even	6
63.4.p.a.26.3	yes	16	4.3	odd	2
63.4.p.a.26.6	yes	16	12.11	even	2
441.4.c.a.440.5		16	84.23	even	6
441.4.c.a.440.6		16	84.47	odd	6
441.4.c.a.440.11		16	28.19	even	6
441.4.c.a.440.12		16	28.23	odd	6
441.4.p.c.80.3		16	84.11	even	6
441.4.p.c.80.6		16	28.11	odd	6
441.4.p.c.215.3		16	28.27	even	2
441.4.p.c.215.6		16	84.83	odd	2
1008.4.bt.a.17.1		16	21.17	even	6	inner
1008.4.bt.a.17.8		16	7.3	odd	6	inner
1008.4.bt.a.593.1		16	1.1	even	1	trivial
1008.4.bt.a.593.8		16	3.2	odd	2	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)

\(f(q)\)	\(=\)	\(q+(-7.54372 + 13.0661i) q^{5} +(-16.2919 - 8.80760i) q^{7} +O(q^{10})\)	\(q+(-7.54372 + 13.0661i) q^{5} +(-16.2919 - 8.80760i) q^{7} +(8.56529 - 4.94517i) q^{11} +67.8891i q^{13} +(35.0687 + 60.7407i) q^{17} +(53.2242 + 30.7290i) q^{19} +(113.895 + 65.7575i) q^{23} +(-51.3154 - 88.8809i) q^{25} -158.738i q^{29} +(66.2349 - 38.2407i) q^{31} +(237.983 - 146.430i) q^{35} +(-174.341 + 301.967i) q^{37} +138.909 q^{41} -539.651 q^{43} +(-111.821 + 193.680i) q^{47} +(187.852 + 286.985i) q^{49} +(-459.003 + 265.005i) q^{53} +149.220i q^{55} +(-271.438 - 470.145i) q^{59} +(-116.218 - 67.0983i) q^{61} +(-887.046 - 512.136i) q^{65} +(160.290 + 277.630i) q^{67} -416.958i q^{71} +(472.510 - 272.804i) q^{73} +(-183.100 + 5.12660i) q^{77} +(-161.369 + 279.499i) q^{79} -885.170 q^{83} -1058.19 q^{85} +(812.312 - 1406.97i) q^{89} +(597.940 - 1106.04i) q^{91} +(-803.017 + 463.622i) q^{95} -739.155i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 56 q^{7}+O(q^{10}) \) 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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