LMFDB - Embedded newform 2160.3.bs.c.1601.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2160,3,Mod(881,2160)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2160, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 5, 0])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2160.881"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 2160 = 2^{4} \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	2160.bs (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,0,0,0,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$58.8557371018$
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} + 48x^{14} + 912x^{12} + 8704x^{10} + 43602x^{8} + 109032x^{6} + 117844x^{4} + 36000x^{2} + 81 $ x^16 + 48x^14 + 912x^12 + 8704x^10 + 43602x^8 + 109032x^6 + 117844x^4 + 36000*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3^{6} $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1601.1
Root			$-3.73655i$ of defining polynomial
Character	$\chi$	$=$	2160.1601
Dual form			2160.3.bs.c.881.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.93649 + 1.11803i) q^{5} +(-3.63061 + 6.28840i) q^{7} +(6.50668 + 3.75663i) q^{11} +(-1.46668 - 2.54036i) q^{13} -1.90107i q^{17} +7.38378 q^{19} +(-30.6549 + 17.6986i) q^{23} +(2.50000 - 4.33013i) q^{25} +(14.2015 + 8.19922i) q^{29} +(13.3206 + 23.0720i) q^{31} -16.2366i q^{35} -44.6613 q^{37} +(-14.8634 + 8.58140i) q^{41} +(20.5554 - 35.6031i) q^{43} +(36.4950 + 21.0704i) q^{47} +(-1.86263 - 3.22616i) q^{49} +100.474i q^{53} -16.8002 q^{55} +(-4.12003 + 2.37870i) q^{59} +(38.4629 - 66.6197i) q^{61} +(5.68041 + 3.27959i) q^{65} +(-41.9225 - 72.6119i) q^{67} +23.1134i q^{71} -103.753 q^{73} +(-47.2464 + 27.2777i) q^{77} +(40.2610 - 69.7340i) q^{79} +(-17.1034 - 9.87463i) q^{83} +(2.12546 + 3.68141i) q^{85} +29.0566i q^{89} +21.2997 q^{91} +(-14.2986 + 8.25532i) q^{95} +(47.7972 - 82.7872i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{7} - 18 q^{11} - 10 q^{13} + 52 q^{19} - 54 q^{23} + 40 q^{25} + 54 q^{29} - 32 q^{31} + 44 q^{37} - 144 q^{41} + 124 q^{43} - 216 q^{47} - 54 q^{49} - 486 q^{59} + 62 q^{61} + 90 q^{65} - 14 q^{67}+ \cdots - 142 q^{97}+O(q^{100}) $ 16 * q - 2 * q^7 - 18 * q^11 - 10 * q^13 + 52 * q^19 - 54 * q^23 + 40 * q^25 + 54 * q^29 - 32 * q^31 + 44 * q^37 - 144 * q^41 + 124 * q^43 - 216 * q^47 - 54 * q^49 - 486 * q^59 + 62 * q^61 + 90 * q^65 - 14 * q^67 - 268 * q^73 - 702 * q^77 + 40 * q^79 + 522 * q^83 + 30 * q^85 - 136 * q^91 + 180 * q^95 - 142 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2160\mathbb{Z}\right)^\times$.

$n$	$271$	$1297$	$1621$	$2081$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{1}{6}\right)$

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
$5$	−1.93649	+	1.11803i	−0.387298	+	0.223607i
$5$	−1.93649	+	1.11803i	−0.387298	+	0.223607i
$6$		0			0
$7$	−3.63061	+	6.28840i	−0.518658	+	0.898342i	0.481107	+	0.876662i	$0.340235\pi$
$7$	−3.63061	+	6.28840i	−0.518658	+	0.898342i	−0.999765	+	0.0216804i	$0.993098\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	6.50668	+	3.75663i	0.591516	+	0.341512i	0.765697	−	0.643202i	$-0.222394\pi$
$11$	6.50668	+	3.75663i	0.591516	+	0.341512i	−0.174181	+	0.984714i	$0.555728\pi$
$12$		0			0
$13$	−1.46668	−	2.54036i	−0.112821	−	0.195412i	0.804085	−	0.594514i	$-0.202655\pi$
$13$	−1.46668	−	2.54036i	−0.112821	−	0.195412i	−0.916907	+	0.399102i	$0.869322\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$		−	1.90107i		−	0.111828i	−0.998436	−	0.0559139i	$-0.982193\pi$
$17$		−	1.90107i		−	0.111828i	0.998436	−	0.0559139i	$-0.0178072\pi$
$18$		0			0
$19$	7.38378			0.388620			0.194310	−	0.980940i	$-0.437753\pi$
$19$	7.38378			0.388620			0.194310	+	0.980940i	$0.437753\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−30.6549	+	17.6986i	−1.33282	+	0.769506i	−0.985731	−	0.168326i	$-0.946164\pi$
$23$	−30.6549	+	17.6986i	−1.33282	+	0.769506i	−0.347091	+	0.937831i	$0.612831\pi$
$24$		0			0
$25$	2.50000	−	4.33013i	0.100000	−	0.173205i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	14.2015	+	8.19922i	0.489705	+	0.282732i	0.724452	−	0.689325i	$-0.242093\pi$
$29$	14.2015	+	8.19922i	0.489705	+	0.282732i	−0.234747	+	0.972057i	$0.575426\pi$
$30$		0			0
$31$	13.3206	+	23.0720i	0.429697	+	0.744257i	0.996846	−	0.0793581i	$-0.0252871\pi$
$31$	13.3206	+	23.0720i	0.429697	+	0.744257i	−0.567149	+	0.823615i	$0.691954\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$		−	16.2366i		−	0.463902i
$36$		0			0
$37$	−44.6613			−1.20706			−0.603531	−	0.797340i	$-0.706240\pi$
$37$	−44.6613			−1.20706			−0.603531	+	0.797340i	$0.706240\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−14.8634	+	8.58140i	−0.362522	+	0.209302i	−0.670187	−	0.742193i	$-0.733786\pi$
$41$	−14.8634	+	8.58140i	−0.362522	+	0.209302i	0.307664	+	0.951495i	$0.400453\pi$
$42$		0			0
$43$	20.5554	−	35.6031i	0.478033	−	0.827978i	−0.521650	−	0.853160i	$-0.674683\pi$
$43$	20.5554	−	35.6031i	0.478033	−	0.827978i	0.999683	+	0.0251818i	$0.00801646\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	36.4950	+	21.0704i	0.776490	+	0.448307i	0.835185	−	0.549969i	$-0.185361\pi$
$47$	36.4950	+	21.0704i	0.776490	+	0.448307i	−0.0586949	+	0.998276i	$0.518694\pi$
$48$		0			0
$49$	−1.86263	−	3.22616i	−0.0380128	−	0.0658401i
$50$		0			0
$51$		0			0
$52$		0			0
$53$			100.474i			1.89573i	0.318671	+	0.947865i	$0.396764\pi$
$53$			100.474i			1.89573i	−0.318671	+	0.947865i	$0.603236\pi$
$54$		0			0
$55$	−16.8002			−0.305458
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−4.12003	+	2.37870i	−0.0698310	+	0.0403169i	−0.534509	−	0.845163i	$-0.679503\pi$
$59$	−4.12003	+	2.37870i	−0.0698310	+	0.0403169i	0.464678	+	0.885480i	$0.346170\pi$
$60$		0			0
$61$	38.4629	−	66.6197i	0.630539	−	1.09213i	−0.356902	−	0.934142i	$-0.616167\pi$
$61$	38.4629	−	66.6197i	0.630539	−	1.09213i	0.987442	−	0.157985i	$-0.0504996\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	5.68041	+	3.27959i	0.0873910	+	0.0504552i
$66$		0			0
$67$	−41.9225	−	72.6119i	−0.625709	−	1.08376i	−0.988403	−	0.151852i	$-0.951476\pi$
$67$	−41.9225	−	72.6119i	−0.625709	−	1.08376i	0.362694	−	0.931908i	$-0.381857\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			23.1134i			0.325540i	0.986664	+	0.162770i	$0.0520429\pi$
$71$			23.1134i			0.325540i	−0.986664	+	0.162770i	$0.947957\pi$
$72$		0			0
$73$	−103.753			−1.42127			−0.710637	−	0.703559i	$-0.751593\pi$
$73$	−103.753			−1.42127			−0.710637	+	0.703559i	$0.751593\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−47.2464	+	27.2777i	−0.613589	+	0.354256i
$78$		0			0
$79$	40.2610	−	69.7340i	0.509633	−	0.882709i	−0.490305	−	0.871551i	$-0.663115\pi$
$79$	40.2610	−	69.7340i	0.509633	−	0.882709i	0.999938	−	0.0111586i	$-0.00355198\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−17.1034	−	9.87463i	−0.206065	−	0.118971i	0.393417	−	0.919360i	$-0.371293\pi$
$83$	−17.1034	−	9.87463i	−0.206065	−	0.118971i	−0.599481	+	0.800389i	$0.704626\pi$
$84$		0			0
$85$	2.12546	+	3.68141i	0.0250055	+	0.0433107i
$86$		0			0
$87$		0			0
$88$		0			0
$89$			29.0566i			0.326478i	0.986587	+	0.163239i	$0.0521942\pi$
$89$			29.0566i			0.326478i	−0.986587	+	0.163239i	$0.947806\pi$
$90$		0			0
$91$	21.2997			0.234063
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−14.2986	+	8.25532i	−0.150512	+	0.0868981i
$96$		0			0
$97$	47.7972	−	82.7872i	0.492755	−	0.853476i	−0.507210	−	0.861822i	$-0.669323\pi$
$97$	47.7972	−	82.7872i	0.492755	−	0.853476i	0.999965	+	0.00834602i	$0.00265665\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−117.817	−	68.0219i	−1.16651	−	0.673484i	−0.213653	−	0.976910i	$-0.568536\pi$
$101$	−117.817	−	68.0219i	−1.16651	−	0.673484i	−0.952855	+	0.303426i	$0.901870\pi$
$102$		0			0
$103$	−85.9401	−	148.853i	−0.834370	−	1.44517i	−0.894542	−	0.446983i	$-0.852498\pi$
$103$	−85.9401	−	148.853i	−0.834370	−	1.44517i	0.0601721	−	0.998188i	$-0.480835\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	98.6056i		−	0.921548i	−0.887518	−	0.460774i	$-0.847572\pi$
$107$		−	98.6056i		−	0.921548i	0.887518	−	0.460774i	$-0.152428\pi$
$108$		0			0
$109$	2.62651			0.0240965			0.0120482	−	0.999927i	$-0.496165\pi$
$109$	2.62651			0.0240965			0.0120482	+	0.999927i	$0.496165\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−2.36782	+	1.36706i	−0.0209542	+	0.0120979i	−0.510440	−	0.859913i	$-0.670518\pi$
$113$	−2.36782	+	1.36706i	−0.0209542	+	0.0120979i	0.489486	+	0.872011i	$0.337184\pi$
$114$		0			0
$115$	39.5753	−	68.5465i	0.344133	−	0.596056i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	11.9547	+	6.90205i	0.100460	+	0.0580004i
$120$		0			0
$121$	−32.2754	−	55.9027i	−0.266739	−	0.462006i
$122$		0			0
$123$		0			0
$124$		0			0
$125$			11.1803i			0.0894427i
$126$		0			0
$127$	−193.060			−1.52015			−0.760077	−	0.649833i	$-0.774839\pi$
$127$	−193.060			−1.52015			−0.760077	+	0.649833i	$0.774839\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−201.259	+	116.197i	−1.53633	+	0.886999i	−0.537278	+	0.843405i	$0.680547\pi$
$131$	−201.259	+	116.197i	−1.53633	+	0.886999i	−0.999049	+	0.0435937i	$0.986119\pi$
$132$		0			0
$133$	−26.8076	+	46.4322i	−0.201561	+	0.349114i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−154.172	−	89.0111i	−1.12534	−	0.649716i	−0.182582	−	0.983191i	$-0.558445\pi$
$137$	−154.172	−	89.0111i	−1.12534	−	0.649716i	−0.942759	+	0.333475i	$0.891779\pi$
$138$		0			0
$139$	16.0343	+	27.7722i	0.115355	+	0.199800i	0.917922	−	0.396762i	$-0.129866\pi$
$139$	16.0343	+	27.7722i	0.115355	+	0.199800i	−0.802567	+	0.596562i	$0.796533\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		−	22.0390i		−	0.154119i
$144$		0			0
$145$	−36.6680			−0.252883
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−80.4653	+	46.4567i	−0.540036	+	0.311790i	−0.745093	−	0.666960i	$-0.767595\pi$
$149$	−80.4653	+	46.4567i	−0.540036	+	0.311790i	0.205058	+	0.978750i	$0.434262\pi$
$150$		0			0
$151$	−113.614	+	196.785i	−0.752408	+	1.30321i	0.194245	+	0.980953i	$0.437774\pi$
$151$	−113.614	+	196.785i	−0.752408	+	1.30321i	−0.946653	+	0.322256i	$0.895559\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−51.5905	−	29.7858i	−0.332842	−	0.192166i
$156$		0			0
$157$	0.792406	+	1.37249i	0.00504717	+	0.00874196i	0.868538	−	0.495623i	$-0.165060\pi$
$157$	0.792406	+	1.37249i	0.00504717	+	0.00874196i	−0.863491	+	0.504365i	$0.831727\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		−	257.027i		−	1.59644i
$162$		0			0
$163$	41.6801			0.255706			0.127853	−	0.991793i	$-0.459191\pi$
$163$	41.6801			0.255706			0.127853	+	0.991793i	$0.459191\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	8.01405	−	4.62692i	0.0479884	−	0.0277061i	−0.475814	−	0.879546i	$-0.657846\pi$
$167$	8.01405	−	4.62692i	0.0479884	−	0.0277061i	0.523802	+	0.851840i	$0.324513\pi$
$168$		0			0
$169$	80.1977	−	138.907i	0.474543	−	0.821932i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	127.637	+	73.6913i	0.737787	+	0.425962i	0.821264	−	0.570548i	$-0.193269\pi$
$173$	127.637	+	73.6913i	0.737787	+	0.425962i	−0.0834771	+	0.996510i	$0.526603\pi$
$174$		0			0
$175$	18.1530	+	31.4420i	0.103732	+	0.179668i
$176$		0			0
$177$		0			0
$178$		0			0
$179$			160.022i			0.893977i	0.894540	+	0.446988i	$0.147504\pi$
$179$			160.022i			0.893977i	−0.894540	+	0.446988i	$0.852496\pi$
$180$		0			0
$181$	−30.3346			−0.167595			−0.0837973	−	0.996483i	$-0.526705\pi$
$181$	−30.3346			−0.167595			−0.0837973	+	0.996483i	$0.526705\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	86.4862	−	49.9328i	0.467493	−	0.269907i
$186$		0			0
$187$	7.14163	−	12.3697i	0.0381905	−	0.0661480i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−249.938	−	144.302i	−1.30857	−	0.755506i	−0.326716	−	0.945122i	$-0.605942\pi$
$191$	−249.938	−	144.302i	−1.30857	−	0.755506i	−0.981858	+	0.189617i	$0.939275\pi$
$192$		0			0
$193$	47.3339	+	81.9847i	0.245253	+	0.424791i	0.962203	−	0.272334i	$-0.0877955\pi$
$193$	47.3339	+	81.9847i	0.245253	+	0.424791i	−0.716949	+	0.697125i	$0.754462\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	129.755i		−	0.658657i	−0.944215	−	0.329329i	$-0.893178\pi$
$197$		−	129.755i		−	0.658657i	0.944215	−	0.329329i	$-0.106822\pi$
$198$		0			0
$199$	−136.428			−0.685570			−0.342785	−	0.939414i	$-0.611370\pi$
$199$	−136.428			−0.685570			−0.342785	+	0.939414i	$0.611370\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−103.120	+	59.5363i	−0.507980	+	0.293282i
$204$		0			0
$205$	19.1886	−	33.2356i	0.0936029	−	0.162125i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	48.0439	+	27.7382i	0.229875	+	0.132718i
$210$		0			0
$211$	79.1144	+	137.030i	0.374950	+	0.649432i	0.990320	−	0.138806i	$-0.0443266\pi$
$211$	79.1144	+	137.030i	0.374950	+	0.649432i	−0.615370	+	0.788239i	$0.710993\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$			91.9267i			0.427566i
$216$		0			0
$217$	−193.448			−0.891463
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−4.82941	+	2.78826i	−0.0218525	+	0.0126166i
$222$		0			0
$223$	−103.124	+	178.616i	−0.462440	+	0.800969i	−0.999082	−	0.0428406i	$-0.986359\pi$
$223$	−103.124	+	178.616i	−0.462440	+	0.800969i	0.536642	+	0.843810i	$0.319693\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−127.562	−	73.6481i	−0.561948	−	0.324441i	0.191979	−	0.981399i	$-0.438510\pi$
$227$	−127.562	−	73.6481i	−0.561948	−	0.324441i	−0.753927	+	0.656958i	$0.771843\pi$
$228$		0			0
$229$	13.5751	+	23.5127i	0.0592798	+	0.102676i	0.894142	−	0.447783i	$-0.147786\pi$
$229$	13.5751	+	23.5127i	0.0592798	+	0.102676i	−0.834863	+	0.550458i	$0.814453\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$			39.6011i			0.169962i	0.996383	+	0.0849808i	$0.0270829\pi$
$233$			39.6011i			0.169962i	−0.996383	+	0.0849808i	$0.972917\pi$
$234$		0			0
$235$	−94.2298			−0.400978
$236$		0			0
$237$		0			0
$238$		0			0
$239$	54.9394	−	31.7193i	0.229872	−	0.132717i	−0.380641	−	0.924723i	$-0.624297\pi$
$239$	54.9394	−	31.7193i	0.229872	−	0.132717i	0.610513	+	0.792006i	$0.290963\pi$
$240$		0			0
$241$	69.1161	−	119.713i	0.286789	−	0.496733i	−0.686253	−	0.727363i	$-0.740746\pi$
$241$	69.1161	−	119.713i	0.286789	−	0.496733i	0.973041	+	0.230630i	$0.0740789\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	7.21392	+	4.16496i	0.0294446	+	0.0169998i
$246$		0			0
$247$	−10.8296	−	18.7575i	−0.0438446	−	0.0759411i
$248$		0			0
$249$		0			0
$250$		0			0
$251$			186.477i			0.742936i	0.928446	+	0.371468i	$0.121145\pi$
$251$			186.477i			0.742936i	−0.928446	+	0.371468i	$0.878855\pi$
$252$		0			0
$253$	−265.949			−1.05118
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−201.713	+	116.459i	−0.784877	+	0.453149i	−0.838156	−	0.545431i	$-0.816366\pi$
$257$	−201.713	+	116.459i	−0.784877	+	0.453149i	0.0532790	+	0.998580i	$0.483033\pi$
$258$		0			0
$259$	162.148	−	280.848i	0.626053	−	1.08435i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−9.34728	−	5.39665i	−0.0355410	−	0.0205196i	0.482124	−	0.876103i	$-0.339865\pi$
$263$	−9.34728	−	5.39665i	−0.0355410	−	0.0205196i	−0.517665	+	0.855583i	$0.673199\pi$
$264$		0			0
$265$	−112.333	−	194.567i	−0.423898	−	0.734213i
$266$		0			0
$267$		0			0
$268$		0			0
$269$		−	58.4601i		−	0.217324i	−0.994079	−	0.108662i	$-0.965343\pi$
$269$		−	58.4601i		−	0.217324i	0.994079	−	0.108662i	$-0.0346566\pi$
$270$		0			0
$271$	65.5995			0.242065			0.121032	−	0.992649i	$-0.461380\pi$
$271$	65.5995			0.242065			0.121032	+	0.992649i	$0.461380\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	32.5334	−	18.7832i	0.118303	−	0.0683024i
$276$		0			0
$277$	−134.128	+	232.317i	−0.484218	+	0.838690i	−0.999836	−	0.0181286i	$-0.994229\pi$
$277$	−134.128	+	232.317i	−0.484218	+	0.838690i	0.515618	+	0.856819i	$0.327562\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−159.428	−	92.0461i	−0.567361	−	0.327566i	0.188734	−	0.982028i	$-0.439562\pi$
$281$	−159.428	−	92.0461i	−0.567361	−	0.327566i	−0.756095	+	0.654462i	$0.772895\pi$
$282$		0			0
$283$	−231.303	−	400.628i	−0.817324	−	1.41565i	−0.907647	−	0.419734i	$-0.862123\pi$
$283$	−231.303	−	400.628i	−0.817324	−	1.41565i	0.0903234	−	0.995912i	$-0.471210\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		−	124.623i		−	0.434226i
$288$		0			0
$289$	285.386			0.987495
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−248.349	+	143.384i	−0.847608	+	0.489367i	−0.859843	−	0.510559i	$-0.829439\pi$
$293$	−248.349	+	143.384i	−0.847608	+	0.489367i	0.0122351	+	0.999925i	$0.496105\pi$
$294$		0			0
$295$	5.31893	−	9.21266i	0.0180303	−	0.0312294i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	89.9217	+	51.9163i	0.300741	+	0.173633i
$300$		0			0
$301$	149.257	+	258.521i	0.495872	+	0.858875i
$302$		0			0
$303$		0			0
$304$		0			0
$305$			172.011i			0.563972i
$306$		0			0
$307$	236.738			0.771133			0.385567	−	0.922680i	$-0.374006\pi$
$307$	236.738			0.771133			0.385567	+	0.922680i	$0.374006\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	448.597	−	258.997i	1.44243	−	0.832789i	0.444421	−	0.895818i	$-0.353409\pi$
$311$	448.597	−	258.997i	1.44243	−	0.832789i	0.998012	+	0.0630292i	$0.0200761\pi$
$312$		0			0
$313$	247.615	−	428.882i	0.791102	−	1.37023i	−0.134183	−	0.990957i	$-0.542841\pi$
$313$	247.615	−	428.882i	0.791102	−	1.37023i	0.925285	−	0.379272i	$-0.123826\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	189.840	+	109.604i	0.598864	+	0.345754i	0.768595	−	0.639736i	$-0.220956\pi$
$317$	189.840	+	109.604i	0.598864	+	0.345754i	−0.169731	+	0.985491i	$0.554290\pi$
$318$		0			0
$319$	61.6029	+	106.699i	0.193112	+	0.334481i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	14.0371i		−	0.0434586i
$324$		0			0
$325$	−14.6668			−0.0451285
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−264.998	+	152.997i	−0.805466	+	0.465036i
$330$		0			0
$331$	−47.4838	+	82.2443i	−0.143455	+	0.248472i	−0.928796	−	0.370592i	$-0.879155\pi$
$331$	−47.4838	+	82.2443i	−0.143455	+	0.248472i	0.785340	+	0.619064i	$0.212488\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	162.365	+	93.7416i	0.484672	+	0.279826i
$336$		0			0
$337$	257.989	+	446.850i	0.765547	+	1.32597i	0.939957	+	0.341293i	$0.110865\pi$
$337$	257.989	+	446.850i	0.765547	+	1.32597i	−0.174411	+	0.984673i	$0.555802\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$			200.162i			0.586986i
$342$		0			0
$343$	−328.750			−0.958454
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−96.4994	+	55.7140i	−0.278096	+	0.160559i	−0.632561	−	0.774510i	$-0.717996\pi$
$347$	−96.4994	+	55.7140i	−0.278096	+	0.160559i	0.354465	+	0.935069i	$0.384663\pi$
$348$		0			0
$349$	−310.131	+	537.162i	−0.888627	+	1.53915i	−0.0471279	+	0.998889i	$0.515007\pi$
$349$	−310.131	+	537.162i	−0.888627	+	1.53915i	−0.841499	+	0.540258i	$0.818327\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−488.067	−	281.786i	−1.38263	−	0.798260i	−0.390157	−	0.920748i	$-0.627579\pi$
$353$	−488.067	−	281.786i	−1.38263	−	0.798260i	−0.992470	+	0.122488i	$0.960913\pi$
$354$		0			0
$355$	−25.8415	−	44.7588i	−0.0727930	−	0.126081i
$356$		0			0
$357$		0			0
$358$		0			0
$359$		−	415.128i		−	1.15635i	−0.815915	−	0.578173i	$-0.803766\pi$
$359$		−	415.128i		−	1.15635i	0.815915	−	0.578173i	$-0.196234\pi$
$360$		0			0
$361$	−306.480			−0.848974
$362$		0			0
$363$		0			0
$364$		0			0
$365$	200.917	−	115.999i	0.550457	−	0.317807i
$366$		0			0
$367$	313.940	−	543.761i	0.855423	−	1.48164i	−0.0208286	−	0.999783i	$-0.506630\pi$
$367$	313.940	−	543.761i	0.855423	−	1.48164i	0.876252	−	0.481853i	$-0.160036\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−631.819	−	364.781i	−1.70302	−	0.983237i
$372$		0			0
$373$	−195.467	−	338.559i	−0.524040	−	0.907665i	−0.999608	−	0.0279857i	$-0.991091\pi$
$373$	−195.467	−	338.559i	−0.524040	−	0.907665i	0.475568	−	0.879679i	$-0.342243\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	48.1024i		−	0.127593i
$378$		0			0
$379$	−52.4430			−0.138372			−0.0691860	−	0.997604i	$-0.522040\pi$
$379$	−52.4430			−0.138372			−0.0691860	+	0.997604i	$0.522040\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−96.0614	+	55.4610i	−0.250813	+	0.144807i	−0.620136	−	0.784494i	$-0.712923\pi$
$383$	−96.0614	+	55.4610i	−0.250813	+	0.144807i	0.369324	+	0.929301i	$0.379589\pi$
$384$		0			0
$385$	60.9948	−	105.646i	0.158428	−	0.274405i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	91.6114	+	52.8918i	0.235505	+	0.135969i	0.613109	−	0.789998i	$-0.289919\pi$
$389$	91.6114	+	52.8918i	0.235505	+	0.135969i	−0.377604	+	0.925967i	$0.623252\pi$
$390$		0			0
$391$	33.6464	+	58.2773i	0.0860521	+	0.149047i
$392$		0			0
$393$		0			0
$394$		0			0
$395$			180.053i			0.455829i
$396$		0			0
$397$	99.8892			0.251610			0.125805	−	0.992055i	$-0.459849\pi$
$397$	99.8892			0.251610			0.125805	+	0.992055i	$0.459849\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	136.080	−	78.5658i	0.339352	−	0.195925i	−0.320634	−	0.947203i	$-0.603896\pi$
$401$	136.080	−	78.5658i	0.339352	−	0.195925i	0.659985	+	0.751279i	$0.270563\pi$
$402$		0			0
$403$	39.0740	−	67.6782i	0.0969579	−	0.167936i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−290.597	−	167.776i	−0.713996	−	0.412226i
$408$		0			0
$409$	−342.619	−	593.434i	−0.837700	−	1.45094i	−0.891813	−	0.452404i	$-0.850567\pi$
$409$	−342.619	−	593.434i	−0.837700	−	1.45094i	0.0541134	−	0.998535i	$-0.482767\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		−	34.5445i		−	0.0836428i
$414$		0			0
$415$	44.1607			0.106411
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−44.6836	+	25.7981i	−0.106643	+	0.0615706i	−0.552373	−	0.833597i	$-0.686278\pi$
$419$	−44.6836	+	25.7981i	−0.106643	+	0.0615706i	0.445730	+	0.895168i	$0.352944\pi$
$420$		0			0
$421$	−7.37620	+	12.7760i	−0.0175207	+	0.0303467i	−0.874653	−	0.484750i	$-0.838911\pi$
$421$	−7.37620	+	12.7760i	−0.0175207	+	0.0303467i	0.857132	+	0.515097i	$0.172244\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−8.23189	−	4.75268i	−0.0193691	−	0.0111828i
$426$		0			0
$427$	279.287	+	483.740i	0.654069	+	1.13288i
$428$		0			0
$429$		0			0
$430$		0			0
$431$		−	38.6810i		−	0.0897472i	−0.998993	−	0.0448736i	$-0.985711\pi$
$431$		−	38.6810i		−	0.0897472i	0.998993	−	0.0448736i	$-0.0142885\pi$
$432$		0			0
$433$	−544.647			−1.25784			−0.628922	−	0.777468i	$-0.716504\pi$
$433$	−544.647			−1.25784			−0.628922	+	0.777468i	$0.716504\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−226.349	+	130.683i	−0.517962	+	0.299045i
$438$		0			0
$439$	125.709	−	217.735i	0.286353	−	0.495978i	−0.686583	−	0.727051i	$-0.740890\pi$
$439$	125.709	−	217.735i	0.286353	−	0.495978i	0.972936	+	0.231073i	$0.0742236\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	632.952	+	365.435i	1.42878	+	0.824909i	0.997025	−	0.0770796i	$-0.0245596\pi$
$443$	632.952	+	365.435i	1.42878	+	0.824909i	0.431760	+	0.901989i	$0.357893\pi$
$444$		0			0
$445$	−32.4862	−	56.2678i	−0.0730028	−	0.126445i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			94.7211i			0.210960i	0.994421	+	0.105480i	$0.0336379\pi$
$449$			94.7211i			0.210960i	−0.994421	+	0.105480i	$0.966362\pi$
$450$		0			0
$451$	−128.949			−0.285917
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−41.2467	+	23.8138i	−0.0906521	+	0.0523380i
$456$		0			0
$457$	204.206	−	353.695i	0.446840	−	0.773949i	−0.551339	−	0.834282i	$-0.685883\pi$
$457$	204.206	−	353.695i	0.446840	−	0.773949i	0.998178	+	0.0603323i	$0.0192160\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	511.735	+	295.450i	1.11005	+	0.640890i	0.938843	−	0.344344i	$-0.111899\pi$
$461$	511.735	+	295.450i	1.11005	+	0.640890i	0.171211	+	0.985234i	$0.445232\pi$
$462$		0			0
$463$	400.967	+	694.496i	0.866020	+	1.49999i	0.866031	+	0.499991i	$0.166663\pi$
$463$	400.967	+	694.496i	0.866020	+	1.49999i	−1.04649e−5		1.00000i	$0.500003\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		−	20.6432i		−	0.0442039i	−0.999756	−	0.0221019i	$-0.992964\pi$
$467$		−	20.6432i		−	0.0442039i	0.999756	−	0.0221019i	$-0.00703584\pi$
$468$		0			0
$469$	608.817			1.29812
$470$		0			0
$471$		0			0
$472$		0			0
$473$	267.495	−	154.438i	0.565529	−	0.326508i
$474$		0			0
$475$	18.4595	−	31.9727i	0.0388620	−	0.0673110i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	435.378	+	251.366i	0.908931	+	0.524771i	0.880087	−	0.474812i	$-0.157484\pi$
$479$	435.378	+	251.366i	0.908931	+	0.524771i	0.0288439	+	0.999584i	$0.490817\pi$
$480$		0			0
$481$	65.5037	+	113.456i	0.136182	+	0.235875i
$482$		0			0
$483$		0			0
$484$		0			0
$485$			213.756i			0.440733i
$486$		0			0
$487$	−80.4336			−0.165161			−0.0825807	−	0.996584i	$-0.526316\pi$
$487$	−80.4336			−0.165161			−0.0825807	+	0.996584i	$0.526316\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−417.972	+	241.316i	−0.851267	+	0.491479i	−0.861078	−	0.508473i	$-0.830210\pi$
$491$	−417.972	+	241.316i	−0.851267	+	0.491479i	0.00981129	+	0.999952i	$0.496877\pi$
$492$		0			0
$493$	15.5873	−	26.9980i	0.0316173	−	0.0547627i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−145.346	−	83.9155i	−0.292447	−	0.168844i
$498$		0			0
$499$	−17.5059	−	30.3212i	−0.0350820	−	0.0607638i	0.847951	−	0.530074i	$-0.177836\pi$
$499$	−17.5059	−	30.3212i	−0.0350820	−	0.0607638i	−0.883033	+	0.469310i	$0.844503\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$			211.016i			0.419514i	0.977754	+	0.209757i	$0.0672673\pi$
$503$			211.016i			0.419514i	−0.977754	+	0.209757i	$0.932733\pi$
$504$		0			0
$505$	304.203			0.602382
$506$		0			0
$507$		0			0
$508$		0			0
$509$	732.292	−	422.789i	1.43869	−	0.830627i	0.440930	−	0.897542i	$-0.354649\pi$
$509$	732.292	−	422.789i	1.43869	−	0.830627i	0.997759	+	0.0669144i	$0.0213154\pi$
$510$		0			0
$511$	376.687	−	652.440i	0.737156	−	1.27679i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	332.845	+	192.168i	0.646300	+	0.373142i
$516$		0			0
$517$	158.308	+	274.197i	0.306204	+	0.530361i
$518$		0			0
$519$		0			0
$520$		0			0
$521$		−	260.960i		−	0.500883i	−0.968132	−	0.250442i	$-0.919424\pi$
$521$		−	260.960i		−	0.500883i	0.968132	−	0.250442i	$-0.0805758\pi$
$522$		0			0
$523$	−553.330			−1.05799			−0.528996	−	0.848624i	$-0.677431\pi$
$523$	−553.330			−1.05799			−0.528996	+	0.848624i	$0.677431\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	43.8615	−	25.3234i	0.0832286	−	0.0480521i
$528$		0			0
$529$	361.983	−	626.973i	0.684278	−	1.18520i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	43.5996	+	25.1723i	0.0818005	+	0.0472275i
$534$		0			0
$535$	110.244	+	190.949i	0.206064	+	0.356914i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		−	27.9888i		−	0.0519273i
$540$		0			0
$541$	−795.168			−1.46981			−0.734906	−	0.678169i	$-0.762774\pi$
$541$	−795.168			−1.46981			−0.734906	+	0.678169i	$0.762774\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−5.08622	+	2.93653i	−0.00933252	+	0.00538813i
$546$		0			0
$547$	−303.604	+	525.858i	−0.555035	+	0.961348i	0.442866	+	0.896588i	$0.353962\pi$
$547$	−303.604	+	525.858i	−0.555035	+	0.961348i	−0.997901	+	0.0647606i	$0.979372\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	104.861	+	60.5412i	0.190309	+	0.109875i
$552$		0			0
$553$	292.344	+	506.354i	0.528650	+	0.915649i
$554$		0			0
$555$		0			0
$556$		0			0
$557$			686.808i			1.23305i	0.787336	+	0.616524i	$0.211460\pi$
$557$			686.808i			1.23305i	−0.787336	+	0.616524i	$0.788540\pi$
$558$		0			0
$559$	−120.593			−0.215729
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−208.976	+	120.652i	−0.371182	+	0.214302i	−0.673975	−	0.738754i	$-0.735414\pi$
$563$	−208.976	+	120.652i	−0.371182	+	0.214302i	0.302792	+	0.953057i	$0.402081\pi$
$564$		0			0
$565$	3.05685	−	5.29461i	0.00541035	−	0.00937099i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	666.084	+	384.564i	1.17062	+	0.675859i	0.953827	−	0.300358i	$-0.0971061\pi$
$569$	666.084	+	384.564i	1.17062	+	0.675859i	0.216796	+	0.976217i	$0.430439\pi$
$570$		0			0
$571$	48.7253	+	84.3947i	0.0853333	+	0.147802i	0.905533	−	0.424275i	$-0.139471\pi$
$571$	48.7253	+	84.3947i	0.0853333	+	0.147802i	−0.820200	+	0.572077i	$0.806138\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			176.986i			0.307802i
$576$		0			0
$577$	277.283			0.480560			0.240280	−	0.970704i	$-0.422761\pi$
$577$	277.283			0.480560			0.240280	+	0.970704i	$0.422761\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	124.191	−	71.7018i	0.213754	−	0.123411i
$582$		0			0
$583$	−377.443	+	653.750i	−0.647415	+	1.12136i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	405.017	+	233.836i	0.689977	+	0.398358i	0.803603	−	0.595165i	$-0.202913\pi$
$587$	405.017	+	233.836i	0.689977	+	0.398358i	−0.113626	+	0.993524i	$0.536247\pi$
$588$		0			0
$589$	98.3565	+	170.358i	0.166989	+	0.289233i
$590$		0			0
$591$		0			0
$592$		0			0
$593$		−	254.411i		−	0.429023i	−0.976721	−	0.214512i	$-0.931184\pi$
$593$		−	254.411i		−	0.429023i	0.976721	−	0.214512i	$-0.0688160\pi$
$594$		0			0
$595$	−30.8669			−0.0518772
$596$		0			0
$597$		0			0
$598$		0			0
$599$	352.081	−	203.274i	0.587780	−	0.339355i	−0.176439	−	0.984312i	$-0.556458\pi$
$599$	352.081	−	203.274i	0.587780	−	0.339355i	0.764219	+	0.644956i	$0.223124\pi$
$600$		0			0
$601$	−249.967	+	432.956i	−0.415919	+	0.720393i	−0.995524	−	0.0945042i	$-0.969873\pi$
$601$	−249.967	+	432.956i	−0.415919	+	0.720393i	0.579605	+	0.814897i	$0.303207\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	125.002	+	72.1701i	0.206615	+	0.119289i
$606$		0			0
$607$	29.9627	+	51.8970i	0.0493620	+	0.0854975i	0.889651	−	0.456642i	$-0.150948\pi$
$607$	29.9627	+	51.8970i	0.0493620	+	0.0854975i	−0.840289	+	0.542139i	$0.817615\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		−	123.614i		−	0.202314i
$612$		0			0
$613$	−373.866			−0.609896			−0.304948	−	0.952369i	$-0.598639\pi$
$613$	−373.866			−0.609896			−0.304948	+	0.952369i	$0.598639\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	320.088	−	184.803i	0.518782	−	0.299519i	−0.217654	−	0.976026i	$-0.569841\pi$
$617$	320.088	−	184.803i	0.518782	−	0.299519i	0.736436	+	0.676507i	$0.236507\pi$
$618$		0			0
$619$	598.225	−	1036.16i	0.966438	−	1.67392i	0.260738	−	0.965410i	$-0.416034\pi$
$619$	598.225	−	1036.16i	0.966438	−	1.67392i	0.705701	−	0.708510i	$-0.250632\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−182.719	−	105.493i	−0.293289	−	0.169331i
$624$		0			0
$625$	−12.5000	−	21.6506i	−0.0200000	−	0.0346410i
$626$		0			0
$627$		0			0
$628$		0			0
$629$			84.9044i			0.134983i
$630$		0			0
$631$	−628.525			−0.996078			−0.498039	−	0.867155i	$-0.665946\pi$
$631$	−628.525			−0.996078			−0.498039	+	0.867155i	$0.665946\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	373.858	−	215.847i	0.588753	−	0.339917i
$636$		0			0
$637$	−5.46374	+	9.46347i	−0.00857730	+	0.0148563i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−824.417	−	475.977i	−1.28614	−	0.742554i	−0.308178	−	0.951329i	$-0.599719\pi$
$641$	−824.417	−	475.977i	−1.28614	−	0.742554i	−0.977964	+	0.208774i	$0.933053\pi$
$642$		0			0
$643$	−35.7759	−	61.9656i	−0.0556390	−	0.0963696i	0.836864	−	0.547410i	$-0.184386\pi$
$643$	−35.7759	−	61.9656i	−0.0556390	−	0.0963696i	−0.892503	+	0.451041i	$0.851053\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			900.292i			1.39149i	0.718290	+	0.695744i	$0.244925\pi$
$647$			900.292i			1.39149i	−0.718290	+	0.695744i	$0.755075\pi$
$648$		0			0
$649$	−35.7436			−0.0550748
$650$		0			0
$651$		0			0
$652$		0			0
$653$	222.825	−	128.648i	0.341233	−	0.197011i	−0.319584	−	0.947558i	$-0.603543\pi$
$653$	222.825	−	128.648i	0.341233	−	0.197011i	0.660817	+	0.750547i	$0.270210\pi$
$654$		0			0
$655$	259.824	−	450.029i	0.396678	−	0.687066i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	477.967	+	275.954i	0.725291	+	0.418747i	0.816697	−	0.577067i	$-0.195803\pi$
$659$	477.967	+	275.954i	0.725291	+	0.418747i	−0.0914057	+	0.995814i	$0.529136\pi$
$660$		0			0
$661$	523.413	+	906.578i	0.791851	+	1.37153i	0.924820	+	0.380405i	$0.124216\pi$
$661$	523.413	+	906.578i	0.791851	+	1.37153i	−0.132969	+	0.991120i	$0.542451\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		−	119.887i		−	0.180282i
$666$		0			0
$667$	−580.460			−0.870254
$668$		0			0
$669$		0			0
$670$		0			0
$671$	500.531	−	288.982i	0.745948	−	0.430673i
$672$		0			0
$673$	−118.875	+	205.898i	−0.176635	+	0.305940i	−0.940726	−	0.339168i	$-0.889854\pi$
$673$	−118.875	+	205.898i	−0.176635	+	0.305940i	0.764091	+	0.645108i	$0.223188\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	145.591	+	84.0570i	0.215053	+	0.124161i	0.603658	−	0.797244i	$-0.293709\pi$
$677$	145.591	+	84.0570i	0.215053	+	0.124161i	−0.388605	+	0.921405i	$0.627043\pi$
$678$		0			0
$679$	347.066	+	601.136i	0.511143	+	0.885325i
$680$		0			0
$681$		0			0
$682$		0			0
$683$		−	995.446i		−	1.45746i	−0.684800	−	0.728731i	$-0.740111\pi$
$683$		−	995.446i		−	1.45746i	0.684800	−	0.728731i	$-0.259889\pi$
$684$		0			0
$685$	398.070			0.581123
$686$		0			0
$687$		0			0
$688$		0			0
$689$	255.239	−	147.362i	0.370449	−	0.213879i
$690$		0			0
$691$	−298.570	+	517.138i	−0.432084	+	0.748391i	−0.997053	−	0.0767211i	$-0.975555\pi$
$691$	−298.570	+	517.138i	−0.432084	+	0.748391i	0.564969	+	0.825112i	$0.308888\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−62.1006	−	35.8538i	−0.0893534	−	0.0515882i
$696$		0			0
$697$	16.3139	+	28.2564i	0.0234058	+	0.0405401i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			413.729i			0.590199i	0.955467	+	0.295099i	$0.0953528\pi$
$701$			413.729i			0.590199i	−0.955467	+	0.295099i	$0.904647\pi$
$702$		0			0
$703$	−329.769			−0.469089
$704$		0			0
$705$		0			0
$706$		0			0
$707$	855.497	−	493.921i	1.21004	−	0.698616i
$708$		0			0
$709$	328.568	−	569.096i	0.463424	−	0.802674i	−0.535705	−	0.844405i	$-0.679954\pi$
$709$	328.568	−	569.096i	0.463424	−	0.802674i	0.999129	+	0.0417311i	$0.0132873\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−816.684	−	471.513i	−1.14542	−	0.661308i
$714$		0			0
$715$	24.6404	+	42.6784i	0.0344621	+	0.0596901i
$716$		0			0
$717$		0			0
$718$		0			0
$719$			217.226i			0.302122i	0.988524	+	0.151061i	$0.0482690\pi$
$719$			217.226i			0.302122i	−0.988524	+	0.151061i	$0.951731\pi$
$720$		0			0
$721$	1248.06			1.73101
$722$		0			0
$723$		0			0
$724$		0			0
$725$	71.0073	−	40.9961i	0.0979411	−	0.0565463i
$726$		0			0
$727$	304.437	−	527.300i	0.418757	−	0.725309i	−0.577057	−	0.816704i	$-0.695799\pi$
$727$	304.437	−	527.300i	0.418757	−	0.725309i	0.995815	+	0.0913946i	$0.0291325\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−67.6840	−	39.0774i	−0.0925910	−	0.0534574i
$732$		0			0
$733$	440.351	+	762.709i	0.600751	+	1.04053i	0.992708	+	0.120548i	$0.0384650\pi$
$733$	440.351	+	762.709i	0.600751	+	1.04053i	−0.391957	+	0.919984i	$0.628202\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	629.950i		−	0.854749i
$738$		0			0
$739$	917.157			1.24108			0.620540	−	0.784175i	$-0.286914\pi$
$739$	917.157			1.24108			0.620540	+	0.784175i	$0.286914\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−956.492	+	552.231i	−1.28734	+	0.743245i	−0.978179	−	0.207765i	$-0.933381\pi$
$743$	−956.492	+	552.231i	−1.28734	+	0.743245i	−0.309159	+	0.951010i	$0.600048\pi$
$744$		0			0
$745$	103.880	−	179.926i	0.139437	−	0.241511i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	620.071	+	357.998i	0.827866	+	0.477968i
$750$		0			0
$751$	330.239	+	571.990i	0.439732	+	0.761638i	0.997669	−	0.0682453i	$-0.0217401\pi$
$751$	330.239	+	571.990i	0.439732	+	0.761638i	−0.557936	+	0.829884i	$0.688407\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		−	508.096i		−	0.672974i
$756$		0			0
$757$	−353.728			−0.467276			−0.233638	−	0.972324i	$-0.575063\pi$
$757$	−353.728			−0.467276			−0.233638	+	0.972324i	$0.575063\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−708.380	+	408.983i	−0.930854	+	0.537429i	−0.887081	−	0.461613i	$-0.847271\pi$
$761$	−708.380	+	408.983i	−0.930854	+	0.537429i	−0.0437722	+	0.999042i	$0.513938\pi$
$762$		0			0
$763$	−9.53584	+	16.5166i	−0.0124978	+	0.0216469i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	12.0855	+	6.97756i	0.0157568	+	0.00909721i
$768$		0			0
$769$	500.408	+	866.732i	0.650725	+	1.12709i	0.982947	+	0.183888i	$0.0588684\pi$
$769$	500.408	+	866.732i	0.650725	+	1.12709i	−0.332222	+	0.943201i	$0.607798\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$			860.440i			1.11312i	0.830808	+	0.556559i	$0.187879\pi$
$773$			860.440i			1.11312i	−0.830808	+	0.556559i	$0.812121\pi$
$774$		0			0
$775$	133.206			0.171879
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−109.748	+	63.3632i	−0.140884	+	0.0813391i
$780$		0			0
$781$	−86.8283	+	150.391i	−0.111176	+	0.192562i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−3.06898	−	1.77187i	−0.00390952	−	0.00225716i
$786$		0			0
$787$	463.491	+	802.789i	0.588933	+	1.02006i	0.994372	+	0.105940i	$0.0337853\pi$
$787$	463.491	+	802.789i	0.588933	+	1.02006i	−0.405439	+	0.914122i	$0.632881\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		−	19.8531i		−	0.0250987i
$792$		0			0
$793$	−225.651			−0.284553
$794$		0			0
$795$		0			0
$796$		0			0
$797$	825.230	−	476.447i	1.03542	−	0.597800i	0.116888	−	0.993145i	$-0.462708\pi$
$797$	825.230	−	476.447i	1.03542	−	0.597800i	0.918533	+	0.395345i	$0.129375\pi$
$798$		0			0
$799$	40.0564	−	69.3797i	0.0501332	−	0.0868332i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−675.087	−	389.762i	−0.840707	−	0.485382i
$804$		0			0
$805$	287.365	+	497.731i	0.356975	+	0.618299i
$806$		0			0
$807$		0			0
$808$		0			0
$809$		−	1425.22i		−	1.76171i	−0.473387	−	0.880855i	$-0.656969\pi$
$809$		−	1425.22i		−	1.76171i	0.473387	−	0.880855i	$-0.343031\pi$
$810$		0			0
$811$	473.774			0.584185			0.292093	−	0.956390i	$-0.405648\pi$
$811$	473.774			0.584185			0.292093	+	0.956390i	$0.405648\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−80.7131	+	46.5997i	−0.0990345	+	0.0571776i
$816$		0			0
$817$	151.777	−	262.885i	0.185773	−	0.321769i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	63.4905	+	36.6562i	0.0773331	+	0.0446483i	0.538168	−	0.842838i	$-0.319117\pi$
$821$	63.4905	+	36.6562i	0.0773331	+	0.0446483i	−0.460835	+	0.887486i	$0.652450\pi$
$822$		0			0
$823$	316.027	+	547.374i	0.383994	+	0.665096i	0.991629	−	0.129120i	$-0.0412151\pi$
$823$	316.027	+	547.374i	0.383994	+	0.665096i	−0.607635	+	0.794216i	$0.707882\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	226.153i		−	0.273462i	−0.990608	−	0.136731i	$-0.956340\pi$
$827$		−	226.153i		−	0.273462i	0.990608	−	0.136731i	$-0.0436597\pi$
$828$		0			0
$829$	−522.396			−0.630152			−0.315076	−	0.949067i	$-0.602030\pi$
$829$	−522.396			−0.630152			−0.315076	+	0.949067i	$0.602030\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−6.13317	+	3.54099i	−0.00736275	+	0.00425089i
$834$		0			0
$835$	−10.3461	+	17.9200i	−0.0123905	+	0.0214610i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	511.329	+	295.216i	0.609450	+	0.351866i	0.772750	−	0.634710i	$-0.218881\pi$
$839$	511.329	+	295.216i	0.609450	+	0.351866i	−0.163300	+	0.986576i	$0.552214\pi$
$840$		0			0
$841$	−286.046	−	495.446i	−0.340126	−	0.589115i
$842$		0			0
$843$		0			0
$844$		0			0
$845$			358.655i			0.424444i
$846$		0			0
$847$	468.718			0.553386
$848$		0			0
$849$		0			0
$850$		0			0
$851$	1369.09	−	790.444i	1.60880	−	0.928841i
$852$		0			0
$853$	−693.749	+	1201.61i	−0.813305	+	1.40869i	0.0972332	+	0.995262i	$0.469001\pi$
$853$	−693.749	+	1201.61i	−0.813305	+	1.40869i	−0.910538	+	0.413424i	$0.864333\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	683.058	+	394.363i	0.797033	+	0.460167i	0.842433	−	0.538801i	$-0.181123\pi$
$857$	683.058	+	394.363i	0.797033	+	0.460167i	−0.0453994	+	0.998969i	$0.514456\pi$
$858$		0			0
$859$	413.601	+	716.378i	0.481491	+	0.833968i	0.999774	−	0.0212416i	$-0.00676191\pi$
$859$	413.601	+	716.378i	0.481491	+	0.833968i	−0.518283	+	0.855209i	$0.673429\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		−	1089.70i		−	1.26268i	−0.775504	−	0.631342i	$-0.782504\pi$
$863$		−	1089.70i		−	1.26268i	0.775504	−	0.631342i	$-0.217496\pi$
$864$		0			0
$865$	−329.558			−0.380992
$866$		0			0
$867$		0			0
$868$		0			0
$869$	523.930	−	302.491i	0.602912	−	0.348091i
$870$		0			0
$871$	−122.974	+	212.996i	−0.141187	+	0.244542i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−70.3064	−	40.5914i	−0.0803502	−	0.0463902i
$876$		0			0
$877$	−213.875	−	370.443i	−0.243872	−	0.422398i	0.717942	−	0.696103i	$-0.245084\pi$
$877$	−213.875	−	370.443i	−0.243872	−	0.422398i	−0.961814	+	0.273705i	$0.911751\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		−	1113.87i		−	1.26432i	−0.774837	−	0.632161i	$-0.782168\pi$
$881$		−	1113.87i		−	1.26432i	0.774837	−	0.632161i	$-0.217832\pi$
$882$		0			0
$883$	408.581			0.462719			0.231359	−	0.972868i	$-0.425683\pi$
$883$	408.581			0.462719			0.231359	+	0.972868i	$0.425683\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−755.098	+	435.956i	−0.851294	+	0.491495i	−0.861087	−	0.508457i	$-0.830216\pi$
$887$	−755.098	+	435.956i	−0.851294	+	0.491495i	0.00979311	+	0.999952i	$0.496883\pi$
$888$		0			0
$889$	700.924	−	1214.04i	0.788441	−	1.36562i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	269.471	+	155.579i	0.301760	+	0.174221i
$894$		0			0
$895$	−178.910	−	309.881i	−0.199899	−	0.346236i
$896$		0			0
$897$		0			0
$898$		0			0
$899$			436.874i			0.485956i
$900$		0			0
$901$	191.008			0.211995
$902$		0			0
$903$		0			0
$904$		0			0
$905$	58.7427	−	33.9151i	0.0649091	−	0.0374753i
$906$		0			0
$907$	−843.097	+	1460.29i	−0.929544	+	1.61002i	−0.145459	+	0.989364i	$0.546466\pi$
$907$	−843.097	+	1460.29i	−0.929544	+	1.61002i	−0.784085	+	0.620653i	$0.786867\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−383.084	−	221.173i	−0.420509	−	0.242781i	0.274786	−	0.961505i	$-0.411393\pi$
$911$	−383.084	−	221.173i	−0.420509	−	0.242781i	−0.695295	+	0.718724i	$0.744726\pi$
$912$		0			0
$913$	−74.1907	−	128.502i	−0.0812603	−	0.140747i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		−	1687.46i		−	1.84020i
$918$		0			0
$919$	182.236			0.198298			0.0991489	−	0.995073i	$-0.468388\pi$
$919$	182.236			0.198298			0.0991489	+	0.995073i	$0.468388\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	58.7162	−	33.8998i	0.0636145	−	0.0367279i
$924$		0			0
$925$	−111.653	+	193.389i	−0.120706	+	0.209069i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	1150.27	+	664.111i	1.23819	+	0.714867i	0.968723	−	0.248144i	$-0.0798205\pi$
$929$	1150.27	+	664.111i	1.23819	+	0.714867i	0.269463	+	0.963011i	$0.413154\pi$
$930$		0			0
$931$	−13.7532	−	23.8213i	−0.0147725	−	0.0255868i
$932$		0			0
$933$		0			0
$934$		0			0
$935$			31.9383i			0.0341587i
$936$		0			0
$937$	−276.582			−0.295178			−0.147589	−	0.989049i	$-0.547151\pi$
$937$	−276.582			−0.295178			−0.147589	+	0.989049i	$0.547151\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−1083.50	+	625.557i	−1.15143	+	0.664779i	−0.949236	−	0.314566i	$-0.898141\pi$
$941$	−1083.50	+	625.557i	−1.15143	+	0.664779i	−0.202196	+	0.979345i	$0.564808\pi$
$942$		0			0
$943$	303.758	−	526.124i	0.322119	−	0.557926i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−935.323	−	540.009i	−0.987670	−	0.570232i	−0.0830930	−	0.996542i	$-0.526480\pi$
$947$	−935.323	−	540.009i	−0.987670	−	0.570232i	−0.904577	+	0.426310i	$0.859813\pi$
$948$		0			0
$949$	152.172	+	263.570i	0.160350	+	0.277734i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	328.534i		−	0.344737i	−0.985033	−	0.172369i	$-0.944858\pi$
$953$		−	328.534i		−	0.344737i	0.985033	−	0.172369i	$-0.0551420\pi$
$954$		0			0
$955$	645.336			0.675745
$956$		0			0
$957$		0			0
$958$		0			0
$959$	1119.47	−	646.328i	1.16733	−	0.673961i
$960$		0			0
$961$	125.623	−	217.585i	0.130721	−	0.226416i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−183.323	−	105.842i	−0.189972	−	0.109681i
$966$		0			0
$967$	−298.854	−	517.631i	−0.309053	−	0.535296i	0.669102	−	0.743170i	$-0.266679\pi$
$967$	−298.854	−	517.631i	−0.309053	−	0.535296i	−0.978155	+	0.207875i	$0.933345\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$			711.597i			0.732850i	0.930448	+	0.366425i	$0.119418\pi$
$971$			711.597i			0.732850i	−0.930448	+	0.366425i	$0.880582\pi$
$972$		0			0
$973$	−232.857			−0.239319
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−292.262	+	168.738i	−0.299142	+	0.172710i	−0.642058	−	0.766656i	$-0.721919\pi$
$977$	−292.262	+	168.738i	−0.299142	+	0.172710i	0.342915	+	0.939366i	$0.388586\pi$
$978$		0			0
$979$	−109.155	+	189.062i	−0.111496	+	0.193117i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−274.504	−	158.485i	−0.279252	−	0.161226i	0.353833	−	0.935309i	$-0.384878\pi$
$983$	−274.504	−	158.485i	−0.279252	−	0.161226i	−0.633085	+	0.774083i	$0.718211\pi$
$984$		0			0
$985$	145.071	+	251.270i	0.147280	+	0.255097i
$986$		0			0
$987$		0			0
$988$		0			0
$989$			1455.21i			1.47140i
$990$		0			0
$991$	−685.922			−0.692152			−0.346076	−	0.938207i	$-0.612486\pi$
$991$	−685.922			−0.692152			−0.346076	+	0.938207i	$0.612486\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	264.192	−	152.532i	0.265520	−	0.153298i
$996$		0			0
$997$	−293.035	+	507.551i	−0.293917	+	0.509078i	−0.974732	−	0.223376i	$-0.928292\pi$
$997$	−293.035	+	507.551i	−0.293917	+	0.509078i	0.680816	+	0.732455i	$0.261625\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2160.3.bs.c.1601.1		16
3.2	odd	2		720.3.bs.c.641.2		16
4.3	odd	2		135.3.i.a.116.8		16
9.4	even	3		720.3.bs.c.401.2		16
9.5	odd	6	inner	2160.3.bs.c.881.1		16
12.11	even	2		45.3.i.a.11.1	✓	16
20.3	even	4		675.3.i.c.224.16		32
20.7	even	4		675.3.i.c.224.1		32
20.19	odd	2		675.3.j.b.251.1		16
36.7	odd	6		405.3.c.a.161.1		16
36.11	even	6		405.3.c.a.161.16		16
36.23	even	6		135.3.i.a.71.8		16
36.31	odd	6		45.3.i.a.41.1	yes	16
60.23	odd	4		225.3.i.b.74.1		32
60.47	odd	4		225.3.i.b.74.16		32
60.59	even	2		225.3.j.b.101.8		16
180.23	odd	12		675.3.i.c.449.1		32
180.59	even	6		675.3.j.b.476.1		16
180.67	even	12		225.3.i.b.149.1		32
180.103	even	12		225.3.i.b.149.16		32
180.139	odd	6		225.3.j.b.176.8		16
180.167	odd	12		675.3.i.c.449.16		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.3.i.a.11.1	✓	16	12.11	even	2
45.3.i.a.41.1	yes	16	36.31	odd	6
135.3.i.a.71.8		16	36.23	even	6
135.3.i.a.116.8		16	4.3	odd	2
225.3.i.b.74.1		32	60.23	odd	4
225.3.i.b.74.16		32	60.47	odd	4
225.3.i.b.149.1		32	180.67	even	12
225.3.i.b.149.16		32	180.103	even	12
225.3.j.b.101.8		16	60.59	even	2
225.3.j.b.176.8		16	180.139	odd	6
405.3.c.a.161.1		16	36.7	odd	6
405.3.c.a.161.16		16	36.11	even	6
675.3.i.c.224.1		32	20.7	even	4
675.3.i.c.224.16		32	20.3	even	4
675.3.i.c.449.1		32	180.23	odd	12
675.3.i.c.449.16		32	180.167	odd	12
675.3.j.b.251.1		16	20.19	odd	2
675.3.j.b.476.1		16	180.59	even	6
720.3.bs.c.401.2		16	9.4	even	3
720.3.bs.c.641.2		16	3.2	odd	2
2160.3.bs.c.881.1		16	9.5	odd	6	inner
2160.3.bs.c.1601.1		16	1.1	even	1	trivial

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Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2160 = 2^{4} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	2160.bs (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.93649 + 1.11803i) q^{5} +(-3.63061 + 6.28840i) q^{7} +(6.50668 + 3.75663i) q^{11} +(-1.46668 - 2.54036i) q^{13} -1.90107i q^{17} +7.38378 q^{19} +(-30.6549 + 17.6986i) q^{23} +(2.50000 - 4.33013i) q^{25} +(14.2015 + 8.19922i) q^{29} +(13.3206 + 23.0720i) q^{31} -16.2366i q^{35} -44.6613 q^{37} +(-14.8634 + 8.58140i) q^{41} +(20.5554 - 35.6031i) q^{43} +(36.4950 + 21.0704i) q^{47} +(-1.86263 - 3.22616i) q^{49} +100.474i q^{53} -16.8002 q^{55} +(-4.12003 + 2.37870i) q^{59} +(38.4629 - 66.6197i) q^{61} +(5.68041 + 3.27959i) q^{65} +(-41.9225 - 72.6119i) q^{67} +23.1134i q^{71} -103.753 q^{73} +(-47.2464 + 27.2777i) q^{77} +(40.2610 - 69.7340i) q^{79} +(-17.1034 - 9.87463i) q^{83} +(2.12546 + 3.68141i) q^{85} +29.0566i q^{89} +21.2997 q^{91} +(-14.2986 + 8.25532i) q^{95} +(47.7972 - 82.7872i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{7} - 18 q^{11} - 10 q^{13} + 52 q^{19} - 54 q^{23} + 40 q^{25} + 54 q^{29} - 32 q^{31} + 44 q^{37} - 144 q^{41} + 124 q^{43} - 216 q^{47} - 54 q^{49} - 486 q^{59} + 62 q^{61} + 90 q^{65} - 14 q^{67}+ \cdots - 142 q^{97}+O(q^{100}) \) 16 * q - 2 * q^7 - 18 * q^11 - 10 * q^13 + 52 * q^19 - 54 * q^23 + 40 * q^25 + 54 * q^29 - 32 * q^31 + 44 * q^37 - 144 * q^41 + 124 * q^43 - 216 * q^47 - 54 * q^49 - 486 * q^59 + 62 * q^61 + 90 * q^65 - 14 * q^67 - 268 * q^73 - 702 * q^77 + 40 * q^79 + 522 * q^83 + 30 * q^85 - 136 * q^91 + 180 * q^95 - 142 * q^97

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