LMFDB - Embedded newform 648.4.i.g.433.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [648,4,Mod(217,648)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(648, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("648.217");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 648 = 2^{3} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	648.i (of order $3$, 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:	$38.2332376837$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 216)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			433.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	648.433
Dual form			648.4.i.g.217.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{5} +(4.50000 + 7.79423i) q^{7} +O(q^{10})$	$q+(0.500000 - 0.866025i) q^{5} +(4.50000 + 7.79423i) q^{7} +(-8.50000 - 14.7224i) q^{11} +(22.0000 - 38.1051i) q^{13} -56.0000 q^{17} -94.0000 q^{19} +(-25.0000 + 43.3013i) q^{23} +(62.0000 + 107.387i) q^{25} +(-15.0000 - 25.9808i) q^{29} +(69.5000 - 120.378i) q^{31} +9.00000 q^{35} -174.000 q^{37} +(159.000 - 275.396i) q^{41} +(121.000 + 209.578i) q^{43} +(-315.000 - 545.596i) q^{47} +(131.000 - 226.899i) q^{49} -547.000 q^{53} -17.0000 q^{55} +(-118.000 + 204.382i) q^{59} +(-164.000 - 284.056i) q^{61} +(-22.0000 - 38.1051i) q^{65} +(-307.000 + 531.740i) q^{67} -296.000 q^{71} +433.000 q^{73} +(76.5000 - 132.502i) q^{77} +(28.0000 + 48.4974i) q^{79} +(-612.500 - 1060.88i) q^{83} +(-28.0000 + 48.4974i) q^{85} -1506.00 q^{89} +396.000 q^{91} +(-47.0000 + 81.4064i) q^{95} +(-695.500 - 1204.64i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{5} + 9 q^{7}+O(q^{10}) $ 2 * q + q^5 + 9 * q^7	$ 2 q + q^{5} + 9 q^{7} - 17 q^{11} + 44 q^{13} - 112 q^{17} - 188 q^{19} - 50 q^{23} + 124 q^{25} - 30 q^{29} + 139 q^{31} + 18 q^{35} - 348 q^{37} + 318 q^{41} + 242 q^{43} - 630 q^{47} + 262 q^{49} - 1094 q^{53} - 34 q^{55} - 236 q^{59} - 328 q^{61} - 44 q^{65} - 614 q^{67} - 592 q^{71} + 866 q^{73} + 153 q^{77} + 56 q^{79} - 1225 q^{83} - 56 q^{85} - 3012 q^{89} + 792 q^{91} - 94 q^{95} - 1391 q^{97}+O(q^{100}) $ 2 * q + q^5 + 9 * q^7 - 17 * q^11 + 44 * q^13 - 112 * q^17 - 188 * q^19 - 50 * q^23 + 124 * q^25 - 30 * q^29 + 139 * q^31 + 18 * q^35 - 348 * q^37 + 318 * q^41 + 242 * q^43 - 630 * q^47 + 262 * q^49 - 1094 * q^53 - 34 * q^55 - 236 * q^59 - 328 * q^61 - 44 * q^65 - 614 * q^67 - 592 * q^71 + 866 * q^73 + 153 * q^77 + 56 * q^79 - 1225 * q^83 - 56 * q^85 - 3012 * q^89 + 792 * q^91 - 94 * q^95 - 1391 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/648\mathbb{Z}\right)^\times$.

$n$	$325$	$487$	$569$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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
$5$	0.500000	−	0.866025i	0.0447214	−	0.0774597i	−0.842798	−	0.538230i	$-0.819093\pi$
$5$	0.500000	−	0.866025i	0.0447214	−	0.0774597i	0.887520	+	0.460770i	$0.152427\pi$
$6$		0			0
$7$	4.50000	+	7.79423i	0.242977	+	0.420849i	0.961561	−	0.274592i	$-0.0885427\pi$
$7$	4.50000	+	7.79423i	0.242977	+	0.420849i	−0.718584	+	0.695440i	$0.755209\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−8.50000	−	14.7224i	−0.232986	−	0.403544i	0.725699	−	0.688012i	$-0.241516\pi$
$11$	−8.50000	−	14.7224i	−0.232986	−	0.403544i	−0.958685	+	0.284468i	$0.908183\pi$
$12$		0			0
$13$	22.0000	−	38.1051i	0.469362	−	0.812958i	−0.530025	−	0.847982i	$-0.677817\pi$
$13$	22.0000	−	38.1051i	0.469362	−	0.812958i	0.999386	+	0.0350238i	$0.0111507\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−56.0000			−0.798941			−0.399470	−	0.916746i	$-0.630806\pi$
$17$	−56.0000			−0.798941			−0.399470	+	0.916746i	$0.630806\pi$
$18$		0			0
$19$	−94.0000			−1.13500			−0.567502	−	0.823372i	$-0.692090\pi$
$19$	−94.0000			−1.13500			−0.567502	+	0.823372i	$0.692090\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−25.0000	+	43.3013i	−0.226646	+	0.392563i	−0.956812	−	0.290707i	$-0.906109\pi$
$23$	−25.0000	+	43.3013i	−0.226646	+	0.392563i	0.730166	+	0.683270i	$0.239443\pi$
$24$		0			0
$25$	62.0000	+	107.387i	0.496000	+	0.859097i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−15.0000	−	25.9808i	−0.0960493	−	0.166362i	0.813997	−	0.580869i	$-0.197287\pi$
$29$	−15.0000	−	25.9808i	−0.0960493	−	0.166362i	−0.910046	+	0.414507i	$0.863954\pi$
$30$		0			0
$31$	69.5000	−	120.378i	0.402663	−	0.697434i	−0.591383	−	0.806391i	$-0.701418\pi$
$31$	69.5000	−	120.378i	0.402663	−	0.697434i	0.994046	+	0.108957i	$0.0347512\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	9.00000			0.0434651
$36$		0			0
$37$	−174.000			−0.773120			−0.386560	−	0.922264i	$-0.626337\pi$
$37$	−174.000			−0.773120			−0.386560	+	0.922264i	$0.626337\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	159.000	−	275.396i	0.605649	−	1.04902i	−0.386299	−	0.922374i	$-0.626247\pi$
$41$	159.000	−	275.396i	0.605649	−	1.04902i	0.991948	−	0.126642i	$-0.0404200\pi$
$42$		0			0
$43$	121.000	+	209.578i	0.429124	+	0.743264i	0.996796	−	0.0799906i	$-0.0254890\pi$
$43$	121.000	+	209.578i	0.429124	+	0.743264i	−0.567672	+	0.823255i	$0.692156\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−315.000	−	545.596i	−0.977606	−	1.69326i	−0.671053	−	0.741409i	$-0.734158\pi$
$47$	−315.000	−	545.596i	−0.977606	−	1.69326i	−0.306553	−	0.951854i	$-0.599176\pi$
$48$		0			0
$49$	131.000	−	226.899i	0.381924	−	0.661512i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−547.000			−1.41766			−0.708832	−	0.705377i	$-0.750778\pi$
$53$	−547.000			−1.41766			−0.708832	+	0.705377i	$0.750778\pi$
$54$		0			0
$55$	−17.0000			−0.0416778
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−118.000	+	204.382i	−0.260378	+	0.450988i	−0.966342	−	0.257260i	$-0.917180\pi$
$59$	−118.000	+	204.382i	−0.260378	+	0.450988i	0.705965	+	0.708247i	$0.250514\pi$
$60$		0			0
$61$	−164.000	−	284.056i	−0.344230	−	0.596224i	0.640983	−	0.767555i	$-0.278527\pi$
$61$	−164.000	−	284.056i	−0.344230	−	0.596224i	−0.985214	+	0.171330i	$0.945193\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−22.0000	−	38.1051i	−0.0419810	−	0.0727132i
$66$		0			0
$67$	−307.000	+	531.740i	−0.559791	+	0.969587i	0.437722	+	0.899110i	$0.355785\pi$
$67$	−307.000	+	531.740i	−0.559791	+	0.969587i	−0.997513	+	0.0704767i	$0.977548\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−296.000			−0.494771			−0.247385	−	0.968917i	$-0.579571\pi$
$71$	−296.000			−0.494771			−0.247385	+	0.968917i	$0.579571\pi$
$72$		0			0
$73$	433.000			0.694230			0.347115	−	0.937823i	$-0.387161\pi$
$73$	433.000			0.694230			0.347115	+	0.937823i	$0.387161\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	76.5000	−	132.502i	0.113221	−	0.196104i
$78$		0			0
$79$	28.0000	+	48.4974i	0.0398765	+	0.0690682i	0.885275	−	0.465068i	$-0.153970\pi$
$79$	28.0000	+	48.4974i	0.0398765	+	0.0690682i	−0.845398	+	0.534136i	$0.820637\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−612.500	−	1060.88i	−0.810007	−	1.40297i	−0.912858	−	0.408277i	$-0.866130\pi$
$83$	−612.500	−	1060.88i	−0.810007	−	1.40297i	0.102851	−	0.994697i	$-0.467204\pi$
$84$		0			0
$85$	−28.0000	+	48.4974i	−0.0357297	+	0.0618857i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−1506.00			−1.79366			−0.896830	−	0.442376i	$-0.854136\pi$
$89$	−1506.00			−1.79366			−0.896830	+	0.442376i	$0.854136\pi$
$90$		0			0
$91$	396.000			0.456177
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−47.0000	+	81.4064i	−0.0507589	+	0.0879170i
$96$		0			0
$97$	−695.500	−	1204.64i	−0.728014	−	1.26096i	−0.957721	−	0.287697i	$-0.907110\pi$
$97$	−695.500	−	1204.64i	−0.728014	−	1.26096i	0.229708	−	0.973260i	$-0.426223\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−832.500	−	1441.93i	−0.820167	−	1.42057i	−0.905558	−	0.424223i	$-0.860547\pi$
$101$	−832.500	−	1441.93i	−0.820167	−	1.42057i	0.0853909	−	0.996348i	$-0.472786\pi$
$102$		0			0
$103$	−734.000	+	1271.33i	−0.702167	+	1.21619i	0.265538	+	0.964100i	$0.414451\pi$
$103$	−734.000	+	1271.33i	−0.702167	+	1.21619i	−0.967704	+	0.252088i	$0.918883\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−627.000			−0.566490			−0.283245	−	0.959048i	$-0.591411\pi$
$107$	−627.000			−0.566490			−0.283245	+	0.959048i	$0.591411\pi$
$108$		0			0
$109$	610.000			0.536031			0.268016	−	0.963415i	$-0.413632\pi$
$109$	610.000			0.536031			0.268016	+	0.963415i	$0.413632\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	567.000	−	982.073i	0.472025	−	0.817572i	−0.527462	−	0.849578i	$-0.676856\pi$
$113$	567.000	−	982.073i	0.472025	−	0.817572i	0.999488	+	0.0320065i	$0.0101897\pi$
$114$		0			0
$115$	25.0000	+	43.3013i	0.0202718	+	0.0351119i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−252.000	−	436.477i	−0.194124	−	0.336233i
$120$		0			0
$121$	521.000	−	902.398i	0.391435	−	0.677985i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	249.000			0.178170
$126$		0			0
$127$	505.000			0.352846			0.176423	−	0.984314i	$-0.443547\pi$
$127$	505.000			0.352846			0.176423	+	0.984314i	$0.443547\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	257.500	−	446.003i	0.171740	−	0.297462i	−0.767289	−	0.641302i	$-0.778395\pi$
$131$	257.500	−	446.003i	0.171740	−	0.297462i	0.939028	+	0.343840i	$0.111728\pi$
$132$		0			0
$133$	−423.000	−	732.657i	−0.275780	−	0.477665i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−3.00000	−	5.19615i	−0.00187086	−	0.00324042i	0.865088	−	0.501619i	$-0.167262\pi$
$137$	−3.00000	−	5.19615i	−0.00187086	−	0.00324042i	−0.866959	+	0.498379i	$0.833929\pi$
$138$		0			0
$139$	−318.000	+	550.792i	−0.194046	+	0.336098i	−0.946587	−	0.322447i	$-0.895494\pi$
$139$	−318.000	+	550.792i	−0.194046	+	0.336098i	0.752541	+	0.658545i	$0.228828\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−748.000			−0.437419
$144$		0			0
$145$	−30.0000			−0.0171818
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−1119.50	+	1939.03i	−0.615524	+	1.06612i	0.374769	+	0.927118i	$0.377722\pi$
$149$	−1119.50	+	1939.03i	−0.615524	+	1.06612i	−0.990292	+	0.139000i	$0.955611\pi$
$150$		0			0
$151$	1347.50	+	2333.94i	0.726212	+	1.25784i	0.958473	+	0.285182i	$0.0920542\pi$
$151$	1347.50	+	2333.94i	0.726212	+	1.25784i	−0.232261	+	0.972653i	$0.574612\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−69.5000	−	120.378i	−0.0360153	−	0.0623804i
$156$		0			0
$157$	994.000	−	1721.66i	0.505286	−	0.875180i	−0.494696	−	0.869066i	$-0.664720\pi$
$157$	994.000	−	1721.66i	0.505286	−	0.875180i	0.999981	−	0.00611406i	$-0.00194618\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−450.000			−0.220279
$162$		0			0
$163$	−2580.00			−1.23976			−0.619881	−	0.784696i	$-0.712819\pi$
$163$	−2580.00			−1.23976			−0.619881	+	0.784696i	$0.712819\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	939.000	−	1626.40i	0.435102	−	0.753618i	−0.562202	−	0.827000i	$-0.690046\pi$
$167$	939.000	−	1626.40i	0.435102	−	0.753618i	0.997304	+	0.0733814i	$0.0233790\pi$
$168$		0			0
$169$	130.500	+	226.033i	0.0593992	+	0.102882i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−1081.50	−	1873.21i	−0.475289	−	0.823224i	0.524311	−	0.851527i	$-0.324323\pi$
$173$	−1081.50	−	1873.21i	−0.475289	−	0.823224i	−0.999599	+	0.0283030i	$0.990990\pi$
$174$		0			0
$175$	−558.000	+	966.484i	−0.241033	+	0.417482i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−2181.00			−0.910702			−0.455351	−	0.890312i	$-0.650486\pi$
$179$	−2181.00			−0.910702			−0.455351	+	0.890312i	$0.650486\pi$
$180$		0			0
$181$	−1488.00			−0.611062			−0.305531	−	0.952182i	$-0.598834\pi$
$181$	−1488.00			−0.611062			−0.305531	+	0.952182i	$0.598834\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−87.0000	+	150.688i	−0.0345750	+	0.0598856i
$186$		0			0
$187$	476.000	+	824.456i	0.186142	+	0.322408i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	882.000	+	1527.67i	0.334132	+	0.578734i	0.983318	−	0.181896i	$-0.0582234\pi$
$191$	882.000	+	1527.67i	0.334132	+	0.578734i	−0.649185	+	0.760630i	$0.724890\pi$
$192$		0			0
$193$	1773.50	−	3071.79i	0.661447	−	1.14566i	−0.318788	−	0.947826i	$-0.603276\pi$
$193$	1773.50	−	3071.79i	0.661447	−	1.14566i	0.980235	−	0.197834i	$-0.0633908\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	4941.00			1.78696			0.893481	−	0.449100i	$-0.148255\pi$
$197$	4941.00			1.78696			0.893481	+	0.449100i	$0.148255\pi$
$198$		0			0
$199$	−1487.00			−0.529702			−0.264851	−	0.964289i	$-0.585323\pi$
$199$	−1487.00			−0.529702			−0.264851	+	0.964289i	$0.585323\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	135.000	−	233.827i	0.0466756	−	0.0808445i
$204$		0			0
$205$	−159.000	−	275.396i	−0.0541709	−	0.0938268i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	799.000	+	1383.91i	0.264440	+	0.458024i
$210$		0			0
$211$	−221.000	+	382.783i	−0.0721055	+	0.124890i	−0.899824	−	0.436253i	$-0.856305\pi$
$211$	−221.000	+	382.783i	−0.0721055	+	0.124890i	0.827718	+	0.561144i	$0.189639\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	242.000			0.0767640
$216$		0			0
$217$	1251.00			0.391352
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−1232.00	+	2133.89i	−0.374992	+	0.649506i
$222$		0			0
$223$	2548.00	+	4413.27i	0.765142	+	1.32527i	0.940171	+	0.340702i	$0.110665\pi$
$223$	2548.00	+	4413.27i	0.765142	+	1.32527i	−0.175029	+	0.984563i	$0.556002\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	2742.00	+	4749.28i	0.801731	+	1.38864i	0.918476	+	0.395477i	$0.129421\pi$
$227$	2742.00	+	4749.28i	0.801731	+	1.38864i	−0.116745	+	0.993162i	$0.537246\pi$
$228$		0			0
$229$	1765.00	−	3057.07i	0.509321	−	0.882170i	−0.490621	−	0.871373i	$-0.663230\pi$
$229$	1765.00	−	3057.07i	0.509321	−	0.882170i	0.999942	−	0.0107965i	$-0.00343669\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−1630.00			−0.458304			−0.229152	−	0.973391i	$-0.573595\pi$
$233$	−1630.00			−0.458304			−0.229152	+	0.973391i	$0.573595\pi$
$234$		0			0
$235$	−630.000			−0.174879
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−995.000	+	1723.39i	−0.269294	+	0.466430i	−0.968680	−	0.248314i	$-0.920124\pi$
$239$	−995.000	+	1723.39i	−0.269294	+	0.466430i	0.699386	+	0.714744i	$0.253457\pi$
$240$		0			0
$241$	−1107.00	−	1917.38i	−0.295884	−	0.512487i	0.679306	−	0.733855i	$-0.262281\pi$
$241$	−1107.00	−	1917.38i	−0.295884	−	0.512487i	−0.975190	+	0.221368i	$0.928948\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−131.000	−	226.899i	−0.0341603	−	0.0591674i
$246$		0			0
$247$	−2068.00	+	3581.88i	−0.532727	+	0.922711i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	4480.00			1.12659			0.563297	−	0.826254i	$-0.309533\pi$
$251$	4480.00			1.12659			0.563297	+	0.826254i	$0.309533\pi$
$252$		0			0
$253$	850.000			0.211222
$254$		0			0
$255$		0			0
$256$		0			0
$257$	1102.00	−	1908.72i	0.267474	−	0.463279i	−0.700735	−	0.713422i	$-0.747144\pi$
$257$	1102.00	−	1908.72i	0.267474	−	0.463279i	0.968209	+	0.250143i	$0.0804777\pi$
$258$		0			0
$259$	−783.000	−	1356.20i	−0.187850	−	0.325366i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	971.000	+	1681.82i	0.227659	+	0.394318i	0.957114	−	0.289712i	$-0.0935594\pi$
$263$	971.000	+	1681.82i	0.227659	+	0.394318i	−0.729455	+	0.684029i	$0.760226\pi$
$264$		0			0
$265$	−273.500	+	473.716i	−0.0633999	+	0.109812i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	7606.00			1.72396			0.861981	−	0.506940i	$-0.169223\pi$
$269$	7606.00			1.72396			0.861981	+	0.506940i	$0.169223\pi$
$270$		0			0
$271$	4391.00			0.984259			0.492130	−	0.870522i	$-0.336219\pi$
$271$	4391.00			0.984259			0.492130	+	0.870522i	$0.336219\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	1054.00	−	1825.58i	0.231122	−	0.400315i
$276$		0			0
$277$	−3500.00	−	6062.18i	−0.759186	−	1.31495i	−0.943266	−	0.332038i	$-0.892264\pi$
$277$	−3500.00	−	6062.18i	−0.759186	−	1.31495i	0.184080	−	0.982911i	$-0.441070\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	4456.00	+	7718.02i	0.945988	+	1.63850i	0.753761	+	0.657149i	$0.228238\pi$
$281$	4456.00	+	7718.02i	0.945988	+	1.63850i	0.192228	+	0.981350i	$0.438429\pi$
$282$		0			0
$283$	−1807.00	+	3129.82i	−0.379558	+	0.657414i	−0.990998	−	0.133877i	$-0.957257\pi$
$283$	−1807.00	+	3129.82i	−0.379558	+	0.657414i	0.611440	+	0.791291i	$0.290591\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	2862.00			0.588636
$288$		0			0
$289$	−1777.00			−0.361693
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−2097.00	+	3632.11i	−0.418116	+	0.724199i	−0.995750	−	0.0920975i	$-0.970643\pi$
$293$	−2097.00	+	3632.11i	−0.418116	+	0.724199i	0.577634	+	0.816296i	$0.303976\pi$
$294$		0			0
$295$	118.000	+	204.382i	0.0232889	+	0.0403376i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	1100.00	+	1905.26i	0.212758	+	0.368508i
$300$		0			0
$301$	−1089.00	+	1886.20i	−0.208535	+	0.361193i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−328.000			−0.0615778
$306$		0			0
$307$	840.000			0.156161			0.0780803	−	0.996947i	$-0.475121\pi$
$307$	840.000			0.156161			0.0780803	+	0.996947i	$0.475121\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	303.000	−	524.811i	0.0552462	−	0.0956891i	−0.837080	−	0.547081i	$-0.815739\pi$
$311$	303.000	−	524.811i	0.0552462	−	0.0956891i	0.892326	+	0.451392i	$0.149072\pi$
$312$		0			0
$313$	−1018.50	−	1764.09i	−0.183927	−	0.318570i	0.759288	−	0.650755i	$-0.225548\pi$
$313$	−1018.50	−	1764.09i	−0.183927	−	0.318570i	−0.943214	+	0.332185i	$0.892214\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	259.500	+	449.467i	0.0459778	+	0.0796359i	0.888098	−	0.459653i	$-0.152026\pi$
$317$	259.500	+	449.467i	0.0459778	+	0.0796359i	−0.842121	+	0.539289i	$0.818693\pi$
$318$		0			0
$319$	−255.000	+	441.673i	−0.0447563	+	0.0775202i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	5264.00			0.906801
$324$		0			0
$325$	5456.00			0.931214
$326$		0			0
$327$		0			0
$328$		0			0
$329$	2835.00	−	4910.36i	0.475072	−	0.822848i
$330$		0			0
$331$	−1375.00	−	2381.57i	−0.228329	−	0.395477i	0.728984	−	0.684531i	$-0.239993\pi$
$331$	−1375.00	−	2381.57i	−0.228329	−	0.395477i	−0.957313	+	0.289053i	$0.906659\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	307.000	+	531.740i	0.0500693	+	0.0867225i
$336$		0			0
$337$	−2205.00	+	3819.17i	−0.356421	+	0.617340i	−0.987360	−	0.158493i	$-0.949337\pi$
$337$	−2205.00	+	3819.17i	−0.356421	+	0.617340i	0.630939	+	0.775833i	$0.282670\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−2363.00			−0.375260
$342$		0			0
$343$	5445.00			0.857150
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−5455.50	+	9449.20i	−0.843996	+	1.46184i	0.0424944	+	0.999097i	$0.486470\pi$
$347$	−5455.50	+	9449.20i	−0.843996	+	1.46184i	−0.886490	+	0.462747i	$0.846864\pi$
$348$		0			0
$349$	2325.00	+	4027.02i	0.356603	+	0.617654i	0.987391	−	0.158301i	$-0.0506016\pi$
$349$	2325.00	+	4027.02i	0.356603	+	0.617654i	−0.630788	+	0.775955i	$0.717268\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	4705.00	+	8149.30i	0.709410	+	1.22873i	0.965076	+	0.261970i	$0.0843720\pi$
$353$	4705.00	+	8149.30i	0.709410	+	1.22873i	−0.255666	+	0.966765i	$0.582295\pi$
$354$		0			0
$355$	−148.000	+	256.344i	−0.0221268	+	0.0383248i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	2130.00			0.313140			0.156570	−	0.987667i	$-0.449956\pi$
$359$	2130.00			0.313140			0.156570	+	0.987667i	$0.449956\pi$
$360$		0			0
$361$	1977.00			0.288234
$362$		0			0
$363$		0			0
$364$		0			0
$365$	216.500	−	374.989i	0.0310469	−	0.0537749i
$366$		0			0
$367$	−696.500	−	1206.37i	−0.0990654	−	0.171586i	0.812233	−	0.583334i	$-0.198252\pi$
$367$	−696.500	−	1206.37i	−0.0990654	−	0.171586i	−0.911298	+	0.411747i	$0.864919\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−2461.50	−	4263.44i	−0.344460	−	0.596622i
$372$		0			0
$373$	1460.00	−	2528.79i	0.202670	−	0.351035i	−0.746718	−	0.665141i	$-0.768371\pi$
$373$	1460.00	−	2528.79i	0.202670	−	0.351035i	0.949388	+	0.314106i	$0.101705\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−1320.00			−0.180327
$378$		0			0
$379$	−10780.0			−1.46103			−0.730516	−	0.682895i	$-0.760721\pi$
$379$	−10780.0			−1.46103			−0.730516	+	0.682895i	$0.760721\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−1944.00	+	3367.11i	−0.259357	+	0.449220i	−0.966070	−	0.258281i	$-0.916844\pi$
$383$	−1944.00	+	3367.11i	−0.259357	+	0.449220i	0.706713	+	0.707501i	$0.250177\pi$
$384$		0			0
$385$	−76.5000	−	132.502i	−0.0101268	−	0.0175401i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	2004.50	+	3471.90i	0.261265	+	0.452525i	0.966578	−	0.256371i	$-0.0825269\pi$
$389$	2004.50	+	3471.90i	0.261265	+	0.452525i	−0.705313	+	0.708896i	$0.749194\pi$
$390$		0			0
$391$	1400.00	−	2424.87i	0.181077	−	0.313634i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	56.0000			0.00713333
$396$		0			0
$397$	860.000			0.108721			0.0543604	−	0.998521i	$-0.482688\pi$
$397$	860.000			0.108721			0.0543604	+	0.998521i	$0.482688\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	858.000	−	1486.10i	0.106849	−	0.185068i	−0.807643	−	0.589672i	$-0.799257\pi$
$401$	858.000	−	1486.10i	0.106849	−	0.185068i	0.914492	+	0.404604i	$0.132591\pi$
$402$		0			0
$403$	−3058.00	−	5296.61i	−0.377990	−	0.654697i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	1479.00	+	2561.70i	0.180126	+	0.311987i
$408$		0			0
$409$	1600.50	−	2772.15i	0.193495	−	0.335144i	−0.752911	−	0.658123i	$-0.771351\pi$
$409$	1600.50	−	2772.15i	0.193495	−	0.335144i	0.946406	+	0.322979i	$0.104684\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−2124.00			−0.253063
$414$		0			0
$415$	−1225.00			−0.144899
$416$		0			0
$417$		0			0
$418$		0			0
$419$	2850.00	−	4936.34i	0.332295	−	0.575552i	−0.650666	−	0.759364i	$-0.725510\pi$
$419$	2850.00	−	4936.34i	0.332295	−	0.575552i	0.982961	+	0.183812i	$0.0588437\pi$
$420$		0			0
$421$	5156.00	+	8930.45i	0.596884	+	1.03383i	0.993278	+	0.115753i	$0.0369280\pi$
$421$	5156.00	+	8930.45i	0.596884	+	1.03383i	−0.396394	+	0.918080i	$0.629739\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−3472.00	−	6013.68i	−0.396275	−	0.686368i
$426$		0			0
$427$	1476.00	−	2556.51i	0.167280	−	0.289738i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	10354.0			1.15716			0.578578	−	0.815627i	$-0.303608\pi$
$431$	10354.0			1.15716			0.578578	+	0.815627i	$0.303608\pi$
$432$		0			0
$433$	−10787.0			−1.19721			−0.598603	−	0.801046i	$-0.704277\pi$
$433$	−10787.0			−1.19721			−0.598603	+	0.801046i	$0.704277\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	2350.00	−	4070.32i	0.257244	−	0.445560i
$438$		0			0
$439$	7357.50	+	12743.6i	0.799896	+	1.38546i	0.919683	+	0.392661i	$0.128445\pi$
$439$	7357.50	+	12743.6i	0.799896	+	1.38546i	−0.119787	+	0.992800i	$0.538221\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−3314.00	−	5740.02i	−0.355424	−	0.615613i	0.631766	−	0.775159i	$-0.282330\pi$
$443$	−3314.00	−	5740.02i	−0.355424	−	0.615613i	−0.987190	+	0.159546i	$0.948997\pi$
$444$		0			0
$445$	−753.000	+	1304.23i	−0.0802149	+	0.138936i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−8122.00			−0.853677			−0.426838	−	0.904328i	$-0.640373\pi$
$449$	−8122.00			−0.853677			−0.426838	+	0.904328i	$0.640373\pi$
$450$		0			0
$451$	−5406.00			−0.564431
$452$		0			0
$453$		0			0
$454$		0			0
$455$	198.000	−	342.946i	0.0204008	−	0.0353353i
$456$		0			0
$457$	3276.50	+	5675.06i	0.335379	+	0.580893i	0.983558	−	0.180595i	$-0.0578023\pi$
$457$	3276.50	+	5675.06i	0.335379	+	0.580893i	−0.648179	+	0.761488i	$0.724469\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−2039.50	−	3532.52i	−0.206050	−	0.356889i	0.744417	−	0.667715i	$-0.232728\pi$
$461$	−2039.50	−	3532.52i	−0.206050	−	0.356889i	−0.950467	+	0.310826i	$0.899394\pi$
$462$		0			0
$463$	6342.50	−	10985.5i	0.636633	−	1.10268i	−0.349534	−	0.936924i	$-0.613660\pi$
$463$	6342.50	−	10985.5i	0.636633	−	1.10268i	0.986167	−	0.165757i	$-0.0530066\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−6111.00			−0.605532			−0.302766	−	0.953065i	$-0.597910\pi$
$467$	−6111.00			−0.605532			−0.302766	+	0.953065i	$0.597910\pi$
$468$		0			0
$469$	−5526.00			−0.544066
$470$		0			0
$471$		0			0
$472$		0			0
$473$	2057.00	−	3562.83i	0.199960	−	0.346340i
$474$		0			0
$475$	−5828.00	−	10094.4i	−0.562962	−	0.975079i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−5627.00	−	9746.25i	−0.536752	−	0.929682i	−0.999076	−	0.0429708i	$-0.986318\pi$
$479$	−5627.00	−	9746.25i	−0.536752	−	0.929682i	0.462324	−	0.886711i	$-0.347016\pi$
$480$		0			0
$481$	−3828.00	+	6630.29i	−0.362873	+	0.628514i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−1391.00			−0.130231
$486$		0			0
$487$	13936.0			1.29672			0.648358	−	0.761336i	$-0.275456\pi$
$487$	13936.0			1.29672			0.648358	+	0.761336i	$0.275456\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	3022.50	−	5235.12i	0.277808	−	0.481177i	−0.693032	−	0.720907i	$-0.743726\pi$
$491$	3022.50	−	5235.12i	0.277808	−	0.481177i	0.970840	+	0.239730i	$0.0770589\pi$
$492$		0			0
$493$	840.000	+	1454.92i	0.0767377	+	0.132914i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−1332.00	−	2307.09i	−0.120218	−	0.208224i
$498$		0			0
$499$	9741.00	−	16871.9i	0.873882	−	1.51361i	0.0159328	−	0.999873i	$-0.494928\pi$
$499$	9741.00	−	16871.9i	0.873882	−	1.51361i	0.857949	−	0.513735i	$-0.171738\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−19770.0			−1.75249			−0.876243	−	0.481869i	$-0.839958\pi$
$503$	−19770.0			−1.75249			−0.876243	+	0.481869i	$0.839958\pi$
$504$		0			0
$505$	−1665.00			−0.146716
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−5806.50	+	10057.2i	−0.505636	+	0.875787i	0.494343	+	0.869267i	$0.335409\pi$
$509$	−5806.50	+	10057.2i	−0.505636	+	0.875787i	−0.999979	+	0.00651985i	$0.997925\pi$
$510$		0			0
$511$	1948.50	+	3374.90i	0.168682	+	0.292166i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	734.000	+	1271.33i	0.0628037	+	0.108779i
$516$		0			0
$517$	−5355.00	+	9275.13i	−0.455537	+	0.789013i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	5500.00			0.462494			0.231247	−	0.972895i	$-0.425719\pi$
$521$	5500.00			0.462494			0.231247	+	0.972895i	$0.425719\pi$
$522$		0			0
$523$	−8024.00			−0.670870			−0.335435	−	0.942063i	$-0.608883\pi$
$523$	−8024.00			−0.670870			−0.335435	+	0.942063i	$0.608883\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−3892.00	+	6741.14i	−0.321704	+	0.557208i
$528$		0			0
$529$	4833.50	+	8371.87i	0.397263	+	0.688080i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−6996.00	−	12117.4i	−0.568537	−	0.984736i
$534$		0			0
$535$	−313.500	+	542.998i	−0.0253342	+	0.0438801i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−4454.00			−0.355932
$540$		0			0
$541$	−9036.00			−0.718092			−0.359046	−	0.933320i	$-0.616898\pi$
$541$	−9036.00			−0.718092			−0.359046	+	0.933320i	$0.616898\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	305.000	−	528.275i	0.0239720	−	0.0415208i
$546$		0			0
$547$	−11728.0	−	20313.5i	−0.916733	−	1.58783i	−0.804344	−	0.594164i	$-0.797483\pi$
$547$	−11728.0	−	20313.5i	−0.916733	−	1.58783i	−0.112390	−	0.993664i	$-0.535850\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	1410.00	+	2442.19i	0.109016	+	0.188822i
$552$		0			0
$553$	−252.000	+	436.477i	−0.0193782	+	0.0335640i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−18721.0			−1.42412			−0.712059	−	0.702119i	$-0.752237\pi$
$557$	−18721.0			−1.42412			−0.712059	+	0.702119i	$0.752237\pi$
$558$		0			0
$559$	10648.0			0.805657
$560$		0			0
$561$		0			0
$562$		0			0
$563$	708.500	−	1227.16i	0.0530368	−	0.0918624i	−0.838288	−	0.545227i	$-0.816443\pi$
$563$	708.500	−	1227.16i	0.0530368	−	0.0918624i	0.891325	+	0.453365i	$0.149777\pi$
$564$		0			0
$565$	−567.000	−	982.073i	−0.0422192	−	0.0731259i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−9298.00	−	16104.6i	−0.685048	−	1.18654i	−0.973422	−	0.229020i	$-0.926448\pi$
$569$	−9298.00	−	16104.6i	−0.685048	−	1.18654i	0.288373	−	0.957518i	$-0.406886\pi$
$570$		0			0
$571$	1854.00	−	3211.22i	0.135880	−	0.235351i	−0.790053	−	0.613038i	$-0.789947\pi$
$571$	1854.00	−	3211.22i	0.135880	−	0.235351i	0.925933	+	0.377687i	$0.123281\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−6200.00			−0.449666
$576$		0			0
$577$	21494.0			1.55079			0.775396	−	0.631475i	$-0.217550\pi$
$577$	21494.0			1.55079			0.775396	+	0.631475i	$0.217550\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	5512.50	−	9547.93i	0.393627	−	0.681781i
$582$		0			0
$583$	4649.50	+	8053.17i	0.330296	+	0.572090i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−8024.50	−	13898.8i	−0.564236	−	0.977286i	−0.997120	−	0.0758360i	$-0.975837\pi$
$587$	−8024.50	−	13898.8i	−0.564236	−	0.977286i	0.432884	−	0.901450i	$-0.357496\pi$
$588$		0			0
$589$	−6533.00	+	11315.5i	−0.457025	+	0.791590i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	4658.00			0.322565			0.161283	−	0.986908i	$-0.448437\pi$
$593$	4658.00			0.322565			0.161283	+	0.986908i	$0.448437\pi$
$594$		0			0
$595$	−504.000			−0.0347260
$596$		0			0
$597$		0			0
$598$		0			0
$599$	13269.0	−	22982.6i	0.905103	−	1.56768i	0.0843239	−	0.996438i	$-0.473127\pi$
$599$	13269.0	−	22982.6i	0.905103	−	1.56768i	0.820779	−	0.571246i	$-0.193540\pi$
$600$		0			0
$601$	−573.500	−	993.331i	−0.0389244	−	0.0674190i	0.845907	−	0.533331i	$-0.179060\pi$
$601$	−573.500	−	993.331i	−0.0389244	−	0.0674190i	−0.884831	+	0.465912i	$0.845726\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−521.000	−	902.398i	−0.0350110	−	0.0606409i
$606$		0			0
$607$	−13024.0	+	22558.2i	−0.870886	+	1.50842i	−0.00980461	+	0.999952i	$0.503121\pi$
$607$	−13024.0	+	22558.2i	−0.870886	+	1.50842i	−0.861081	+	0.508467i	$0.830212\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−27720.0			−1.83540
$612$		0			0
$613$	−394.000			−0.0259600			−0.0129800	−	0.999916i	$-0.504132\pi$
$613$	−394.000			−0.0259600			−0.0129800	+	0.999916i	$0.504132\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−13911.0	+	24094.6i	−0.907675	+	1.57214i	−0.0903905	+	0.995906i	$0.528812\pi$
$617$	−13911.0	+	24094.6i	−0.907675	+	1.57214i	−0.817285	+	0.576234i	$0.804522\pi$
$618$		0			0
$619$	−10790.0	−	18688.8i	−0.700625	−	1.21352i	−0.968247	−	0.249994i	$-0.919571\pi$
$619$	−10790.0	−	18688.8i	−0.700625	−	1.21352i	0.267623	−	0.963524i	$-0.413762\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−6777.00	−	11738.1i	−0.435818	−	0.754859i
$624$		0			0
$625$	−7625.50	+	13207.8i	−0.488032	+	0.845296i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	9744.00			0.617677
$630$		0			0
$631$	7855.00			0.495567			0.247783	−	0.968815i	$-0.420298\pi$
$631$	7855.00			0.495567			0.247783	+	0.968815i	$0.420298\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	252.500	−	437.343i	0.0157798	−	0.0273314i
$636$		0			0
$637$	−5764.00	−	9983.54i	−0.358521	−	0.620977i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−15385.0	−	26647.6i	−0.948005	−	1.64199i	−0.749621	−	0.661868i	$-0.769764\pi$
$641$	−15385.0	−	26647.6i	−0.948005	−	1.64199i	−0.198384	−	0.980124i	$-0.563569\pi$
$642$		0			0
$643$	9210.00	−	15952.2i	0.564863	−	0.978372i	−0.432199	−	0.901778i	$-0.642262\pi$
$643$	9210.00	−	15952.2i	0.564863	−	0.978372i	0.997062	−	0.0765934i	$-0.0244043\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−10448.0			−0.634858			−0.317429	−	0.948282i	$-0.602820\pi$
$647$	−10448.0			−0.634858			−0.317429	+	0.948282i	$0.602820\pi$
$648$		0			0
$649$	4012.00			0.242658
$650$		0			0
$651$		0			0
$652$		0			0
$653$	9610.50	−	16645.9i	0.575939	−	0.997555i	−0.420000	−	0.907524i	$-0.637970\pi$
$653$	9610.50	−	16645.9i	0.575939	−	0.997555i	0.995939	−	0.0900310i	$-0.0286966\pi$
$654$		0			0
$655$	−257.500	−	446.003i	−0.0153609	−	0.0266058i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	14824.5	+	25676.8i	0.876298	+	1.51779i	0.855373	+	0.518012i	$0.173328\pi$
$659$	14824.5	+	25676.8i	0.876298	+	1.51779i	0.0209249	+	0.999781i	$0.493339\pi$
$660$		0			0
$661$	−2239.00	+	3878.06i	−0.131750	+	0.228198i	−0.924351	−	0.381542i	$-0.875393\pi$
$661$	−2239.00	+	3878.06i	−0.131750	+	0.228198i	0.792601	+	0.609741i	$0.208726\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−846.000			−0.0493330
$666$		0			0
$667$	1500.00			0.0870768
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−2788.00	+	4828.96i	−0.160402	+	0.277824i
$672$		0			0
$673$	7049.50	+	12210.1i	0.403772	+	0.699353i	0.994178	−	0.107753i	$-0.0343657\pi$
$673$	7049.50	+	12210.1i	0.403772	+	0.699353i	−0.590406	+	0.807106i	$0.701032\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	7391.00	+	12801.6i	0.419585	+	0.726743i	0.995898	−	0.0904865i	$-0.0288422\pi$
$677$	7391.00	+	12801.6i	0.419585	+	0.726743i	−0.576312	+	0.817229i	$0.695509\pi$
$678$		0			0
$679$	6259.50	−	10841.8i	0.353781	−	0.612767i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	24620.0			1.37929			0.689647	−	0.724145i	$-0.257766\pi$
$683$	24620.0			1.37929			0.689647	+	0.724145i	$0.257766\pi$
$684$		0			0
$685$	−6.00000			−0.000334669
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−12034.0	+	20843.5i	−0.665398	+	1.15250i
$690$		0			0
$691$	−15358.0	−	26600.8i	−0.845508	−	1.46446i	−0.885180	−	0.465250i	$-0.845965\pi$
$691$	−15358.0	−	26600.8i	−0.845508	−	1.46446i	0.0396718	−	0.999213i	$-0.487369\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	318.000	+	550.792i	0.0173560	+	0.0300615i
$696$		0			0
$697$	−8904.00	+	15422.2i	−0.483878	+	0.838101i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−3147.00			−0.169559			−0.0847793	−	0.996400i	$-0.527019\pi$
$701$	−3147.00			−0.169559			−0.0847793	+	0.996400i	$0.527019\pi$
$702$		0			0
$703$	16356.0			0.877494
$704$		0			0
$705$		0			0
$706$		0			0
$707$	7492.50	−	12977.4i	0.398564	−	0.690332i
$708$		0			0
$709$	11330.0	+	19624.1i	0.600151	+	1.03949i	0.992798	+	0.119803i	$0.0382262\pi$
$709$	11330.0	+	19624.1i	0.600151	+	1.03949i	−0.392647	+	0.919689i	$0.628440\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	3475.00	+	6018.88i	0.182524	+	0.316141i
$714$		0			0
$715$	−374.000	+	647.787i	−0.0195620	+	0.0338823i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−4828.00			−0.250423			−0.125211	−	0.992130i	$-0.539961\pi$
$719$	−4828.00			−0.250423			−0.125211	+	0.992130i	$0.539961\pi$
$720$		0			0
$721$	−13212.0			−0.682442
$722$		0			0
$723$		0			0
$724$		0			0
$725$	1860.00	−	3221.61i	0.0952809	−	0.165031i
$726$		0			0
$727$	1924.50	+	3333.33i	0.0981785	+	0.170050i	0.910931	−	0.412559i	$-0.135365\pi$
$727$	1924.50	+	3333.33i	0.0981785	+	0.170050i	−0.812752	+	0.582609i	$0.802032\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−6776.00	−	11736.4i	−0.342845	−	0.593824i
$732$		0			0
$733$	−5869.00	+	10165.4i	−0.295739	+	0.512234i	−0.975156	−	0.221517i	$-0.928899\pi$
$733$	−5869.00	+	10165.4i	−0.295739	+	0.512234i	0.679418	+	0.733752i	$0.262232\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	10438.0			0.521694
$738$		0			0
$739$	−26824.0			−1.33523			−0.667616	−	0.744506i	$-0.732685\pi$
$739$	−26824.0			−1.33523			−0.667616	+	0.744506i	$0.732685\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−34.0000	+	58.8897i	−0.00167879	+	0.00290775i	−0.866864	−	0.498545i	$-0.833868\pi$
$743$	−34.0000	+	58.8897i	−0.00167879	+	0.00290775i	0.865185	+	0.501453i	$0.167201\pi$
$744$		0			0
$745$	1119.50	+	1939.03i	0.0550541	+	0.0953565i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−2821.50	−	4886.98i	−0.137644	−	0.238406i
$750$		0			0
$751$	18019.5	−	31210.7i	0.875554	−	1.51650i	0.0193821	−	0.999812i	$-0.493830\pi$
$751$	18019.5	−	31210.7i	0.875554	−	1.51650i	0.856172	−	0.516691i	$-0.172837\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	2695.00			0.129909
$756$		0			0
$757$	18650.0			0.895437			0.447718	−	0.894175i	$-0.352237\pi$
$757$	18650.0			0.895437			0.447718	+	0.894175i	$0.352237\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	9424.00	−	16322.8i	0.448909	−	0.777533i	−0.549406	−	0.835555i	$-0.685146\pi$
$761$	9424.00	−	16322.8i	0.448909	−	0.777533i	0.998315	+	0.0580222i	$0.0184794\pi$
$762$		0			0
$763$	2745.00	+	4754.48i	0.130243	+	0.225588i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	5192.00	+	8992.81i	0.244423	+	0.423353i
$768$		0			0
$769$	14607.5	−	25300.9i	0.684993	−	1.18644i	−0.288445	−	0.957496i	$-0.593138\pi$
$769$	14607.5	−	25300.9i	0.684993	−	1.18644i	0.973439	−	0.228947i	$-0.0735283\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−26586.0			−1.23704			−0.618520	−	0.785769i	$-0.712267\pi$
$773$	−26586.0			−1.23704			−0.618520	+	0.785769i	$0.712267\pi$
$774$		0			0
$775$	17236.0			0.798884
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−14946.0	+	25887.2i	−0.687415	+	1.19064i
$780$		0			0
$781$	2516.00	+	4357.84i	0.115275	+	0.199662i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−994.000	−	1721.66i	−0.0451941	−	0.0782785i
$786$		0			0
$787$	−7760.00	+	13440.7i	−0.351479	+	0.608780i	−0.986509	−	0.163708i	$-0.947655\pi$
$787$	−7760.00	+	13440.7i	−0.351479	+	0.608780i	0.635030	+	0.772488i	$0.280988\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	10206.0			0.458766
$792$		0			0
$793$	−14432.0			−0.646274
$794$		0			0
$795$		0			0
$796$		0			0
$797$	3738.50	−	6475.27i	0.166154	−	0.287787i	−0.770911	−	0.636943i	$-0.780199\pi$
$797$	3738.50	−	6475.27i	0.166154	−	0.287787i	0.937064	+	0.349157i	$0.113532\pi$
$798$		0			0
$799$	17640.0	+	30553.4i	0.781049	+	1.35282i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−3680.50	−	6374.81i	−0.161746	−	0.280152i
$804$		0			0
$805$	−225.000	+	389.711i	−0.00985119	+	0.0170628i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	25282.0			1.09872			0.549362	−	0.835584i	$-0.314871\pi$
$809$	25282.0			1.09872			0.549362	+	0.835584i	$0.314871\pi$
$810$		0			0
$811$	−35582.0			−1.54063			−0.770316	−	0.637662i	$-0.779902\pi$
$811$	−35582.0			−1.54063			−0.770316	+	0.637662i	$0.779902\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−1290.00	+	2234.35i	−0.0554438	+	0.0960315i
$816$		0			0
$817$	−11374.0	−	19700.3i	−0.487057	−	0.843608i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	18753.0	+	32481.1i	0.797179	+	1.38076i	0.921446	+	0.388506i	$0.127009\pi$
$821$	18753.0	+	32481.1i	0.797179	+	1.38076i	−0.124267	+	0.992249i	$0.539658\pi$
$822$		0			0
$823$	−6092.50	+	10552.5i	−0.258045	+	0.446947i	−0.965718	−	0.259593i	$-0.916412\pi$
$823$	−6092.50	+	10552.5i	−0.258045	+	0.446947i	0.707673	+	0.706540i	$0.249745\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	8128.00			0.341763			0.170882	−	0.985292i	$-0.445338\pi$
$827$	8128.00			0.341763			0.170882	+	0.985292i	$0.445338\pi$
$828$		0			0
$829$	−39542.0			−1.65664			−0.828318	−	0.560259i	$-0.810702\pi$
$829$	−39542.0			−1.65664			−0.828318	+	0.560259i	$0.810702\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−7336.00	+	12706.3i	−0.305135	+	0.528509i
$834$		0			0
$835$	−939.000	−	1626.40i	−0.0389167	−	0.0674057i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	20184.0	+	34959.7i	0.830547	+	1.43855i	0.897605	+	0.440801i	$0.145305\pi$
$839$	20184.0	+	34959.7i	0.830547	+	1.43855i	−0.0670578	+	0.997749i	$0.521361\pi$
$840$		0			0
$841$	11744.5	−	20342.1i	0.481549	−	0.834067i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	261.000			0.0106256
$846$		0			0
$847$	9378.00			0.380439
$848$		0			0
$849$		0			0
$850$		0			0
$851$	4350.00	−	7534.42i	0.175225	−	0.303498i
$852$		0			0
$853$	10097.0	+	17488.5i	0.405293	+	0.701988i	0.994355	−	0.106100i	$-0.0338363\pi$
$853$	10097.0	+	17488.5i	0.405293	+	0.701988i	−0.589063	+	0.808087i	$0.700503\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	4332.00	+	7503.24i	0.172670	+	0.299073i	0.939353	−	0.342953i	$-0.111427\pi$
$857$	4332.00	+	7503.24i	0.172670	+	0.299073i	−0.766682	+	0.642027i	$0.778094\pi$
$858$		0			0
$859$	7836.00	−	13572.4i	0.311247	−	0.539095i	−0.667386	−	0.744712i	$-0.732587\pi$
$859$	7836.00	−	13572.4i	0.311247	−	0.539095i	0.978633	+	0.205617i	$0.0659201\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	46076.0			1.81743			0.908717	−	0.417413i	$-0.137063\pi$
$863$	46076.0			1.81743			0.908717	+	0.417413i	$0.137063\pi$
$864$		0			0
$865$	−2163.00			−0.0850222
$866$		0			0
$867$		0			0
$868$		0			0
$869$	476.000	−	824.456i	0.0185814	−	0.0321838i
$870$		0			0
$871$	13508.0	+	23396.5i	0.525489	+	0.910174i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	1120.50	+	1940.76i	0.0432912	+	0.0749826i
$876$		0			0
$877$	14463.0	−	25050.7i	0.556877	−	0.964539i	−0.440878	−	0.897567i	$-0.645333\pi$
$877$	14463.0	−	25050.7i	0.556877	−	0.964539i	0.997755	−	0.0669717i	$-0.0213337\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	10372.0			0.396642			0.198321	−	0.980137i	$-0.436451\pi$
$881$	10372.0			0.396642			0.198321	+	0.980137i	$0.436451\pi$
$882$		0			0
$883$	−15502.0			−0.590808			−0.295404	−	0.955372i	$-0.595454\pi$
$883$	−15502.0			−0.590808			−0.295404	+	0.955372i	$0.595454\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−14762.0	+	25568.5i	−0.558804	+	0.967878i	0.438792	+	0.898589i	$0.355406\pi$
$887$	−14762.0	+	25568.5i	−0.558804	+	0.967878i	−0.997597	+	0.0692890i	$0.977927\pi$
$888$		0			0
$889$	2272.50	+	3936.09i	0.0857336	+	0.148495i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	29610.0	+	51286.0i	1.10959	+	1.92186i
$894$		0			0
$895$	−1090.50	+	1888.80i	−0.0407278	+	0.0705426i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−4170.00			−0.154702
$900$		0			0
$901$	30632.0			1.13263
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−744.000	+	1288.65i	−0.0273275	+	0.0473326i
$906$		0			0
$907$	−13613.0	−	23578.4i	−0.498360	−	0.863184i	0.501639	−	0.865077i	$-0.332731\pi$
$907$	−13613.0	−	23578.4i	−0.498360	−	0.863184i	−0.999998	+	0.00189302i	$0.999397\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−26755.0	−	46341.0i	−0.973033	−	1.68534i	−0.686280	−	0.727337i	$-0.740758\pi$
$911$	−26755.0	−	46341.0i	−0.973033	−	1.68534i	−0.286752	−	0.958005i	$-0.592576\pi$
$912$		0			0
$913$	−10412.5	+	18035.0i	−0.377441	+	0.653747i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	4635.00			0.166915
$918$		0			0
$919$	−443.000			−0.0159012			−0.00795061	−	0.999968i	$-0.502531\pi$
$919$	−443.000			−0.0159012			−0.00795061	+	0.999968i	$0.502531\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−6512.00	+	11279.1i	−0.232227	+	0.402228i
$924$		0			0
$925$	−10788.0	−	18685.4i	−0.383467	−	0.664185i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	13630.0	+	23607.9i	0.481363	+	0.833744i	0.999771	−	0.0213886i	$-0.00680873\pi$
$929$	13630.0	+	23607.9i	0.481363	+	0.833744i	−0.518409	+	0.855133i	$0.673475\pi$
$930$		0			0
$931$	−12314.0	+	21328.5i	−0.433486	+	0.750819i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	952.000			0.0332981
$936$		0			0
$937$	21075.0			0.734781			0.367391	−	0.930067i	$-0.380251\pi$
$937$	21075.0			0.734781			0.367391	+	0.930067i	$0.380251\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	11374.5	−	19701.2i	0.394047	−	0.682509i	−0.598932	−	0.800800i	$-0.704408\pi$
$941$	11374.5	−	19701.2i	0.394047	−	0.682509i	0.992979	+	0.118291i	$0.0377414\pi$
$942$		0			0
$943$	7950.00	+	13769.8i	0.274536	+	0.475511i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	18100.5	+	31351.0i	0.621106	+	1.07579i	0.989280	+	0.146030i	$0.0466496\pi$
$947$	18100.5	+	31351.0i	0.621106	+	1.07579i	−0.368174	+	0.929757i	$0.620017\pi$
$948$		0			0
$949$	9526.00	−	16499.5i	0.325845	−	0.564380i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	4428.00			0.150511			0.0752555	−	0.997164i	$-0.476023\pi$
$953$	4428.00			0.150511			0.0752555	+	0.997164i	$0.476023\pi$
$954$		0			0
$955$	1764.00			0.0597714
$956$		0			0
$957$		0			0
$958$		0			0
$959$	27.0000	−	46.7654i	0.000909151	−	0.00157470i
$960$		0			0
$961$	5235.00	+	9067.29i	0.175724	+	0.304363i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−1773.50	−	3071.79i	−0.0591616	−	0.102471i
$966$		0			0
$967$	−13463.5	+	23319.5i	−0.447732	+	0.775495i	−0.998238	−	0.0593365i	$-0.981102\pi$
$967$	−13463.5	+	23319.5i	−0.447732	+	0.775495i	0.550506	+	0.834831i	$0.314435\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	47961.0			1.58511			0.792555	−	0.609800i	$-0.208750\pi$
$971$	47961.0			1.58511			0.792555	+	0.609800i	$0.208750\pi$
$972$		0			0
$973$	−5724.00			−0.188595
$974$		0			0
$975$		0			0
$976$		0			0
$977$	8373.00	−	14502.5i	0.274182	−	0.474897i	−0.695746	−	0.718288i	$-0.744926\pi$
$977$	8373.00	−	14502.5i	0.274182	−	0.474897i	0.969928	+	0.243390i	$0.0782595\pi$
$978$		0			0
$979$	12801.0	+	22172.0i	0.417898	+	0.723820i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	18573.0	+	32169.4i	0.602631	+	1.04379i	0.992421	+	0.122884i	$0.0392144\pi$
$983$	18573.0	+	32169.4i	0.602631	+	1.04379i	−0.389790	+	0.920904i	$0.627452\pi$
$984$		0			0
$985$	2470.50	−	4279.03i	0.0799154	−	0.138418i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−12100.0			−0.389037
$990$		0			0
$991$	42079.0			1.34882			0.674411	−	0.738356i	$-0.264397\pi$
$991$	42079.0			1.34882			0.674411	+	0.738356i	$0.264397\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−743.500	+	1287.78i	−0.0236890	+	0.0410305i
$996$		0			0
$997$	−23246.0	−	40263.3i	−0.738423	−	1.27899i	−0.953205	−	0.302325i	$-0.902237\pi$
$997$	−23246.0	−	40263.3i	−0.738423	−	1.27899i	0.214781	−	0.976662i	$-0.431096\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	648.4.i.g.433.1		2
3.2	odd	2		648.4.i.f.433.1		2
9.2	odd	6		648.4.i.f.217.1		2
9.4	even	3		216.4.a.b.1.1	✓	1
9.5	odd	6		216.4.a.c.1.1	yes	1
9.7	even	3	inner	648.4.i.g.217.1		2
36.23	even	6		432.4.a.i.1.1		1
36.31	odd	6		432.4.a.f.1.1		1
72.5	odd	6		1728.4.a.m.1.1		1
72.13	even	6		1728.4.a.s.1.1		1
72.59	even	6		1728.4.a.n.1.1		1
72.67	odd	6		1728.4.a.t.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.4.a.b.1.1	✓	1	9.4	even	3
216.4.a.c.1.1	yes	1	9.5	odd	6
432.4.a.f.1.1		1	36.31	odd	6
432.4.a.i.1.1		1	36.23	even	6
648.4.i.f.217.1		2	9.2	odd	6
648.4.i.f.433.1		2	3.2	odd	2
648.4.i.g.217.1		2	9.7	even	3	inner
648.4.i.g.433.1		2	1.1	even	1	trivial
1728.4.a.m.1.1		1	72.5	odd	6
1728.4.a.n.1.1		1	72.59	even	6
1728.4.a.s.1.1		1	72.13	even	6
1728.4.a.t.1.1		1	72.67	odd	6

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:	\( N \)	\(=\)	\( 648 = 2^{3} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	648.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{5} +(4.50000 + 7.79423i) q^{7} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{5} +(4.50000 + 7.79423i) q^{7} +(-8.50000 - 14.7224i) q^{11} +(22.0000 - 38.1051i) q^{13} -56.0000 q^{17} -94.0000 q^{19} +(-25.0000 + 43.3013i) q^{23} +(62.0000 + 107.387i) q^{25} +(-15.0000 - 25.9808i) q^{29} +(69.5000 - 120.378i) q^{31} +9.00000 q^{35} -174.000 q^{37} +(159.000 - 275.396i) q^{41} +(121.000 + 209.578i) q^{43} +(-315.000 - 545.596i) q^{47} +(131.000 - 226.899i) q^{49} -547.000 q^{53} -17.0000 q^{55} +(-118.000 + 204.382i) q^{59} +(-164.000 - 284.056i) q^{61} +(-22.0000 - 38.1051i) q^{65} +(-307.000 + 531.740i) q^{67} -296.000 q^{71} +433.000 q^{73} +(76.5000 - 132.502i) q^{77} +(28.0000 + 48.4974i) q^{79} +(-612.500 - 1060.88i) q^{83} +(-28.0000 + 48.4974i) q^{85} -1506.00 q^{89} +396.000 q^{91} +(-47.0000 + 81.4064i) q^{95} +(-695.500 - 1204.64i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{5} + 9 q^{7}+O(q^{10}) \) 2 * q + q^5 + 9 * q^7	\( 2 q + q^{5} + 9 q^{7} - 17 q^{11} + 44 q^{13} - 112 q^{17} - 188 q^{19} - 50 q^{23} + 124 q^{25} - 30 q^{29} + 139 q^{31} + 18 q^{35} - 348 q^{37} + 318 q^{41} + 242 q^{43} - 630 q^{47} + 262 q^{49} - 1094 q^{53} - 34 q^{55} - 236 q^{59} - 328 q^{61} - 44 q^{65} - 614 q^{67} - 592 q^{71} + 866 q^{73} + 153 q^{77} + 56 q^{79} - 1225 q^{83} - 56 q^{85} - 3012 q^{89} + 792 q^{91} - 94 q^{95} - 1391 q^{97}+O(q^{100}) \) 2 * q + q^5 + 9 * q^7 - 17 * q^11 + 44 * q^13 - 112 * q^17 - 188 * q^19 - 50 * q^23 + 124 * q^25 - 30 * q^29 + 139 * q^31 + 18 * q^35 - 348 * q^37 + 318 * q^41 + 242 * q^43 - 630 * q^47 + 262 * q^49 - 1094 * q^53 - 34 * q^55 - 236 * q^59 - 328 * q^61 - 44 * q^65 - 614 * q^67 - 592 * q^71 + 866 * q^73 + 153 * q^77 + 56 * q^79 - 1225 * q^83 - 56 * q^85 - 3012 * q^89 + 792 * q^91 - 94 * q^95 - 1391 * q^97

Introduction

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