LMFDB - Embedded newform 1512.2.q.c.793.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1512,2,Mod(793,1512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1512, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2, 2]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1512.793");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1512 = 2^{3} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1512.q (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:	$12.0733807856$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			793.11
Character	$\chi$	$=$	1512.793
Dual form			1512.2.q.c.1369.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.92048 + 3.32636i) q^{5} +(-2.55336 - 0.693065i) q^{7} +O(q^{10})$	$q+(1.92048 + 3.32636i) q^{5} +(-2.55336 - 0.693065i) q^{7} +(0.903316 - 1.56459i) q^{11} +(-0.692713 + 1.19981i) q^{13} +(0.833405 + 1.44350i) q^{17} +(-0.0802084 + 0.138925i) q^{19} +(1.60019 + 2.77161i) q^{23} +(-4.87646 + 8.44627i) q^{25} +(3.78000 + 6.54716i) q^{29} +3.22021 q^{31} +(-2.59829 - 9.82442i) q^{35} +(1.58395 - 2.74348i) q^{37} +(-6.00329 + 10.3980i) q^{41} +(3.45480 + 5.98389i) q^{43} -11.4384 q^{47} +(6.03932 + 3.53929i) q^{49} +(-1.37450 - 2.38071i) q^{53} +6.93918 q^{55} -15.0705 q^{59} -9.20285 q^{61} -5.32136 q^{65} -12.3366 q^{67} +6.93289 q^{71} +(-6.22457 - 10.7813i) q^{73} +(-3.39085 + 3.36891i) q^{77} +16.0743 q^{79} +(1.45280 + 2.51633i) q^{83} +(-3.20107 + 5.54441i) q^{85} +(-5.04034 + 8.73012i) q^{89} +(2.60030 - 2.58347i) q^{91} -0.616153 q^{95} +(4.18830 + 7.25435i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 3 q^{5} - 5 q^{7}+O(q^{10}) $ 22 * q - 3 * q^5 - 5 * q^7	$ 22 q - 3 q^{5} - 5 q^{7} + 3 q^{11} - 3 q^{13} - 7 q^{17} - q^{19} - 2 q^{23} - 10 q^{25} - 9 q^{29} + 8 q^{31} - 14 q^{35} + 2 q^{37} - 16 q^{41} + 10 q^{47} + 15 q^{49} - 11 q^{53} + 22 q^{55} - 38 q^{59} + 26 q^{61} + 26 q^{65} - 52 q^{67} + 48 q^{71} - 35 q^{73} - 17 q^{77} - 20 q^{79} + 28 q^{83} - 20 q^{85} - 6 q^{89} - 37 q^{91} + 24 q^{95} - 29 q^{97}+O(q^{100}) $ 22 * q - 3 * q^5 - 5 * q^7 + 3 * q^11 - 3 * q^13 - 7 * q^17 - q^19 - 2 * q^23 - 10 * q^25 - 9 * q^29 + 8 * q^31 - 14 * q^35 + 2 * q^37 - 16 * q^41 + 10 * q^47 + 15 * q^49 - 11 * q^53 + 22 * q^55 - 38 * q^59 + 26 * q^61 + 26 * q^65 - 52 * q^67 + 48 * q^71 - 35 * q^73 - 17 * q^77 - 20 * q^79 + 28 * q^83 - 20 * q^85 - 6 * q^89 - 37 * q^91 + 24 * q^95 - 29 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1081$	$1135$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	1.92048	+	3.32636i	0.858863	+	1.48759i	0.873014	+	0.487694i	$0.162162\pi$
$5$	1.92048	+	3.32636i	0.858863	+	1.48759i	−0.0141515	+	0.999900i	$0.504505\pi$
$6$		0			0
$7$	−2.55336	−	0.693065i	−0.965080	−	0.261954i
$7$	−2.55336	−	0.693065i	−0.965080	−	0.261954i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	0.903316	−	1.56459i	0.272360	−	0.471741i	−0.697106	−	0.716968i	$-0.745529\pi$
$11$	0.903316	−	1.56459i	0.272360	−	0.471741i	0.969466	+	0.245227i	$0.0788625\pi$
$12$		0			0
$13$	−0.692713	+	1.19981i	−0.192124	+	0.332769i	−0.945954	−	0.324301i	$-0.894871\pi$
$13$	−0.692713	+	1.19981i	−0.192124	+	0.332769i	0.753830	+	0.657070i	$0.228204\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.833405	+	1.44350i	0.202130	+	0.350100i	0.949215	−	0.314629i	$-0.101880\pi$
$17$	0.833405	+	1.44350i	0.202130	+	0.350100i	−0.747084	+	0.664729i	$0.768547\pi$
$18$		0			0
$19$	−0.0802084	+	0.138925i	−0.0184011	+	0.0318716i	−0.875079	−	0.483980i	$-0.839191\pi$
$19$	−0.0802084	+	0.138925i	−0.0184011	+	0.0318716i	0.856678	+	0.515851i	$0.172524\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	1.60019	+	2.77161i	0.333663	+	0.577921i	0.983227	−	0.182386i	$-0.0583819\pi$
$23$	1.60019	+	2.77161i	0.333663	+	0.577921i	−0.649564	+	0.760307i	$0.725049\pi$
$24$		0			0
$25$	−4.87646	+	8.44627i	−0.975291	+	1.68925i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	3.78000	+	6.54716i	0.701929	+	1.21578i	0.967788	+	0.251765i	$0.0810110\pi$
$29$	3.78000	+	6.54716i	0.701929	+	1.21578i	−0.265859	+	0.964012i	$0.585656\pi$
$30$		0			0
$31$	3.22021			0.578367			0.289184	−	0.957274i	$-0.406616\pi$
$31$	3.22021			0.578367			0.289184	+	0.957274i	$0.406616\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−2.59829	−	9.82442i	−0.439190	−	1.66063i
$36$		0			0
$37$	1.58395	−	2.74348i	0.260399	−	0.451025i	−0.705949	−	0.708263i	$-0.749479\pi$
$37$	1.58395	−	2.74348i	0.260399	−	0.451025i	0.966348	+	0.257238i	$0.0828124\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−6.00329	+	10.3980i	−0.937556	+	1.62389i	−0.167545	+	0.985864i	$0.553584\pi$
$41$	−6.00329	+	10.3980i	−0.937556	+	1.62389i	−0.770011	+	0.638030i	$0.779750\pi$
$42$		0			0
$43$	3.45480	+	5.98389i	0.526852	+	0.912535i	0.999510	+	0.0312891i	$0.00996125\pi$
$43$	3.45480	+	5.98389i	0.526852	+	0.912535i	−0.472658	+	0.881246i	$0.656705\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−11.4384			−1.66846			−0.834232	−	0.551414i	$-0.814089\pi$
$47$	−11.4384			−1.66846			−0.834232	+	0.551414i	$0.814089\pi$
$48$		0			0
$49$	6.03932	+	3.53929i	0.862760	+	0.505613i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−1.37450	−	2.38071i	−0.188802	−	0.327015i	0.756049	−	0.654515i	$-0.227127\pi$
$53$	−1.37450	−	2.38071i	−0.188802	−	0.327015i	−0.944851	+	0.327500i	$0.893794\pi$
$54$		0			0
$55$	6.93918			0.935679
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−15.0705			−1.96202			−0.981009	−	0.193964i	$-0.937866\pi$
$59$	−15.0705			−1.96202			−0.981009	+	0.193964i	$0.937866\pi$
$60$		0			0
$61$	−9.20285			−1.17830			−0.589152	−	0.808022i	$-0.700538\pi$
$61$	−9.20285			−1.17830			−0.589152	+	0.808022i	$0.700538\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−5.32136			−0.660033
$66$		0			0
$67$	−12.3366			−1.50716			−0.753578	−	0.657359i	$-0.771674\pi$
$67$	−12.3366			−1.50716			−0.753578	+	0.657359i	$0.771674\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	6.93289			0.822783			0.411391	−	0.911459i	$-0.365043\pi$
$71$	6.93289			0.822783			0.411391	+	0.911459i	$0.365043\pi$
$72$		0			0
$73$	−6.22457	−	10.7813i	−0.728531	−	1.26185i	−0.957504	−	0.288420i	$-0.906870\pi$
$73$	−6.22457	−	10.7813i	−0.728531	−	1.26185i	0.228973	−	0.973433i	$-0.426463\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−3.39085	+	3.36891i	−0.386424	+	0.383922i
$78$		0			0
$79$	16.0743			1.80850			0.904251	−	0.427001i	$-0.140430\pi$
$79$	16.0743			1.80850			0.904251	+	0.427001i	$0.140430\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	1.45280	+	2.51633i	0.159466	+	0.276203i	0.934676	−	0.355500i	$-0.115689\pi$
$83$	1.45280	+	2.51633i	0.159466	+	0.276203i	−0.775210	+	0.631703i	$0.782356\pi$
$84$		0			0
$85$	−3.20107	+	5.54441i	−0.347205	+	0.601376i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−5.04034	+	8.73012i	−0.534275	+	0.925391i	0.464923	+	0.885351i	$0.346082\pi$
$89$	−5.04034	+	8.73012i	−0.534275	+	0.925391i	−0.999198	+	0.0400399i	$0.987251\pi$
$90$		0			0
$91$	2.60030	−	2.58347i	0.272585	−	0.270821i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−0.616153			−0.0632160
$96$		0			0
$97$	4.18830	+	7.25435i	0.425257	+	0.736567i	0.996444	−	0.0842527i	$-0.0268503\pi$
$97$	4.18830	+	7.25435i	0.425257	+	0.736567i	−0.571187	+	0.820820i	$0.693517\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	4.05750	−	7.02780i	0.403736	−	0.699292i	−0.590437	−	0.807084i	$-0.701045\pi$
$101$	4.05750	−	7.02780i	0.403736	−	0.699292i	0.994173	+	0.107792i	$0.0343780\pi$
$102$		0			0
$103$	3.76891	+	6.52794i	0.371362	+	0.643217i	0.989775	−	0.142635i	$-0.0455577\pi$
$103$	3.76891	+	6.52794i	0.371362	+	0.643217i	−0.618414	+	0.785853i	$0.712224\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	2.95731	−	5.12221i	0.285894	−	0.495183i	−0.686932	−	0.726722i	$-0.741043\pi$
$107$	2.95731	−	5.12221i	0.285894	−	0.495183i	0.972826	+	0.231539i	$0.0743762\pi$
$108$		0			0
$109$	−4.48409	−	7.76668i	−0.429498	−	0.743913i	0.567331	−	0.823490i	$-0.307976\pi$
$109$	−4.48409	−	7.76668i	−0.429498	−	0.743913i	−0.996829	+	0.0795776i	$0.974643\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	7.98131	−	13.8240i	0.750819	−	1.30046i	−0.196608	−	0.980482i	$-0.562993\pi$
$113$	7.98131	−	13.8240i	0.750819	−	1.30046i	0.947426	−	0.319974i	$-0.103674\pi$
$114$		0			0
$115$	−6.14626	+	10.6456i	−0.573142	+	0.992710i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−1.12755	−	4.26338i	−0.103362	−	0.390824i
$120$		0			0
$121$	3.86804	+	6.69964i	0.351640	+	0.609059i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−18.2557			−1.63284
$126$		0			0
$127$	8.60913			0.763937			0.381968	−	0.924175i	$-0.375246\pi$
$127$	8.60913			0.763937			0.381968	+	0.924175i	$0.375246\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−0.964831	−	1.67114i	−0.0842976	−	0.146008i	0.820794	−	0.571224i	$-0.193531\pi$
$131$	−0.964831	−	1.67114i	−0.0842976	−	0.146008i	−0.905092	+	0.425216i	$0.860198\pi$
$132$		0			0
$133$	0.301085	−	0.299136i	0.0261074	−	0.0259384i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−1.85442	+	3.21195i	−0.158434	+	0.274416i	−0.934304	−	0.356477i	$-0.883978\pi$
$137$	−1.85442	+	3.21195i	−0.158434	+	0.274416i	0.775870	+	0.630893i	$0.217311\pi$
$138$		0			0
$139$	0.134568	−	0.233079i	0.0114139	−	0.0197695i	−0.860262	−	0.509852i	$-0.829700\pi$
$139$	0.134568	−	0.233079i	0.0114139	−	0.0197695i	0.871676	+	0.490083i	$0.163033\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	1.25148	+	2.16762i	0.104654	+	0.181266i
$144$		0			0
$145$	−14.5188	+	25.1473i	−1.20572	+	2.08837i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	4.15880	+	7.20325i	0.340702	+	0.590113i	0.984563	−	0.175029i	$-0.0560019\pi$
$149$	4.15880	+	7.20325i	0.340702	+	0.590113i	−0.643861	+	0.765142i	$0.722669\pi$
$150$		0			0
$151$	−4.87069	+	8.43628i	−0.396371	+	0.686535i	−0.993275	−	0.115778i	$-0.963064\pi$
$151$	−4.87069	+	8.43628i	−0.396371	+	0.686535i	0.596904	+	0.802313i	$0.296397\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	6.18434	+	10.7116i	0.496738	+	0.860376i
$156$		0			0
$157$	24.2580			1.93600			0.968001	−	0.250947i	$-0.0807420\pi$
$157$	24.2580			1.93600			0.968001	+	0.250947i	$0.0807420\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−2.16496	−	8.18597i	−0.170623	−	0.645145i
$162$		0			0
$163$	3.91401	−	6.77927i	0.306569	−	0.530993i	−0.671040	−	0.741421i	$-0.734152\pi$
$163$	3.91401	−	6.77927i	0.306569	−	0.530993i	0.977609	+	0.210428i	$0.0674857\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	2.15395	−	3.73076i	0.166678	−	0.288695i	−0.770572	−	0.637353i	$-0.780029\pi$
$167$	2.15395	−	3.73076i	0.166678	−	0.288695i	0.937250	+	0.348658i	$0.113363\pi$
$168$		0			0
$169$	5.54030	+	9.59608i	0.426177	+	0.738160i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	17.3359			1.31803			0.659014	−	0.752131i	$-0.270974\pi$
$173$	17.3359			1.31803			0.659014	+	0.752131i	$0.270974\pi$
$174$		0			0
$175$	18.3052	−	18.1867i	1.38374	−	1.37478i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	9.68644	+	16.7774i	0.723998	+	1.25400i	0.959385	+	0.282100i	$0.0910310\pi$
$179$	9.68644	+	16.7774i	0.723998	+	1.25400i	−0.235387	+	0.971902i	$0.575636\pi$
$180$		0			0
$181$	2.89036			0.214839			0.107420	−	0.994214i	$-0.465741\pi$
$181$	2.89036			0.214839			0.107420	+	0.994214i	$0.465741\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	12.1677			0.894590
$186$		0			0
$187$	3.01131			0.220209
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−3.70044			−0.267755			−0.133877	−	0.990998i	$-0.542743\pi$
$191$	−3.70044			−0.267755			−0.133877	+	0.990998i	$0.542743\pi$
$192$		0			0
$193$	−12.7670			−0.918991			−0.459495	−	0.888180i	$-0.651970\pi$
$193$	−12.7670			−0.918991			−0.459495	+	0.888180i	$0.651970\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−2.44715			−0.174352			−0.0871762	−	0.996193i	$-0.527784\pi$
$197$	−2.44715			−0.174352			−0.0871762	+	0.996193i	$0.527784\pi$
$198$		0			0
$199$	2.24829	+	3.89415i	0.159377	+	0.276049i	0.934644	−	0.355584i	$-0.115718\pi$
$199$	2.24829	+	3.89415i	0.159377	+	0.276049i	−0.775267	+	0.631633i	$0.782385\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−5.11411	−	19.3371i	−0.358940	−	1.35720i
$204$		0			0
$205$	−46.1167			−3.22093
$206$		0			0
$207$		0			0
$208$		0			0
$209$	0.144907	+	0.250986i	0.0100234	+	0.0173611i
$210$		0			0
$211$	1.09087	−	1.88945i	0.0750987	−	0.130075i	−0.826030	−	0.563625i	$-0.809406\pi$
$211$	1.09087	−	1.88945i	0.0750987	−	0.130075i	0.901129	+	0.433551i	$0.142739\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−13.2697	+	22.9838i	−0.904988	+	1.56749i
$216$		0			0
$217$	−8.22237	−	2.23182i	−0.558171	−	0.151506i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−2.30924			−0.155336
$222$		0			0
$223$	−2.87967	−	4.98773i	−0.192837	−	0.334003i	0.753352	−	0.657617i	$-0.228436\pi$
$223$	−2.87967	−	4.98773i	−0.192837	−	0.334003i	−0.946189	+	0.323614i	$0.895102\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	8.29135	−	14.3610i	0.550316	−	0.953175i	−0.447935	−	0.894066i	$-0.647841\pi$
$227$	8.29135	−	14.3610i	0.550316	−	0.953175i	0.998252	−	0.0591094i	$-0.0188261\pi$
$228$		0			0
$229$	7.29688	+	12.6386i	0.482191	+	0.835180i	0.999791	−	0.0204432i	$-0.00650771\pi$
$229$	7.29688	+	12.6386i	0.482191	+	0.835180i	−0.517600	+	0.855623i	$0.673174\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−0.949438	+	1.64448i	−0.0621998	+	0.107733i	−0.895448	−	0.445165i	$-0.853145\pi$
$233$	−0.949438	+	1.64448i	−0.0621998	+	0.107733i	0.833249	+	0.552898i	$0.186478\pi$
$234$		0			0
$235$	−21.9672	−	38.0483i	−1.43298	−	2.48200i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	4.46351	−	7.73103i	0.288721	−	0.500079i	−0.684784	−	0.728746i	$-0.740103\pi$
$239$	4.46351	−	7.73103i	0.288721	−	0.500079i	0.973505	+	0.228667i	$0.0734368\pi$
$240$		0			0
$241$	12.1465	−	21.0383i	0.782423	−	1.35520i	−0.148104	−	0.988972i	$-0.547317\pi$
$241$	12.1465	−	21.0383i	0.782423	−	1.35520i	0.930527	−	0.366224i	$-0.119350\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−0.174600	+	26.8861i	−0.0111548	+	1.71769i
$246$		0			0
$247$	−0.111123	−	0.192470i	−0.00707057	−	0.0122466i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	5.64873			0.356545			0.178272	−	0.983981i	$-0.442949\pi$
$251$	5.64873			0.356545			0.178272	+	0.983981i	$0.442949\pi$
$252$		0			0
$253$	5.78191			0.363506
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−11.7856	−	20.4132i	−0.735163	−	1.27334i	−0.954652	−	0.297724i	$-0.903772\pi$
$257$	−11.7856	−	20.4132i	−0.735163	−	1.27334i	0.219489	−	0.975615i	$-0.429561\pi$
$258$		0			0
$259$	−5.94580	+	5.90731i	−0.369454	+	0.367063i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	12.8203	−	22.2053i	0.790531	−	1.36924i	−0.135108	−	0.990831i	$-0.543138\pi$
$263$	12.8203	−	22.2053i	0.790531	−	1.36924i	0.925639	−	0.378409i	$-0.123529\pi$
$264$		0			0
$265$	5.27940	−	9.14419i	0.324311	−	0.561723i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	8.27239	+	14.3282i	0.504376	+	0.873606i	0.999987	+	0.00506090i	$0.00161094\pi$
$269$	8.27239	+	14.3282i	0.504376	+	0.873606i	−0.495611	+	0.868545i	$0.665056\pi$
$270$		0			0
$271$	8.90748	−	15.4282i	0.541091	−	0.937197i	−0.457751	−	0.889081i	$-0.651345\pi$
$271$	8.90748	−	15.4282i	0.541091	−	0.937197i	0.998842	−	0.0481166i	$-0.0153219\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	8.80996	+	15.2593i	0.531260	+	0.920170i
$276$		0			0
$277$	2.92191	−	5.06089i	0.175560	−	0.304080i	−0.764795	−	0.644274i	$-0.777160\pi$
$277$	2.92191	−	5.06089i	0.175560	−	0.304080i	0.940355	+	0.340194i	$0.110493\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	10.5591	+	18.2889i	0.629905	+	1.09103i	0.987570	+	0.157177i	$0.0502394\pi$
$281$	10.5591	+	18.2889i	0.629905	+	1.09103i	−0.357666	+	0.933850i	$0.616427\pi$
$282$		0			0
$283$	−12.7762			−0.759468			−0.379734	−	0.925096i	$-0.623984\pi$
$283$	−12.7762			−0.759468			−0.379734	+	0.925096i	$0.623984\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	22.5351	−	22.3892i	1.33020	−	1.32159i
$288$		0			0
$289$	7.11087	−	12.3164i	0.418287	−	0.724494i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−5.93828	+	10.2854i	−0.346918	+	0.600880i	−0.985700	−	0.168508i	$-0.946105\pi$
$293$	−5.93828	+	10.2854i	−0.346918	+	0.600880i	0.638782	+	0.769388i	$0.279439\pi$
$294$		0			0
$295$	−28.9426	−	50.1301i	−1.68510	−	2.91869i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−4.43389			−0.256419
$300$		0			0
$301$	−4.67413	−	17.6734i	−0.269413	−	1.01868i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−17.6739	−	30.6120i	−1.01200	−	1.75284i
$306$		0			0
$307$	−3.93298			−0.224467			−0.112234	−	0.993682i	$-0.535800\pi$
$307$	−3.93298			−0.224467			−0.112234	+	0.993682i	$0.535800\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−1.98221			−0.112401			−0.0562005	−	0.998420i	$-0.517899\pi$
$311$	−1.98221			−0.112401			−0.0562005	+	0.998420i	$0.517899\pi$
$312$		0			0
$313$	20.4995			1.15870			0.579349	−	0.815080i	$-0.303307\pi$
$313$	20.4995			1.15870			0.579349	+	0.815080i	$0.303307\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−9.51416			−0.534369			−0.267184	−	0.963645i	$-0.586093\pi$
$317$	−9.51416			−0.534369			−0.267184	+	0.963645i	$0.586093\pi$
$318$		0			0
$319$	13.6581			0.764709
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−0.267384			−0.0148777
$324$		0			0
$325$	−6.75597	−	11.7017i	−0.374754	−	0.649093i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	29.2064	+	7.92756i	1.61020	+	0.437061i
$330$		0			0
$331$	1.52986			0.0840886			0.0420443	−	0.999116i	$-0.486613\pi$
$331$	1.52986			0.0840886			0.0420443	+	0.999116i	$0.486613\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−23.6921	−	41.0360i	−1.29444	−	2.24204i
$336$		0			0
$337$	10.6972	−	18.5281i	0.582714	−	1.00929i	−0.412442	−	0.910984i	$-0.635324\pi$
$337$	10.6972	−	18.5281i	0.582714	−	1.00929i	0.995156	−	0.0983063i	$-0.0313425\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	2.90887	−	5.03831i	0.157524	−	0.272840i
$342$		0			0
$343$	−12.9676	−	13.2227i	−0.700185	−	0.713961i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−5.14381			−0.276134			−0.138067	−	0.990423i	$-0.544089\pi$
$347$	−5.14381			−0.276134			−0.138067	+	0.990423i	$0.544089\pi$
$348$		0			0
$349$	0.207526	+	0.359446i	0.0111086	+	0.0192407i	0.871526	−	0.490349i	$-0.163131\pi$
$349$	0.207526	+	0.359446i	0.0111086	+	0.0192407i	−0.860418	+	0.509590i	$0.829797\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−6.04122	+	10.4637i	−0.321542	+	0.556926i	−0.980806	−	0.194985i	$-0.937534\pi$
$353$	−6.04122	+	10.4637i	−0.321542	+	0.556926i	0.659265	+	0.751911i	$0.270868\pi$
$354$		0			0
$355$	13.3145	+	23.0613i	0.706658	+	1.22397i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	8.14926	−	14.1149i	0.430102	−	0.744958i	−0.566780	−	0.823869i	$-0.691811\pi$
$359$	8.14926	−	14.1149i	0.430102	−	0.744958i	0.996882	+	0.0789113i	$0.0251444\pi$
$360$		0			0
$361$	9.48713	+	16.4322i	0.499323	+	0.864852i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	23.9083	−	41.4104i	1.25142	−	2.16752i
$366$		0			0
$367$	−17.3500	+	30.0511i	−0.905664	+	1.56866i	−0.0856404	+	0.996326i	$0.527294\pi$
$367$	−17.3500	+	30.0511i	−0.905664	+	1.56866i	−0.820024	+	0.572330i	$0.806040\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	1.85962	+	7.03143i	0.0965465	+	0.365054i
$372$		0			0
$373$	7.75329	+	13.4291i	0.401450	+	0.695332i	0.993901	−	0.110274i	$-0.0351730\pi$
$373$	7.75329	+	13.4291i	0.401450	+	0.695332i	−0.592451	+	0.805606i	$0.701840\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−10.4738			−0.539430
$378$		0			0
$379$	−16.1820			−0.831214			−0.415607	−	0.909544i	$-0.636431\pi$
$379$	−16.1820			−0.831214			−0.415607	+	0.909544i	$0.636431\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	2.17027	+	3.75902i	0.110896	+	0.192077i	0.916132	−	0.400877i	$-0.131295\pi$
$383$	2.17027	+	3.75902i	0.110896	+	0.192077i	−0.805236	+	0.592955i	$0.797961\pi$
$384$		0			0
$385$	−17.7183	−	4.80931i	−0.903006	−	0.245105i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	12.7731	−	22.1237i	0.647624	−	1.12172i	−0.336065	−	0.941839i	$-0.609096\pi$
$389$	12.7731	−	22.1237i	0.647624	−	1.12172i	0.983689	−	0.179879i	$-0.0575705\pi$
$390$		0			0
$391$	−2.66722	+	4.61975i	−0.134887	+	0.233631i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	30.8703	+	53.4690i	1.55326	+	2.69032i
$396$		0			0
$397$	2.28225	−	3.95297i	0.114543	−	0.198394i	−0.803054	−	0.595906i	$-0.796793\pi$
$397$	2.28225	−	3.95297i	0.114543	−	0.198394i	0.917597	+	0.397512i	$0.130126\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	0.668128	+	1.15723i	0.0333647	+	0.0577894i	0.882226	−	0.470827i	$-0.156044\pi$
$401$	0.668128	+	1.15723i	0.0333647	+	0.0577894i	−0.848861	+	0.528616i	$0.822711\pi$
$402$		0			0
$403$	−2.23068	+	3.86366i	−0.111118	+	0.192463i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−2.86161	−	4.95645i	−0.141845	−	0.245682i
$408$		0			0
$409$	20.6664			1.02189			0.510944	−	0.859614i	$-0.329296\pi$
$409$	20.6664			1.02189			0.510944	+	0.859614i	$0.329296\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	38.4806	+	10.4449i	1.89350	+	0.513958i
$414$		0			0
$415$	−5.58015	+	9.66510i	−0.273919	+	0.474441i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−10.5227	+	18.2259i	−0.514069	+	0.890394i	0.485797	+	0.874071i	$0.338529\pi$
$419$	−10.5227	+	18.2259i	−0.514069	+	0.890394i	−0.999867	+	0.0163228i	$0.994804\pi$
$420$		0			0
$421$	−8.51630	−	14.7507i	−0.415059	−	0.718903i	0.580376	−	0.814349i	$-0.302906\pi$
$421$	−8.51630	−	14.7507i	−0.415059	−	0.718903i	−0.995435	+	0.0954456i	$0.969572\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−16.2563			−0.788544
$426$		0			0
$427$	23.4982	+	6.37818i	1.13716	+	0.308662i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−18.2925	−	31.6836i	−0.881121	−	1.52615i	−0.850096	−	0.526627i	$-0.823456\pi$
$431$	−18.2925	−	31.6836i	−0.881121	−	1.52615i	−0.0310244	−	0.999519i	$-0.509877\pi$
$432$		0			0
$433$	−23.6571			−1.13689			−0.568444	−	0.822722i	$-0.692454\pi$
$433$	−23.6571			−1.13689			−0.568444	+	0.822722i	$0.692454\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−0.513395			−0.0245590
$438$		0			0
$439$	20.7864			0.992082			0.496041	−	0.868299i	$-0.334787\pi$
$439$	20.7864			0.992082			0.496041	+	0.868299i	$0.334787\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−7.42807			−0.352918			−0.176459	−	0.984308i	$-0.556464\pi$
$443$	−7.42807			−0.352918			−0.176459	+	0.984308i	$0.556464\pi$
$444$		0			0
$445$	−38.7194			−1.83547
$446$		0			0
$447$		0			0
$448$		0			0
$449$	8.15800			0.385000			0.192500	−	0.981297i	$-0.438340\pi$
$449$	8.15800			0.385000			0.192500	+	0.981297i	$0.438340\pi$
$450$		0			0
$451$	10.8457	+	18.7854i	0.510705	+	0.884568i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	13.5873	+	3.68805i	0.636985	+	0.172898i
$456$		0			0
$457$	14.3058			0.669199			0.334600	−	0.942360i	$-0.391399\pi$
$457$	14.3058			0.669199			0.334600	+	0.942360i	$0.391399\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−7.71961	−	13.3708i	−0.359538	−	0.622738i	0.628346	−	0.777934i	$-0.283732\pi$
$461$	−7.71961	−	13.3708i	−0.359538	−	0.622738i	−0.987884	+	0.155196i	$0.950399\pi$
$462$		0			0
$463$	10.5531	−	18.2785i	0.490444	−	0.849474i	−0.509496	−	0.860473i	$-0.670168\pi$
$463$	10.5531	−	18.2785i	0.490444	−	0.849474i	0.999940	+	0.0109995i	$0.00350132\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−3.49896	+	6.06037i	−0.161912	+	0.280440i	−0.935555	−	0.353182i	$-0.885100\pi$
$467$	−3.49896	+	6.06037i	−0.161912	+	0.280440i	0.773642	+	0.633623i	$0.218433\pi$
$468$		0			0
$469$	31.4998	+	8.55007i	1.45453	+	0.394805i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	12.4831			0.573974
$474$		0			0
$475$	−0.782265	−	1.35492i	−0.0358928	−	0.0621681i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	1.54406	−	2.67440i	0.0705500	−	0.122196i	−0.828592	−	0.559852i	$-0.810858\pi$
$479$	1.54406	−	2.67440i	0.0705500	−	0.122196i	0.899142	+	0.437656i	$0.144191\pi$
$480$		0			0
$481$	2.19444	+	3.80089i	0.100058	+	0.173305i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−16.0871	+	27.8636i	−0.730475	+	1.26522i
$486$		0			0
$487$	4.90011	+	8.48725i	0.222045	+	0.384594i	0.955429	−	0.295221i	$-0.0953934\pi$
$487$	4.90011	+	8.48725i	0.222045	+	0.384594i	−0.733384	+	0.679815i	$0.762060\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−9.98641	+	17.2970i	−0.450680	+	0.780601i	−0.998428	−	0.0560419i	$-0.982152\pi$
$491$	−9.98641	+	17.2970i	−0.450680	+	0.780601i	0.547748	+	0.836643i	$0.315485\pi$
$492$		0			0
$493$	−6.30055	+	10.9129i	−0.283762	+	0.491491i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−17.7022	−	4.80495i	−0.794052	−	0.215531i
$498$		0			0
$499$	10.1650	+	17.6062i	0.455046	+	0.788163i	0.998691	−	0.0511526i	$-0.0162895\pi$
$499$	10.1650	+	17.6062i	0.455046	+	0.788163i	−0.543645	+	0.839315i	$0.682956\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	23.9595			1.06830			0.534151	−	0.845389i	$-0.320631\pi$
$503$	23.9595			1.06830			0.534151	+	0.845389i	$0.320631\pi$
$504$		0			0
$505$	31.1693			1.38702
$506$		0			0
$507$		0			0
$508$		0			0
$509$	5.03046	+	8.71302i	0.222971	+	0.386198i	0.955709	−	0.294314i	$-0.0950910\pi$
$509$	5.03046	+	8.71302i	0.222971	+	0.386198i	−0.732737	+	0.680511i	$0.761758\pi$
$510$		0			0
$511$	8.42146	+	31.8425i	0.372544	+	1.40863i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−14.4762	+	25.0735i	−0.637898	+	1.10487i
$516$		0			0
$517$	−10.3325	+	17.8964i	−0.454423	+	0.787083i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−7.99821	−	13.8533i	−0.350408	−	0.606924i	0.635913	−	0.771761i	$-0.280624\pi$
$521$	−7.99821	−	13.8533i	−0.350408	−	0.606924i	−0.986321	+	0.164836i	$0.947290\pi$
$522$		0			0
$523$	−18.7103	+	32.4072i	−0.818146	+	1.41707i	0.0889016	+	0.996040i	$0.471664\pi$
$523$	−18.7103	+	32.4072i	−0.818146	+	1.41707i	−0.907047	+	0.421029i	$0.861669\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	2.68374	+	4.64838i	0.116906	+	0.202487i
$528$		0			0
$529$	6.37877	−	11.0484i	0.277338	−	0.480364i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−8.31711	−	14.4057i	−0.360254	−	0.623978i
$534$		0			0
$535$	22.7178			0.982175
$536$		0			0
$537$		0			0
$538$		0			0
$539$	10.9930	−	6.25195i	0.473500	−	0.269291i
$540$		0			0
$541$	0.229159	−	0.396916i	0.00985233	−	0.0170647i	−0.861057	−	0.508508i	$-0.830197\pi$
$541$	0.229159	−	0.396916i	0.00985233	−	0.0170647i	0.870910	+	0.491443i	$0.163531\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	17.2232	−	29.8314i	0.737760	−	1.27784i
$546$		0			0
$547$	−11.2013	−	19.4011i	−0.478931	−	0.829533i	0.520777	−	0.853693i	$-0.325642\pi$
$547$	−11.2013	−	19.4011i	−0.478931	−	0.829533i	−0.999708	+	0.0241596i	$0.992309\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−1.21275			−0.0516650
$552$		0			0
$553$	−41.0436	−	11.1405i	−1.74535	−	0.473744i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−10.4155	−	18.0401i	−0.441317	−	0.764383i	0.556471	−	0.830867i	$-0.312155\pi$
$557$	−10.4155	−	18.0401i	−0.441317	−	0.764383i	−0.997787	+	0.0664841i	$0.978822\pi$
$558$		0			0
$559$	−9.57275			−0.404884
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−8.80605			−0.371131			−0.185565	−	0.982632i	$-0.559412\pi$
$563$	−8.80605			−0.371131			−0.185565	+	0.982632i	$0.559412\pi$
$564$		0			0
$565$	61.3117			2.57940
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−18.9857			−0.795923			−0.397962	−	0.917402i	$-0.630282\pi$
$569$	−18.9857			−0.795923			−0.397962	+	0.917402i	$0.630282\pi$
$570$		0			0
$571$	−15.7597			−0.659523			−0.329762	−	0.944064i	$-0.606968\pi$
$571$	−15.7597			−0.659523			−0.329762	+	0.944064i	$0.606968\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−31.2131			−1.30167
$576$		0			0
$577$	−15.9306	−	27.5927i	−0.663201	−	1.14870i	−0.979770	−	0.200128i	$-0.935864\pi$
$577$	−15.9306	−	27.5927i	−0.663201	−	1.14870i	0.316569	−	0.948570i	$-0.397469\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−1.96555	−	7.43199i	−0.0815449	−	0.308331i
$582$		0			0
$583$	−4.96644			−0.205689
$584$		0			0
$585$		0			0
$586$		0			0
$587$	20.3597	+	35.2640i	0.840333	+	1.45550i	0.889613	+	0.456715i	$0.150974\pi$
$587$	20.3597	+	35.2640i	0.840333	+	1.45550i	−0.0492799	+	0.998785i	$0.515693\pi$
$588$		0			0
$589$	−0.258288	+	0.447368i	−0.0106426	+	0.0184335i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	14.0693	−	24.3688i	0.577759	−	1.00071i	−0.417977	−	0.908458i	$-0.637261\pi$
$593$	14.0693	−	24.3688i	0.577759	−	1.00071i	0.995736	−	0.0922500i	$-0.0294059\pi$
$594$		0			0
$595$	12.0161	−	11.9383i	0.492613	−	0.489425i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−32.9926			−1.34804			−0.674020	−	0.738713i	$-0.735434\pi$
$599$	−32.9926			−1.34804			−0.674020	+	0.738713i	$0.735434\pi$
$600$		0			0
$601$	−1.98103	−	3.43124i	−0.0808079	−	0.139963i	0.822789	−	0.568347i	$-0.192417\pi$
$601$	−1.98103	−	3.43124i	−0.0808079	−	0.139963i	−0.903597	+	0.428383i	$0.859083\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−14.8570	+	25.7330i	−0.604021	+	1.04620i
$606$		0			0
$607$	−17.0132	−	29.4676i	−0.690543	−	1.19605i	−0.971660	−	0.236382i	$-0.924038\pi$
$607$	−17.0132	−	29.4676i	−0.690543	−	1.19605i	0.281118	−	0.959673i	$-0.409295\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	7.92354	−	13.7240i	0.320552	−	0.555212i
$612$		0			0
$613$	−15.2967	−	26.4946i	−0.617827	−	1.07011i	−0.989881	−	0.141897i	$-0.954680\pi$
$613$	−15.2967	−	26.4946i	−0.617827	−	1.07011i	0.372054	−	0.928211i	$-0.378654\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−18.7646	+	32.5013i	−0.755435	+	1.30845i	0.189723	+	0.981838i	$0.439241\pi$
$617$	−18.7646	+	32.5013i	−0.755435	+	1.30845i	−0.945158	+	0.326614i	$0.894092\pi$
$618$		0			0
$619$	2.92302	−	5.06282i	0.117486	−	0.203492i	−0.801285	−	0.598283i	$-0.795850\pi$
$619$	2.92302	−	5.06282i	0.117486	−	0.203492i	0.918771	+	0.394791i	$0.129183\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	18.9203	−	18.7979i	0.758028	−	0.753121i
$624$		0			0
$625$	−10.6774	−	18.4937i	−0.427095	−	0.739749i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	5.28028			0.210539
$630$		0			0
$631$	25.6347			1.02050			0.510251	−	0.860025i	$-0.329552\pi$
$631$	25.6347			1.02050			0.510251	+	0.860025i	$0.329552\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	16.5336	+	28.6371i	0.656117	+	1.13643i
$636$		0			0
$637$	−8.43001	+	4.79435i	−0.334009	+	0.189959i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	12.9824	−	22.4861i	0.512772	−	0.888147i	−0.487118	−	0.873336i	$-0.661952\pi$
$641$	12.9824	−	22.4861i	0.512772	−	0.888147i	0.999890	−	0.0148113i	$-0.00471476\pi$
$642$		0			0
$643$	−22.5634	+	39.0809i	−0.889812	+	1.54120i	−0.0497151	+	0.998763i	$0.515831\pi$
$643$	−22.5634	+	39.0809i	−0.889812	+	1.54120i	−0.840097	+	0.542436i	$0.817502\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−2.70324	−	4.68215i	−0.106275	−	0.184074i	0.807983	−	0.589206i	$-0.200559\pi$
$647$	−2.70324	−	4.68215i	−0.106275	−	0.184074i	−0.914259	+	0.405131i	$0.867226\pi$
$648$		0			0
$649$	−13.6135	+	23.5792i	−0.534375	+	0.925564i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−15.9515	−	27.6288i	−0.624231	−	1.08120i	−0.988689	−	0.149980i	$-0.952079\pi$
$653$	−15.9515	−	27.6288i	−0.624231	−	1.08120i	0.364458	−	0.931220i	$-0.381254\pi$
$654$		0			0
$655$	3.70587	−	6.41875i	0.144800	−	0.250801i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−2.50215	−	4.33385i	−0.0974699	−	0.168823i	0.813167	−	0.582031i	$-0.197742\pi$
$659$	−2.50215	−	4.33385i	−0.0974699	−	0.168823i	−0.910637	+	0.413208i	$0.864408\pi$
$660$		0			0
$661$	9.63406			0.374721			0.187361	−	0.982291i	$-0.440007\pi$
$661$	9.63406			0.374721			0.187361	+	0.982291i	$0.440007\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	1.57326	+	0.427034i	0.0610085	+	0.0165597i
$666$		0			0
$667$	−12.0975	+	20.9534i	−0.468415	+	0.811319i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−8.31308	+	14.3987i	−0.320923	+	0.555855i
$672$		0			0
$673$	13.5885	+	23.5359i	0.523797	+	0.907243i	0.999616	+	0.0276998i	$0.00881825\pi$
$673$	13.5885	+	23.5359i	0.523797	+	0.907243i	−0.475819	+	0.879543i	$0.657848\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	38.0502			1.46239			0.731194	−	0.682169i	$-0.238963\pi$
$677$	38.0502			1.46239			0.731194	+	0.682169i	$0.238963\pi$
$678$		0			0
$679$	−5.66651	−	21.4257i	−0.217461	−	0.822244i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−15.0571	−	26.0797i	−0.576146	−	0.997913i	−0.995916	−	0.0902831i	$-0.971223\pi$
$683$	−15.0571	−	26.0797i	−0.576146	−	0.997913i	0.419771	−	0.907630i	$-0.362111\pi$
$684$		0			0
$685$	−14.2455			−0.544293
$686$		0			0
$687$		0			0
$688$		0			0
$689$	3.80854			0.145094
$690$		0			0
$691$	14.3902			0.547429			0.273714	−	0.961811i	$-0.411748\pi$
$691$	14.3902			0.547429			0.273714	+	0.961811i	$0.411748\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	1.03374			0.0392120
$696$		0			0
$697$	−20.0127			−0.758034
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−14.4170			−0.544521			−0.272261	−	0.962224i	$-0.587771\pi$
$701$	−14.4170			−0.544521			−0.272261	+	0.962224i	$0.587771\pi$
$702$		0			0
$703$	0.254092	+	0.440100i	0.00958325	+	0.0165987i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−15.2310	+	15.1324i	−0.572820	+	0.569113i
$708$		0			0
$709$	11.4882			0.431448			0.215724	−	0.976454i	$-0.430789\pi$
$709$	11.4882			0.431448			0.215724	+	0.976454i	$0.430789\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	5.15296	+	8.92519i	0.192980	+	0.334251i
$714$		0			0
$715$	−4.80686	+	8.32573i	−0.179766	+	0.311365i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−17.9451	+	31.0818i	−0.669240	+	1.15916i	0.308877	+	0.951102i	$0.400047\pi$
$719$	−17.9451	+	31.0818i	−0.669240	+	1.15916i	−0.978117	+	0.208055i	$0.933287\pi$
$720$		0			0
$721$	−5.09910	−	19.2803i	−0.189901	−	0.718036i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−73.7321			−2.73834
$726$		0			0
$727$	−5.03060	−	8.71326i	−0.186575	−	0.323157i	0.757531	−	0.652799i	$-0.226405\pi$
$727$	−5.03060	−	8.71326i	−0.186575	−	0.323157i	−0.944106	+	0.329642i	$0.893072\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−5.75850	+	9.97401i	−0.212986	+	0.368902i
$732$		0			0
$733$	−16.5690	−	28.6984i	−0.611992	−	1.06000i	−0.990904	−	0.134568i	$-0.957035\pi$
$733$	−16.5690	−	28.6984i	−0.611992	−	1.06000i	0.378913	−	0.925432i	$-0.376298\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−11.1438	+	19.3017i	−0.410489	+	0.710987i
$738$		0			0
$739$	21.9237	+	37.9729i	0.806475	+	1.39686i	0.915291	+	0.402793i	$0.131961\pi$
$739$	21.9237	+	37.9729i	0.806475	+	1.39686i	−0.108816	+	0.994062i	$0.534706\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−4.50115	+	7.79622i	−0.165131	+	0.286016i	−0.936702	−	0.350128i	$-0.886138\pi$
$743$	−4.50115	+	7.79622i	−0.165131	+	0.286016i	0.771571	+	0.636144i	$0.219471\pi$
$744$		0			0
$745$	−15.9738	+	27.6673i	−0.585233	+	1.01365i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−11.1011	+	11.0293i	−0.405626	+	0.403000i
$750$		0			0
$751$	−5.59141	−	9.68460i	−0.204033	−	0.353396i	0.745791	−	0.666180i	$-0.232072\pi$
$751$	−5.59141	−	9.68460i	−0.204033	−	0.353396i	−0.949824	+	0.312784i	$0.898738\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−37.4162			−1.36171
$756$		0			0
$757$	42.1431			1.53172			0.765859	−	0.643009i	$-0.222314\pi$
$757$	42.1431			1.53172			0.765859	+	0.643009i	$0.222314\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	1.14155	+	1.97721i	0.0413810	+	0.0716740i	0.885974	−	0.463735i	$-0.153491\pi$
$761$	1.14155	+	1.97721i	0.0413810	+	0.0716740i	−0.844593	+	0.535409i	$0.820158\pi$
$762$		0			0
$763$	6.06670	+	22.9389i	0.219629	+	0.830444i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	10.4396	−	18.0819i	0.376951	−	0.652898i
$768$		0			0
$769$	8.96676	−	15.5309i	0.323350	−	0.560058i	−0.657827	−	0.753169i	$-0.728524\pi$
$769$	8.96676	−	15.5309i	0.323350	−	0.560058i	0.981177	+	0.193111i	$0.0618577\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−17.4807	−	30.2775i	−0.628737	−	1.08901i	−0.987805	−	0.155694i	$-0.950239\pi$
$773$	−17.4807	−	30.2775i	−0.628737	−	1.08901i	0.359068	−	0.933311i	$-0.383095\pi$
$774$		0			0
$775$	−15.7032	+	27.1988i	−0.564077	+	0.977009i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−0.963028	−	1.66801i	−0.0345041	−	0.0597628i
$780$		0			0
$781$	6.26259	−	10.8471i	0.224093	−	0.388141i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	46.5870	+	80.6910i	1.66276	+	2.87998i
$786$		0			0
$787$	−28.3564			−1.01079			−0.505397	−	0.862887i	$-0.668654\pi$
$787$	−28.3564			−1.01079			−0.505397	+	0.862887i	$0.668654\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−29.9601	+	29.7662i	−1.06526	+	1.05836i
$792$		0			0
$793$	6.37494	−	11.0417i	0.226381	−	0.392103i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	9.51922	−	16.4878i	0.337188	−	0.584027i	−0.646715	−	0.762732i	$-0.723857\pi$
$797$	9.51922	−	16.4878i	0.337188	−	0.584027i	0.983903	+	0.178705i	$0.0571908\pi$
$798$		0			0
$799$	−9.53283	−	16.5113i	−0.337247	−	0.584129i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−22.4910			−0.793691
$804$		0			0
$805$	23.0717	−	22.9224i	0.813172	−	0.807908i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	10.4529	+	18.1050i	0.367505	+	0.636538i	0.989175	−	0.146742i	$-0.0468787\pi$
$809$	10.4529	+	18.1050i	0.367505	+	0.636538i	−0.621670	+	0.783280i	$0.713545\pi$
$810$		0			0
$811$	17.5392			0.615884			0.307942	−	0.951405i	$-0.400360\pi$
$811$	17.5392			0.615884			0.307942	+	0.951405i	$0.400360\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	30.0671			1.05320
$816$		0			0
$817$	−1.10842			−0.0387786
$818$		0			0
$819$		0			0
$820$		0			0
$821$	34.9762			1.22068			0.610339	−	0.792140i	$-0.291033\pi$
$821$	34.9762			1.22068			0.610339	+	0.792140i	$0.291033\pi$
$822$		0			0
$823$	−30.4235			−1.06050			−0.530249	−	0.847842i	$-0.677901\pi$
$823$	−30.4235			−1.06050			−0.530249	+	0.847842i	$0.677901\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	25.6276			0.891158			0.445579	−	0.895243i	$-0.352998\pi$
$827$	25.6276			0.891158			0.445579	+	0.895243i	$0.352998\pi$
$828$		0			0
$829$	23.9403	+	41.4658i	0.831481	+	1.44017i	0.896864	+	0.442307i	$0.145840\pi$
$829$	23.9403	+	41.4658i	0.831481	+	1.44017i	−0.0653833	+	0.997860i	$0.520827\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−0.0757689	+	11.6674i	−0.00262524	+	0.404252i
$834$		0			0
$835$	16.5465			0.572614
$836$		0			0
$837$		0			0
$838$		0			0
$839$	21.8466	+	37.8394i	0.754227	+	1.30636i	0.945758	+	0.324873i	$0.105322\pi$
$839$	21.8466	+	37.8394i	0.754227	+	1.30636i	−0.191530	+	0.981487i	$0.561345\pi$
$840$		0			0
$841$	−14.0769	+	24.3818i	−0.485409	+	0.840753i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−21.2800	+	36.8581i	−0.732055	+	1.26796i
$846$		0			0
$847$	−5.23322	−	19.7874i	−0.179816	−	0.679904i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	10.1385			0.347543
$852$		0			0
$853$	8.33994	+	14.4452i	0.285554	+	0.494594i	0.972743	−	0.231884i	$-0.0744890\pi$
$853$	8.33994	+	14.4452i	0.285554	+	0.494594i	−0.687189	+	0.726478i	$0.741156\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	7.21452	−	12.4959i	0.246443	−	0.426852i	−0.716093	−	0.698005i	$-0.754071\pi$
$857$	7.21452	−	12.4959i	0.246443	−	0.426852i	0.962536	+	0.271152i	$0.0874048\pi$
$858$		0			0
$859$	−11.3867	−	19.7223i	−0.388508	−	0.672915i	0.603741	−	0.797180i	$-0.293676\pi$
$859$	−11.3867	−	19.7223i	−0.388508	−	0.672915i	−0.992249	+	0.124265i	$0.960343\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	5.97266	−	10.3450i	0.203312	−	0.352146i	−0.746282	−	0.665630i	$-0.768163\pi$
$863$	5.97266	−	10.3450i	0.203312	−	0.352146i	0.949594	+	0.313484i	$0.101496\pi$
$864$		0			0
$865$	33.2933	+	57.6656i	1.13200	+	1.96069i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	14.5202	−	25.1497i	0.492563	−	0.853145i
$870$		0			0
$871$	8.54572	−	14.8016i	0.289561	−	0.501534i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	46.6134	+	12.6524i	1.57582	+	0.427729i
$876$		0			0
$877$	28.3099	+	49.0342i	0.955957	+	1.65577i	0.732163	+	0.681130i	$0.238511\pi$
$877$	28.3099	+	49.0342i	0.955957	+	1.65577i	0.223794	+	0.974636i	$0.428156\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	6.41130			0.216002			0.108001	−	0.994151i	$-0.465555\pi$
$881$	6.41130			0.216002			0.108001	+	0.994151i	$0.465555\pi$
$882$		0			0
$883$	−25.7180			−0.865481			−0.432741	−	0.901518i	$-0.642453\pi$
$883$	−25.7180			−0.865481			−0.432741	+	0.901518i	$0.642453\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	9.99472	+	17.3114i	0.335590	+	0.581259i	0.983598	−	0.180375i	$-0.0577311\pi$
$887$	9.99472	+	17.3114i	0.335590	+	0.581259i	−0.648008	+	0.761633i	$0.724398\pi$
$888$		0			0
$889$	−21.9822	−	5.96669i	−0.737261	−	0.200116i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	0.917456	−	1.58908i	0.0307015	−	0.0531766i
$894$		0			0
$895$	−37.2051	+	64.4412i	−1.24363	+	2.15403i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	12.1724	+	21.0832i	0.405973	+	0.703166i
$900$		0			0
$901$	2.29104	−	3.96819i	0.0763254	−	0.132200i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	5.55087	+	9.61439i	0.184517	+	0.319593i
$906$		0			0
$907$	−12.1517	+	21.0474i	−0.403491	+	0.698866i	−0.994145	−	0.108059i	$-0.965537\pi$
$907$	−12.1517	+	21.0474i	−0.403491	+	0.698866i	0.590654	+	0.806925i	$0.298870\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−19.7871	−	34.2723i	−0.655577	−	1.13549i	−0.981749	−	0.190183i	$-0.939092\pi$
$911$	−19.7871	−	34.2723i	−0.655577	−	1.13549i	0.326171	−	0.945311i	$-0.394241\pi$
$912$		0			0
$913$	5.24936			0.173728
$914$		0			0
$915$		0			0
$916$		0			0
$917$	1.30536	+	4.93571i	0.0431067	+	0.162991i
$918$		0			0
$919$	−12.9220	+	22.3815i	−0.426257	+	0.738298i	−0.996537	−	0.0831519i	$-0.973501\pi$
$919$	−12.9220	+	22.3815i	−0.426257	+	0.738298i	0.570280	+	0.821450i	$0.306835\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−4.80251	+	8.31818i	−0.158076	+	0.273796i
$924$		0			0
$925$	15.4481	+	26.7569i	0.507930	+	0.879761i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−50.8506			−1.66836			−0.834178	−	0.551496i	$-0.814057\pi$
$929$	−50.8506			−1.66836			−0.834178	+	0.551496i	$0.814057\pi$
$930$		0			0
$931$	−0.976100	+	0.555132i	−0.0319904	+	0.0181937i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	5.78315	+	10.0167i	0.189129	+	0.327581i
$936$		0			0
$937$	32.7623			1.07030			0.535149	−	0.844758i	$-0.320256\pi$
$937$	32.7623			1.07030			0.535149	+	0.844758i	$0.320256\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−50.6793			−1.65210			−0.826048	−	0.563599i	$-0.809416\pi$
$941$	−50.6793			−1.65210			−0.826048	+	0.563599i	$0.809416\pi$
$942$		0			0
$943$	−38.4256			−1.25131
$944$		0			0
$945$		0			0
$946$		0			0
$947$	11.5255			0.374530			0.187265	−	0.982309i	$-0.440038\pi$
$947$	11.5255			0.374530			0.187265	+	0.982309i	$0.440038\pi$
$948$		0			0
$949$	17.2474			0.559873
$950$		0			0
$951$		0			0
$952$		0			0
$953$	45.7747			1.48279			0.741395	−	0.671069i	$-0.234165\pi$
$953$	45.7747			1.48279			0.741395	+	0.671069i	$0.234165\pi$
$954$		0			0
$955$	−7.10661	−	12.3090i	−0.229965	−	0.398310i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	6.96111	−	6.91605i	0.224786	−	0.223331i
$960$		0			0
$961$	−20.6302			−0.665491
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−24.5188	−	42.4678i	−0.789287	−	1.36709i
$966$		0			0
$967$	−4.07666	+	7.06098i	−0.131097	+	0.227066i	−0.924100	−	0.382152i	$-0.875183\pi$
$967$	−4.07666	+	7.06098i	−0.131097	+	0.227066i	0.793003	+	0.609218i	$0.208516\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−14.1137	+	24.4457i	−0.452932	+	0.784501i	−0.998567	−	0.0535223i	$-0.982955\pi$
$971$	−14.1137	+	24.4457i	−0.452932	+	0.784501i	0.545635	+	0.838023i	$0.316288\pi$
$972$		0			0
$973$	−0.505141	+	0.501871i	−0.0161941	+	0.0160893i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	15.6502			0.500694			0.250347	−	0.968156i	$-0.419455\pi$
$977$	15.6502			0.500694			0.250347	+	0.968156i	$0.419455\pi$
$978$		0			0
$979$	9.10603	+	15.7721i	0.291030	+	0.504079i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	1.47581	−	2.55617i	0.0470710	−	0.0815293i	−0.841530	−	0.540210i	$-0.818345\pi$
$983$	1.47581	−	2.55617i	0.0470710	−	0.0815293i	0.888601	+	0.458681i	$0.151678\pi$
$984$		0			0
$985$	−4.69970	−	8.14012i	−0.149745	−	0.259366i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−11.0567	+	19.1507i	−0.351582	+	0.608958i
$990$		0			0
$991$	15.8182	+	27.3979i	0.502482	+	0.870324i	0.999996	+	0.00286819i	$0.000912976\pi$
$991$	15.8182	+	27.3979i	0.502482	+	0.870324i	−0.497514	+	0.867456i	$0.665754\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−8.63557	+	14.9572i	−0.273766	+	0.474176i
$996$		0			0
$997$	0.792608	−	1.37284i	0.0251021	−	0.0434782i	−0.853201	−	0.521582i	$-0.825342\pi$
$997$	0.792608	−	1.37284i	0.0251021	−	0.0434782i	0.878304	+	0.478103i	$0.158676\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.q.c.793.11		22
3.2	odd	2		504.2.q.d.121.10	yes	22
4.3	odd	2		3024.2.q.k.2305.11		22
7.4	even	3		1512.2.t.d.361.1		22
9.2	odd	6		504.2.t.d.457.2	yes	22
9.7	even	3		1512.2.t.d.289.1		22
12.11	even	2		1008.2.q.k.625.2		22
21.11	odd	6		504.2.t.d.193.2	yes	22
28.11	odd	6		3024.2.t.l.1873.1		22
36.7	odd	6		3024.2.t.l.289.1		22
36.11	even	6		1008.2.t.k.961.10		22
63.11	odd	6		504.2.q.d.25.10	✓	22
63.25	even	3	inner	1512.2.q.c.1369.11		22
84.11	even	6		1008.2.t.k.193.10		22
252.11	even	6		1008.2.q.k.529.2		22
252.151	odd	6		3024.2.q.k.2881.11		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.d.25.10	✓	22	63.11	odd	6
504.2.q.d.121.10	yes	22	3.2	odd	2
504.2.t.d.193.2	yes	22	21.11	odd	6
504.2.t.d.457.2	yes	22	9.2	odd	6
1008.2.q.k.529.2		22	252.11	even	6
1008.2.q.k.625.2		22	12.11	even	2
1008.2.t.k.193.10		22	84.11	even	6
1008.2.t.k.961.10		22	36.11	even	6
1512.2.q.c.793.11		22	1.1	even	1	trivial
1512.2.q.c.1369.11		22	63.25	even	3	inner
1512.2.t.d.289.1		22	9.7	even	3
1512.2.t.d.361.1		22	7.4	even	3
3024.2.q.k.2305.11		22	4.3	odd	2
3024.2.q.k.2881.11		22	252.151	odd	6
3024.2.t.l.289.1		22	36.7	odd	6
3024.2.t.l.1873.1		22	28.11	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:	\( N \)	\(=\)	\( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1512.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.92048 + 3.32636i) q^{5} +(-2.55336 - 0.693065i) q^{7} +O(q^{10})\)	\(q+(1.92048 + 3.32636i) q^{5} +(-2.55336 - 0.693065i) q^{7} +(0.903316 - 1.56459i) q^{11} +(-0.692713 + 1.19981i) q^{13} +(0.833405 + 1.44350i) q^{17} +(-0.0802084 + 0.138925i) q^{19} +(1.60019 + 2.77161i) q^{23} +(-4.87646 + 8.44627i) q^{25} +(3.78000 + 6.54716i) q^{29} +3.22021 q^{31} +(-2.59829 - 9.82442i) q^{35} +(1.58395 - 2.74348i) q^{37} +(-6.00329 + 10.3980i) q^{41} +(3.45480 + 5.98389i) q^{43} -11.4384 q^{47} +(6.03932 + 3.53929i) q^{49} +(-1.37450 - 2.38071i) q^{53} +6.93918 q^{55} -15.0705 q^{59} -9.20285 q^{61} -5.32136 q^{65} -12.3366 q^{67} +6.93289 q^{71} +(-6.22457 - 10.7813i) q^{73} +(-3.39085 + 3.36891i) q^{77} +16.0743 q^{79} +(1.45280 + 2.51633i) q^{83} +(-3.20107 + 5.54441i) q^{85} +(-5.04034 + 8.73012i) q^{89} +(2.60030 - 2.58347i) q^{91} -0.616153 q^{95} +(4.18830 + 7.25435i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 3 q^{5} - 5 q^{7}+O(q^{10}) \) 22 * q - 3 * q^5 - 5 * q^7	\( 22 q - 3 q^{5} - 5 q^{7} + 3 q^{11} - 3 q^{13} - 7 q^{17} - q^{19} - 2 q^{23} - 10 q^{25} - 9 q^{29} + 8 q^{31} - 14 q^{35} + 2 q^{37} - 16 q^{41} + 10 q^{47} + 15 q^{49} - 11 q^{53} + 22 q^{55} - 38 q^{59} + 26 q^{61} + 26 q^{65} - 52 q^{67} + 48 q^{71} - 35 q^{73} - 17 q^{77} - 20 q^{79} + 28 q^{83} - 20 q^{85} - 6 q^{89} - 37 q^{91} + 24 q^{95} - 29 q^{97}+O(q^{100}) \) 22 * q - 3 * q^5 - 5 * q^7 + 3 * q^11 - 3 * q^13 - 7 * q^17 - q^19 - 2 * q^23 - 10 * q^25 - 9 * q^29 + 8 * q^31 - 14 * q^35 + 2 * q^37 - 16 * q^41 + 10 * q^47 + 15 * q^49 - 11 * q^53 + 22 * q^55 - 38 * q^59 + 26 * q^61 + 26 * q^65 - 52 * q^67 + 48 * q^71 - 35 * q^73 - 17 * q^77 - 20 * q^79 + 28 * q^83 - 20 * q^85 - 6 * q^89 - 37 * q^91 + 24 * q^95 - 29 * q^97

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