LMFDB - Embedded newform 5292.2.j.g.3529.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5292,2,Mod(1765,5292)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5292, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("5292.1765");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5292 = 2^{2} \cdot 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5292.j (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:	$42.2568327497$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 5x^{12} - 3x^{11} + 7x^{10} + 30x^{9} - 117x^{7} + 270x^{5} + 189x^{4} - 243x^{3} - 1215x^{2} + 2187 $ x^14 - 5x^12 - 3x^11 + 7x^10 + 30x^9 - 117x^7 + 270x^5 + 189x^4 - 243x^3 - 1215*x^2 + 2187
Coefficient ring:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 3^{8} $
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			3529.4
Root			$1.64515 - 0.541745i$ of defining polynomial
Character	$\chi$	$=$	5292.3529
Dual form			5292.2.j.g.1765.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.381918 + 0.661502i) q^{5} +O(q^{10})$	$q+(0.381918 + 0.661502i) q^{5} +(3.01695 - 5.22551i) q^{11} +(1.26032 + 2.18294i) q^{13} -3.88888 q^{17} -4.27006 q^{19} +(-0.732124 - 1.26808i) q^{23} +(2.20828 - 3.82485i) q^{25} +(3.00732 - 5.20884i) q^{29} +(3.28482 + 5.68948i) q^{31} -9.64983 q^{37} +(-2.24844 - 3.89442i) q^{41} +(-2.13503 + 3.69798i) q^{43} +(3.38924 - 5.87034i) q^{47} -0.531162 q^{53} +4.60891 q^{55} +(-5.59926 - 9.69821i) q^{59} +(4.19144 - 7.25979i) q^{61} +(-0.962681 + 1.66741i) q^{65} +(0.961979 + 1.66620i) q^{67} -9.90353 q^{71} -4.26198 q^{73} +(3.70372 - 6.41503i) q^{79} +(-8.05178 + 13.9461i) q^{83} +(-1.48523 - 2.57250i) q^{85} -3.52619 q^{89} +(-1.63081 - 2.82465i) q^{95} +(-2.33513 + 4.04456i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 2 q^{5}+O(q^{10}) $ 14 * q - 2 * q^5	$ 14 q - 2 q^{5} - 2 q^{11} - 2 q^{13} - 4 q^{17} + 14 q^{19} - 11 q^{23} - 9 q^{25} - q^{29} + q^{31} - 20 q^{37} - 33 q^{41} + 7 q^{43} - 3 q^{47} - 30 q^{53} + 28 q^{55} - 14 q^{59} + 10 q^{61} - 15 q^{65} + 6 q^{67} - 2 q^{71} + 42 q^{73} - 10 q^{79} - 25 q^{83} + 8 q^{85} + 12 q^{89} + 28 q^{95} + 18 q^{97}+O(q^{100}) $ 14 * q - 2 * q^5 - 2 * q^11 - 2 * q^13 - 4 * q^17 + 14 * q^19 - 11 * q^23 - 9 * q^25 - q^29 + q^31 - 20 * q^37 - 33 * q^41 + 7 * q^43 - 3 * q^47 - 30 * q^53 + 28 * q^55 - 14 * q^59 + 10 * q^61 - 15 * q^65 + 6 * q^67 - 2 * q^71 + 42 * q^73 - 10 * q^79 - 25 * q^83 + 8 * q^85 + 12 * q^89 + 28 * q^95 + 18 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/5292\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$	$2647$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	0.381918	+	0.661502i	0.170799	+	0.295833i	0.938699	−	0.344737i	$-0.112032\pi$
$5$	0.381918	+	0.661502i	0.170799	+	0.295833i	−0.767900	+	0.640569i	$0.778698\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$		0			0
$10$		0			0
$11$	3.01695	−	5.22551i	0.909644	−	1.57555i	0.0950845	−	0.995469i	$-0.469688\pi$
$11$	3.01695	−	5.22551i	0.909644	−	1.57555i	0.814559	−	0.580080i	$-0.196979\pi$
$12$		0			0
$13$	1.26032	+	2.18294i	0.349551	+	0.605440i	0.986170	−	0.165739i	$-0.0530009\pi$
$13$	1.26032	+	2.18294i	0.349551	+	0.605440i	−0.636619	+	0.771179i	$0.719668\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−3.88888			−0.943192			−0.471596	−	0.881815i	$-0.656322\pi$
$17$	−3.88888			−0.943192			−0.471596	+	0.881815i	$0.656322\pi$
$18$		0			0
$19$	−4.27006			−0.979619			−0.489809	−	0.871830i	$-0.662934\pi$
$19$	−4.27006			−0.979619			−0.489809	+	0.871830i	$0.662934\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−0.732124	−	1.26808i	−0.152658	−	0.264412i	0.779546	−	0.626346i	$-0.215450\pi$
$23$	−0.732124	−	1.26808i	−0.152658	−	0.264412i	−0.932204	+	0.361933i	$0.882117\pi$
$24$		0			0
$25$	2.20828	−	3.82485i	0.441655	−	0.764970i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	3.00732	−	5.20884i	0.558446	−	0.967257i	−0.439180	−	0.898399i	$-0.644731\pi$
$29$	3.00732	−	5.20884i	0.558446	−	0.967257i	0.997626	−	0.0688580i	$-0.0219355\pi$
$30$		0			0
$31$	3.28482	+	5.68948i	0.589972	+	1.02186i	0.994235	+	0.107219i	$0.0341945\pi$
$31$	3.28482	+	5.68948i	0.589972	+	1.02186i	−0.404264	+	0.914642i	$0.632472\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−9.64983			−1.58642			−0.793211	−	0.608947i	$-0.791592\pi$
$37$	−9.64983			−1.58642			−0.793211	+	0.608947i	$0.791592\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−2.24844	−	3.89442i	−0.351148	−	0.608206i	0.635303	−	0.772263i	$-0.280875\pi$
$41$	−2.24844	−	3.89442i	−0.351148	−	0.608206i	−0.986451	+	0.164057i	$0.947542\pi$
$42$		0			0
$43$	−2.13503	+	3.69798i	−0.325589	+	0.563937i	−0.981631	−	0.190787i	$-0.938896\pi$
$43$	−2.13503	+	3.69798i	−0.325589	+	0.563937i	0.656042	+	0.754724i	$0.272229\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	3.38924	−	5.87034i	0.494372	−	0.856277i	−0.505607	−	0.862764i	$-0.668731\pi$
$47$	3.38924	−	5.87034i	0.494372	−	0.856277i	0.999979	+	0.00648676i	$0.00206481\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−0.531162			−0.0729607			−0.0364804	−	0.999334i	$-0.511615\pi$
$53$	−0.531162			−0.0729607			−0.0364804	+	0.999334i	$0.511615\pi$
$54$		0			0
$55$	4.60891			0.621465
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−5.59926	−	9.69821i	−0.728962	−	1.26260i	−0.957322	−	0.289023i	$-0.906670\pi$
$59$	−5.59926	−	9.69821i	−0.728962	−	1.26260i	0.228360	−	0.973577i	$-0.426664\pi$
$60$		0			0
$61$	4.19144	−	7.25979i	0.536659	−	0.929521i	−0.462422	−	0.886660i	$-0.653019\pi$
$61$	4.19144	−	7.25979i	0.536659	−	0.929521i	0.999081	−	0.0428608i	$-0.0136472\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−0.962681	+	1.66741i	−0.119406	+	0.206817i
$66$		0			0
$67$	0.961979	+	1.66620i	0.117524	+	0.203558i	0.918786	−	0.394756i	$-0.129171\pi$
$67$	0.961979	+	1.66620i	0.117524	+	0.203558i	−0.801262	+	0.598314i	$0.795838\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−9.90353			−1.17533			−0.587666	−	0.809103i	$-0.699953\pi$
$71$	−9.90353			−1.17533			−0.587666	+	0.809103i	$0.699953\pi$
$72$		0			0
$73$	−4.26198			−0.498827			−0.249413	−	0.968397i	$-0.580238\pi$
$73$	−4.26198			−0.498827			−0.249413	+	0.968397i	$0.580238\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$	3.70372	−	6.41503i	0.416701	−	0.721748i	−0.578904	−	0.815396i	$-0.696519\pi$
$79$	3.70372	−	6.41503i	0.416701	−	0.721748i	0.995605	+	0.0936479i	$0.0298528\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−8.05178	+	13.9461i	−0.883798	+	1.53078i	−0.0367125	+	0.999326i	$0.511689\pi$
$83$	−8.05178	+	13.9461i	−0.883798	+	1.53078i	−0.847085	+	0.531457i	$0.821645\pi$
$84$		0			0
$85$	−1.48523	−	2.57250i	−0.161096	−	0.279027i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−3.52619			−0.373776			−0.186888	−	0.982381i	$-0.559840\pi$
$89$	−3.52619			−0.373776			−0.186888	+	0.982381i	$0.559840\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−1.63081	−	2.82465i	−0.167318	−	0.289803i
$96$		0			0
$97$	−2.33513	+	4.04456i	−0.237096	+	0.410662i	−0.959880	−	0.280412i	$-0.909529\pi$
$97$	−2.33513	+	4.04456i	−0.237096	+	0.410662i	0.722784	+	0.691074i	$0.242862\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	2.35982	−	4.08734i	0.234811	−	0.406705i	−0.724407	−	0.689373i	$-0.757886\pi$
$101$	2.35982	−	4.08734i	0.234811	−	0.406705i	0.959218	+	0.282668i	$0.0912194\pi$
$102$		0			0
$103$	1.58266	+	2.74124i	0.155944	+	0.270103i	0.933402	−	0.358832i	$-0.116825\pi$
$103$	1.58266	+	2.74124i	0.155944	+	0.270103i	−0.777458	+	0.628934i	$0.783491\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	15.3107			1.48015			0.740073	−	0.672527i	$-0.234791\pi$
$107$	15.3107			1.48015			0.740073	+	0.672527i	$0.234791\pi$
$108$		0			0
$109$	−15.3074			−1.46618			−0.733092	−	0.680129i	$-0.761924\pi$
$109$	−15.3074			−1.46618			−0.733092	+	0.680129i	$0.761924\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	1.56114	+	2.70397i	0.146860	+	0.254368i	0.930065	−	0.367395i	$-0.119750\pi$
$113$	1.56114	+	2.70397i	0.146860	+	0.254368i	−0.783206	+	0.621763i	$0.786417\pi$
$114$		0			0
$115$	0.559223	−	0.968602i	0.0521478	−	0.0903226i
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−12.7039	−	22.0039i	−1.15490	−	2.00035i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	7.19271			0.643335
$126$		0			0
$127$	1.27814			0.113416			0.0567082	−	0.998391i	$-0.481940\pi$
$127$	1.27814			0.113416			0.0567082	+	0.998391i	$0.481940\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−3.88733	−	6.73305i	−0.339637	−	0.588269i	0.644727	−	0.764413i	$-0.276971\pi$
$131$	−3.88733	−	6.73305i	−0.339637	−	0.588269i	−0.984364	+	0.176144i	$0.943638\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$		0			0
$137$	1.41153	−	2.44485i	0.120596	−	0.208878i	−0.799407	−	0.600790i	$-0.794853\pi$
$137$	1.41153	−	2.44485i	0.120596	−	0.208878i	0.920003	+	0.391912i	$0.128186\pi$
$138$		0			0
$139$	11.2206	+	19.4346i	0.951718	+	1.64842i	0.741705	+	0.670726i	$0.234017\pi$
$139$	11.2206	+	19.4346i	0.951718	+	1.64842i	0.210013	+	0.977699i	$0.432649\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	15.2093			1.27187
$144$		0			0
$145$	4.59421			0.381528
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−10.0851	−	17.4679i	−0.826206	−	1.43103i	−0.900994	−	0.433831i	$-0.857162\pi$
$149$	−10.0851	−	17.4679i	−0.826206	−	1.43103i	0.0747887	−	0.997199i	$-0.476172\pi$
$150$		0			0
$151$	−4.14725	+	7.18325i	−0.337498	+	0.584564i	−0.983962	−	0.178381i	$-0.942914\pi$
$151$	−4.14725	+	7.18325i	−0.337498	+	0.584564i	0.646463	+	0.762945i	$0.276247\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−2.50907	+	4.34583i	−0.201533	+	0.349066i
$156$		0			0
$157$	−3.33332	−	5.77348i	−0.266028	−	0.460774i	0.701804	−	0.712370i	$-0.252378\pi$
$157$	−3.33332	−	5.77348i	−0.266028	−	0.460774i	−0.967832	+	0.251596i	$0.919045\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−7.39502			−0.579223			−0.289611	−	0.957144i	$-0.593526\pi$
$163$	−7.39502			−0.579223			−0.289611	+	0.957144i	$0.593526\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−0.475526	−	0.823635i	−0.0367973	−	0.0637348i	0.847040	−	0.531529i	$-0.178382\pi$
$167$	−0.475526	−	0.823635i	−0.0367973	−	0.0637348i	−0.883838	+	0.467794i	$0.845049\pi$
$168$		0			0
$169$	3.32317	−	5.75590i	0.255629	−	0.442762i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−2.33554	+	4.04527i	−0.177568	+	0.307557i	−0.941047	−	0.338276i	$-0.890156\pi$
$173$	−2.33554	+	4.04527i	−0.177568	+	0.307557i	0.763479	+	0.645833i	$0.223490\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−14.9897			−1.12038			−0.560192	−	0.828363i	$-0.689273\pi$
$179$	−14.9897			−1.12038			−0.560192	+	0.828363i	$0.689273\pi$
$180$		0			0
$181$	13.6525			1.01478			0.507391	−	0.861716i	$-0.330610\pi$
$181$	13.6525			1.01478			0.507391	+	0.861716i	$0.330610\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−3.68545	−	6.38338i	−0.270959	−	0.469316i
$186$		0			0
$187$	−11.7325	+	20.3214i	−0.857969	+	1.48605i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	6.14528	−	10.6439i	0.444657	−	0.770168i	−0.553372	−	0.832934i	$-0.686659\pi$
$191$	6.14528	−	10.6439i	0.444657	−	0.770168i	0.998028	+	0.0627667i	$0.0199924\pi$
$192$		0			0
$193$	−3.58578	−	6.21075i	−0.258110	−	0.447060i	0.707626	−	0.706588i	$-0.249766\pi$
$193$	−3.58578	−	6.21075i	−0.258110	−	0.447060i	−0.965736	+	0.259528i	$0.916433\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	13.0286			0.928247			0.464124	−	0.885770i	$-0.346369\pi$
$197$	13.0286			0.928247			0.464124	+	0.885770i	$0.346369\pi$
$198$		0			0
$199$	−4.96174			−0.351728			−0.175864	−	0.984414i	$-0.556272\pi$
$199$	−4.96174			−0.351728			−0.175864	+	0.984414i	$0.556272\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$	1.71744	−	2.97470i	0.119951	−	0.207762i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−12.8825	+	22.3132i	−0.891104	+	1.54344i
$210$		0			0
$211$	2.07384	+	3.59199i	0.142769	+	0.247283i	0.928538	−	0.371237i	$-0.121066\pi$
$211$	2.07384	+	3.59199i	0.142769	+	0.247283i	−0.785769	+	0.618519i	$0.787733\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−3.26163			−0.222441
$216$		0			0
$217$		0			0
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−4.90125	−	8.48921i	−0.329694	−	0.571046i
$222$		0			0
$223$	4.63830	−	8.03378i	0.310604	−	0.537982i	−0.667889	−	0.744261i	$-0.732802\pi$
$223$	4.63830	−	8.03378i	0.310604	−	0.537982i	0.978493	+	0.206279i	$0.0661354\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	10.6801	−	18.4985i	0.708863	−	1.22779i	−0.256416	−	0.966567i	$-0.582542\pi$
$227$	10.6801	−	18.4985i	0.708863	−	1.22779i	0.965279	−	0.261221i	$-0.0841250\pi$
$228$		0			0
$229$	−10.0035	−	17.3266i	−0.661052	−	1.14498i	−0.980339	−	0.197318i	$-0.936777\pi$
$229$	−10.0035	−	17.3266i	−0.661052	−	1.14498i	0.319287	−	0.947658i	$-0.396557\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	15.2731			1.00058			0.500288	−	0.865859i	$-0.333227\pi$
$233$	15.2731			1.00058			0.500288	+	0.865859i	$0.333227\pi$
$234$		0			0
$235$	5.17765			0.337753
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−9.03828	−	15.6548i	−0.584638	−	1.01262i	−0.994920	−	0.100664i	$-0.967903\pi$
$239$	−9.03828	−	15.6548i	−0.584638	−	1.01262i	0.410283	−	0.911958i	$-0.365430\pi$
$240$		0			0
$241$	2.15522	−	3.73296i	0.138830	−	0.240461i	−0.788224	−	0.615389i	$-0.788999\pi$
$241$	2.15522	−	3.73296i	0.138830	−	0.240461i	0.927054	+	0.374928i	$0.122332\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−5.38165	−	9.32130i	−0.342426	−	0.593100i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	16.3348			1.03104			0.515521	−	0.856877i	$-0.327599\pi$
$251$	16.3348			1.03104			0.515521	+	0.856877i	$0.327599\pi$
$252$		0			0
$253$	−8.83512			−0.555459
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−0.647698	−	1.12185i	−0.0404023	−	0.0699788i	0.845117	−	0.534581i	$-0.179531\pi$
$257$	−0.647698	−	1.12185i	−0.0404023	−	0.0699788i	−0.885519	+	0.464602i	$0.846197\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$	14.1364	−	24.4850i	0.871687	−	1.50981i	0.0114371	−	0.999935i	$-0.496359\pi$
$263$	14.1364	−	24.4850i	0.871687	−	1.50981i	0.860250	−	0.509872i	$-0.170307\pi$
$264$		0			0
$265$	−0.202861	−	0.351365i	−0.0124616	−	0.0215842i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−14.2194			−0.866970			−0.433485	−	0.901161i	$-0.642716\pi$
$269$	−14.2194			−0.866970			−0.433485	+	0.901161i	$0.642716\pi$
$270$		0			0
$271$	−14.3783			−0.873418			−0.436709	−	0.899603i	$-0.643856\pi$
$271$	−14.3783			−0.873418			−0.436709	+	0.899603i	$0.643856\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−13.3245	−	23.0787i	−0.803498	−	1.39170i
$276$		0			0
$277$	7.71807	−	13.3681i	0.463734	−	0.803211i	−0.535409	−	0.844593i	$-0.679843\pi$
$277$	7.71807	−	13.3681i	0.463734	−	0.803211i	0.999143	+	0.0413818i	$0.0131760\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	9.39609	−	16.2745i	0.560524	−	0.970856i	−0.436927	−	0.899497i	$-0.643933\pi$
$281$	9.39609	−	16.2745i	0.560524	−	0.970856i	0.997451	−	0.0713587i	$-0.0227335\pi$
$282$		0			0
$283$	−16.2864	−	28.2089i	−0.968128	−	1.67685i	−0.700965	−	0.713196i	$-0.747247\pi$
$283$	−16.2864	−	28.2089i	−0.968128	−	1.67685i	−0.267163	−	0.963651i	$-0.586086\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−1.87661			−0.110389
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−1.69821	−	2.94138i	−0.0992103	−	0.171837i	0.812148	−	0.583452i	$-0.198298\pi$
$293$	−1.69821	−	2.94138i	−0.0992103	−	0.171837i	−0.911358	+	0.411615i	$0.864965\pi$
$294$		0			0
$295$	4.27692	−	7.40785i	0.249012	−	0.431302i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	1.84543	−	3.19637i	0.106724	−	0.184851i
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$	6.40315			0.366643
$306$		0			0
$307$	−3.69564			−0.210921			−0.105461	−	0.994423i	$-0.533632\pi$
$307$	−3.69564			−0.210921			−0.105461	+	0.994423i	$0.533632\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	8.58119	+	14.8631i	0.486594	+	0.842806i	0.999881	−	0.0154108i	$-0.00490561\pi$
$311$	8.58119	+	14.8631i	0.486594	+	0.842806i	−0.513287	+	0.858217i	$0.671572\pi$
$312$		0			0
$313$	2.64824	−	4.58688i	0.149687	−	0.259266i	−0.781425	−	0.624000i	$-0.785507\pi$
$313$	2.64824	−	4.58688i	0.149687	−	0.259266i	0.931112	+	0.364734i	$0.118840\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	14.0890	−	24.4028i	0.791315	−	1.37060i	−0.133838	−	0.991003i	$-0.542730\pi$
$317$	14.0890	−	24.4028i	0.791315	−	1.37060i	0.925153	−	0.379594i	$-0.123936\pi$
$318$		0			0
$319$	−18.1459	−	31.4296i	−1.01597	−	1.75972i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	16.6057			0.923968
$324$		0			0
$325$	11.1326			0.617524
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−14.5860	+	25.2637i	−0.801720	+	1.38862i	0.116762	+	0.993160i	$0.462748\pi$
$331$	−14.5860	+	25.2637i	−0.801720	+	1.38862i	−0.918483	+	0.395461i	$0.870585\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−0.734794	+	1.27270i	−0.0401461	+	0.0695351i
$336$		0			0
$337$	−0.447174	−	0.774528i	−0.0243591	−	0.0421912i	0.853589	−	0.520947i	$-0.174421\pi$
$337$	−0.447174	−	0.774528i	−0.0243591	−	0.0421912i	−0.877948	+	0.478756i	$0.841088\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	39.6406			2.14666
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$		0			0
$347$	9.98982	+	17.3029i	0.536282	+	0.928867i	0.999100	+	0.0424143i	$0.0135049\pi$
$347$	9.98982	+	17.3029i	0.536282	+	0.928867i	−0.462818	+	0.886453i	$0.653162\pi$
$348$		0			0
$349$	−2.58530	+	4.47788i	−0.138388	+	0.239695i	−0.926887	−	0.375341i	$-0.877525\pi$
$349$	−2.58530	+	4.47788i	−0.138388	+	0.239695i	0.788499	+	0.615037i	$0.210859\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−16.5611	+	28.6847i	−0.881459	+	1.52673i	−0.0317390	+	0.999496i	$0.510105\pi$
$353$	−16.5611	+	28.6847i	−0.881459	+	1.52673i	−0.849720	+	0.527235i	$0.823229\pi$
$354$		0			0
$355$	−3.78234	−	6.55120i	−0.200746	−	0.347702i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−34.5930			−1.82575			−0.912874	−	0.408242i	$-0.866142\pi$
$359$	−34.5930			−1.82575			−0.912874	+	0.408242i	$0.866142\pi$
$360$		0			0
$361$	−0.766602			−0.0403475
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−1.62773	−	2.81931i	−0.0851992	−	0.147569i
$366$		0			0
$367$	−1.64805	+	2.85451i	−0.0860277	+	0.149004i	−0.905829	−	0.423644i	$-0.860751\pi$
$367$	−1.64805	+	2.85451i	−0.0860277	+	0.149004i	0.819801	+	0.572649i	$0.194084\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$	11.8377	+	20.5035i	0.612933	+	1.06163i	0.990743	+	0.135748i	$0.0433436\pi$
$373$	11.8377	+	20.5035i	0.612933	+	1.06163i	−0.377811	+	0.925883i	$0.623323\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	15.1608			0.780821
$378$		0			0
$379$	−25.4415			−1.30684			−0.653421	−	0.756995i	$-0.726667\pi$
$379$	−25.4415			−1.30684			−0.653421	+	0.756995i	$0.726667\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−11.8639	−	20.5489i	−0.606218	−	1.05000i	−0.991858	−	0.127351i	$-0.959353\pi$
$383$	−11.8639	−	20.5489i	−0.606218	−	1.05000i	0.385640	−	0.922649i	$-0.373981\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$	9.76374	−	16.9113i	0.495041	−	0.857436i	−0.504943	−	0.863153i	$-0.668486\pi$
$389$	9.76374	−	16.9113i	0.495041	−	0.857436i	0.999984	+	0.00571663i	$0.00181967\pi$
$390$		0			0
$391$	2.84714	+	4.93139i	0.143986	+	0.249391i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	5.65808			0.284689
$396$		0			0
$397$	28.8936			1.45013			0.725064	−	0.688682i	$-0.241810\pi$
$397$	28.8936			1.45013			0.725064	+	0.688682i	$0.241810\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	2.75292	+	4.76820i	0.137474	+	0.238112i	0.926540	−	0.376196i	$-0.122768\pi$
$401$	2.75292	+	4.76820i	0.137474	+	0.238112i	−0.789066	+	0.614309i	$0.789435\pi$
$402$		0			0
$403$	−8.27988	+	14.3412i	−0.412450	+	0.714385i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−29.1130	+	50.4253i	−1.44308	+	2.49949i
$408$		0			0
$409$	−0.511954	−	0.886731i	−0.0253145	−	0.0438460i	0.853091	−	0.521763i	$-0.174725\pi$
$409$	−0.511954	−	0.886731i	−0.0253145	−	0.0438460i	−0.878405	+	0.477917i	$0.841392\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−12.3005			−0.603807
$416$		0			0
$417$		0			0
$418$		0			0
$419$	16.9398	+	29.3405i	0.827562	+	1.43338i	0.899946	+	0.436002i	$0.143606\pi$
$419$	16.9398	+	29.3405i	0.827562	+	1.43338i	−0.0723837	+	0.997377i	$0.523061\pi$
$420$		0			0
$421$	0.563823	−	0.976570i	0.0274790	−	0.0475951i	−0.851959	−	0.523609i	$-0.824585\pi$
$421$	0.563823	−	0.976570i	0.0274790	−	0.0475951i	0.879438	+	0.476014i	$0.157919\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−8.58772	+	14.8744i	−0.416566	+	0.721513i
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−2.88343			−0.138890			−0.0694450	−	0.997586i	$-0.522123\pi$
$431$	−2.88343			−0.138890			−0.0694450	+	0.997586i	$0.522123\pi$
$432$		0			0
$433$	14.3808			0.691097			0.345548	−	0.938401i	$-0.387693\pi$
$433$	14.3808			0.691097			0.345548	+	0.938401i	$0.387693\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	3.12621	+	5.41476i	0.149547	+	0.259023i
$438$		0			0
$439$	10.4958	−	18.1792i	0.500936	−	0.867646i	−0.499064	−	0.866565i	$-0.666323\pi$
$439$	10.4958	−	18.1792i	0.500936	−	0.867646i	0.999999	−	0.00108089i	$-0.000344059\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−10.0293	+	17.3713i	−0.476507	+	0.825335i	−0.999638	−	0.0269179i	$-0.991431\pi$
$443$	−10.0293	+	17.3713i	−0.476507	+	0.825335i	0.523130	+	0.852253i	$0.324764\pi$
$444$		0			0
$445$	−1.34672	−	2.33258i	−0.0638405	−	0.110575i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	11.4192			0.538903			0.269452	−	0.963014i	$-0.413158\pi$
$449$	11.4192			0.538903			0.269452	+	0.963014i	$0.413158\pi$
$450$		0			0
$451$	−27.1337			−1.27768
$452$		0			0
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	9.10294	−	15.7667i	0.425817	−	0.737537i	−0.570679	−	0.821173i	$-0.693320\pi$
$457$	9.10294	−	15.7667i	0.425817	−	0.737537i	0.996496	+	0.0836359i	$0.0266533\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−18.6430	+	32.2906i	−0.868289	+	1.50392i	−0.00454533	+	0.999990i	$0.501447\pi$
$461$	−18.6430	+	32.2906i	−0.868289	+	1.50392i	−0.863744	+	0.503931i	$0.831887\pi$
$462$		0			0
$463$	−0.530345	−	0.918584i	−0.0246472	−	0.0426902i	0.853439	−	0.521193i	$-0.174513\pi$
$463$	−0.530345	−	0.918584i	−0.0246472	−	0.0426902i	−0.878086	+	0.478503i	$0.841180\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	28.0747			1.29914			0.649571	−	0.760301i	$-0.274948\pi$
$467$	28.0747			1.29914			0.649571	+	0.760301i	$0.274948\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$	12.8825	+	22.3132i	0.592340	+	1.02596i
$474$		0			0
$475$	−9.42947	+	16.3323i	−0.432654	+	0.749378i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−3.61705	+	6.26492i	−0.165267	+	0.286251i	−0.936750	−	0.349999i	$-0.886182\pi$
$479$	−3.61705	+	6.26492i	−0.165267	+	0.286251i	0.771483	+	0.636250i	$0.219515\pi$
$480$		0			0
$481$	−12.1619	−	21.0650i	−0.554535	−	0.960483i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−3.56731			−0.161983
$486$		0			0
$487$	−33.8290			−1.53294			−0.766470	−	0.642280i	$-0.777988\pi$
$487$	−33.8290			−1.53294			−0.766470	+	0.642280i	$0.777988\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	0.300406	+	0.520319i	0.0135572	+	0.0234817i	0.872724	−	0.488213i	$-0.162351\pi$
$491$	0.300406	+	0.520319i	0.0135572	+	0.0234817i	−0.859167	+	0.511695i	$0.829018\pi$
$492$		0			0
$493$	−11.6951	+	20.2565i	−0.526722	+	0.912309i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−2.82067	−	4.88554i	−0.126271	−	0.218707i	0.795958	−	0.605351i	$-0.206967\pi$
$499$	−2.82067	−	4.88554i	−0.126271	−	0.218707i	−0.922229	+	0.386644i	$0.873634\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−31.0034			−1.38237			−0.691186	−	0.722677i	$-0.742911\pi$
$503$	−31.0034			−1.38237			−0.691186	+	0.722677i	$0.742911\pi$
$504$		0			0
$505$	3.60504			0.160422
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−17.3480	−	30.0475i	−0.768935	−	1.33183i	−0.938141	−	0.346253i	$-0.887454\pi$
$509$	−17.3480	−	30.0475i	−0.768935	−	1.33183i	0.169206	−	0.985581i	$-0.445880\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−1.20889	+	2.09386i	−0.0532701	+	0.0922665i
$516$		0			0
$517$	−20.4503	−	35.4210i	−0.899405	−	1.55781i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	25.0166			1.09600			0.547998	−	0.836479i	$-0.315390\pi$
$521$	25.0166			1.09600			0.547998	+	0.836479i	$0.315390\pi$
$522$		0			0
$523$	−3.18639			−0.139331			−0.0696656	−	0.997570i	$-0.522193\pi$
$523$	−3.18639			−0.139331			−0.0696656	+	0.997570i	$0.522193\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−12.7743	−	22.1257i	−0.556457	−	0.963811i
$528$		0			0
$529$	10.4280	−	18.0618i	0.453391	−	0.785296i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	5.66753	−	9.81645i	0.245488	−	0.425198i
$534$		0			0
$535$	5.84745	+	10.1281i	0.252808	+	0.437875i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		0			0
$540$		0			0
$541$	13.6139			0.585306			0.292653	−	0.956219i	$-0.405462\pi$
$541$	13.6139			0.585306			0.292653	+	0.956219i	$0.405462\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−5.84618	−	10.1259i	−0.250423	−	0.433745i
$546$		0			0
$547$	−5.91254	+	10.2408i	−0.252802	+	0.437866i	−0.964296	−	0.264826i	$-0.914685\pi$
$547$	−5.91254	+	10.2408i	−0.252802	+	0.437866i	0.711494	+	0.702692i	$0.248019\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−12.8414	+	22.2420i	−0.547064	+	0.947543i
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−18.6582			−0.790574			−0.395287	−	0.918558i	$-0.629355\pi$
$557$	−18.6582			−0.790574			−0.395287	+	0.918558i	$0.629355\pi$
$558$		0			0
$559$	−10.7633			−0.455239
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−11.3196	−	19.6060i	−0.477062	−	0.826296i	0.522592	−	0.852583i	$-0.324965\pi$
$563$	−11.3196	−	19.6060i	−0.477062	−	0.826296i	−0.999654	+	0.0262866i	$0.991632\pi$
$564$		0			0
$565$	−1.19246	+	2.06539i	−0.0501670	+	0.0868917i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	5.45277	−	9.44447i	0.228592	−	0.395933i	−0.728799	−	0.684728i	$-0.759921\pi$
$569$	5.45277	−	9.44447i	0.228592	−	0.395933i	0.957391	+	0.288795i	$0.0932545\pi$
$570$		0			0
$571$	13.8055	+	23.9119i	0.577743	+	1.00068i	0.995738	+	0.0922313i	$0.0293999\pi$
$571$	13.8055	+	23.9119i	0.577743	+	1.00068i	−0.417994	+	0.908450i	$0.637267\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−6.46693			−0.269690
$576$		0			0
$577$	−20.5184			−0.854193			−0.427096	−	0.904206i	$-0.640463\pi$
$577$	−20.5184			−0.854193			−0.427096	+	0.904206i	$0.640463\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−1.60249	+	2.77559i	−0.0663683	+	0.114953i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	7.59632	−	13.1572i	0.313534	−	0.543056i	−0.665591	−	0.746317i	$-0.731820\pi$
$587$	7.59632	−	13.1572i	0.313534	−	0.543056i	0.979125	+	0.203260i	$0.0651538\pi$
$588$		0			0
$589$	−14.0264	−	24.2944i	−0.577947	−	1.00103i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−6.78747			−0.278728			−0.139364	−	0.990241i	$-0.544506\pi$
$593$	−6.78747			−0.278728			−0.139364	+	0.990241i	$0.544506\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$	6.32519	+	10.9555i	0.258440	+	0.447632i	0.965824	−	0.259198i	$-0.0834582\pi$
$599$	6.32519	+	10.9555i	0.258440	+	0.447632i	−0.707384	+	0.706829i	$0.750125\pi$
$600$		0			0
$601$	11.3699	−	19.6932i	0.463787	−	0.803303i	−0.535359	−	0.844625i	$-0.679824\pi$
$601$	11.3699	−	19.6932i	0.463787	−	0.803303i	0.999146	+	0.0413219i	$0.0131569\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	9.70374	−	16.8074i	0.394513	−	0.683317i
$606$		0			0
$607$	20.9613	+	36.3061i	0.850794	+	1.47362i	0.880493	+	0.474059i	$0.157212\pi$
$607$	20.9613	+	36.3061i	0.850794	+	1.47362i	−0.0296994	+	0.999559i	$0.509455\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	17.0862			0.691232
$612$		0			0
$613$	27.4075			1.10698			0.553490	−	0.832856i	$-0.313296\pi$
$613$	27.4075			1.10698			0.553490	+	0.832856i	$0.313296\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−5.75420	−	9.96656i	−0.231655	−	0.401239i	0.726640	−	0.687018i	$-0.241081\pi$
$617$	−5.75420	−	9.96656i	−0.231655	−	0.401239i	−0.958295	+	0.285780i	$0.907747\pi$
$618$		0			0
$619$	18.8780	−	32.6976i	0.758770	−	1.31423i	−0.184708	−	0.982793i	$-0.559134\pi$
$619$	18.8780	−	32.6976i	0.758770	−	1.31423i	0.943478	−	0.331435i	$-0.107533\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−8.29436	−	14.3662i	−0.331774	−	0.574650i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	37.5270			1.49630
$630$		0			0
$631$	45.4466			1.80920			0.904600	−	0.426262i	$-0.140170\pi$
$631$	45.4466			1.80920			0.904600	+	0.426262i	$0.140170\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	0.488144	+	0.845490i	0.0193714	+	0.0335523i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−0.149803	+	0.259467i	−0.00591687	+	0.0102483i	−0.868969	−	0.494867i	$-0.835217\pi$
$641$	−0.149803	+	0.259467i	−0.00591687	+	0.0102483i	0.863052	+	0.505115i	$0.168550\pi$
$642$		0			0
$643$	3.61580	+	6.26275i	0.142593	+	0.246979i	0.928472	−	0.371401i	$-0.121123\pi$
$643$	3.61580	+	6.26275i	0.142593	+	0.246979i	−0.785879	+	0.618380i	$0.787789\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	9.56597			0.376077			0.188039	−	0.982162i	$-0.439787\pi$
$647$	9.56597			0.376077			0.188039	+	0.982162i	$0.439787\pi$
$648$		0			0
$649$	−67.5707			−2.65238
$650$		0			0
$651$		0			0
$652$		0			0
$653$	19.5035	+	33.7811i	0.763232	+	1.32196i	0.941176	+	0.337915i	$0.109722\pi$
$653$	19.5035	+	33.7811i	0.763232	+	1.32196i	−0.177945	+	0.984040i	$0.556945\pi$
$654$		0			0
$655$	2.96928	−	5.14295i	0.116019	−	0.200952i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	0.251281	−	0.435231i	0.00978851	−	0.0169542i	−0.861090	−	0.508453i	$-0.830218\pi$
$659$	0.251281	−	0.435231i	0.00978851	−	0.0169542i	0.870878	+	0.491499i	$0.163551\pi$
$660$		0			0
$661$	−1.09910	−	1.90370i	−0.0427501	−	0.0740453i	0.843859	−	0.536566i	$-0.180279\pi$
$661$	−1.09910	−	1.90370i	−0.0427501	−	0.0740453i	−0.886609	+	0.462520i	$0.846945\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−8.80693			−0.341006
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−25.2907	−	43.8048i	−0.976337	−	1.69107i
$672$		0			0
$673$	7.50630	−	13.0013i	0.289346	−	0.501163i	−0.684307	−	0.729194i	$-0.739895\pi$
$673$	7.50630	−	13.0013i	0.289346	−	0.501163i	0.973654	+	0.228031i	$0.0732287\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−14.8304	+	25.6869i	−0.569977	+	0.987229i	0.426591	+	0.904445i	$0.359715\pi$
$677$	−14.8304	+	25.6869i	−0.569977	+	0.987229i	−0.996568	+	0.0827841i	$0.973619\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−25.4591			−0.974165			−0.487083	−	0.873356i	$-0.661939\pi$
$683$	−25.4591			−0.974165			−0.487083	+	0.873356i	$0.661939\pi$
$684$		0			0
$685$	2.15636			0.0823904
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−0.669436	−	1.15950i	−0.0255035	−	0.0441733i
$690$		0			0
$691$	−5.95499	+	10.3143i	−0.226538	+	0.392376i	−0.956780	−	0.290813i	$-0.906074\pi$
$691$	−5.95499	+	10.3143i	−0.226538	+	0.392376i	0.730241	+	0.683189i	$0.239408\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−8.57070	+	14.8449i	−0.325105	+	0.563099i
$696$		0			0
$697$	8.74393	+	15.1449i	0.331200	+	0.573655i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	3.84543			0.145240			0.0726199	−	0.997360i	$-0.476864\pi$
$701$	3.84543			0.145240			0.0726199	+	0.997360i	$0.476864\pi$
$702$		0			0
$703$	41.2053			1.55409
$704$		0			0
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	13.3533	−	23.1286i	0.501494	−	0.868614i	−0.498504	−	0.866887i	$-0.666117\pi$
$709$	13.3533	−	23.1286i	0.501494	−	0.868614i	0.999999	−	0.00172652i	$-0.000549569\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	4.80979	−	8.33081i	0.180128	−	0.311991i
$714$		0			0
$715$	5.80872	+	10.0610i	0.217234	+	0.376260i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−26.7221			−0.996567			−0.498284	−	0.867014i	$-0.666036\pi$
$719$	−26.7221			−0.996567			−0.498284	+	0.867014i	$0.666036\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−13.2820	−	23.0051i	−0.493281	−	0.854388i
$726$		0			0
$727$	1.13012	−	1.95743i	0.0419139	−	0.0725970i	−0.844307	−	0.535859i	$-0.819988\pi$
$727$	1.13012	−	1.95743i	0.0419139	−	0.0725970i	0.886221	+	0.463262i	$0.153321\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	8.30287	−	14.3810i	0.307093	−	0.531900i
$732$		0			0
$733$	18.3702	+	31.8181i	0.678519	+	1.17523i	0.975427	+	0.220323i	$0.0707113\pi$
$733$	18.3702	+	31.8181i	0.678519	+	1.17523i	−0.296908	+	0.954906i	$0.595955\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	11.6090			0.427621
$738$		0			0
$739$	34.1817			1.25739			0.628697	−	0.777650i	$-0.283588\pi$
$739$	34.1817			1.25739			0.628697	+	0.777650i	$0.283588\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	4.56487	+	7.90658i	0.167469	+	0.290064i	0.937529	−	0.347907i	$-0.113107\pi$
$743$	4.56487	+	7.90658i	0.167469	+	0.290064i	−0.770061	+	0.637971i	$0.779774\pi$
$744$		0			0
$745$	7.70339	−	13.3427i	0.282230	−	0.488837i
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$	19.0648	+	33.0212i	0.695683	+	1.20496i	0.969950	+	0.243305i	$0.0782316\pi$
$751$	19.0648	+	33.0212i	0.695683	+	1.20496i	−0.274266	+	0.961654i	$0.588435\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−6.33564			−0.230578
$756$		0			0
$757$	18.6952			0.679488			0.339744	−	0.940518i	$-0.389660\pi$
$757$	18.6952			0.679488			0.339744	+	0.940518i	$0.389660\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	8.07859	+	13.9925i	0.292849	+	0.507229i	0.974482	−	0.224465i	$-0.0720635\pi$
$761$	8.07859	+	13.9925i	0.292849	+	0.507229i	−0.681634	+	0.731694i	$0.738730\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$	14.1138	−	24.4458i	0.509618	−	0.882685i
$768$		0			0
$769$	16.9628	+	29.3804i	0.611694	+	1.05949i	0.990955	+	0.134195i	$0.0428449\pi$
$769$	16.9628	+	29.3804i	0.611694	+	1.05949i	−0.379261	+	0.925290i	$0.623822\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−39.6903			−1.42756			−0.713781	−	0.700369i	$-0.753019\pi$
$773$	−39.6903			−1.42756			−0.713781	+	0.700369i	$0.753019\pi$
$774$		0			0
$775$	29.0152			1.04226
$776$		0			0
$777$		0			0
$778$		0			0
$779$	9.60099	+	16.6294i	0.343991	+	0.595810i
$780$		0			0
$781$	−29.8784	+	51.7509i	−1.06913	+	1.85179i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	2.54611	−	4.41000i	0.0908746	−	0.157400i
$786$		0			0
$787$	−0.158840	−	0.275119i	−0.00566204	−	0.00980695i	0.863180	−	0.504895i	$-0.168469\pi$
$787$	−0.158840	−	0.275119i	−0.00566204	−	0.00980695i	−0.868843	+	0.495089i	$0.835136\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	21.1303			0.750358
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−21.0702	−	36.4946i	−0.746344	−	1.29271i	−0.949564	−	0.313572i	$-0.898474\pi$
$797$	−21.0702	−	36.4946i	−0.746344	−	1.29271i	0.203221	−	0.979133i	$-0.434859\pi$
$798$		0			0
$799$	−13.1804	+	22.8290i	−0.466288	+	0.807634i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−12.8582	+	22.2710i	−0.453755	+	0.785926i
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−12.8010			−0.450061			−0.225030	−	0.974352i	$-0.572248\pi$
$809$	−12.8010			−0.450061			−0.225030	+	0.974352i	$0.572248\pi$
$810$		0			0
$811$	−27.1410			−0.953051			−0.476526	−	0.879161i	$-0.658104\pi$
$811$	−27.1410			−0.953051			−0.476526	+	0.879161i	$0.658104\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−2.82429	−	4.89182i	−0.0989307	−	0.171353i
$816$		0			0
$817$	9.11670	−	15.7906i	0.318953	−	0.552443i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−5.95924	+	10.3217i	−0.207979	+	0.360230i	−0.951078	−	0.308952i	$-0.900022\pi$
$821$	−5.95924	+	10.3217i	−0.207979	+	0.360230i	0.743099	+	0.669182i	$0.233355\pi$
$822$		0			0
$823$	9.26505	+	16.0475i	0.322959	+	0.559382i	0.981097	−	0.193515i	$-0.0619890\pi$
$823$	9.26505	+	16.0475i	0.322959	+	0.559382i	−0.658138	+	0.752897i	$0.728656\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−9.64616			−0.335430			−0.167715	−	0.985836i	$-0.553639\pi$
$827$	−9.64616			−0.335430			−0.167715	+	0.985836i	$0.553639\pi$
$828$		0			0
$829$	20.4310			0.709599			0.354800	−	0.934942i	$-0.384549\pi$
$829$	20.4310			0.709599			0.354800	+	0.934942i	$0.384549\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$	0.363224	−	0.629122i	0.0125699	−	0.0217717i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−7.18866	+	12.4511i	−0.248180	+	0.429861i	−0.963021	−	0.269427i	$-0.913166\pi$
$839$	−7.18866	+	12.4511i	−0.248180	+	0.429861i	0.714841	+	0.699287i	$0.246499\pi$
$840$		0			0
$841$	−3.58799	−	6.21459i	−0.123724	−	0.214296i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	5.07672			0.174644
$846$		0			0
$847$		0			0
$848$		0			0
$849$		0			0
$850$		0			0
$851$	7.06487	+	12.2367i	0.242181	+	0.419469i
$852$		0			0
$853$	2.05636	−	3.56173i	0.0704085	−	0.121951i	−0.828672	−	0.559735i	$-0.810903\pi$
$853$	2.05636	−	3.56173i	0.0704085	−	0.121951i	0.899080	+	0.437784i	$0.144236\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−25.5542	+	44.2612i	−0.872915	+	1.51193i	−0.0139471	+	0.999903i	$0.504440\pi$
$857$	−25.5542	+	44.2612i	−0.872915	+	1.51193i	−0.858968	+	0.512030i	$0.828894\pi$
$858$		0			0
$859$	7.65825	+	13.2645i	0.261296	+	0.452578i	0.966587	−	0.256340i	$-0.0825168\pi$
$859$	7.65825	+	13.2645i	0.261296	+	0.452578i	−0.705290	+	0.708918i	$0.749183\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	24.9730			0.850090			0.425045	−	0.905172i	$-0.360258\pi$
$863$	24.9730			0.850090			0.425045	+	0.905172i	$0.360258\pi$
$864$		0			0
$865$	−3.56794			−0.121314
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−22.3479	−	38.7076i	−0.758099	−	1.31307i
$870$		0			0
$871$	−2.42481	+	4.19989i	−0.0821615	+	0.142308i
$872$		0			0
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−18.1959	−	31.5162i	−0.614432	−	1.06423i	−0.990484	−	0.137628i	$-0.956052\pi$
$877$	−18.1959	−	31.5162i	−0.614432	−	1.06423i	0.376052	−	0.926598i	$-0.377281\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	56.1807			1.89277			0.946387	−	0.323035i	$-0.104703\pi$
$881$	56.1807			1.89277			0.946387	+	0.323035i	$0.104703\pi$
$882$		0			0
$883$	−22.7585			−0.765884			−0.382942	−	0.923772i	$-0.625089\pi$
$883$	−22.7585			−0.765884			−0.382942	+	0.923772i	$0.625089\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	5.01568	+	8.68742i	0.168410	+	0.291695i	0.937861	−	0.347011i	$-0.112803\pi$
$887$	5.01568	+	8.68742i	0.168410	+	0.291695i	−0.769451	+	0.638706i	$0.779470\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−14.4723	+	25.0667i	−0.484296	+	0.838825i
$894$		0			0
$895$	−5.72485	−	9.91573i	−0.191361	−	0.331446i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	39.5141			1.31787
$900$		0			0
$901$	2.06563			0.0688160
$902$		0			0
$903$		0			0
$904$		0			0
$905$	5.21414	+	9.03115i	0.173324	+	0.300206i
$906$		0			0
$907$	10.2856	−	17.8151i	0.341527	−	0.591542i	−0.643189	−	0.765707i	$-0.722389\pi$
$907$	10.2856	−	17.8151i	0.341527	−	0.591542i	0.984716	+	0.174165i	$0.0557226\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	1.19047	−	2.06196i	0.0394421	−	0.0683157i	−0.845630	−	0.533769i	$-0.820775\pi$
$911$	1.19047	−	2.06196i	0.0394421	−	0.0683157i	0.885073	+	0.465453i	$0.154109\pi$
$912$		0			0
$913$	48.5836	+	84.1493i	1.60788	+	2.78493i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	23.6261			0.779352			0.389676	−	0.920952i	$-0.372587\pi$
$919$	23.6261			0.779352			0.389676	+	0.920952i	$0.372587\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−12.4816	−	21.6188i	−0.410838	−	0.711593i
$924$		0			0
$925$	−21.3095	+	36.9091i	−0.700652	+	1.21356i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	29.6884	−	51.4219i	0.974046	−	1.68710i	0.290999	−	0.956723i	$-0.406012\pi$
$929$	29.6884	−	51.4219i	0.974046	−	1.68710i	0.683047	−	0.730374i	$-0.260654\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−17.9235			−0.586161
$936$		0			0
$937$	−16.1455			−0.527451			−0.263725	−	0.964598i	$-0.584951\pi$
$937$	−16.1455			−0.527451			−0.263725	+	0.964598i	$0.584951\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−9.88063	−	17.1137i	−0.322099	−	0.557892i	0.658822	−	0.752299i	$-0.271055\pi$
$941$	−9.88063	−	17.1137i	−0.322099	−	0.557892i	−0.980921	+	0.194407i	$0.937722\pi$
$942$		0			0
$943$	−3.29228	+	5.70239i	−0.107211	+	0.185695i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−24.4618	+	42.3691i	−0.794902	+	1.37681i	0.128000	+	0.991774i	$0.459144\pi$
$947$	−24.4618	+	42.3691i	−0.794902	+	1.37681i	−0.922902	+	0.385036i	$0.874189\pi$
$948$		0			0
$949$	−5.37147	−	9.30366i	−0.174365	−	0.302010i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	48.6464			1.57581			0.787905	−	0.615797i	$-0.211166\pi$
$953$	48.6464			1.57581			0.787905	+	0.615797i	$0.211166\pi$
$954$		0			0
$955$	9.38797			0.303788
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−6.08013	+	10.5311i	−0.196133	+	0.339713i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	2.73895	−	4.74400i	0.0881699	−	0.152715i
$966$		0			0
$967$	22.1435	+	38.3537i	0.712087	+	1.23337i	0.964072	+	0.265639i	$0.0855831\pi$
$967$	22.1435	+	38.3537i	0.712087	+	1.23337i	−0.251986	+	0.967731i	$0.581084\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	37.2709			1.19608			0.598040	−	0.801466i	$-0.295946\pi$
$971$	37.2709			1.19608			0.598040	+	0.801466i	$0.295946\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	30.9312	+	53.5744i	0.989577	+	1.71400i	0.619499	+	0.784997i	$0.287336\pi$
$977$	30.9312	+	53.5744i	0.989577	+	1.71400i	0.370078	+	0.929001i	$0.379331\pi$
$978$		0			0
$979$	−10.6383	+	18.4261i	−0.340003	+	0.588902i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	5.48825	−	9.50593i	0.175048	−	0.303192i	−0.765130	−	0.643876i	$-0.777325\pi$
$983$	5.48825	−	9.50593i	0.175048	−	0.303192i	0.940178	+	0.340684i	$0.110659\pi$
$984$		0			0
$985$	4.97585	+	8.61843i	0.158544	+	0.274606i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	6.25242			0.198815
$990$		0			0
$991$	10.8634			0.345087			0.172543	−	0.985002i	$-0.444802\pi$
$991$	10.8634			0.345087			0.172543	+	0.985002i	$0.444802\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−1.89498	−	3.28220i	−0.0600749	−	0.104053i
$996$		0			0
$997$	−20.4646	+	35.4457i	−0.648119	+	1.12258i	0.335452	+	0.942057i	$0.391111\pi$
$997$	−20.4646	+	35.4457i	−0.648119	+	1.12258i	−0.983572	+	0.180519i	$0.942222\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5292.2.j.g.3529.4		14
3.2	odd	2		1764.2.j.h.1177.4		14
7.2	even	3		5292.2.i.i.2125.4		14
7.3	odd	6		756.2.l.b.289.4		14
7.4	even	3		5292.2.l.i.3313.4		14
7.5	odd	6		756.2.i.b.613.4		14
7.6	odd	2		5292.2.j.h.3529.4		14
9.4	even	3	inner	5292.2.j.g.1765.4		14
9.5	odd	6		1764.2.j.h.589.4		14
21.2	odd	6		1764.2.i.i.1537.7		14
21.5	even	6		252.2.i.b.25.1	✓	14
21.11	odd	6		1764.2.l.i.961.2		14
21.17	even	6		252.2.l.b.205.6	yes	14
21.20	even	2		1764.2.j.g.1177.4		14
28.3	even	6		3024.2.t.j.289.4		14
28.19	even	6		3024.2.q.j.2881.4		14
63.4	even	3		5292.2.i.i.1549.4		14
63.5	even	6		252.2.l.b.193.6	yes	14
63.13	odd	6		5292.2.j.h.1765.4		14
63.23	odd	6		1764.2.l.i.949.2		14
63.31	odd	6		756.2.i.b.37.4		14
63.32	odd	6		1764.2.i.i.373.7		14
63.38	even	6		2268.2.k.e.1297.4		14
63.40	odd	6		756.2.l.b.361.4		14
63.41	even	6		1764.2.j.g.589.4		14
63.47	even	6		2268.2.k.e.1621.4		14
63.52	odd	6		2268.2.k.f.1297.4		14
63.58	even	3		5292.2.l.i.361.4		14
63.59	even	6		252.2.i.b.121.1	yes	14
63.61	odd	6		2268.2.k.f.1621.4		14
84.47	odd	6		1008.2.q.j.529.7		14
84.59	odd	6		1008.2.t.j.961.2		14
252.31	even	6		3024.2.q.j.2305.4		14
252.59	odd	6		1008.2.q.j.625.7		14
252.103	even	6		3024.2.t.j.1873.4		14
252.131	odd	6		1008.2.t.j.193.2		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.i.b.25.1	✓	14	21.5	even	6
252.2.i.b.121.1	yes	14	63.59	even	6
252.2.l.b.193.6	yes	14	63.5	even	6
252.2.l.b.205.6	yes	14	21.17	even	6
756.2.i.b.37.4		14	63.31	odd	6
756.2.i.b.613.4		14	7.5	odd	6
756.2.l.b.289.4		14	7.3	odd	6
756.2.l.b.361.4		14	63.40	odd	6
1008.2.q.j.529.7		14	84.47	odd	6
1008.2.q.j.625.7		14	252.59	odd	6
1008.2.t.j.193.2		14	252.131	odd	6
1008.2.t.j.961.2		14	84.59	odd	6
1764.2.i.i.373.7		14	63.32	odd	6
1764.2.i.i.1537.7		14	21.2	odd	6
1764.2.j.g.589.4		14	63.41	even	6
1764.2.j.g.1177.4		14	21.20	even	2
1764.2.j.h.589.4		14	9.5	odd	6
1764.2.j.h.1177.4		14	3.2	odd	2
1764.2.l.i.949.2		14	63.23	odd	6
1764.2.l.i.961.2		14	21.11	odd	6
2268.2.k.e.1297.4		14	63.38	even	6
2268.2.k.e.1621.4		14	63.47	even	6
2268.2.k.f.1297.4		14	63.52	odd	6
2268.2.k.f.1621.4		14	63.61	odd	6
3024.2.q.j.2305.4		14	252.31	even	6
3024.2.q.j.2881.4		14	28.19	even	6
3024.2.t.j.289.4		14	28.3	even	6
3024.2.t.j.1873.4		14	252.103	even	6
5292.2.i.i.1549.4		14	63.4	even	3
5292.2.i.i.2125.4		14	7.2	even	3
5292.2.j.g.1765.4		14	9.4	even	3	inner
5292.2.j.g.3529.4		14	1.1	even	1	trivial
5292.2.j.h.1765.4		14	63.13	odd	6
5292.2.j.h.3529.4		14	7.6	odd	2
5292.2.l.i.361.4		14	63.58	even	3
5292.2.l.i.3313.4		14	7.4	even	3

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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:	\( N \)	\(=\)	\( 5292 = 2^{2} \cdot 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5292.j (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.381918 + 0.661502i) q^{5} +O(q^{10})\)	\(q+(0.381918 + 0.661502i) q^{5} +(3.01695 - 5.22551i) q^{11} +(1.26032 + 2.18294i) q^{13} -3.88888 q^{17} -4.27006 q^{19} +(-0.732124 - 1.26808i) q^{23} +(2.20828 - 3.82485i) q^{25} +(3.00732 - 5.20884i) q^{29} +(3.28482 + 5.68948i) q^{31} -9.64983 q^{37} +(-2.24844 - 3.89442i) q^{41} +(-2.13503 + 3.69798i) q^{43} +(3.38924 - 5.87034i) q^{47} -0.531162 q^{53} +4.60891 q^{55} +(-5.59926 - 9.69821i) q^{59} +(4.19144 - 7.25979i) q^{61} +(-0.962681 + 1.66741i) q^{65} +(0.961979 + 1.66620i) q^{67} -9.90353 q^{71} -4.26198 q^{73} +(3.70372 - 6.41503i) q^{79} +(-8.05178 + 13.9461i) q^{83} +(-1.48523 - 2.57250i) q^{85} -3.52619 q^{89} +(-1.63081 - 2.82465i) q^{95} +(-2.33513 + 4.04456i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 2 q^{5}+O(q^{10}) \) 14 * q - 2 * q^5	\( 14 q - 2 q^{5} - 2 q^{11} - 2 q^{13} - 4 q^{17} + 14 q^{19} - 11 q^{23} - 9 q^{25} - q^{29} + q^{31} - 20 q^{37} - 33 q^{41} + 7 q^{43} - 3 q^{47} - 30 q^{53} + 28 q^{55} - 14 q^{59} + 10 q^{61} - 15 q^{65} + 6 q^{67} - 2 q^{71} + 42 q^{73} - 10 q^{79} - 25 q^{83} + 8 q^{85} + 12 q^{89} + 28 q^{95} + 18 q^{97}+O(q^{100}) \) 14 * q - 2 * q^5 - 2 * q^11 - 2 * q^13 - 4 * q^17 + 14 * q^19 - 11 * q^23 - 9 * q^25 - q^29 + q^31 - 20 * q^37 - 33 * q^41 + 7 * q^43 - 3 * q^47 - 30 * q^53 + 28 * q^55 - 14 * q^59 + 10 * q^61 - 15 * q^65 + 6 * q^67 - 2 * q^71 + 42 * q^73 - 10 * q^79 - 25 * q^83 + 8 * q^85 + 12 * q^89 + 28 * q^95 + 18 * q^97

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