LMFDB - Embedded newform 5292.2.j.h.3529.1

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			3529.1
Root			$-1.58203 + 0.705117i$ of defining polynomial
Character	$\chi$	$=$	5292.3529
Dual form			5292.2.j.h.1765.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.26013 - 2.18261i) q^{5} +O(q^{10})$	$q+(-1.26013 - 2.18261i) q^{5} +(-0.687041 + 1.18999i) q^{11} +(-2.80008 - 4.84989i) q^{13} -5.39225 q^{17} -4.89435 q^{19} +(2.08765 + 3.61591i) q^{23} +(-0.675864 + 1.17063i) q^{25} +(1.56761 - 2.71518i) q^{29} +(-2.40060 - 4.15797i) q^{31} +5.39677 q^{37} +(3.02991 + 5.24797i) q^{41} +(2.44717 - 4.23863i) q^{43} +(-2.82774 + 4.89779i) q^{47} -14.0056 q^{53} +3.46305 q^{55} +(7.13442 + 12.3572i) q^{59} +(3.42860 - 5.93852i) q^{61} +(-7.05695 + 12.2230i) q^{65} +(4.05678 + 7.02655i) q^{67} +2.25704 q^{71} -7.02911 q^{73} +(-1.37843 + 2.38750i) q^{79} +(-7.48876 + 12.9709i) q^{83} +(6.79495 + 11.7692i) q^{85} +5.51608 q^{89} +(6.16752 + 10.6825i) q^{95} +(0.894003 - 1.54846i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−1.26013	−	2.18261i	−0.563548	−	0.976094i	−0.997183	−	0.0750053i	$-0.976103\pi$
$5$	−1.26013	−	2.18261i	−0.563548	−	0.976094i	0.433635	−	0.901089i	$-0.357231\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.687041	+	1.18999i	−0.207151	+	0.358796i	−0.950816	−	0.309757i	$-0.899752\pi$
$11$	−0.687041	+	1.18999i	−0.207151	+	0.358796i	0.743665	+	0.668552i	$0.233086\pi$
$12$		0			0
$13$	−2.80008	−	4.84989i	−0.776603	−	1.34512i	−0.933889	−	0.357563i	$-0.883608\pi$
$13$	−2.80008	−	4.84989i	−0.776603	−	1.34512i	0.157285	−	0.987553i	$-0.449726\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−5.39225			−1.30781			−0.653907	−	0.756575i	$-0.726871\pi$
$17$	−5.39225			−1.30781			−0.653907	+	0.756575i	$0.726871\pi$
$18$		0			0
$19$	−4.89435			−1.12284			−0.561420	−	0.827531i	$-0.689745\pi$
$19$	−4.89435			−1.12284			−0.561420	+	0.827531i	$0.689745\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.08765	+	3.61591i	0.435304	+	0.753969i	0.997320	−	0.0731570i	$-0.0233074\pi$
$23$	2.08765	+	3.61591i	0.435304	+	0.753969i	−0.562016	+	0.827126i	$0.689974\pi$
$24$		0			0
$25$	−0.675864	+	1.17063i	−0.135173	+	0.234126i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	1.56761	−	2.71518i	0.291097	−	0.504195i	−0.682972	−	0.730444i	$-0.739313\pi$
$29$	1.56761	−	2.71518i	0.291097	−	0.504195i	0.974069	+	0.226249i	$0.0726463\pi$
$30$		0			0
$31$	−2.40060	−	4.15797i	−0.431161	−	0.746793i	0.565812	−	0.824534i	$-0.308563\pi$
$31$	−2.40060	−	4.15797i	−0.431161	−	0.746793i	−0.996974	+	0.0777407i	$0.975229\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$		0			0
$36$		0			0
$37$	5.39677			0.887224			0.443612	−	0.896219i	$-0.353697\pi$
$37$	5.39677			0.887224			0.443612	+	0.896219i	$0.353697\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	3.02991	+	5.24797i	0.473193	+	0.819595i	0.999529	−	0.0306820i	$-0.00976793\pi$
$41$	3.02991	+	5.24797i	0.473193	+	0.819595i	−0.526336	+	0.850277i	$0.676435\pi$
$42$		0			0
$43$	2.44717	−	4.23863i	0.373190	−	0.646385i	−0.616864	−	0.787070i	$-0.711597\pi$
$43$	2.44717	−	4.23863i	0.373190	−	0.646385i	0.990054	+	0.140685i	$0.0449305\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−2.82774	+	4.89779i	−0.412468	+	0.714416i	−0.995159	−	0.0982782i	$-0.968667\pi$
$47$	−2.82774	+	4.89779i	−0.412468	+	0.714416i	0.582691	+	0.812694i	$0.302000\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−14.0056			−1.92382			−0.961910	−	0.273365i	$-0.911863\pi$
$53$	−14.0056			−1.92382			−0.961910	+	0.273365i	$0.911863\pi$
$54$		0			0
$55$	3.46305			0.466958
$56$		0			0
$57$		0			0
$58$		0			0
$59$	7.13442	+	12.3572i	0.928823	+	1.60877i	0.785294	+	0.619122i	$0.212512\pi$
$59$	7.13442	+	12.3572i	0.928823	+	1.60877i	0.143529	+	0.989646i	$0.454155\pi$
$60$		0			0
$61$	3.42860	−	5.93852i	0.438988	−	0.760349i	−0.558624	−	0.829421i	$-0.688670\pi$
$61$	3.42860	−	5.93852i	0.438988	−	0.760349i	0.997612	+	0.0690720i	$0.0220038\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−7.05695	+	12.2230i	−0.875307	+	1.51608i
$66$		0			0
$67$	4.05678	+	7.02655i	0.495615	+	0.858430i	0.999987	−	0.00505643i	$-0.00160952\pi$
$67$	4.05678	+	7.02655i	0.495615	+	0.858430i	−0.504373	+	0.863486i	$0.668276\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	2.25704			0.267861			0.133931	−	0.990991i	$-0.457240\pi$
$71$	2.25704			0.267861			0.133931	+	0.990991i	$0.457240\pi$
$72$		0			0
$73$	−7.02911			−0.822695			−0.411348	−	0.911479i	$-0.634942\pi$
$73$	−7.02911			−0.822695			−0.411348	+	0.911479i	$0.634942\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−1.37843	+	2.38750i	−0.155085	+	0.268615i	−0.933090	−	0.359643i	$-0.882898\pi$
$79$	−1.37843	+	2.38750i	−0.155085	+	0.268615i	0.778005	+	0.628258i	$0.216232\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−7.48876	+	12.9709i	−0.821998	+	1.42374i	0.0821933	+	0.996616i	$0.473808\pi$
$83$	−7.48876	+	12.9709i	−0.821998	+	1.42374i	−0.904192	+	0.427127i	$0.859526\pi$
$84$		0			0
$85$	6.79495	+	11.7692i	0.737016	+	1.27655i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	5.51608			0.584703			0.292352	−	0.956311i	$-0.405562\pi$
$89$	5.51608			0.584703			0.292352	+	0.956311i	$0.405562\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$	6.16752	+	10.6825i	0.632774	+	1.09600i
$96$		0			0
$97$	0.894003	−	1.54846i	0.0907722	−	0.157222i	−0.817064	−	0.576547i	$-0.804400\pi$
$97$	0.894003	−	1.54846i	0.0907722	−	0.157222i	0.907836	+	0.419325i	$0.137733\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	6.69534	−	11.5967i	0.666211	−	1.15391i	−0.312744	−	0.949837i	$-0.601248\pi$
$101$	6.69534	−	11.5967i	0.666211	−	1.15391i	0.978955	−	0.204074i	$-0.0654183\pi$
$102$		0			0
$103$	−1.10164	−	1.90810i	−0.108548	−	0.188010i	0.806634	−	0.591051i	$-0.201287\pi$
$103$	−1.10164	−	1.90810i	−0.108548	−	0.188010i	−0.915182	+	0.403040i	$0.867953\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	9.86567			0.953750			0.476875	−	0.878971i	$-0.341769\pi$
$107$	9.86567			0.953750			0.476875	+	0.878971i	$0.341769\pi$
$108$		0			0
$109$	−3.08680			−0.295662			−0.147831	−	0.989013i	$-0.547229\pi$
$109$	−3.08680			−0.295662			−0.147831	+	0.989013i	$0.547229\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−0.218815	−	0.378999i	−0.0205844	−	0.0356532i	0.855550	−	0.517721i	$-0.173219\pi$
$113$	−0.218815	−	0.378999i	−0.0205844	−	0.0356532i	−0.876134	+	0.482067i	$0.839886\pi$
$114$		0			0
$115$	5.26142	−	9.11304i	0.490630	−	0.849796i
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	4.55595	+	7.89113i	0.414177	+	0.717376i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−9.19461			−0.822391
$126$		0			0
$127$	−5.75958			−0.511080			−0.255540	−	0.966798i	$-0.582253\pi$
$127$	−5.75958			−0.511080			−0.255540	+	0.966798i	$0.582253\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−0.714865	−	1.23818i	−0.0624580	−	0.108180i	0.833106	−	0.553114i	$-0.186561\pi$
$131$	−0.714865	−	1.23818i	−0.0624580	−	0.108180i	−0.895564	+	0.444934i	$0.853227\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$		0			0
$137$	5.59335	−	9.68796i	0.477872	−	0.827698i	−0.521806	−	0.853064i	$-0.674742\pi$
$137$	5.59335	−	9.68796i	0.477872	−	0.827698i	0.999678	+	0.0253656i	$0.00807500\pi$
$138$		0			0
$139$	7.87024	+	13.6317i	0.667545	+	1.15622i	0.978589	+	0.205826i	$0.0659881\pi$
$139$	7.87024	+	13.6317i	0.667545	+	1.15622i	−0.311044	+	0.950396i	$0.600679\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	7.69509			0.643496
$144$		0			0
$145$	−7.90157			−0.656189
$146$		0			0
$147$		0			0
$148$		0			0
$149$	3.96513	+	6.86780i	0.324836	+	0.562632i	0.981479	−	0.191569i	$-0.0613576\pi$
$149$	3.96513	+	6.86780i	0.324836	+	0.562632i	−0.656643	+	0.754201i	$0.728024\pi$
$150$		0			0
$151$	5.39683	−	9.34758i	0.439188	−	0.760696i	−0.558439	−	0.829545i	$-0.688600\pi$
$151$	5.39683	−	9.34758i	0.439188	−	0.760696i	0.997627	+	0.0688499i	$0.0219329\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−6.05016	+	10.4792i	−0.485960	+	0.841708i
$156$		0			0
$157$	−10.5884	−	18.3396i	−0.845045	−	1.46366i	−0.885582	−	0.464483i	$-0.846240\pi$
$157$	−10.5884	−	18.3396i	−0.845045	−	1.46366i	0.0405373	−	0.999178i	$-0.487093\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−1.07310			−0.0840520			−0.0420260	−	0.999117i	$-0.513381\pi$
$163$	−1.07310			−0.0840520			−0.0420260	+	0.999117i	$0.513381\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	7.71638	+	13.3652i	0.597112	+	1.03423i	0.993245	+	0.116035i	$0.0370185\pi$
$167$	7.71638	+	13.3652i	0.597112	+	1.03423i	−0.396133	+	0.918193i	$0.629648\pi$
$168$		0			0
$169$	−9.18094	+	15.9018i	−0.706226	+	1.22322i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	10.1810	−	17.6340i	0.774046	−	1.34069i	−0.161283	−	0.986908i	$-0.551563\pi$
$173$	10.1810	−	17.6340i	0.774046	−	1.34069i	0.935329	−	0.353779i	$-0.115103\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$		0			0
$179$	6.09920			0.455876			0.227938	−	0.973676i	$-0.426802\pi$
$179$	6.09920			0.455876			0.227938	+	0.973676i	$0.426802\pi$
$180$		0			0
$181$	10.0056			0.743714			0.371857	−	0.928290i	$-0.378721\pi$
$181$	10.0056			0.743714			0.371857	+	0.928290i	$0.378721\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−6.80065	−	11.7791i	−0.499993	−	0.866014i
$186$		0			0
$187$	3.70470	−	6.41673i	0.270915	−	0.469238i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−11.0993	+	19.2246i	−0.803120	+	1.39104i	0.114433	+	0.993431i	$0.463495\pi$
$191$	−11.0993	+	19.2246i	−0.803120	+	1.39104i	−0.917553	+	0.397613i	$0.869839\pi$
$192$		0			0
$193$	13.3080	+	23.0501i	0.957930	+	1.65918i	0.727516	+	0.686091i	$0.240675\pi$
$193$	13.3080	+	23.0501i	0.957930	+	1.65918i	0.230414	+	0.973093i	$0.425992\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−10.1696			−0.724551			−0.362276	−	0.932071i	$-0.618000\pi$
$197$	−10.1696			−0.724551			−0.362276	+	0.932071i	$0.618000\pi$
$198$		0			0
$199$	3.32485			0.235693			0.117846	−	0.993032i	$-0.462401\pi$
$199$	3.32485			0.235693			0.117846	+	0.993032i	$0.462401\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$	7.63618	−	13.2263i	0.533334	−	0.923762i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	3.36262	−	5.82423i	0.232597	−	0.402870i
$210$		0			0
$211$	−1.29535	−	2.24361i	−0.0891755	−	0.154456i	0.817987	−	0.575236i	$-0.195090\pi$
$211$	−1.29535	−	2.24361i	−0.0891755	−	0.154456i	−0.907163	+	0.420780i	$0.861757\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−12.3350			−0.841243
$216$		0			0
$217$		0			0
$218$		0			0
$219$		0			0
$220$		0			0
$221$	15.0988	+	26.1518i	1.01565	+	1.75916i
$222$		0			0
$223$	−12.4029	+	21.4824i	−0.830556	+	1.43857i	0.0670411	+	0.997750i	$0.478644\pi$
$223$	−12.4029	+	21.4824i	−0.830556	+	1.43857i	−0.897598	+	0.440816i	$0.854689\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	3.55125	−	6.15095i	0.235705	−	0.408253i	−0.723772	−	0.690039i	$-0.757593\pi$
$227$	3.55125	−	6.15095i	0.235705	−	0.408253i	0.959477	+	0.281786i	$0.0909267\pi$
$228$		0			0
$229$	3.23252	+	5.59889i	0.213611	+	0.369985i	0.952842	−	0.303467i	$-0.0981442\pi$
$229$	3.23252	+	5.59889i	0.213611	+	0.369985i	−0.739231	+	0.673452i	$0.764811\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−8.85900			−0.580372			−0.290186	−	0.956970i	$-0.593717\pi$
$233$	−8.85900			−0.580372			−0.290186	+	0.956970i	$0.593717\pi$
$234$		0			0
$235$	14.2533			0.929782
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−8.60836	−	14.9101i	−0.556828	−	0.964455i	−0.997759	−	0.0669138i	$-0.978685\pi$
$239$	−8.60836	−	14.9101i	−0.556828	−	0.964455i	0.440930	−	0.897541i	$-0.354649\pi$
$240$		0			0
$241$	−10.1106	+	17.5120i	−0.651279	+	1.12805i	0.331534	+	0.943443i	$0.392434\pi$
$241$	−10.1106	+	17.5120i	−0.651279	+	1.12805i	−0.982813	+	0.184604i	$0.940900\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$		0			0
$246$		0			0
$247$	13.7046	+	23.7370i	0.872001	+	1.51035i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−7.32214			−0.462169			−0.231085	−	0.972934i	$-0.574227\pi$
$251$	−7.32214			−0.462169			−0.231085	+	0.972934i	$0.574227\pi$
$252$		0			0
$253$	−5.73720			−0.360695
$254$		0			0
$255$		0			0
$256$		0			0
$257$	3.07308	+	5.32274i	0.191694	+	0.332023i	0.945812	−	0.324716i	$-0.105269\pi$
$257$	3.07308	+	5.32274i	0.191694	+	0.332023i	−0.754118	+	0.656739i	$0.771935\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−0.0824634	+	0.142831i	−0.00508491	+	0.00880732i	−0.868557	−	0.495590i	$-0.834952\pi$
$263$	−0.0824634	+	0.142831i	−0.00508491	+	0.00880732i	0.863472	+	0.504397i	$0.168285\pi$
$264$		0			0
$265$	17.6489	+	30.5689i	1.08417	+	1.87783i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−3.72954			−0.227394			−0.113697	−	0.993515i	$-0.536269\pi$
$269$	−3.72954			−0.227394			−0.113697	+	0.993515i	$0.536269\pi$
$270$		0			0
$271$	0.787304			0.0478253			0.0239127	−	0.999714i	$-0.492388\pi$
$271$	0.787304			0.0478253			0.0239127	+	0.999714i	$0.492388\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−0.928693	−	1.60854i	−0.0560023	−	0.0969988i
$276$		0			0
$277$	1.62954	−	2.82245i	0.0979096	−	0.169584i	−0.812910	−	0.582390i	$-0.802118\pi$
$277$	1.62954	−	2.82245i	0.0979096	−	0.169584i	0.910819	+	0.412805i	$0.135451\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−9.39147	+	16.2665i	−0.560248	+	0.970379i	0.437226	+	0.899352i	$0.355961\pi$
$281$	−9.39147	+	16.2665i	−0.560248	+	0.970379i	−0.997474	+	0.0710269i	$0.977372\pi$
$282$		0			0
$283$	6.41848	+	11.1171i	0.381539	+	0.660845i	0.991282	−	0.131754i	$-0.0420608\pi$
$283$	6.41848	+	11.1171i	0.381539	+	0.660845i	−0.609743	+	0.792599i	$0.708727\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$		0			0
$289$	12.0764			0.710377
$290$		0			0
$291$		0			0
$292$		0			0
$293$	13.6293	+	23.6066i	0.796230	+	1.37911i	0.922055	+	0.387058i	$0.126509\pi$
$293$	13.6293	+	23.6066i	0.796230	+	1.37911i	−0.125825	+	0.992052i	$0.540158\pi$
$294$		0			0
$295$	17.9806	−	31.1434i	1.04687	−	1.81324i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	11.6912	−	20.2497i	0.676118	−	1.17107i
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−17.2820			−0.989563
$306$		0			0
$307$	24.4623			1.39614			0.698069	−	0.716030i	$-0.254043\pi$
$307$	24.4623			1.39614			0.698069	+	0.716030i	$0.254043\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−8.58916	−	14.8769i	−0.487047	−	0.843590i	0.512842	−	0.858483i	$-0.328593\pi$
$311$	−8.58916	−	14.8769i	−0.487047	−	0.843590i	−0.999889	+	0.0148930i	$0.995259\pi$
$312$		0			0
$313$	−7.93226	+	13.7391i	−0.448358	+	0.776578i	−0.998279	−	0.0586380i	$-0.981324\pi$
$313$	−7.93226	+	13.7391i	−0.448358	+	0.776578i	0.549922	+	0.835216i	$0.314658\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−11.3626	+	19.6806i	−0.638188	+	1.10537i	0.347642	+	0.937627i	$0.386983\pi$
$317$	−11.3626	+	19.6806i	−0.638188	+	1.10537i	−0.985830	+	0.167747i	$0.946351\pi$
$318$		0			0
$319$	2.15402	+	3.73088i	0.120602	+	0.208889i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	26.3916			1.46847
$324$		0			0
$325$	7.56990			0.419903
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−12.1140	+	20.9821i	−0.665848	+	1.15328i	0.313207	+	0.949685i	$0.398597\pi$
$331$	−12.1140	+	20.9821i	−0.665848	+	1.15328i	−0.979055	+	0.203597i	$0.934737\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	10.2242	−	17.7088i	0.558605	−	0.967533i
$336$		0			0
$337$	−2.20181	−	3.81365i	−0.119940	−	0.207743i	0.799803	−	0.600262i	$-0.204937\pi$
$337$	−2.20181	−	3.81365i	−0.119940	−	0.207743i	−0.919744	+	0.392519i	$0.871604\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	6.59726			0.357262
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−6.12528	−	10.6093i	−0.328823	−	0.569537i	0.653456	−	0.756965i	$-0.273318\pi$
$347$	−6.12528	−	10.6093i	−0.328823	−	0.569537i	−0.982278	+	0.187427i	$0.939985\pi$
$348$		0			0
$349$	7.19444	−	12.4611i	0.385110	−	0.667030i	−0.606675	−	0.794950i	$-0.707497\pi$
$349$	7.19444	−	12.4611i	0.385110	−	0.667030i	0.991784	+	0.127921i	$0.0408303\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−4.40835	+	7.63549i	−0.234633	+	0.406396i	−0.959166	−	0.282844i	$-0.908722\pi$
$353$	−4.40835	+	7.63549i	−0.234633	+	0.406396i	0.724533	+	0.689240i	$0.242055\pi$
$354$		0			0
$355$	−2.84417	−	4.92624i	−0.150953	−	0.261458i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−6.09819			−0.321850			−0.160925	−	0.986967i	$-0.551448\pi$
$359$	−6.09819			−0.321850			−0.160925	+	0.986967i	$0.551448\pi$
$360$		0			0
$361$	4.95462			0.260770
$362$		0			0
$363$		0			0
$364$		0			0
$365$	8.85761	+	15.3418i	0.463628	+	0.803028i
$366$		0			0
$367$	3.45814	−	5.98967i	0.180513	−	0.312658i	−0.761542	−	0.648115i	$-0.775557\pi$
$367$	3.45814	−	5.98967i	0.180513	−	0.312658i	0.942055	+	0.335457i	$0.108891\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$	11.9489	+	20.6961i	0.618691	+	1.07160i	0.989725	+	0.142985i	$0.0456701\pi$
$373$	11.9489	+	20.6961i	0.618691	+	1.07160i	−0.371034	+	0.928619i	$0.620997\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−17.5577			−0.904269
$378$		0			0
$379$	34.6719			1.78097			0.890487	−	0.455008i	$-0.150364\pi$
$379$	34.6719			1.78097			0.890487	+	0.455008i	$0.150364\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	9.71507	+	16.8270i	0.496417	+	0.859820i	0.999991	−	0.00413220i	$-0.00131532\pi$
$383$	9.71507	+	16.8270i	0.496417	+	0.859820i	−0.503574	+	0.863952i	$0.667982\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−16.3172	+	28.2623i	−0.827317	+	1.43295i	0.0728190	+	0.997345i	$0.476800\pi$
$389$	−16.3172	+	28.2623i	−0.827317	+	1.43295i	−0.900136	+	0.435610i	$0.856533\pi$
$390$		0			0
$391$	−11.2571	−	19.4979i	−0.569297	−	0.986051i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	6.94799			0.349591
$396$		0			0
$397$	6.23613			0.312982			0.156491	−	0.987679i	$-0.449982\pi$
$397$	6.23613			0.312982			0.156491	+	0.987679i	$0.449982\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−12.3672	−	21.4207i	−0.617591	−	1.06970i	−0.989924	−	0.141599i	$-0.954776\pi$
$401$	−12.3672	−	21.4207i	−0.617591	−	1.06970i	0.372333	−	0.928099i	$-0.378558\pi$
$402$		0			0
$403$	−13.4438	+	23.2853i	−0.669683	+	1.15992i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−3.70781	+	6.42211i	−0.183789	+	0.318332i
$408$		0			0
$409$	11.5749	+	20.0484i	0.572344	+	0.991329i	0.996325	+	0.0856575i	$0.0272991\pi$
$409$	11.5749	+	20.0484i	0.572344	+	0.991329i	−0.423981	+	0.905671i	$0.639368\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$	37.7473			1.85294
$416$		0			0
$417$		0			0
$418$		0			0
$419$	0.703260	+	1.21808i	0.0343565	+	0.0595072i	0.882692	−	0.469951i	$-0.155729\pi$
$419$	0.703260	+	1.21808i	0.0343565	+	0.0595072i	−0.848336	+	0.529458i	$0.822395\pi$
$420$		0			0
$421$	−0.663904	+	1.14992i	−0.0323567	+	0.0560435i	−0.881750	−	0.471716i	$-0.843635\pi$
$421$	−0.663904	+	1.14992i	−0.0323567	+	0.0560435i	0.849394	+	0.527760i	$0.176968\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	3.64443	−	6.31234i	0.176781	−	0.306193i
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−5.66756			−0.272997			−0.136498	−	0.990640i	$-0.543585\pi$
$431$	−5.66756			−0.272997			−0.136498	+	0.990640i	$0.543585\pi$
$432$		0			0
$433$	1.60371			0.0770696			0.0385348	−	0.999257i	$-0.487731\pi$
$433$	1.60371			0.0770696			0.0385348	+	0.999257i	$0.487731\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−10.2177	−	17.6975i	−0.488777	−	0.846587i
$438$		0			0
$439$	0.227323	−	0.393735i	0.0108495	−	0.0187919i	−0.860550	−	0.509367i	$-0.829880\pi$
$439$	0.227323	−	0.393735i	0.0108495	−	0.0187919i	0.871399	+	0.490575i	$0.163213\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	9.31442	−	16.1331i	0.442542	−	0.766505i	−0.555336	−	0.831626i	$-0.687410\pi$
$443$	9.31442	−	16.1331i	0.442542	−	0.766505i	0.997877	+	0.0651217i	$0.0207436\pi$
$444$		0			0
$445$	−6.95099	−	12.0395i	−0.329508	−	0.570725i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	14.2330			0.671696			0.335848	−	0.941916i	$-0.390977\pi$
$449$	14.2330			0.671696			0.335848	+	0.941916i	$0.390977\pi$
$450$		0			0
$451$	−8.32671			−0.392089
$452$		0			0
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−14.6729	+	25.4142i	−0.686370	+	1.18883i	0.286634	+	0.958040i	$0.407464\pi$
$457$	−14.6729	+	25.4142i	−0.686370	+	1.18883i	−0.973004	+	0.230788i	$0.925870\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	12.6587	−	21.9254i	0.589572	−	1.02117i	−0.404716	−	0.914442i	$-0.632630\pi$
$461$	12.6587	−	21.9254i	0.589572	−	1.02117i	0.994288	−	0.106727i	$-0.0340371\pi$
$462$		0			0
$463$	−11.6503	−	20.1789i	−0.541435	−	0.937793i	−0.998822	−	0.0485250i	$-0.984548\pi$
$463$	−11.6503	−	20.1789i	−0.541435	−	0.937793i	0.457387	−	0.889268i	$-0.348785\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−41.6819			−1.92881			−0.964403	−	0.264436i	$-0.914814\pi$
$467$	−41.6819			−1.92881			−0.964403	+	0.264436i	$0.914814\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$	3.36262	+	5.82423i	0.154613	+	0.267798i
$474$		0			0
$475$	3.30791	−	5.72947i	0.151777	−	0.262886i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	2.76946	−	4.79684i	0.126540	−	0.219173i	−0.795794	−	0.605567i	$-0.792946\pi$
$479$	2.76946	−	4.79684i	0.126540	−	0.219173i	0.922334	+	0.386394i	$0.126280\pi$
$480$		0			0
$481$	−15.1114	−	26.1737i	−0.689021	−	1.19342i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−4.50624			−0.204618
$486$		0			0
$487$	−24.6714			−1.11797			−0.558985	−	0.829178i	$-0.688809\pi$
$487$	−24.6714			−1.11797			−0.558985	+	0.829178i	$0.688809\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	10.0509	+	17.4087i	0.453590	+	0.785642i	0.998606	−	0.0527842i	$-0.0168096\pi$
$491$	10.0509	+	17.4087i	0.453590	+	0.785642i	−0.545015	+	0.838426i	$0.683476\pi$
$492$		0			0
$493$	−8.45294	+	14.6409i	−0.380701	+	0.659394i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−17.7587	−	30.7589i	−0.794987	−	1.37696i	−0.922848	−	0.385166i	$-0.874144\pi$
$499$	−17.7587	−	30.7589i	−0.794987	−	1.37696i	0.127861	−	0.991792i	$-0.459189\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−24.2236			−1.08008			−0.540039	−	0.841640i	$-0.681590\pi$
$503$	−24.2236			−1.08008			−0.540039	+	0.841640i	$0.681590\pi$
$504$		0			0
$505$	−33.7480			−1.50177
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−3.86723	−	6.69824i	−0.171412	−	0.296894i	0.767502	−	0.641047i	$-0.221500\pi$
$509$	−3.86723	−	6.69824i	−0.171412	−	0.296894i	−0.938914	+	0.344153i	$0.888166\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−2.77642	+	4.80891i	−0.122344	+	0.211906i
$516$		0			0
$517$	−3.88555	−	6.72997i	−0.170886	−	0.295984i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−29.8099			−1.30600			−0.652998	−	0.757360i	$-0.726489\pi$
$521$	−29.8099			−1.30600			−0.652998	+	0.757360i	$0.726489\pi$
$522$		0			0
$523$	3.52436			0.154109			0.0770547	−	0.997027i	$-0.475448\pi$
$523$	3.52436			0.154109			0.0770547	+	0.997027i	$0.475448\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	12.9447	+	22.4208i	0.563879	+	0.976667i
$528$		0			0
$529$	2.78347	−	4.82110i	0.121020	−	0.209613i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	16.9680	−	29.3895i	0.734967	−	1.27300i
$534$		0			0
$535$	−12.4320	−	21.5329i	−0.537484	−	0.930950i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−27.6871			−1.19036			−0.595180	−	0.803593i	$-0.702919\pi$
$541$	−27.6871			−1.19036			−0.595180	+	0.803593i	$0.702919\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	3.88977	+	6.73729i	0.166620	+	0.288594i
$546$		0			0
$547$	−16.6136	+	28.7756i	−0.710347	+	1.23036i	0.254380	+	0.967104i	$0.418129\pi$
$547$	−16.6136	+	28.7756i	−0.710347	+	1.23036i	−0.964727	+	0.263253i	$0.915205\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−7.67241	+	13.2890i	−0.326856	+	0.566131i
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$	15.6175			0.661733			0.330866	−	0.943678i	$-0.392659\pi$
$557$	15.6175			0.661733			0.330866	+	0.943678i	$0.392659\pi$
$558$		0			0
$559$	−27.4092			−1.15928
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−9.75592	−	16.8977i	−0.411163	−	0.712155i	0.583854	−	0.811858i	$-0.301544\pi$
$563$	−9.75592	−	16.8977i	−0.411163	−	0.712155i	−0.995017	+	0.0997034i	$0.968211\pi$
$564$		0			0
$565$	−0.551472	+	0.955177i	−0.0232006	+	0.0401846i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	3.59181	−	6.22119i	0.150576	−	0.260806i	−0.780863	−	0.624702i	$-0.785220\pi$
$569$	3.59181	−	6.22119i	0.150576	−	0.260806i	0.931439	+	0.363896i	$0.118554\pi$
$570$		0			0
$571$	−14.7886	−	25.6147i	−0.618886	−	1.07194i	−0.989689	−	0.143230i	$-0.954251\pi$
$571$	−14.7886	−	25.6147i	−0.618886	−	1.07194i	0.370804	−	0.928711i	$-0.379082\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−5.64386			−0.235365
$576$		0			0
$577$	−10.3782			−0.432051			−0.216025	−	0.976388i	$-0.569309\pi$
$577$	−10.3782			−0.432051			−0.216025	+	0.976388i	$0.569309\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	9.62244	−	16.6666i	0.398521	−	0.690259i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−14.4563	+	25.0391i	−0.596677	+	1.03348i	0.396630	+	0.917978i	$0.370179\pi$
$587$	−14.4563	+	25.0391i	−0.596677	+	1.03348i	−0.993308	+	0.115497i	$0.963154\pi$
$588$		0			0
$589$	11.7494	+	20.3505i	0.484125	+	0.838530i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−20.5290			−0.843024			−0.421512	−	0.906823i	$-0.638500\pi$
$593$	−20.5290			−0.843024			−0.421512	+	0.906823i	$0.638500\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$	3.91652	+	6.78361i	0.160025	+	0.277171i	0.934877	−	0.354971i	$-0.115509\pi$
$599$	3.91652	+	6.78361i	0.160025	+	0.277171i	−0.774853	+	0.632142i	$0.782176\pi$
$600$		0			0
$601$	−7.27021	+	12.5924i	−0.296558	+	0.513654i	−0.975346	−	0.220681i	$-0.929172\pi$
$601$	−7.27021	+	12.5924i	−0.296558	+	0.513654i	0.678788	+	0.734334i	$0.262505\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	11.4822	−	19.8877i	0.466817	−	0.808551i
$606$		0			0
$607$	15.2755	+	26.4579i	0.620013	+	1.07389i	0.989483	+	0.144651i	$0.0462060\pi$
$607$	15.2755	+	26.4579i	0.620013	+	1.07389i	−0.369470	+	0.929243i	$0.620461\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	31.6716			1.28130
$612$		0			0
$613$	28.9292			1.16844			0.584220	−	0.811595i	$-0.301401\pi$
$613$	28.9292			1.16844			0.584220	+	0.811595i	$0.301401\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−20.2106	−	35.0059i	−0.813650	−	1.40928i	−0.910293	−	0.413964i	$-0.864144\pi$
$617$	−20.2106	−	35.0059i	−0.813650	−	1.40928i	0.0966430	−	0.995319i	$-0.469189\pi$
$618$		0			0
$619$	9.05857	−	15.6899i	0.364095	−	0.630631i	−0.624536	−	0.780996i	$-0.714712\pi$
$619$	9.05857	−	15.6899i	0.364095	−	0.630631i	0.988630	+	0.150366i	$0.0480451\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	14.9657	+	25.9214i	0.598629	+	1.03686i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−29.1008			−1.16032
$630$		0			0
$631$	8.50373			0.338528			0.169264	−	0.985571i	$-0.445861\pi$
$631$	8.50373			0.338528			0.169264	+	0.985571i	$0.445861\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	7.25783	+	12.5709i	0.288018	+	0.498862i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	11.0020	−	19.0561i	0.434554	−	0.752669i	−0.562705	−	0.826658i	$-0.690239\pi$
$641$	11.0020	−	19.0561i	0.434554	−	0.752669i	0.997259	+	0.0739883i	$0.0235727\pi$
$642$		0			0
$643$	13.1156	+	22.7170i	0.517230	+	0.895869i	0.999800	+	0.0200115i	$0.00637029\pi$
$643$	13.1156	+	22.7170i	0.517230	+	0.895869i	−0.482569	+	0.875858i	$0.660296\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	39.1690			1.53989			0.769946	−	0.638108i	$-0.220283\pi$
$647$	39.1690			1.53989			0.769946	+	0.638108i	$0.220283\pi$
$648$		0			0
$649$	−19.6066			−0.769626
$650$		0			0
$651$		0			0
$652$		0			0
$653$	6.83467	+	11.8380i	0.267461	+	0.463257i	0.968206	−	0.250156i	$-0.0804819\pi$
$653$	6.83467	+	11.8380i	0.267461	+	0.463257i	−0.700744	+	0.713413i	$0.747149\pi$
$654$		0			0
$655$	−1.80165	+	3.12054i	−0.0703962	+	0.121930i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	3.06683	−	5.31191i	0.119467	−	0.206923i	−0.800090	−	0.599880i	$-0.795215\pi$
$659$	3.06683	−	5.31191i	0.119467	−	0.206923i	0.919557	+	0.392958i	$0.128548\pi$
$660$		0			0
$661$	22.3118	+	38.6451i	0.867828	+	1.50312i	0.864212	+	0.503128i	$0.167818\pi$
$661$	22.3118	+	38.6451i	0.867828	+	1.50312i	0.00361604	+	0.999993i	$0.498849\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$	13.0904			0.506864
$668$		0			0
$669$		0			0
$670$		0			0
$671$	4.71119	+	8.16001i	0.181873	+	0.315014i
$672$		0			0
$673$	−16.3833	+	28.3767i	−0.631531	+	1.09384i	0.355708	+	0.934597i	$0.384240\pi$
$673$	−16.3833	+	28.3767i	−0.631531	+	1.09384i	−0.987239	+	0.159246i	$0.949094\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	13.5764	−	23.5150i	0.521782	−	0.903753i	−0.477897	−	0.878416i	$-0.658601\pi$
$677$	13.5764	−	23.5150i	0.521782	−	0.903753i	0.999679	−	0.0253373i	$-0.00806596\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−38.0668			−1.45659			−0.728293	−	0.685266i	$-0.759686\pi$
$683$	−38.0668			−1.45659			−0.728293	+	0.685266i	$0.759686\pi$
$684$		0			0
$685$	−28.1934			−1.07721
$686$		0			0
$687$		0			0
$688$		0			0
$689$	39.2169	+	67.9257i	1.49405	+	2.58776i
$690$		0			0
$691$	6.37848	−	11.0478i	0.242649	−	0.420280i	−0.718819	−	0.695197i	$-0.755317\pi$
$691$	6.37848	−	11.0478i	0.242649	−	0.420280i	0.961468	+	0.274917i	$0.0886504\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	19.8351	−	34.3554i	0.752387	−	1.30317i
$696$		0			0
$697$	−16.3381	−	28.2984i	−0.618849	−	1.07188i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−40.6428			−1.53506			−0.767528	−	0.641015i	$-0.778514\pi$
$701$	−40.6428			−1.53506			−0.767528	+	0.641015i	$0.778514\pi$
$702$		0			0
$703$	−26.4137			−0.996211
$704$		0			0
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	3.74552	−	6.48743i	0.140666	−	0.243640i	−0.787082	−	0.616849i	$-0.788409\pi$
$709$	3.74552	−	6.48743i	0.140666	−	0.243640i	0.927748	+	0.373208i	$0.121742\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	10.0232	−	17.3607i	0.375373	−	0.650165i
$714$		0			0
$715$	−9.69683	−	16.7954i	−0.362641	−	0.628112i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−3.28113			−0.122365			−0.0611827	−	0.998127i	$-0.519487\pi$
$719$	−3.28113			−0.122365			−0.0611827	+	0.998127i	$0.519487\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$		0			0
$724$		0			0
$725$	2.11898	+	3.67018i	0.0786969	+	0.136307i
$726$		0			0
$727$	8.01088	−	13.8753i	0.297107	−	0.514605i	−0.678366	−	0.734724i	$-0.737311\pi$
$727$	8.01088	−	13.8753i	0.297107	−	0.514605i	0.975473	+	0.220120i	$0.0706448\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−13.1958	+	22.8558i	−0.488064	+	0.845351i
$732$		0			0
$733$	−14.8123	−	25.6556i	−0.547104	−	0.947611i	−0.998471	−	0.0552733i	$-0.982397\pi$
$733$	−14.8123	−	25.6556i	−0.547104	−	0.947611i	0.451368	−	0.892338i	$-0.350936\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−11.1487			−0.410668
$738$		0			0
$739$	44.5733			1.63966			0.819829	−	0.572609i	$-0.194069\pi$
$739$	44.5733			1.63966			0.819829	+	0.572609i	$0.194069\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	5.67364	+	9.82704i	0.208146	+	0.360519i	0.951130	−	0.308789i	$-0.0999238\pi$
$743$	5.67364	+	9.82704i	0.208146	+	0.360519i	−0.742985	+	0.669308i	$0.766590\pi$
$744$		0			0
$745$	9.99317	−	17.3087i	0.366121	−	0.634141i
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−17.5928	−	30.4716i	−0.641970	−	1.11192i	−0.984992	−	0.172597i	$-0.944784\pi$
$751$	−17.5928	−	30.4716i	−0.641970	−	1.11192i	0.343023	−	0.939327i	$-0.388549\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−27.2029			−0.990014
$756$		0			0
$757$	40.9186			1.48721			0.743605	−	0.668619i	$-0.233114\pi$
$757$	40.9186			1.48721			0.743605	+	0.668619i	$0.233114\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	5.72243	+	9.91155i	0.207438	+	0.359293i	0.950907	−	0.309477i	$-0.100154\pi$
$761$	5.72243	+	9.91155i	0.207438	+	0.359293i	−0.743469	+	0.668771i	$0.766821\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$	39.9540	−	69.2023i	1.44265	−	2.49875i
$768$		0			0
$769$	−14.9723	−	25.9328i	−0.539916	−	0.935162i	−0.998908	−	0.0467217i	$-0.985123\pi$
$769$	−14.9723	−	25.9328i	−0.539916	−	0.935162i	0.458992	−	0.888440i	$-0.348211\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−7.93155			−0.285278			−0.142639	−	0.989775i	$-0.545559\pi$
$773$	−7.93155			−0.285278			−0.142639	+	0.989775i	$0.545559\pi$
$774$		0			0
$775$	6.48993			0.233125
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−14.8295	−	25.6854i	−0.531320	−	0.920274i
$780$		0			0
$781$	−1.55068	+	2.68586i	−0.0554877	+	0.0961075i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−26.6855	+	46.2207i	−0.952447	+	1.64969i
$786$		0			0
$787$	−21.6037	−	37.4187i	−0.770089	−	1.33383i	−0.937514	−	0.347949i	$-0.886878\pi$
$787$	−21.6037	−	37.4187i	−0.770089	−	1.33383i	0.167425	−	0.985885i	$-0.446455\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−38.4015			−1.36368
$794$		0			0
$795$		0			0
$796$		0			0
$797$	8.34385	+	14.4520i	0.295554	+	0.511915i	0.975114	−	0.221706i	$-0.0711624\pi$
$797$	8.34385	+	14.4520i	0.295554	+	0.511915i	−0.679559	+	0.733620i	$0.737829\pi$
$798$		0			0
$799$	15.2479	−	26.4101i	0.539432	−	0.934323i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	4.82929	−	8.36458i	0.170422	−	0.295180i
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−5.09692			−0.179198			−0.0895992	−	0.995978i	$-0.528559\pi$
$809$	−5.09692			−0.179198			−0.0895992	+	0.995978i	$0.528559\pi$
$810$		0			0
$811$	10.2996			0.361666			0.180833	−	0.983514i	$-0.442121\pi$
$811$	10.2996			0.361666			0.180833	+	0.983514i	$0.442121\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	1.35225	+	2.34217i	0.0473674	+	0.0820427i
$816$		0			0
$817$	−11.9773	+	20.7453i	−0.419033	+	0.725787i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−12.6369	+	21.8878i	−0.441031	+	0.763889i	−0.997766	−	0.0668013i	$-0.978721\pi$
$821$	−12.6369	+	21.8878i	−0.441031	+	0.763889i	0.556735	+	0.830690i	$0.312054\pi$
$822$		0			0
$823$	−4.44391	−	7.69707i	−0.154905	−	0.268303i	0.778120	−	0.628116i	$-0.216174\pi$
$823$	−4.44391	−	7.69707i	−0.154905	−	0.268303i	−0.933024	+	0.359813i	$0.882840\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	13.1680			0.457895			0.228947	−	0.973439i	$-0.426472\pi$
$827$	13.1680			0.457895			0.228947	+	0.973439i	$0.426472\pi$
$828$		0			0
$829$	22.6917			0.788117			0.394058	−	0.919085i	$-0.371071\pi$
$829$	22.6917			0.788117			0.394058	+	0.919085i	$0.371071\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$	19.4473	−	33.6838i	0.673002	−	1.16567i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	14.9632	−	25.9171i	0.516588	−	0.894757i	−0.483226	−	0.875496i	$-0.660535\pi$
$839$	14.9632	−	25.9171i	0.516588	−	0.894757i	0.999814	−	0.0192618i	$-0.00613161\pi$
$840$		0			0
$841$	9.58522	+	16.6021i	0.330525	+	0.572486i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	46.2768			1.59197
$846$		0			0
$847$		0			0
$848$		0			0
$849$		0			0
$850$		0			0
$851$	11.2666	+	19.5142i	0.386213	+	0.668940i
$852$		0			0
$853$	6.46929	−	11.2051i	0.221504	−	0.383657i	−0.733761	−	0.679408i	$-0.762237\pi$
$853$	6.46929	−	11.2051i	0.221504	−	0.383657i	0.955265	+	0.295751i	$0.0955699\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−4.12252	+	7.14042i	−0.140823	+	0.243912i	−0.927807	−	0.373061i	$-0.878308\pi$
$857$	−4.12252	+	7.14042i	−0.140823	+	0.243912i	0.786984	+	0.616973i	$0.211641\pi$
$858$		0			0
$859$	−1.73399	−	3.00336i	−0.0591630	−	0.102473i	0.834927	−	0.550361i	$-0.185510\pi$
$859$	−1.73399	−	3.00336i	−0.0591630	−	0.102473i	−0.894090	+	0.447888i	$0.852177\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−0.512788			−0.0174555			−0.00872775	−	0.999962i	$-0.502778\pi$
$863$	−0.512788			−0.0174555			−0.00872775	+	0.999962i	$0.502778\pi$
$864$		0			0
$865$	−51.3175			−1.74485
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−1.89407	−	3.28063i	−0.0642519	−	0.111288i
$870$		0			0
$871$	22.7186	−	39.3499i	0.769792	−	1.33332i
$872$		0			0
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−18.1880	−	31.5026i	−0.614166	−	1.06377i	−0.990530	−	0.137295i	$-0.956159\pi$
$877$	−18.1880	−	31.5026i	−0.614166	−	1.06377i	0.376365	−	0.926472i	$-0.377174\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	23.3999			0.788363			0.394181	−	0.919033i	$-0.371028\pi$
$881$	23.3999			0.788363			0.394181	+	0.919033i	$0.371028\pi$
$882$		0			0
$883$	−22.8345			−0.768442			−0.384221	−	0.923241i	$-0.625530\pi$
$883$	−22.8345			−0.768442			−0.384221	+	0.923241i	$0.625530\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	22.0791	+	38.2421i	0.741344	+	1.28405i	0.951883	+	0.306460i	$0.0991446\pi$
$887$	22.0791	+	38.2421i	0.741344	+	1.28405i	−0.210539	+	0.977585i	$0.567522\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$	13.8399	−	23.9715i	0.463136	−	0.802175i
$894$		0			0
$895$	−7.68579	−	13.3122i	−0.256908	−	0.444977i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−15.0528			−0.502040
$900$		0			0
$901$	75.5219			2.51600
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−12.6084	−	21.8384i	−0.419118	−	0.725934i
$906$		0			0
$907$	−3.53884	+	6.12946i	−0.117505	+	0.203525i	−0.918778	−	0.394773i	$-0.870823\pi$
$907$	−3.53884	+	6.12946i	−0.117505	+	0.203525i	0.801273	+	0.598299i	$0.204156\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	23.6764	−	41.0088i	0.784435	−	1.35868i	−0.144901	−	0.989446i	$-0.546286\pi$
$911$	23.6764	−	41.0088i	0.784435	−	1.35868i	0.929336	−	0.369235i	$-0.120380\pi$
$912$		0			0
$913$	−10.2902	−	17.8231i	−0.340555	−	0.589859i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−25.9503			−0.856022			−0.428011	−	0.903773i	$-0.640786\pi$
$919$	−25.9503			−0.856022			−0.428011	+	0.903773i	$0.640786\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−6.31990	−	10.9464i	−0.208022	−	0.360305i
$924$		0			0
$925$	−3.64748	+	6.31763i	−0.119929	+	0.207722i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−2.66110	+	4.60917i	−0.0873080	+	0.151222i	−0.906372	−	0.422480i	$-0.861160\pi$
$929$	−2.66110	+	4.60917i	−0.0873080	+	0.151222i	0.819064	+	0.573702i	$0.194493\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−18.6736			−0.610694
$936$		0			0
$937$	−30.4266			−0.993994			−0.496997	−	0.867752i	$-0.665564\pi$
$937$	−30.4266			−0.993994			−0.496997	+	0.867752i	$0.665564\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	10.8818	+	18.8479i	0.354738	+	0.614424i	0.987073	−	0.160271i	$-0.0512368\pi$
$941$	10.8818	+	18.8479i	0.354738	+	0.614424i	−0.632335	+	0.774695i	$0.717903\pi$
$942$		0			0
$943$	−12.6508	+	21.9118i	−0.411966	+	0.713546i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−17.4392	+	30.2055i	−0.566697	+	0.981548i	0.430192	+	0.902737i	$0.358446\pi$
$947$	−17.4392	+	30.2055i	−0.566697	+	0.981548i	−0.996890	+	0.0788112i	$0.974888\pi$
$948$		0			0
$949$	19.6821	+	34.0904i	0.638908	+	1.10662i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−27.3744			−0.886742			−0.443371	−	0.896338i	$-0.646218\pi$
$953$	−27.3744			−0.886742			−0.443371	+	0.896338i	$0.646218\pi$
$954$		0			0
$955$	55.9465			1.81039
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	3.97419	−	6.88350i	0.128200	−	0.222048i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	33.5396	−	58.0924i	1.07968	−	1.87006i
$966$		0			0
$967$	7.21327	+	12.4937i	0.231963	+	0.401772i	0.958386	−	0.285476i	$-0.0921518\pi$
$967$	7.21327	+	12.4937i	0.231963	+	0.401772i	−0.726423	+	0.687248i	$0.758819\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−26.5185			−0.851018			−0.425509	−	0.904954i	$-0.639905\pi$
$971$	−26.5185			−0.851018			−0.425509	+	0.904954i	$0.639905\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−20.1867	−	34.9643i	−0.645829	−	1.11861i	−0.984109	−	0.177563i	$-0.943179\pi$
$977$	−20.1867	−	34.9643i	−0.645829	−	1.11861i	0.338281	−	0.941045i	$-0.390155\pi$
$978$		0			0
$979$	−3.78978	+	6.56408i	−0.121122	+	0.209789i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−10.7299	+	18.5847i	−0.342230	+	0.592759i	−0.984846	−	0.173429i	$-0.944515\pi$
$983$	−10.7299	+	18.5847i	−0.342230	+	0.592759i	0.642617	+	0.766188i	$0.277849\pi$
$984$		0			0
$985$	12.8150	+	22.1962i	0.408319	+	0.707230i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	20.4353			0.649806
$990$		0			0
$991$	−14.5068			−0.460824			−0.230412	−	0.973093i	$-0.574007\pi$
$991$	−14.5068			−0.460824			−0.230412	+	0.973093i	$0.574007\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−4.18975	−	7.25687i	−0.132824	−	0.230058i
$996$		0			0
$997$	−18.2204	+	31.5587i	−0.577047	+	0.999475i	0.418769	+	0.908093i	$0.362462\pi$
$997$	−18.2204	+	31.5587i	−0.577047	+	0.999475i	−0.995816	+	0.0913822i	$0.970871\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5292.2.j.h.3529.1		14
3.2	odd	2		1764.2.j.g.1177.5		14
7.2	even	3		756.2.i.b.613.1		14
7.3	odd	6		5292.2.l.i.3313.1		14
7.4	even	3		756.2.l.b.289.7		14
7.5	odd	6		5292.2.i.i.2125.7		14
7.6	odd	2		5292.2.j.g.3529.7		14
9.4	even	3	inner	5292.2.j.h.1765.1		14
9.5	odd	6		1764.2.j.g.589.5		14
21.2	odd	6		252.2.i.b.25.6	✓	14
21.5	even	6		1764.2.i.i.1537.2		14
21.11	odd	6		252.2.l.b.205.2	yes	14
21.17	even	6		1764.2.l.i.961.6		14
21.20	even	2		1764.2.j.h.1177.3		14
28.11	odd	6		3024.2.t.j.289.7		14
28.23	odd	6		3024.2.q.j.2881.1		14
63.2	odd	6		2268.2.k.e.1621.7		14
63.4	even	3		756.2.i.b.37.1		14
63.5	even	6		1764.2.l.i.949.6		14
63.11	odd	6		2268.2.k.e.1297.7		14
63.13	odd	6		5292.2.j.g.1765.7		14
63.16	even	3		2268.2.k.f.1621.1		14
63.23	odd	6		252.2.l.b.193.2	yes	14
63.25	even	3		2268.2.k.f.1297.1		14
63.31	odd	6		5292.2.i.i.1549.7		14
63.32	odd	6		252.2.i.b.121.6	yes	14
63.40	odd	6		5292.2.l.i.361.1		14
63.41	even	6		1764.2.j.h.589.3		14
63.58	even	3		756.2.l.b.361.7		14
63.59	even	6		1764.2.i.i.373.2		14
84.11	even	6		1008.2.t.j.961.6		14
84.23	even	6		1008.2.q.j.529.2		14
252.23	even	6		1008.2.t.j.193.6		14
252.67	odd	6		3024.2.q.j.2305.1		14
252.95	even	6		1008.2.q.j.625.2		14
252.247	odd	6		3024.2.t.j.1873.7		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.i.b.25.6	✓	14	21.2	odd	6
252.2.i.b.121.6	yes	14	63.32	odd	6
252.2.l.b.193.2	yes	14	63.23	odd	6
252.2.l.b.205.2	yes	14	21.11	odd	6
756.2.i.b.37.1		14	63.4	even	3
756.2.i.b.613.1		14	7.2	even	3
756.2.l.b.289.7		14	7.4	even	3
756.2.l.b.361.7		14	63.58	even	3
1008.2.q.j.529.2		14	84.23	even	6
1008.2.q.j.625.2		14	252.95	even	6
1008.2.t.j.193.6		14	252.23	even	6
1008.2.t.j.961.6		14	84.11	even	6
1764.2.i.i.373.2		14	63.59	even	6
1764.2.i.i.1537.2		14	21.5	even	6
1764.2.j.g.589.5		14	9.5	odd	6
1764.2.j.g.1177.5		14	3.2	odd	2
1764.2.j.h.589.3		14	63.41	even	6
1764.2.j.h.1177.3		14	21.20	even	2
1764.2.l.i.949.6		14	63.5	even	6
1764.2.l.i.961.6		14	21.17	even	6
2268.2.k.e.1297.7		14	63.11	odd	6
2268.2.k.e.1621.7		14	63.2	odd	6
2268.2.k.f.1297.1		14	63.25	even	3
2268.2.k.f.1621.1		14	63.16	even	3
3024.2.q.j.2305.1		14	252.67	odd	6
3024.2.q.j.2881.1		14	28.23	odd	6
3024.2.t.j.289.7		14	28.11	odd	6
3024.2.t.j.1873.7		14	252.247	odd	6
5292.2.i.i.1549.7		14	63.31	odd	6
5292.2.i.i.2125.7		14	7.5	odd	6
5292.2.j.g.1765.7		14	63.13	odd	6
5292.2.j.g.3529.7		14	7.6	odd	2
5292.2.j.h.1765.1		14	9.4	even	3	inner
5292.2.j.h.3529.1		14	1.1	even	1	trivial
5292.2.l.i.361.1		14	63.40	odd	6
5292.2.l.i.3313.1		14	7.3	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:	\( N \)	\(=\)	\( 5292 = 2^{2} \cdot 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5292.j (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.26013 - 2.18261i) q^{5} +O(q^{10})\)	\(q+(-1.26013 - 2.18261i) q^{5} +(-0.687041 + 1.18999i) q^{11} +(-2.80008 - 4.84989i) q^{13} -5.39225 q^{17} -4.89435 q^{19} +(2.08765 + 3.61591i) q^{23} +(-0.675864 + 1.17063i) q^{25} +(1.56761 - 2.71518i) q^{29} +(-2.40060 - 4.15797i) q^{31} +5.39677 q^{37} +(3.02991 + 5.24797i) q^{41} +(2.44717 - 4.23863i) q^{43} +(-2.82774 + 4.89779i) q^{47} -14.0056 q^{53} +3.46305 q^{55} +(7.13442 + 12.3572i) q^{59} +(3.42860 - 5.93852i) q^{61} +(-7.05695 + 12.2230i) q^{65} +(4.05678 + 7.02655i) q^{67} +2.25704 q^{71} -7.02911 q^{73} +(-1.37843 + 2.38750i) q^{79} +(-7.48876 + 12.9709i) q^{83} +(6.79495 + 11.7692i) q^{85} +5.51608 q^{89} +(6.16752 + 10.6825i) q^{95} +(0.894003 - 1.54846i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 2 q^{5}+O(q^{10}) \) 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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