LMFDB - Embedded newform 3024.2.q.k.2305.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3024,2,Mod(2305,3024)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3024, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("3024.2305");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3024 = 2^{4} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3024.q (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$24.1467615712$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			2305.4
Character	$\chi$	$=$	3024.2305
Dual form			3024.2.q.k.2881.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.918286 - 1.59052i) q^{5} +(0.361656 - 2.62092i) q^{7} +O(q^{10})$	$q+(-0.918286 - 1.59052i) q^{5} +(0.361656 - 2.62092i) q^{7} +(1.54860 - 2.68225i) q^{11} +(2.40225 - 4.16081i) q^{13} +(-1.87185 - 3.24214i) q^{17} +(2.71408 - 4.70093i) q^{19} +(3.97914 + 6.89208i) q^{23} +(0.813503 - 1.40903i) q^{25} +(0.325267 + 0.563379i) q^{29} -1.03668 q^{31} +(-4.50072 + 1.83153i) q^{35} +(0.873712 - 1.51331i) q^{37} +(-2.52260 + 4.36927i) q^{41} +(6.09645 + 10.5594i) q^{43} -4.61383 q^{47} +(-6.73841 - 1.89574i) q^{49} +(-4.55082 - 7.88226i) q^{53} -5.68821 q^{55} -5.79727 q^{59} -4.81245 q^{61} -8.82379 q^{65} +14.4774 q^{67} -5.00714 q^{71} +(-1.81364 - 3.14131i) q^{73} +(-6.46989 - 5.02879i) q^{77} +14.3581 q^{79} +(3.83139 + 6.63616i) q^{83} +(-3.43778 + 5.95441i) q^{85} +(5.76798 - 9.99043i) q^{89} +(-10.0364 - 7.80087i) q^{91} -9.96922 q^{95} +(-1.04480 - 1.80964i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 3 q^{5} + 5 q^{7}+O(q^{10}) $ 22 * q - 3 * q^5 + 5 * q^7	$ 22 q - 3 q^{5} + 5 q^{7} - 3 q^{11} - 3 q^{13} - 7 q^{17} + q^{19} + 2 q^{23} - 10 q^{25} - 9 q^{29} - 8 q^{31} + 14 q^{35} + 2 q^{37} - 16 q^{41} - 10 q^{47} + 15 q^{49} - 11 q^{53} - 22 q^{55} + 38 q^{59} + 26 q^{61} + 26 q^{65} + 52 q^{67} - 48 q^{71} - 35 q^{73} - 17 q^{77} + 20 q^{79} - 28 q^{83} - 20 q^{85} - 6 q^{89} + 37 q^{91} - 24 q^{95} - 29 q^{97}+O(q^{100}) $ 22 * q - 3 * q^5 + 5 * q^7 - 3 * q^11 - 3 * q^13 - 7 * q^17 + q^19 + 2 * q^23 - 10 * q^25 - 9 * q^29 - 8 * q^31 + 14 * q^35 + 2 * q^37 - 16 * q^41 - 10 * q^47 + 15 * q^49 - 11 * q^53 - 22 * q^55 + 38 * q^59 + 26 * q^61 + 26 * q^65 + 52 * q^67 - 48 * q^71 - 35 * q^73 - 17 * q^77 + 20 * q^79 - 28 * q^83 - 20 * q^85 - 6 * q^89 + 37 * q^91 - 24 * q^95 - 29 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1135$	$2593$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−0.918286	−	1.59052i	−0.410670	−	0.711301i	0.584293	−	0.811543i	$-0.301372\pi$
$5$	−0.918286	−	1.59052i	−0.410670	−	0.711301i	−0.994963	+	0.100242i	$0.968038\pi$
$6$		0			0
$7$	0.361656	−	2.62092i	0.136693	−	0.990613i
$7$	0.361656	−	2.62092i	0.136693	−	0.990613i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.54860	−	2.68225i	0.466919	−	0.808728i	−0.532367	−	0.846514i	$-0.678697\pi$
$11$	1.54860	−	2.68225i	0.466919	−	0.808728i	0.999286	+	0.0377862i	$0.0120306\pi$
$12$		0			0
$13$	2.40225	−	4.16081i	0.666263	−	1.15400i	−0.312678	−	0.949859i	$-0.601226\pi$
$13$	2.40225	−	4.16081i	0.666263	−	1.15400i	0.978941	−	0.204143i	$-0.0654406\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.87185	−	3.24214i	−0.453990	−	0.786333i	0.544640	−	0.838670i	$-0.316666\pi$
$17$	−1.87185	−	3.24214i	−0.453990	−	0.786333i	−0.998629	+	0.0523367i	$0.983333\pi$
$18$		0			0
$19$	2.71408	−	4.70093i	0.622654	−	1.07847i	−0.366336	−	0.930483i	$-0.619388\pi$
$19$	2.71408	−	4.70093i	0.622654	−	1.07847i	0.988990	−	0.147985i	$-0.0472788\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	3.97914	+	6.89208i	0.829709	+	1.43710i	0.898267	+	0.439450i	$0.144827\pi$
$23$	3.97914	+	6.89208i	0.829709	+	1.43710i	−0.0685581	+	0.997647i	$0.521840\pi$
$24$		0			0
$25$	0.813503	−	1.40903i	0.162701	−	0.281806i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	0.325267	+	0.563379i	0.0604006	+	0.104617i	0.894645	−	0.446779i	$-0.147429\pi$
$29$	0.325267	+	0.563379i	0.0604006	+	0.104617i	−0.834244	+	0.551396i	$0.814096\pi$
$30$		0			0
$31$	−1.03668			−0.186194			−0.0930970	−	0.995657i	$-0.529677\pi$
$31$	−1.03668			−0.186194			−0.0930970	+	0.995657i	$0.529677\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−4.50072	+	1.83153i	−0.760760	+	0.309585i
$36$		0			0
$37$	0.873712	−	1.51331i	0.143637	−	0.248787i	−0.785226	−	0.619209i	$-0.787453\pi$
$37$	0.873712	−	1.51331i	0.143637	−	0.248787i	0.928864	+	0.370422i	$0.120787\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−2.52260	+	4.36927i	−0.393964	+	0.682365i	−0.992968	−	0.118381i	$-0.962230\pi$
$41$	−2.52260	+	4.36927i	−0.393964	+	0.682365i	0.599005	+	0.800745i	$0.295563\pi$
$42$		0			0
$43$	6.09645	+	10.5594i	0.929699	+	1.61029i	0.783824	+	0.620984i	$0.213267\pi$
$43$	6.09645	+	10.5594i	0.929699	+	1.61029i	0.145876	+	0.989303i	$0.453400\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−4.61383			−0.672996			−0.336498	−	0.941684i	$-0.609243\pi$
$47$	−4.61383			−0.672996			−0.336498	+	0.941684i	$0.609243\pi$
$48$		0			0
$49$	−6.73841	−	1.89574i	−0.962630	−	0.270820i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−4.55082	−	7.88226i	−0.625104	−	1.08271i	−0.988521	−	0.151085i	$-0.951723\pi$
$53$	−4.55082	−	7.88226i	−0.625104	−	1.08271i	0.363417	−	0.931626i	$-0.381610\pi$
$54$		0			0
$55$	−5.68821			−0.766998
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−5.79727			−0.754740			−0.377370	−	0.926063i	$-0.623172\pi$
$59$	−5.79727			−0.754740			−0.377370	+	0.926063i	$0.623172\pi$
$60$		0			0
$61$	−4.81245			−0.616172			−0.308086	−	0.951359i	$-0.599688\pi$
$61$	−4.81245			−0.616172			−0.308086	+	0.951359i	$0.599688\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−8.82379			−1.09446
$66$		0			0
$67$	14.4774			1.76870			0.884348	−	0.466828i	$-0.154603\pi$
$67$	14.4774			1.76870			0.884348	+	0.466828i	$0.154603\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−5.00714			−0.594238			−0.297119	−	0.954840i	$-0.596026\pi$
$71$	−5.00714			−0.594238			−0.297119	+	0.954840i	$0.596026\pi$
$72$		0			0
$73$	−1.81364	−	3.14131i	−0.212270	−	0.367662i	0.740155	−	0.672437i	$-0.234752\pi$
$73$	−1.81364	−	3.14131i	−0.212270	−	0.367662i	−0.952425	+	0.304774i	$0.901419\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−6.46989	−	5.02879i	−0.737312	−	0.573084i
$78$		0			0
$79$	14.3581			1.61541			0.807705	−	0.589587i	$-0.200710\pi$
$79$	14.3581			1.61541			0.807705	+	0.589587i	$0.200710\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	3.83139	+	6.63616i	0.420550	+	0.728414i	0.995993	−	0.0894279i	$-0.0285038\pi$
$83$	3.83139	+	6.63616i	0.420550	+	0.728414i	−0.575443	+	0.817842i	$0.695171\pi$
$84$		0			0
$85$	−3.43778	+	5.95441i	−0.372880	+	0.645847i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	5.76798	−	9.99043i	0.611405	−	1.05898i	−0.379599	−	0.925151i	$-0.623938\pi$
$89$	5.76798	−	9.99043i	0.611405	−	1.05898i	0.991004	−	0.133833i	$-0.0427286\pi$
$90$		0			0
$91$	−10.0364	−	7.80087i	−1.05210	−	0.817753i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−9.96922			−1.02282
$96$		0			0
$97$	−1.04480	−	1.80964i	−0.106083	−	0.183741i	0.808097	−	0.589049i	$-0.200498\pi$
$97$	−1.04480	−	1.80964i	−0.106083	−	0.183741i	−0.914180	+	0.405308i	$0.867164\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−8.22661	+	14.2489i	−0.818578	+	1.41782i	0.0881520	+	0.996107i	$0.471904\pi$
$101$	−8.22661	+	14.2489i	−0.818578	+	1.41782i	−0.906730	+	0.421712i	$0.861429\pi$
$102$		0			0
$103$	−3.87346	−	6.70903i	−0.381663	−	0.661060i	0.609637	−	0.792681i	$-0.291315\pi$
$103$	−3.87346	−	6.70903i	−0.381663	−	0.661060i	−0.991300	+	0.131621i	$0.957982\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	3.74746	−	6.49080i	0.362281	−	0.627489i	−0.626055	−	0.779779i	$-0.715331\pi$
$107$	3.74746	−	6.49080i	0.362281	−	0.627489i	0.988336	+	0.152290i	$0.0486647\pi$
$108$		0			0
$109$	−4.30644	−	7.45897i	−0.412482	−	0.714440i	0.582678	−	0.812703i	$-0.302005\pi$
$109$	−4.30644	−	7.45897i	−0.412482	−	0.714440i	−0.995160	+	0.0982628i	$0.968671\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	1.55747	−	2.69762i	0.146514	−	0.253771i	−0.783422	−	0.621490i	$-0.786528\pi$
$113$	1.55747	−	2.69762i	0.146514	−	0.253771i	0.929937	+	0.367719i	$0.119861\pi$
$114$		0			0
$115$	7.30798	−	12.6578i	0.681473	−	1.18035i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−9.17433	+	3.73342i	−0.841010	+	0.342242i
$120$		0			0
$121$	0.703704	+	1.21885i	0.0639731	+	0.110805i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−12.1710			−1.08860
$126$		0			0
$127$	−10.8866			−0.966033			−0.483017	−	0.875611i	$-0.660459\pi$
$127$	−10.8866			−0.966033			−0.483017	+	0.875611i	$0.660459\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	8.02790	+	13.9047i	0.701401	+	1.21486i	0.967975	+	0.251048i	$0.0807751\pi$
$131$	8.02790	+	13.9047i	0.701401	+	1.21486i	−0.266574	+	0.963815i	$0.585892\pi$
$132$		0			0
$133$	−11.3392	−	8.81351i	−0.983232	−	0.764228i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	6.72031	−	11.6399i	0.574155	−	0.994465i	−0.421978	−	0.906606i	$-0.638664\pi$
$137$	6.72031	−	11.6399i	0.574155	−	0.994465i	0.996133	−	0.0878590i	$-0.0280025\pi$
$138$		0			0
$139$	4.06953	−	7.04863i	0.345173	−	0.597857i	−0.640212	−	0.768198i	$-0.721154\pi$
$139$	4.06953	−	7.04863i	0.345173	−	0.597857i	0.985385	+	0.170341i	$0.0544869\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−7.44022	−	12.8868i	−0.622182	−	1.07765i
$144$		0			0
$145$	0.597376	−	1.03469i	0.0496094	−	0.0859260i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	3.76479	+	6.52081i	0.308424	+	0.534205i	0.978018	−	0.208522i	$-0.0668652\pi$
$149$	3.76479	+	6.52081i	0.308424	+	0.534205i	−0.669594	+	0.742727i	$0.733532\pi$
$150$		0			0
$151$	−2.83616	+	4.91237i	−0.230803	+	0.399763i	−0.958045	−	0.286619i	$-0.907469\pi$
$151$	−2.83616	+	4.91237i	−0.230803	+	0.399763i	0.727241	+	0.686382i	$0.240802\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	0.951973	+	1.64886i	0.0764643	+	0.132440i
$156$		0			0
$157$	0.436763			0.0348575			0.0174287	−	0.999848i	$-0.494452\pi$
$157$	0.436763			0.0348575			0.0174287	+	0.999848i	$0.494452\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	19.5026	−	7.93644i	1.53702	−	0.625479i
$162$		0			0
$163$	−9.12649	+	15.8076i	−0.714842	+	1.23814i	0.248178	+	0.968714i	$0.420168\pi$
$163$	−9.12649	+	15.8076i	−0.714842	+	1.23814i	−0.963020	+	0.269429i	$0.913165\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	0.765108	−	1.32521i	0.0592058	−	0.102548i	−0.834903	−	0.550397i	$-0.814477\pi$
$167$	0.765108	−	1.32521i	0.0592058	−	0.102548i	0.894109	+	0.447849i	$0.147810\pi$
$168$		0			0
$169$	−5.04157	−	8.73226i	−0.387813	−	0.671713i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−2.16949			−0.164943			−0.0824716	−	0.996593i	$-0.526281\pi$
$173$	−2.16949			−0.164943			−0.0824716	+	0.996593i	$0.526281\pi$
$174$		0			0
$175$	−3.39874	−	2.64171i	−0.256921	−	0.199694i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−1.08263	−	1.87517i	−0.0809195	−	0.140157i	0.822726	−	0.568439i	$-0.192452\pi$
$179$	−1.08263	−	1.87517i	−0.0809195	−	0.140157i	−0.903645	+	0.428282i	$0.859119\pi$
$180$		0			0
$181$	0.557838			0.0414638			0.0207319	−	0.999785i	$-0.493400\pi$
$181$	0.557838			0.0414638			0.0207319	+	0.999785i	$0.493400\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−3.20927			−0.235950
$186$		0			0
$187$	−11.5949			−0.847906
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−23.9997			−1.73655			−0.868277	−	0.496079i	$-0.834773\pi$
$191$	−23.9997			−1.73655			−0.868277	+	0.496079i	$0.834773\pi$
$192$		0			0
$193$	−21.2794			−1.53172			−0.765862	−	0.643005i	$-0.777687\pi$
$193$	−21.2794			−1.53172			−0.765862	+	0.643005i	$0.777687\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	14.8768			1.05993			0.529964	−	0.848020i	$-0.322205\pi$
$197$	14.8768			1.05993			0.529964	+	0.848020i	$0.322205\pi$
$198$		0			0
$199$	−6.17884	−	10.7021i	−0.438006	−	0.758649i	0.559530	−	0.828810i	$-0.310982\pi$
$199$	−6.17884	−	10.7021i	−0.438006	−	0.758649i	−0.997536	+	0.0701616i	$0.977649\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	1.59420	−	0.648749i	0.111891	−	0.0455332i
$204$		0			0
$205$	9.26586			0.647156
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−8.40604	−	14.5597i	−0.581458	−	1.00711i
$210$		0			0
$211$	−8.65802	+	14.9961i	−0.596043	+	1.03238i	0.397356	+	0.917664i	$0.369928\pi$
$211$	−8.65802	+	14.9961i	−0.596043	+	1.03238i	−0.993399	+	0.114712i	$0.963406\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	11.1966	−	19.3930i	0.763599	−	1.32259i
$216$		0			0
$217$	−0.374923	+	2.71706i	−0.0254514	+	0.184446i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−17.9866			−1.20991
$222$		0			0
$223$	−1.14489	−	1.98301i	−0.0766677	−	0.132792i	0.825143	−	0.564925i	$-0.191095\pi$
$223$	−1.14489	−	1.98301i	−0.0766677	−	0.132792i	−0.901810	+	0.432132i	$0.857761\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	1.78013	−	3.08328i	0.118152	−	0.204644i	−0.800884	−	0.598820i	$-0.795636\pi$
$227$	1.78013	−	3.08328i	0.118152	−	0.204644i	0.919035	+	0.394176i	$0.128970\pi$
$228$		0			0
$229$	13.4799	+	23.3478i	0.890775	+	1.54287i	0.838949	+	0.544211i	$0.183171\pi$
$229$	13.4799	+	23.3478i	0.890775	+	1.54287i	0.0518260	+	0.998656i	$0.483496\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−10.7321	+	18.5885i	−0.703081	+	1.21777i	0.264298	+	0.964441i	$0.414860\pi$
$233$	−10.7321	+	18.5885i	−0.703081	+	1.21777i	−0.967380	+	0.253332i	$0.918474\pi$
$234$		0			0
$235$	4.23681	+	7.33837i	0.276379	+	0.478703i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	4.65970	−	8.07083i	0.301411	−	0.522059i	−0.675045	−	0.737777i	$-0.735876\pi$
$239$	4.65970	−	8.07083i	0.301411	−	0.522059i	0.976456	+	0.215718i	$0.0692091\pi$
$240$		0			0
$241$	10.1003	−	17.4943i	0.650620	−	1.12691i	−0.332353	−	0.943155i	$-0.607842\pi$
$241$	10.1003	−	17.4943i	0.650620	−	1.12691i	0.982973	−	0.183752i	$-0.0588242\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	3.17258	+	12.4584i	0.202689	+	0.795937i
$246$		0			0
$247$	−13.0398	−	22.5856i	−0.829702	−	1.43709i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	27.1837			1.71582			0.857910	−	0.513800i	$-0.171762\pi$
$251$	27.1837			1.71582			0.857910	+	0.513800i	$0.171762\pi$
$252$		0			0
$253$	24.6483			1.54963
$254$		0			0
$255$		0			0
$256$		0			0
$257$	14.2411	+	24.6662i	0.888333	+	1.53864i	0.841845	+	0.539719i	$0.181469\pi$
$257$	14.2411	+	24.6662i	0.888333	+	1.53864i	0.0464876	+	0.998919i	$0.485197\pi$
$258$		0			0
$259$	−3.65028	−	2.83722i	−0.226818	−	0.176297i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−1.79907	+	3.11608i	−0.110935	+	0.192146i	−0.916148	−	0.400841i	$-0.868718\pi$
$263$	−1.79907	+	3.11608i	−0.110935	+	0.192146i	0.805212	+	0.592987i	$0.202051\pi$
$264$		0			0
$265$	−8.35791	+	14.4763i	−0.513422	+	0.889274i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−11.2261	−	19.4443i	−0.684470	−	1.18554i	−0.973603	−	0.228248i	$-0.926700\pi$
$269$	−11.2261	−	19.4443i	−0.684470	−	1.18554i	0.289133	−	0.957289i	$-0.406633\pi$
$270$		0			0
$271$	14.7935	−	25.6231i	0.898642	−	1.55649i	0.0694115	−	0.997588i	$-0.477888\pi$
$271$	14.7935	−	25.6231i	0.898642	−	1.55649i	0.829231	−	0.558906i	$-0.188779\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−2.51958	−	4.36403i	−0.151936	−	0.263161i
$276$		0			0
$277$	10.1933	−	17.6554i	0.612459	−	1.06081i	−0.378366	−	0.925656i	$-0.623514\pi$
$277$	10.1933	−	17.6554i	0.612459	−	1.06081i	0.990825	−	0.135153i	$-0.0431527\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	2.23968	+	3.87924i	0.133608	+	0.231416i	0.925065	−	0.379809i	$-0.124010\pi$
$281$	2.23968	+	3.87924i	0.133608	+	0.231416i	−0.791457	+	0.611225i	$0.790677\pi$
$282$		0			0
$283$	−2.07680			−0.123453			−0.0617264	−	0.998093i	$-0.519661\pi$
$283$	−2.07680			−0.123453			−0.0617264	+	0.998093i	$0.519661\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	10.5392	+	8.19169i	0.622108	+	0.483540i
$288$		0			0
$289$	1.49237	−	2.58486i	0.0877865	−	0.152051i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	0.887340	−	1.53692i	0.0518389	−	0.0897877i	−0.838942	−	0.544222i	$-0.816825\pi$
$293$	0.887340	−	1.53692i	0.0518389	−	0.0897877i	0.890780	+	0.454434i	$0.150158\pi$
$294$		0			0
$295$	5.32355	+	9.22066i	0.309949	+	0.536847i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	38.2355			2.21122
$300$		0			0
$301$	29.8800	−	12.1594i	1.72225	−	0.700858i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	4.41921	+	7.65429i	0.253043	+	0.438283i
$306$		0			0
$307$	−19.6315			−1.12043			−0.560215	−	0.828347i	$-0.689282\pi$
$307$	−19.6315			−1.12043			−0.560215	+	0.828347i	$0.689282\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−13.3159			−0.755076			−0.377538	−	0.925994i	$-0.623229\pi$
$311$	−13.3159			−0.755076			−0.377538	+	0.925994i	$0.623229\pi$
$312$		0			0
$313$	4.65281			0.262992			0.131496	−	0.991317i	$-0.458022\pi$
$313$	4.65281			0.262992			0.131496	+	0.991317i	$0.458022\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	4.12552			0.231713			0.115856	−	0.993266i	$-0.463039\pi$
$317$	4.12552			0.231713			0.115856	+	0.993266i	$0.463039\pi$
$318$		0			0
$319$	2.01483			0.112809
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−20.3214			−1.13071
$324$		0			0
$325$	−3.90847	−	6.76967i	−0.216803	−	0.375514i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−1.66862	+	12.0925i	−0.0919939	+	0.666679i
$330$		0			0
$331$	−0.0440594			−0.00242172			−0.00121086	−	0.999999i	$-0.500385\pi$
$331$	−0.0440594			−0.00242172			−0.00121086	+	0.999999i	$0.500385\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−13.2944	−	23.0266i	−0.726350	−	1.25808i
$336$		0			0
$337$	−13.3351	+	23.0970i	−0.726407	+	1.25817i	0.231986	+	0.972719i	$0.425478\pi$
$337$	−13.3351	+	23.0970i	−0.726407	+	1.25817i	−0.958392	+	0.285454i	$0.907856\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−1.60541	+	2.78064i	−0.0869376	+	0.150580i
$342$		0			0
$343$	−7.40556	+	16.9752i	−0.399863	+	0.916575i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	10.8252			0.581126			0.290563	−	0.956856i	$-0.406157\pi$
$347$	10.8252			0.581126			0.290563	+	0.956856i	$0.406157\pi$
$348$		0			0
$349$	−2.69555	−	4.66884i	−0.144290	−	0.249917i	0.784818	−	0.619726i	$-0.212756\pi$
$349$	−2.69555	−	4.66884i	−0.144290	−	0.249917i	−0.929108	+	0.369809i	$0.879423\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−4.47307	+	7.74759i	−0.238078	+	0.412362i	−0.960163	−	0.279442i	$-0.909851\pi$
$353$	−4.47307	+	7.74759i	−0.238078	+	0.412362i	0.722085	+	0.691804i	$0.243184\pi$
$354$		0			0
$355$	4.59798	+	7.96394i	0.244036	+	0.422682i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	1.84157	−	3.18969i	0.0971942	−	0.168345i	−0.813328	−	0.581805i	$-0.802347\pi$
$359$	1.84157	−	3.18969i	0.0971942	−	0.168345i	0.910522	+	0.413460i	$0.135680\pi$
$360$		0			0
$361$	−5.23251	−	9.06297i	−0.275395	−	0.476998i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−3.33087	+	5.76924i	−0.174346	+	0.301976i
$366$		0			0
$367$	−3.74988	+	6.49498i	−0.195742	+	0.339035i	−0.947144	−	0.320810i	$-0.896045\pi$
$367$	−3.74988	+	6.49498i	−0.195742	+	0.339035i	0.751401	+	0.659845i	$0.229378\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−22.3046	+	9.07666i	−1.15800	+	0.471237i
$372$		0			0
$373$	−4.11917	−	7.13461i	−0.213282	−	0.369416i	0.739458	−	0.673203i	$-0.235082\pi$
$373$	−4.11917	−	7.13461i	−0.213282	−	0.369416i	−0.952740	+	0.303787i	$0.901749\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	3.12549			0.160971
$378$		0			0
$379$	3.92853			0.201795			0.100897	−	0.994897i	$-0.467829\pi$
$379$	3.92853			0.201795			0.100897	+	0.994897i	$0.467829\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−11.9632	−	20.7210i	−0.611293	−	1.05879i	−0.991023	−	0.133694i	$-0.957316\pi$
$383$	−11.9632	−	20.7210i	−0.611293	−	1.05879i	0.379729	−	0.925098i	$-0.376017\pi$
$384$		0			0
$385$	−2.05718	+	14.9083i	−0.104843	+	0.759799i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	6.32875	−	10.9617i	0.320881	−	0.555781i	−0.659789	−	0.751451i	$-0.729355\pi$
$389$	6.32875	−	10.9617i	0.320881	−	0.555781i	0.980670	+	0.195669i	$0.0626879\pi$
$390$		0			0
$391$	14.8967	−	25.8018i	0.753359	−	1.30486i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−13.1848	−	22.8368i	−0.663400	−	1.14904i
$396$		0			0
$397$	−17.7703	+	30.7791i	−0.891866	+	1.54476i	−0.0542297	+	0.998528i	$0.517270\pi$
$397$	−17.7703	+	30.7791i	−0.891866	+	1.54476i	−0.837636	+	0.546229i	$0.816063\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−1.66166	−	2.87808i	−0.0829794	−	0.143724i	0.821549	−	0.570138i	$-0.193110\pi$
$401$	−1.66166	−	2.87808i	−0.0829794	−	0.143724i	−0.904528	+	0.426413i	$0.859777\pi$
$402$		0			0
$403$	−2.49037	+	4.31345i	−0.124054	+	0.214868i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−2.70605	−	4.68702i	−0.134134	−	0.232327i
$408$		0			0
$409$	22.5129			1.11319			0.556595	−	0.830784i	$-0.312107\pi$
$409$	22.5129			1.11319			0.556595	+	0.830784i	$0.312107\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−2.09662	+	15.1942i	−0.103168	+	0.747656i
$414$		0			0
$415$	7.03662	−	12.1878i	0.345414	−	0.598275i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−3.59772	+	6.23144i	−0.175760	+	0.304426i	−0.940424	−	0.340004i	$-0.889572\pi$
$419$	−3.59772	+	6.23144i	−0.175760	+	0.304426i	0.764664	+	0.644429i	$0.222905\pi$
$420$		0			0
$421$	16.8121	+	29.1193i	0.819370	+	1.41919i	0.906147	+	0.422962i	$0.139010\pi$
$421$	16.8121	+	29.1193i	0.819370	+	1.41919i	−0.0867773	+	0.996228i	$0.527657\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−6.09102			−0.295458
$426$		0			0
$427$	−1.74045	+	12.6130i	−0.0842264	+	0.610388i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	16.4871	+	28.5565i	0.794156	+	1.37552i	0.923373	+	0.383903i	$0.125420\pi$
$431$	16.4871	+	28.5565i	0.794156	+	1.37552i	−0.129217	+	0.991616i	$0.541246\pi$
$432$		0			0
$433$	19.8977			0.956221			0.478110	−	0.878300i	$-0.341322\pi$
$433$	19.8977			0.956221			0.478110	+	0.878300i	$0.341322\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	43.1989			2.06648
$438$		0			0
$439$	−29.1268			−1.39015			−0.695074	−	0.718938i	$-0.744628\pi$
$439$	−29.1268			−1.39015			−0.695074	+	0.718938i	$0.744628\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	13.7663			0.654058			0.327029	−	0.945014i	$-0.393952\pi$
$443$	13.7663			0.654058			0.327029	+	0.945014i	$0.393952\pi$
$444$		0			0
$445$	−21.1866			−1.00434
$446$		0			0
$447$		0			0
$448$		0			0
$449$	12.0958			0.570838			0.285419	−	0.958403i	$-0.407867\pi$
$449$	12.0958			0.570838			0.285419	+	0.958403i	$0.407867\pi$
$450$		0			0
$451$	7.81297	+	13.5325i	0.367898	+	0.637218i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−3.19118	+	23.1264i	−0.149605	+	1.08418i
$456$		0			0
$457$	−8.35476			−0.390819			−0.195410	−	0.980722i	$-0.562604\pi$
$457$	−8.35476			−0.390819			−0.195410	+	0.980722i	$0.562604\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−11.1673	−	19.3423i	−0.520112	−	0.900860i	−0.999727	−	0.0233807i	$-0.992557\pi$
$461$	−11.1673	−	19.3423i	−0.520112	−	0.900860i	0.479615	−	0.877479i	$-0.340776\pi$
$462$		0			0
$463$	0.0370790	−	0.0642228i	0.00172321	−	0.00298469i	−0.865163	−	0.501492i	$-0.832785\pi$
$463$	0.0370790	−	0.0642228i	0.00172321	−	0.00298469i	0.866886	+	0.498507i	$0.166118\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	14.5828	−	25.2581i	0.674810	−	1.16880i	−0.301715	−	0.953398i	$-0.597559\pi$
$467$	14.5828	−	25.2581i	0.674810	−	1.16880i	0.976524	−	0.215407i	$-0.0691077\pi$
$468$		0			0
$469$	5.23584	−	37.9441i	0.241769	−	1.75209i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	37.7637			1.73638
$474$		0			0
$475$	−4.41583	−	7.64845i	−0.202612	−	0.350935i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−13.9551	+	24.1710i	−0.637626	+	1.10440i	0.348326	+	0.937373i	$0.386750\pi$
$479$	−13.9551	+	24.1710i	−0.637626	+	1.10440i	−0.985952	+	0.167027i	$0.946583\pi$
$480$		0			0
$481$	−4.19774	−	7.27070i	−0.191401	−	0.331515i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−1.91884	+	3.32353i	−0.0871301	+	0.150914i
$486$		0			0
$487$	2.14409	+	3.71367i	0.0971580	+	0.168283i	0.910507	−	0.413493i	$-0.135691\pi$
$487$	2.14409	+	3.71367i	0.0971580	+	0.168283i	−0.813349	+	0.581776i	$0.802358\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−5.22215	+	9.04503i	−0.235672	+	0.408196i	−0.959468	−	0.281818i	$-0.909063\pi$
$491$	−5.22215	+	9.04503i	−0.235672	+	0.408196i	0.723796	+	0.690015i	$0.242396\pi$
$492$		0			0
$493$	1.21770	−	2.10912i	0.0548425	−	0.0949900i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−1.81086	+	13.1233i	−0.0812282	+	0.588660i
$498$		0			0
$499$	−3.06312	−	5.30548i	−0.137124	−	0.237506i	0.789283	−	0.614030i	$-0.210453\pi$
$499$	−3.06312	−	5.30548i	−0.137124	−	0.237506i	−0.926407	+	0.376524i	$0.877119\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−12.4469			−0.554982			−0.277491	−	0.960728i	$-0.589503\pi$
$503$	−12.4469			−0.554982			−0.277491	+	0.960728i	$0.589503\pi$
$504$		0			0
$505$	30.2175			1.34466
$506$		0			0
$507$		0			0
$508$		0			0
$509$	5.90450	+	10.2269i	0.261712	+	0.453299i	0.966697	−	0.255923i	$-0.0823795\pi$
$509$	5.90450	+	10.2269i	0.261712	+	0.453299i	−0.704985	+	0.709222i	$0.749046\pi$
$510$		0			0
$511$	−8.88902	+	3.61731i	−0.393227	+	0.160021i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−7.11388	+	12.3216i	−0.313475	+	0.542955i
$516$		0			0
$517$	−7.14495	+	12.3754i	−0.314235	+	0.544271i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−5.54828	−	9.60991i	−0.243075	−	0.421018i	0.718514	−	0.695513i	$-0.244823\pi$
$521$	−5.54828	−	9.60991i	−0.243075	−	0.421018i	−0.961589	+	0.274495i	$0.911489\pi$
$522$		0			0
$523$	−10.6209	+	18.3960i	−0.464421	+	0.804401i	−0.999175	−	0.0406065i	$-0.987071\pi$
$523$	−10.6209	+	18.3960i	−0.464421	+	0.804401i	0.534754	+	0.845008i	$0.320404\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	1.94052	+	3.36107i	0.0845302	+	0.146411i
$528$		0			0
$529$	−20.1672	+	34.9305i	−0.876833	+	1.51872i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	12.1198	+	20.9921i	0.524967	+	0.909269i
$534$		0			0
$535$	−13.7650			−0.595111
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−15.5199	+	15.1383i	−0.668490	+	0.652054i
$540$		0			0
$541$	−6.33567	+	10.9737i	−0.272392	+	0.471796i	−0.969474	−	0.245195i	$-0.921148\pi$
$541$	−6.33567	+	10.9737i	−0.272392	+	0.471796i	0.697082	+	0.716991i	$0.254481\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−7.90908	+	13.6989i	−0.338788	+	0.586798i
$546$		0			0
$547$	21.4805	+	37.2053i	0.918438	+	1.59078i	0.801788	+	0.597609i	$0.203883\pi$
$547$	21.4805	+	37.2053i	0.918438	+	1.59078i	0.116651	+	0.993173i	$0.462784\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	3.53121			0.150435
$552$		0			0
$553$	5.19268	−	37.6313i	0.220815	−	1.60025i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−16.5129	−	28.6012i	−0.699673	−	1.21187i	−0.968580	−	0.248703i	$-0.919996\pi$
$557$	−16.5129	−	28.6012i	−0.699673	−	1.21187i	0.268906	−	0.963166i	$-0.413338\pi$
$558$		0			0
$559$	58.5807			2.47770
$560$		0			0
$561$		0			0
$562$		0			0
$563$	36.8132			1.55149			0.775746	−	0.631046i	$-0.217374\pi$
$563$	36.8132			1.55149			0.775746	+	0.631046i	$0.217374\pi$
$564$		0			0
$565$	−5.72081			−0.240676
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−44.3571			−1.85955			−0.929774	−	0.368132i	$-0.879998\pi$
$569$	−44.3571			−1.85955			−0.929774	+	0.368132i	$0.879998\pi$
$570$		0			0
$571$	42.5872			1.78222			0.891110	−	0.453787i	$-0.149927\pi$
$571$	42.5872			1.78222			0.891110	+	0.453787i	$0.149927\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	12.9482			0.539977
$576$		0			0
$577$	16.3209	+	28.2687i	0.679450	+	1.17684i	0.975147	+	0.221559i	$0.0711147\pi$
$577$	16.3209	+	28.2687i	0.679450	+	1.17684i	−0.295697	+	0.955282i	$0.595552\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	18.7785	−	7.64175i	0.779063	−	0.317033i
$582$		0			0
$583$	−28.1895			−1.16749
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−13.1270	−	22.7366i	−0.541809	−	0.938441i	−0.998800	−	0.0489701i	$-0.984406\pi$
$587$	−13.1270	−	22.7366i	−0.541809	−	0.938441i	0.456991	−	0.889471i	$-0.348927\pi$
$588$		0			0
$589$	−2.81365	+	4.87338i	−0.115934	+	0.200804i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	2.59998	−	4.50330i	0.106768	−	0.184928i	−0.807691	−	0.589606i	$-0.799283\pi$
$593$	2.59998	−	4.50330i	0.106768	−	0.184928i	0.914459	+	0.404678i	$0.132616\pi$
$594$		0			0
$595$	14.3627	+	11.1636i	0.588814	+	0.457663i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	26.3675			1.07735			0.538673	−	0.842515i	$-0.318926\pi$
$599$	26.3675			1.07735			0.538673	+	0.842515i	$0.318926\pi$
$600$		0			0
$601$	−15.4505	−	26.7611i	−0.630239	−	1.09161i	−0.987503	−	0.157603i	$-0.949623\pi$
$601$	−15.4505	−	26.7611i	−0.630239	−	1.09161i	0.357263	−	0.934004i	$-0.383710\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	1.29240	−	2.23851i	0.0525436	−	0.0910082i
$606$		0			0
$607$	3.83661	+	6.64519i	0.155723	+	0.269720i	0.933322	−	0.359040i	$-0.116896\pi$
$607$	3.83661	+	6.64519i	0.155723	+	0.269720i	−0.777599	+	0.628760i	$0.783563\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−11.0836	+	19.1973i	−0.448393	+	0.776639i
$612$		0			0
$613$	7.97498	+	13.8131i	0.322106	+	0.557905i	0.980922	−	0.194399i	$-0.0622758\pi$
$613$	7.97498	+	13.8131i	0.322106	+	0.557905i	−0.658816	+	0.752304i	$0.728942\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	3.67011	−	6.35682i	0.147753	−	0.255916i	−0.782644	−	0.622470i	$-0.786129\pi$
$617$	3.67011	−	6.35682i	0.147753	−	0.255916i	0.930397	+	0.366554i	$0.119463\pi$
$618$		0			0
$619$	10.2842	−	17.8127i	0.413357	−	0.715955i	−0.581898	−	0.813262i	$-0.697690\pi$
$619$	10.2842	−	17.8127i	0.413357	−	0.715955i	0.995254	+	0.0973072i	$0.0310229\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−24.0981	−	18.7305i	−0.965469	−	0.750421i
$624$		0			0
$625$	7.10891	+	12.3130i	0.284356	+	0.492520i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−6.54182			−0.260840
$630$		0			0
$631$	5.09394			0.202787			0.101393	−	0.994846i	$-0.467670\pi$
$631$	5.09394			0.202787			0.101393	+	0.994846i	$0.467670\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	9.99705	+	17.3154i	0.396721	+	0.687141i
$636$		0			0
$637$	−24.0751	+	23.4832i	−0.953892	+	0.930439i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	6.31861	−	10.9442i	0.249570	−	0.432268i	−0.713836	−	0.700312i	$-0.753044\pi$
$641$	6.31861	−	10.9442i	0.249570	−	0.432268i	0.963407	+	0.268044i	$0.0863773\pi$
$642$		0			0
$643$	−12.4329	+	21.5344i	−0.490306	+	0.849235i	−0.999938	−	0.0111579i	$-0.996448\pi$
$643$	−12.4329	+	21.5344i	−0.490306	+	0.849235i	0.509632	+	0.860393i	$0.329782\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	1.12339	+	1.94577i	0.0441650	+	0.0764960i	0.887263	−	0.461264i	$-0.152604\pi$
$647$	1.12339	+	1.94577i	0.0441650	+	0.0764960i	−0.843098	+	0.537760i	$0.819271\pi$
$648$		0			0
$649$	−8.97762	+	15.5497i	−0.352403	+	0.610379i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	1.02881	+	1.78195i	0.0402604	+	0.0697330i	0.885453	−	0.464728i	$-0.153848\pi$
$653$	1.02881	+	1.78195i	0.0402604	+	0.0697330i	−0.845193	+	0.534461i	$0.820515\pi$
$654$		0			0
$655$	14.7438	−	25.5370i	0.576088	−	0.997815i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−4.16599	−	7.21571i	−0.162284	−	0.281084i	0.773403	−	0.633914i	$-0.218553\pi$
$659$	−4.16599	−	7.21571i	−0.162284	−	0.281084i	−0.935687	+	0.352830i	$0.885219\pi$
$660$		0			0
$661$	34.0926			1.32605			0.663024	−	0.748598i	$-0.269273\pi$
$661$	34.0926			1.32605			0.663024	+	0.748598i	$0.269273\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−3.60543	+	26.1285i	−0.139812	+	1.01322i
$666$		0			0
$667$	−2.58857	+	4.48353i	−0.100230	+	0.173603i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−7.45255	+	12.9082i	−0.287702	+	0.498315i
$672$		0			0
$673$	0.571008	+	0.989016i	0.0220108	+	0.0381237i	0.876821	−	0.480817i	$-0.159660\pi$
$673$	0.571008	+	0.989016i	0.0220108	+	0.0381237i	−0.854810	+	0.518941i	$0.826327\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−36.3812			−1.39824			−0.699121	−	0.715004i	$-0.746425\pi$
$677$	−36.3812			−1.39824			−0.699121	+	0.715004i	$0.746425\pi$
$678$		0			0
$679$	−5.12077	+	2.08386i	−0.196517	+	0.0799711i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	3.11274	+	5.39142i	0.119106	+	0.206297i	0.919414	−	0.393292i	$-0.128664\pi$
$683$	3.11274	+	5.39142i	0.119106	+	0.206297i	−0.800308	+	0.599589i	$0.795331\pi$
$684$		0			0
$685$	−24.6846			−0.943152
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−43.7288			−1.66593
$690$		0			0
$691$	39.8259			1.51505			0.757525	−	0.652806i	$-0.226408\pi$
$691$	39.8259			1.51505			0.757525	+	0.652806i	$0.226408\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−14.9480			−0.567008
$696$		0			0
$697$	18.8877			0.715422
$698$		0			0
$699$		0			0
$700$		0			0
$701$	48.3337			1.82554			0.912769	−	0.408477i	$-0.133940\pi$
$701$	48.3337			1.82554			0.912769	+	0.408477i	$0.133940\pi$
$702$		0			0
$703$	−4.74265	−	8.21452i	−0.178873	−	0.309816i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	34.3700	+	26.7145i	1.29262	+	1.00470i
$708$		0			0
$709$	−16.0840			−0.604046			−0.302023	−	0.953301i	$-0.597662\pi$
$709$	−16.0840			−0.604046			−0.302023	+	0.953301i	$0.597662\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−4.12512	−	7.14491i	−0.154487	−	0.267579i
$714$		0			0
$715$	−13.6645	+	23.6676i	−0.511023	+	0.885117i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	21.0734	−	36.5002i	0.785906	−	1.36123i	−0.142550	−	0.989788i	$-0.545530\pi$
$719$	21.0734	−	36.5002i	0.785906	−	1.36123i	0.928456	−	0.371442i	$-0.121136\pi$
$720$		0			0
$721$	−18.9847	+	7.72566i	−0.707026	+	0.287718i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	1.05842			0.0393089
$726$		0			0
$727$	12.9548	+	22.4384i	0.480467	+	0.832192i	0.999749	−	0.0224103i	$-0.00713401\pi$
$727$	12.9548	+	22.4384i	0.480467	+	0.832192i	−0.519282	+	0.854603i	$0.673801\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	22.8232	−	39.5310i	0.844148	−	1.46211i
$732$		0			0
$733$	−10.2027	−	17.6716i	−0.376846	−	0.652716i	0.613756	−	0.789496i	$-0.289658\pi$
$733$	−10.2027	−	17.6716i	−0.376846	−	0.652716i	−0.990601	+	0.136780i	$0.956325\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	22.4196	−	38.8320i	0.825838	−	1.43039i
$738$		0			0
$739$	11.8953	+	20.6033i	0.437576	+	0.757903i	0.997502	−	0.0706392i	$-0.0225039\pi$
$739$	11.8953	+	20.6033i	0.437576	+	0.757903i	−0.559926	+	0.828542i	$0.689171\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	21.6320	−	37.4678i	0.793603	−	1.37456i	−0.130120	−	0.991498i	$-0.541536\pi$
$743$	21.6320	−	37.4678i	0.793603	−	1.37456i	0.923723	−	0.383062i	$-0.125130\pi$
$744$		0			0
$745$	6.91430	−	11.9759i	0.253321	−	0.438764i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−15.6565	−	12.1692i	−0.572078	−	0.444654i
$750$		0			0
$751$	−7.18465	−	12.4442i	−0.262172	−	0.454095i	0.704647	−	0.709558i	$-0.251105\pi$
$751$	−7.18465	−	12.4442i	−0.262172	−	0.454095i	−0.966819	+	0.255463i	$0.917772\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	10.4176			0.379136
$756$		0			0
$757$	39.7854			1.44603			0.723013	−	0.690835i	$-0.242757\pi$
$757$	39.7854			1.44603			0.723013	+	0.690835i	$0.242757\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−11.1966	−	19.3932i	−0.405878	−	0.703002i	0.588545	−	0.808464i	$-0.299701\pi$
$761$	−11.1966	−	19.3932i	−0.405878	−	0.703002i	−0.994423	+	0.105463i	$0.966368\pi$
$762$		0			0
$763$	−21.1068	+	8.58924i	−0.764117	+	0.310951i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−13.9265	+	24.1213i	−0.502856	+	0.870971i
$768$		0			0
$769$	−1.45546	+	2.52093i	−0.0524853	+	0.0909071i	−0.891074	−	0.453857i	$-0.850048\pi$
$769$	−1.45546	+	2.52093i	−0.0524853	+	0.0909071i	0.838589	+	0.544764i	$0.183381\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	6.68612	+	11.5807i	0.240483	+	0.416529i	0.960852	−	0.277062i	$-0.0893609\pi$
$773$	6.68612	+	11.5807i	0.240483	+	0.416529i	−0.720369	+	0.693591i	$0.756028\pi$
$774$		0			0
$775$	−0.843347	+	1.46072i	−0.0302939	+	0.0524706i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	13.6931	+	23.7171i	0.490606	+	0.849754i
$780$		0			0
$781$	−7.75403	+	13.4304i	−0.277461	+	0.480577i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−0.401073	−	0.694679i	−0.0143149	−	0.0247941i
$786$		0			0
$787$	23.8528			0.850260			0.425130	−	0.905132i	$-0.360228\pi$
$787$	23.8528			0.850260			0.425130	+	0.905132i	$0.360228\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−6.50696	−	5.05761i	−0.231361	−	0.179828i
$792$		0			0
$793$	−11.5607	+	20.0237i	−0.410533	+	0.711063i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	6.10559	−	10.5752i	0.216271	−	0.374593i	−0.737394	−	0.675463i	$-0.763944\pi$
$797$	6.10559	−	10.5752i	0.216271	−	0.374593i	0.953665	+	0.300870i	$0.0972772\pi$
$798$		0			0
$799$	8.63639	+	14.9587i	0.305533	+	0.529199i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−11.2344			−0.396452
$804$		0			0
$805$	−30.5320	−	23.7314i	−1.07611	−	0.836421i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−26.7838	−	46.3910i	−0.941669	−	1.63102i	−0.762287	−	0.647240i	$-0.775923\pi$
$809$	−26.7838	−	46.3910i	−0.941669	−	1.63102i	−0.179383	−	0.983779i	$-0.557410\pi$
$810$		0			0
$811$	−1.81310			−0.0636667			−0.0318334	−	0.999493i	$-0.510135\pi$
$811$	−1.81310			−0.0636667			−0.0318334	+	0.999493i	$0.510135\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	33.5229			1.17426
$816$		0			0
$817$	66.1851			2.31552
$818$		0			0
$819$		0			0
$820$		0			0
$821$	39.6743			1.38464			0.692321	−	0.721590i	$-0.256588\pi$
$821$	39.6743			1.38464			0.692321	+	0.721590i	$0.256588\pi$
$822$		0			0
$823$	−16.8131			−0.586069			−0.293034	−	0.956102i	$-0.594665\pi$
$823$	−16.8131			−0.586069			−0.293034	+	0.956102i	$0.594665\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	37.2198			1.29426			0.647130	−	0.762379i	$-0.275969\pi$
$827$	37.2198			1.29426			0.647130	+	0.762379i	$0.275969\pi$
$828$		0			0
$829$	−11.4365	−	19.8086i	−0.397206	−	0.687981i	0.596174	−	0.802855i	$-0.296687\pi$
$829$	−11.4365	−	19.8086i	−0.397206	−	0.687981i	−0.993380	+	0.114874i	$0.963354\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	6.46703	+	25.3954i	0.224069	+	0.879898i
$834$		0			0
$835$	−2.81035			−0.0972562
$836$		0			0
$837$		0			0
$838$		0			0
$839$	18.4071	+	31.8820i	0.635484	+	1.10069i	0.986412	+	0.164288i	$0.0525326\pi$
$839$	18.4071	+	31.8820i	0.635484	+	1.10069i	−0.350929	+	0.936402i	$0.614134\pi$
$840$		0			0
$841$	14.2884	−	24.7482i	0.492704	−	0.853388i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−9.25921	+	16.0374i	−0.318527	+	0.551704i
$846$		0			0
$847$	3.44901	−	1.40354i	0.118509	−	0.0482264i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	13.9065			0.476709
$852$		0			0
$853$	6.98355	+	12.0959i	0.239112	+	0.414155i	0.960460	−	0.278419i	$-0.0898102\pi$
$853$	6.98355	+	12.0959i	0.239112	+	0.414155i	−0.721347	+	0.692573i	$0.756477\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	8.78386	−	15.2141i	0.300051	−	0.519703i	−0.676096	−	0.736813i	$-0.736330\pi$
$857$	8.78386	−	15.2141i	0.300051	−	0.519703i	0.976147	+	0.217110i	$0.0696630\pi$
$858$		0			0
$859$	1.42288	+	2.46451i	0.0485482	+	0.0840879i	0.889278	−	0.457366i	$-0.151207\pi$
$859$	1.42288	+	2.46451i	0.0485482	+	0.0840879i	−0.840730	+	0.541454i	$0.817874\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−27.7115	+	47.9977i	−0.943310	+	1.63386i	−0.184210	+	0.982887i	$0.558973\pi$
$863$	−27.7115	+	47.9977i	−0.943310	+	1.63386i	−0.759100	+	0.650974i	$0.774361\pi$
$864$		0			0
$865$	1.99221	+	3.45061i	0.0677372	+	0.117324i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	22.2348	−	38.5119i	0.754265	−	1.30643i
$870$		0			0
$871$	34.7783	−	60.2378i	1.17842	−	2.04108i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−4.40170	+	31.8991i	−0.148805	+	1.07839i
$876$		0			0
$877$	−27.4345	−	47.5179i	−0.926396	−	1.60456i	−0.789301	−	0.614006i	$-0.789557\pi$
$877$	−27.4345	−	47.5179i	−0.926396	−	1.60456i	−0.137095	−	0.990558i	$-0.543776\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	51.1572			1.72353			0.861765	−	0.507307i	$-0.169359\pi$
$881$	51.1572			1.72353			0.861765	+	0.507307i	$0.169359\pi$
$882$		0			0
$883$	−38.6438			−1.30047			−0.650234	−	0.759734i	$-0.725329\pi$
$883$	−38.6438			−1.30047			−0.650234	+	0.759734i	$0.725329\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	8.92626	+	15.4607i	0.299714	+	0.519121i	0.976071	−	0.217454i	$-0.0697752\pi$
$887$	8.92626	+	15.4607i	0.299714	+	0.519121i	−0.676356	+	0.736575i	$0.736442\pi$
$888$		0			0
$889$	−3.93722	+	28.5330i	−0.132050	+	0.956966i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−12.5223	+	21.6893i	−0.419043	+	0.725805i
$894$		0			0
$895$	−1.98833	+	3.44388i	−0.0664624	+	0.115116i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−0.337199	−	0.584047i	−0.0112462	−	0.0194790i
$900$		0			0
$901$	−17.0369	+	29.5088i	−0.567581	+	0.983080i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−0.512255	−	0.887252i	−0.0170279	−	0.0294932i
$906$		0			0
$907$	−18.2332	+	31.5807i	−0.605422	+	1.04862i	0.386563	+	0.922263i	$0.373662\pi$
$907$	−18.2332	+	31.5807i	−0.605422	+	1.04862i	−0.991985	+	0.126358i	$0.959671\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	18.9847	+	32.8825i	0.628993	+	1.08945i	0.987754	+	0.156018i	$0.0498658\pi$
$911$	18.9847	+	32.8825i	0.628993	+	1.08945i	−0.358762	+	0.933429i	$0.616801\pi$
$912$		0			0
$913$	23.7331			0.785451
$914$		0			0
$915$		0			0
$916$		0			0
$917$	39.3465	−	16.0117i	1.29934	−	0.528754i
$918$		0			0
$919$	1.21770	−	2.10911i	0.0401681	−	0.0695732i	−0.845242	−	0.534383i	$-0.820544\pi$
$919$	1.21770	−	2.10911i	0.0401681	−	0.0695732i	0.885411	+	0.464810i	$0.153877\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−12.0284	+	20.8338i	−0.395919	+	0.685752i
$924$		0			0
$925$	−1.42153	−	2.46217i	−0.0467398	−	0.0809557i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	35.4808			1.16409			0.582044	−	0.813157i	$-0.302253\pi$
$929$	35.4808			1.16409			0.582044	+	0.813157i	$0.302253\pi$
$930$		0			0
$931$	−27.2004	+	26.5316i	−0.891456	+	0.869538i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	10.6475	+	18.4420i	0.348209	+	0.603116i
$936$		0			0
$937$	−30.0427			−0.981452			−0.490726	−	0.871314i	$-0.663268\pi$
$937$	−30.0427			−0.981452			−0.490726	+	0.871314i	$0.663268\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	30.2499			0.986119			0.493060	−	0.869996i	$-0.335878\pi$
$941$	30.2499			0.986119			0.493060	+	0.869996i	$0.335878\pi$
$942$		0			0
$943$	−40.1511			−1.30750
$944$		0			0
$945$		0			0
$946$		0			0
$947$	33.9889			1.10449			0.552245	−	0.833682i	$-0.313771\pi$
$947$	33.9889			1.10449			0.552245	+	0.833682i	$0.313771\pi$
$948$		0			0
$949$	−17.4272			−0.565711
$950$		0			0
$951$		0			0
$952$		0			0
$953$	21.4324			0.694265			0.347132	−	0.937816i	$-0.387155\pi$
$953$	21.4324			0.694265			0.347132	+	0.937816i	$0.387155\pi$
$954$		0			0
$955$	22.0385	+	38.1719i	0.713151	+	1.23521i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−28.0768	−	21.8230i	−0.906647	−	0.704702i
$960$		0			0
$961$	−29.9253			−0.965332
$962$		0			0
$963$		0			0
$964$		0			0
$965$	19.5406	+	33.8452i	0.629033	+	1.08952i
$966$		0			0
$967$	−12.4095	+	21.4938i	−0.399061	+	0.691194i	−0.993610	−	0.112865i	$-0.963997\pi$
$967$	−12.4095	+	21.4938i	−0.399061	+	0.691194i	0.594549	+	0.804059i	$0.297331\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−13.9437	+	24.1512i	−0.447475	+	0.775050i	−0.998221	−	0.0596234i	$-0.981010\pi$
$971$	−13.9437	+	24.1512i	−0.447475	+	0.775050i	0.550746	+	0.834673i	$0.314343\pi$
$972$		0			0
$973$	−17.0021	−	13.2151i	−0.545062	−	0.423656i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−27.2473			−0.871719			−0.435859	−	0.900015i	$-0.643555\pi$
$977$	−27.2473			−0.871719			−0.435859	+	0.900015i	$0.643555\pi$
$978$		0			0
$979$	−17.8645	−	30.9423i	−0.570953	−	0.988920i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	6.94539	−	12.0298i	0.221523	−	0.383690i	−0.733747	−	0.679422i	$-0.762230\pi$
$983$	6.94539	−	12.0298i	0.221523	−	0.383690i	0.955271	+	0.295733i	$0.0955637\pi$
$984$		0			0
$985$	−13.6611	−	23.6618i	−0.435280	−	0.753928i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−48.5173	+	84.0344i	−1.54276	+	2.67214i
$990$		0			0
$991$	−21.3271	−	36.9397i	−0.677479	−	1.17343i	−0.975738	−	0.218942i	$-0.929739\pi$
$991$	−21.3271	−	36.9397i	−0.677479	−	1.17343i	0.298259	−	0.954485i	$-0.403594\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−11.3479	+	19.6551i	−0.359752	+	0.623108i
$996$		0			0
$997$	−21.5905	+	37.3959i	−0.683779	+	1.18434i	0.290040	+	0.957014i	$0.406331\pi$
$997$	−21.5905	+	37.3959i	−0.683779	+	1.18434i	−0.973819	+	0.227325i	$0.927002\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.q.k.2305.4		22
3.2	odd	2		1008.2.q.k.625.3		22
4.3	odd	2		1512.2.q.c.793.4		22
7.4	even	3		3024.2.t.l.1873.8		22
9.2	odd	6		1008.2.t.k.961.11		22
9.7	even	3		3024.2.t.l.289.8		22
12.11	even	2		504.2.q.d.121.9	yes	22
21.11	odd	6		1008.2.t.k.193.11		22
28.11	odd	6		1512.2.t.d.361.8		22
36.7	odd	6		1512.2.t.d.289.8		22
36.11	even	6		504.2.t.d.457.1	yes	22
63.11	odd	6		1008.2.q.k.529.3		22
63.25	even	3	inner	3024.2.q.k.2881.4		22
84.11	even	6		504.2.t.d.193.1	yes	22
252.11	even	6		504.2.q.d.25.9	✓	22
252.151	odd	6		1512.2.q.c.1369.4		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.d.25.9	✓	22	252.11	even	6
504.2.q.d.121.9	yes	22	12.11	even	2
504.2.t.d.193.1	yes	22	84.11	even	6
504.2.t.d.457.1	yes	22	36.11	even	6
1008.2.q.k.529.3		22	63.11	odd	6
1008.2.q.k.625.3		22	3.2	odd	2
1008.2.t.k.193.11		22	21.11	odd	6
1008.2.t.k.961.11		22	9.2	odd	6
1512.2.q.c.793.4		22	4.3	odd	2
1512.2.q.c.1369.4		22	252.151	odd	6
1512.2.t.d.289.8		22	36.7	odd	6
1512.2.t.d.361.8		22	28.11	odd	6
3024.2.q.k.2305.4		22	1.1	even	1	trivial
3024.2.q.k.2881.4		22	63.25	even	3	inner
3024.2.t.l.289.8		22	9.7	even	3
3024.2.t.l.1873.8		22	7.4	even	3

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:	\( N \)	\(=\)	\( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3024.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.918286 - 1.59052i) q^{5} +(0.361656 - 2.62092i) q^{7} +O(q^{10})\)	\(q+(-0.918286 - 1.59052i) q^{5} +(0.361656 - 2.62092i) q^{7} +(1.54860 - 2.68225i) q^{11} +(2.40225 - 4.16081i) q^{13} +(-1.87185 - 3.24214i) q^{17} +(2.71408 - 4.70093i) q^{19} +(3.97914 + 6.89208i) q^{23} +(0.813503 - 1.40903i) q^{25} +(0.325267 + 0.563379i) q^{29} -1.03668 q^{31} +(-4.50072 + 1.83153i) q^{35} +(0.873712 - 1.51331i) q^{37} +(-2.52260 + 4.36927i) q^{41} +(6.09645 + 10.5594i) q^{43} -4.61383 q^{47} +(-6.73841 - 1.89574i) q^{49} +(-4.55082 - 7.88226i) q^{53} -5.68821 q^{55} -5.79727 q^{59} -4.81245 q^{61} -8.82379 q^{65} +14.4774 q^{67} -5.00714 q^{71} +(-1.81364 - 3.14131i) q^{73} +(-6.46989 - 5.02879i) q^{77} +14.3581 q^{79} +(3.83139 + 6.63616i) q^{83} +(-3.43778 + 5.95441i) q^{85} +(5.76798 - 9.99043i) q^{89} +(-10.0364 - 7.80087i) q^{91} -9.96922 q^{95} +(-1.04480 - 1.80964i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 3 q^{5} + 5 q^{7}+O(q^{10}) \) 22 * q - 3 * q^5 + 5 * q^7	\( 22 q - 3 q^{5} + 5 q^{7} - 3 q^{11} - 3 q^{13} - 7 q^{17} + q^{19} + 2 q^{23} - 10 q^{25} - 9 q^{29} - 8 q^{31} + 14 q^{35} + 2 q^{37} - 16 q^{41} - 10 q^{47} + 15 q^{49} - 11 q^{53} - 22 q^{55} + 38 q^{59} + 26 q^{61} + 26 q^{65} + 52 q^{67} - 48 q^{71} - 35 q^{73} - 17 q^{77} + 20 q^{79} - 28 q^{83} - 20 q^{85} - 6 q^{89} + 37 q^{91} - 24 q^{95} - 29 q^{97}+O(q^{100}) \) 22 * q - 3 * q^5 + 5 * q^7 - 3 * q^11 - 3 * q^13 - 7 * q^17 + q^19 + 2 * q^23 - 10 * q^25 - 9 * q^29 - 8 * q^31 + 14 * q^35 + 2 * q^37 - 16 * q^41 - 10 * q^47 + 15 * q^49 - 11 * q^53 - 22 * q^55 + 38 * q^59 + 26 * q^61 + 26 * q^65 + 52 * q^67 - 48 * q^71 - 35 * q^73 - 17 * q^77 + 20 * q^79 - 28 * q^83 - 20 * q^85 - 6 * q^89 + 37 * q^91 - 24 * q^95 - 29 * q^97

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