LMFDB - Embedded newform 1512.2.t.c.361.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1512,2,Mod(289,1512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 0, 4, 2]))

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

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

chi := DirichletCharacter("1512.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1512 = 2^{3} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1512.t (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$12.0733807856$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.2
Character	$\chi$	$=$	1512.361
Dual form			1512.2.t.c.289.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.19500 q^{5} +(2.61289 - 0.415693i) q^{7} +O(q^{10})$	$q-3.19500 q^{5} +(2.61289 - 0.415693i) q^{7} +2.28279 q^{11} +(-0.675051 + 1.16922i) q^{13} +(-2.21425 + 3.83519i) q^{17} +(-3.69214 - 6.39497i) q^{19} +6.46959 q^{23} +5.20800 q^{25} +(1.06167 + 1.83887i) q^{29} +(0.316154 + 0.547595i) q^{31} +(-8.34818 + 1.32814i) q^{35} +(1.92885 + 3.34087i) q^{37} +(5.05124 - 8.74900i) q^{41} +(4.24701 + 7.35603i) q^{43} +(3.26587 - 5.65664i) q^{47} +(6.65440 - 2.17232i) q^{49} +(-2.39950 + 4.15606i) q^{53} -7.29349 q^{55} +(3.10191 + 5.37267i) q^{59} +(4.45546 - 7.71709i) q^{61} +(2.15679 - 3.73566i) q^{65} +(1.50785 + 2.61167i) q^{67} +15.3791 q^{71} +(4.36577 - 7.56173i) q^{73} +(5.96467 - 0.948938i) q^{77} +(0.938050 - 1.62475i) q^{79} +(3.00140 + 5.19857i) q^{83} +(7.07451 - 12.2534i) q^{85} +(-2.65390 - 4.59668i) q^{89} +(-1.27780 + 3.33566i) q^{91} +(11.7964 + 20.4319i) q^{95} +(7.44539 + 12.8958i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 2 q^{5} - q^{7}+O(q^{10}) $ 22 * q + 2 * q^5 - q^7	$ 22 q + 2 q^{5} - q^{7} + 6 q^{11} + 7 q^{13} + q^{17} + 13 q^{19} + 44 q^{25} + 7 q^{29} + 6 q^{31} - 2 q^{35} + 6 q^{37} - 4 q^{41} + 2 q^{43} - 17 q^{47} + 29 q^{49} - q^{53} + 2 q^{55} + 21 q^{59} + 31 q^{61} + 3 q^{65} - 26 q^{67} + 32 q^{71} + 17 q^{73} + 4 q^{77} - 16 q^{79} + 36 q^{83} + 28 q^{85} + 2 q^{89} + 15 q^{91} + 24 q^{95} + 19 q^{97}+O(q^{100}) $ 22 * q + 2 * q^5 - q^7 + 6 * q^11 + 7 * q^13 + q^17 + 13 * q^19 + 44 * q^25 + 7 * q^29 + 6 * q^31 - 2 * q^35 + 6 * q^37 - 4 * q^41 + 2 * q^43 - 17 * q^47 + 29 * q^49 - q^53 + 2 * q^55 + 21 * q^59 + 31 * q^61 + 3 * q^65 - 26 * q^67 + 32 * q^71 + 17 * q^73 + 4 * q^77 - 16 * q^79 + 36 * q^83 + 28 * q^85 + 2 * q^89 + 15 * q^91 + 24 * q^95 + 19 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$757$	$785$	$1081$	$1135$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−3.19500			−1.42885			−0.714423	−	0.699714i	$-0.753311\pi$
$5$	−3.19500			−1.42885			−0.714423	+	0.699714i	$0.753311\pi$
$6$		0			0
$7$	2.61289	−	0.415693i	0.987580	−	0.157117i
$7$	2.61289	−	0.415693i	0.987580	−	0.157117i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	2.28279			0.688286			0.344143	−	0.938917i	$-0.388170\pi$
$11$	2.28279			0.688286			0.344143	+	0.938917i	$0.388170\pi$
$12$		0			0
$13$	−0.675051	+	1.16922i	−0.187225	+	0.324284i	−0.944324	−	0.329017i	$-0.893283\pi$
$13$	−0.675051	+	1.16922i	−0.187225	+	0.324284i	0.757099	+	0.653300i	$0.226616\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.21425	+	3.83519i	−0.537033	+	0.930169i	0.462028	+	0.886865i	$0.347122\pi$
$17$	−2.21425	+	3.83519i	−0.537033	+	0.930169i	−0.999062	+	0.0433042i	$0.986212\pi$
$18$		0			0
$19$	−3.69214	−	6.39497i	−0.847034	−	1.46711i	−0.883843	−	0.467784i	$-0.845052\pi$
$19$	−3.69214	−	6.39497i	−0.847034	−	1.46711i	0.0368084	−	0.999322i	$-0.488281\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	6.46959			1.34900			0.674501	−	0.738274i	$-0.264359\pi$
$23$	6.46959			1.34900			0.674501	+	0.738274i	$0.264359\pi$
$24$		0			0
$25$	5.20800			1.04160
$26$		0			0
$27$		0			0
$28$		0			0
$29$	1.06167	+	1.83887i	0.197148	+	0.341470i	0.947602	−	0.319452i	$-0.103499\pi$
$29$	1.06167	+	1.83887i	0.197148	+	0.341470i	−0.750455	+	0.660922i	$0.770166\pi$
$30$		0			0
$31$	0.316154	+	0.547595i	0.0567830	+	0.0983510i	0.893020	−	0.450018i	$-0.148582\pi$
$31$	0.316154	+	0.547595i	0.0567830	+	0.0983510i	−0.836237	+	0.548369i	$0.815249\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−8.34818	+	1.32814i	−1.41110	+	0.224496i
$36$		0			0
$37$	1.92885	+	3.34087i	0.317102	+	0.549236i	0.979882	−	0.199578i	$-0.0639570\pi$
$37$	1.92885	+	3.34087i	0.317102	+	0.549236i	−0.662780	+	0.748814i	$0.730624\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	5.05124	−	8.74900i	0.788871	−	1.36636i	−0.137788	−	0.990462i	$-0.543999\pi$
$41$	5.05124	−	8.74900i	0.788871	−	1.36636i	0.926659	−	0.375903i	$-0.122667\pi$
$42$		0			0
$43$	4.24701	+	7.35603i	0.647663	+	1.12178i	0.983680	+	0.179929i	$0.0575867\pi$
$43$	4.24701	+	7.35603i	0.647663	+	1.12178i	−0.336017	+	0.941856i	$0.609080\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	3.26587	−	5.65664i	0.476375	−	0.825106i	−0.523258	−	0.852174i	$-0.675284\pi$
$47$	3.26587	−	5.65664i	0.476375	−	0.825106i	0.999634	+	0.0270678i	$0.00861699\pi$
$48$		0			0
$49$	6.65440	−	2.17232i	0.950628	−	0.310332i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−2.39950	+	4.15606i	−0.329597	+	0.570879i	−0.982432	−	0.186621i	$-0.940246\pi$
$53$	−2.39950	+	4.15606i	−0.329597	+	0.570879i	0.652835	+	0.757500i	$0.273580\pi$
$54$		0			0
$55$	−7.29349			−0.983454
$56$		0			0
$57$		0			0
$58$		0			0
$59$	3.10191	+	5.37267i	0.403835	+	0.699463i	0.994185	−	0.107685i	$-0.0343437\pi$
$59$	3.10191	+	5.37267i	0.403835	+	0.699463i	−0.590350	+	0.807147i	$0.701010\pi$
$60$		0			0
$61$	4.45546	−	7.71709i	0.570464	−	0.988072i	−0.426055	−	0.904697i	$-0.640097\pi$
$61$	4.45546	−	7.71709i	0.570464	−	0.988072i	0.996518	−	0.0833747i	$-0.0265698\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	2.15679	−	3.73566i	0.267516	−	0.463352i
$66$		0			0
$67$	1.50785	+	2.61167i	0.184213	+	0.319067i	0.943311	−	0.331910i	$-0.107693\pi$
$67$	1.50785	+	2.61167i	0.184213	+	0.319067i	−0.759098	+	0.650976i	$0.774360\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	15.3791			1.82516			0.912580	−	0.408899i	$-0.134087\pi$
$71$	15.3791			1.82516			0.912580	+	0.408899i	$0.134087\pi$
$72$		0			0
$73$	4.36577	−	7.56173i	0.510974	−	0.885033i	−0.488945	−	0.872315i	$-0.662618\pi$
$73$	4.36577	−	7.56173i	0.510974	−	0.885033i	0.999919	−	0.0127186i	$-0.00404857\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	5.96467	−	0.948938i	0.679737	−	0.108142i
$78$		0			0
$79$	0.938050	−	1.62475i	0.105539	−	0.182799i	−0.808419	−	0.588607i	$-0.799677\pi$
$79$	0.938050	−	1.62475i	0.105539	−	0.182799i	0.913958	+	0.405808i	$0.133010\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	3.00140	+	5.19857i	0.329446	+	0.570617i	0.982402	−	0.186779i	$-0.0598047\pi$
$83$	3.00140	+	5.19857i	0.329446	+	0.570617i	−0.652956	+	0.757396i	$0.726471\pi$
$84$		0			0
$85$	7.07451	−	12.2534i	0.767338	−	1.32907i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−2.65390	−	4.59668i	−0.281313	−	0.487248i	0.690396	−	0.723432i	$-0.257436\pi$
$89$	−2.65390	−	4.59668i	−0.281313	−	0.487248i	−0.971708	+	0.236184i	$0.924103\pi$
$90$		0			0
$91$	−1.27780	+	3.33566i	−0.133949	+	0.349673i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	11.7964	+	20.4319i	1.21028	+	2.09627i
$96$		0			0
$97$	7.44539	+	12.8958i	0.755965	+	1.30937i	0.944893	+	0.327378i	$0.106165\pi$
$97$	7.44539	+	12.8958i	0.755965	+	1.30937i	−0.188929	+	0.981991i	$0.560502\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	14.0060			1.39365			0.696824	−	0.717242i	$-0.254596\pi$
$101$	14.0060			1.39365			0.696824	+	0.717242i	$0.254596\pi$
$102$		0			0
$103$	16.0611			1.58255			0.791274	−	0.611462i	$-0.209418\pi$
$103$	16.0611			1.58255			0.791274	+	0.611462i	$0.209418\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−1.26820	−	2.19658i	−0.122601	−	0.212352i	0.798191	−	0.602404i	$-0.205790\pi$
$107$	−1.26820	−	2.19658i	−0.122601	−	0.212352i	−0.920793	+	0.390052i	$0.872457\pi$
$108$		0			0
$109$	8.10946	−	14.0460i	0.776746	−	1.34536i	−0.157062	−	0.987589i	$-0.550202\pi$
$109$	8.10946	−	14.0460i	0.776746	−	1.34536i	0.933808	−	0.357775i	$-0.116464\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−1.61499	+	2.79725i	−0.151926	+	0.263143i	−0.931935	−	0.362625i	$-0.881881\pi$
$113$	−1.61499	+	2.79725i	−0.151926	+	0.263143i	0.780010	+	0.625767i	$0.215214\pi$
$114$		0			0
$115$	−20.6703			−1.92752
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−4.19132	+	10.9414i	−0.384218	+	1.00299i
$120$		0			0
$121$	−5.78889			−0.526263
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−0.664575			−0.0594414
$126$		0			0
$127$	−12.6429			−1.12187			−0.560936	−	0.827859i	$-0.689559\pi$
$127$	−12.6429			−1.12187			−0.560936	+	0.827859i	$0.689559\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−19.0686			−1.66603			−0.833015	−	0.553250i	$-0.813387\pi$
$131$	−19.0686			−1.66603			−0.833015	+	0.553250i	$0.813387\pi$
$132$		0			0
$133$	−12.3055	−	15.1746i	−1.06702	−	1.31580i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−6.76473			−0.577949			−0.288975	−	0.957337i	$-0.593314\pi$
$137$	−6.76473			−0.577949			−0.288975	+	0.957337i	$0.593314\pi$
$138$		0			0
$139$	−6.57218	+	11.3834i	−0.557445	+	0.965524i	0.440263	+	0.897869i	$0.354885\pi$
$139$	−6.57218	+	11.3834i	−0.557445	+	0.965524i	−0.997709	+	0.0676550i	$0.978448\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−1.54100	+	2.66908i	−0.128865	+	0.223200i
$144$		0			0
$145$	−3.39204	−	5.87518i	−0.281693	−	0.487907i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−0.280514			−0.0229806			−0.0114903	−	0.999934i	$-0.503658\pi$
$149$	−0.280514			−0.0229806			−0.0114903	+	0.999934i	$0.503658\pi$
$150$		0			0
$151$	8.85798			0.720852			0.360426	−	0.932788i	$-0.382631\pi$
$151$	8.85798			0.720852			0.360426	+	0.932788i	$0.382631\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−1.01011	−	1.74956i	−0.0811341	−	0.140528i
$156$		0			0
$157$	0.964471	+	1.67051i	0.0769731	+	0.133321i	0.901943	−	0.431856i	$-0.142141\pi$
$157$	0.964471	+	1.67051i	0.0769731	+	0.133321i	−0.824969	+	0.565177i	$0.808808\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	16.9043	−	2.68936i	1.33225	−	0.211952i
$162$		0			0
$163$	−12.1983	−	21.1281i	−0.955446	−	1.65488i	−0.733345	−	0.679856i	$-0.762042\pi$
$163$	−12.1983	−	21.1281i	−0.955446	−	1.65488i	−0.222100	−	0.975024i	$-0.571291\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−2.75658	+	4.77453i	−0.213310	+	0.369464i	−0.952749	−	0.303760i	$-0.901758\pi$
$167$	−2.75658	+	4.77453i	−0.213310	+	0.369464i	0.739438	+	0.673224i	$0.235091\pi$
$168$		0			0
$169$	5.58861	+	9.67976i	0.429893	+	0.744597i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	6.30260	−	10.9164i	0.479178	−	0.829960i	−0.520537	−	0.853839i	$-0.674268\pi$
$173$	6.30260	−	10.9164i	0.479178	−	0.829960i	0.999715	+	0.0238790i	$0.00760165\pi$
$174$		0			0
$175$	13.6079	−	2.16493i	1.02866	−	0.163653i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−5.10472	+	8.84164i	−0.381545	+	0.660855i	−0.991283	−	0.131747i	$-0.957941\pi$
$179$	−5.10472	+	8.84164i	−0.381545	+	0.660855i	0.609738	+	0.792603i	$0.291275\pi$
$180$		0			0
$181$	−16.2398			−1.20710			−0.603548	−	0.797327i	$-0.706247\pi$
$181$	−16.2398			−1.20710			−0.603548	+	0.797327i	$0.706247\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−6.16268	−	10.6741i	−0.453089	−	0.784774i
$186$		0			0
$187$	−5.05465	+	8.75491i	−0.369632	+	0.640222i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−1.97060	+	3.41318i	−0.142587	+	0.246969i	−0.928470	−	0.371407i	$-0.878876\pi$
$191$	−1.97060	+	3.41318i	−0.142587	+	0.246969i	0.785883	+	0.618375i	$0.212209\pi$
$192$		0			0
$193$	2.87056	+	4.97196i	0.206627	+	0.357889i	0.950650	−	0.310265i	$-0.100418\pi$
$193$	2.87056	+	4.97196i	0.206627	+	0.357889i	−0.744023	+	0.668154i	$0.767085\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	7.67480			0.546807			0.273403	−	0.961899i	$-0.411851\pi$
$197$	7.67480			0.546807			0.273403	+	0.961899i	$0.411851\pi$
$198$		0			0
$199$	−2.26928	+	3.93050i	−0.160865	+	0.278626i	−0.935179	−	0.354175i	$-0.884762\pi$
$199$	−2.26928	+	3.93050i	−0.160865	+	0.278626i	0.774314	+	0.632801i	$0.218095\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	3.53844	+	4.36344i	0.248350	+	0.306253i
$204$		0			0
$205$	−16.1387	+	27.9530i	−1.12718	+	1.95232i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−8.42836	−	14.5983i	−0.583002	−	1.00979i
$210$		0			0
$211$	9.84097	−	17.0451i	0.677480	−	1.17343i	−0.298257	−	0.954486i	$-0.596405\pi$
$211$	9.84097	−	17.0451i	0.677480	−	1.17343i	0.975737	−	0.218944i	$-0.0702613\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−13.5692	−	23.5025i	−0.925410	−	1.60286i
$216$		0			0
$217$	1.05371	+	1.29938i	0.0715304	+	0.0882079i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−2.98946	−	5.17789i	−0.201093	−	0.348303i
$222$		0			0
$223$	6.63518	+	11.4925i	0.444324	+	0.769592i	0.998005	−	0.0631368i	$-0.0201105\pi$
$223$	6.63518	+	11.4925i	0.444324	+	0.769592i	−0.553681	+	0.832729i	$0.686777\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−22.0610			−1.46424			−0.732118	−	0.681177i	$-0.761468\pi$
$227$	−22.0610			−1.46424			−0.732118	+	0.681177i	$0.761468\pi$
$228$		0			0
$229$	−17.8472			−1.17938			−0.589688	−	0.807631i	$-0.700749\pi$
$229$	−17.8472			−1.17938			−0.589688	+	0.807631i	$0.700749\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	7.84409	+	13.5864i	0.513883	+	0.890072i	0.999870	+	0.0161061i	$0.00512696\pi$
$233$	7.84409	+	13.5864i	0.513883	+	0.890072i	−0.485987	+	0.873966i	$0.661540\pi$
$234$		0			0
$235$	−10.4344	+	18.0730i	−0.680667	+	1.17895i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	0.0639656	−	0.110792i	0.00413759	−	0.00716652i	−0.863949	−	0.503579i	$-0.832016\pi$
$239$	0.0639656	−	0.110792i	0.00413759	−	0.00716652i	0.868087	+	0.496412i	$0.165350\pi$
$240$		0			0
$241$	15.0869			0.971830			0.485915	−	0.874006i	$-0.338486\pi$
$241$	15.0869			0.971830			0.485915	+	0.874006i	$0.338486\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−21.2608	+	6.94056i	−1.35830	+	0.443416i
$246$		0			0
$247$	9.96952			0.634345
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−12.3738			−0.781030			−0.390515	−	0.920596i	$-0.627703\pi$
$251$	−12.3738			−0.781030			−0.390515	+	0.920596i	$0.627703\pi$
$252$		0			0
$253$	14.7687			0.928499
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−22.0867			−1.37773			−0.688865	−	0.724890i	$-0.741891\pi$
$257$	−22.0867			−1.37773			−0.688865	+	0.724890i	$0.741891\pi$
$258$		0			0
$259$	6.42866	+	7.92752i	0.399458	+	0.492592i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	7.79357			0.480572			0.240286	−	0.970702i	$-0.422759\pi$
$263$	7.79357			0.480572			0.240286	+	0.970702i	$0.422759\pi$
$264$		0			0
$265$	7.66641	−	13.2786i	0.470944	−	0.815698i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	3.85738	−	6.68119i	0.235189	−	0.407359i	−0.724139	−	0.689654i	$-0.757762\pi$
$269$	3.85738	−	6.68119i	0.235189	−	0.407359i	0.959328	+	0.282295i	$0.0910958\pi$
$270$		0			0
$271$	12.5744	+	21.7795i	0.763839	+	1.32301i	0.940858	+	0.338801i	$0.110021\pi$
$271$	12.5744	+	21.7795i	0.763839	+	1.32301i	−0.177019	+	0.984207i	$0.556645\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	11.8888			0.716919
$276$		0			0
$277$	−7.96273			−0.478434			−0.239217	−	0.970966i	$-0.576891\pi$
$277$	−7.96273			−0.478434			−0.239217	+	0.970966i	$0.576891\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−13.3385	−	23.1030i	−0.795710	−	1.37821i	−0.922388	−	0.386266i	$-0.873765\pi$
$281$	−13.3385	−	23.1030i	−0.795710	−	1.37821i	0.126678	−	0.991944i	$-0.459569\pi$
$282$		0			0
$283$	−7.21996	−	12.5053i	−0.429182	−	0.743365i	0.567619	−	0.823292i	$-0.307865\pi$
$283$	−7.21996	−	12.5053i	−0.429182	−	0.743365i	−0.996801	+	0.0799265i	$0.974531\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	9.56144	−	24.9600i	0.564394	−	1.47334i
$288$		0			0
$289$	−1.30577	−	2.26166i	−0.0768099	−	0.133039i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	8.27703	−	14.3362i	0.483549	−	0.837532i	−0.516272	−	0.856424i	$-0.672681\pi$
$293$	8.27703	−	14.3362i	0.483549	−	0.837532i	0.999822	+	0.0188927i	$0.00601408\pi$
$294$		0			0
$295$	−9.91061	−	17.1657i	−0.577018	−	0.999424i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−4.36730	+	7.56439i	−0.252568	+	0.437460i
$300$		0			0
$301$	14.1548	+	17.4551i	0.815870	+	1.00609i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−14.2352	+	24.6561i	−0.815105	+	1.41180i
$306$		0			0
$307$	10.9233			0.623425			0.311713	−	0.950176i	$-0.399097\pi$
$307$	10.9233			0.623425			0.311713	+	0.950176i	$0.399097\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−2.62680	−	4.54975i	−0.148952	−	0.257992i	0.781888	−	0.623418i	$-0.214257\pi$
$311$	−2.62680	−	4.54975i	−0.148952	−	0.257992i	−0.930840	+	0.365426i	$0.880923\pi$
$312$		0			0
$313$	−10.7592	+	18.6354i	−0.608145	+	1.05334i	0.383401	+	0.923582i	$0.374753\pi$
$313$	−10.7592	+	18.6354i	−0.608145	+	1.05334i	−0.991546	+	0.129756i	$0.958581\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−8.76613	+	15.1834i	−0.492355	+	0.852784i	−0.999961	−	0.00880525i	$-0.997197\pi$
$317$	−8.76613	+	15.1834i	−0.492355	+	0.852784i	0.507606	+	0.861589i	$0.330530\pi$
$318$		0			0
$319$	2.42357	+	4.19774i	0.135694	+	0.235029i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	32.7012			1.81954
$324$		0			0
$325$	−3.51567	+	6.08932i	−0.195014	+	0.337774i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	6.18192	−	16.1378i	0.340820	−	0.889705i
$330$		0			0
$331$	−3.13795	+	5.43508i	−0.172477	+	0.298739i	−0.939285	−	0.343137i	$-0.888510\pi$
$331$	−3.13795	+	5.43508i	−0.172477	+	0.298739i	0.766808	+	0.641876i	$0.221844\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−4.81757	−	8.34428i	−0.263212	−	0.455897i
$336$		0			0
$337$	13.5924	−	23.5427i	0.740426	−	1.28246i	−0.211876	−	0.977297i	$-0.567957\pi$
$337$	13.5924	−	23.5427i	0.740426	−	1.28246i	0.952302	−	0.305159i	$-0.0987095\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	0.721712	+	1.25004i	0.0390829	+	0.0676936i
$342$		0			0
$343$	16.4842	−	8.44222i	0.890063	−	0.455837i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−9.59040	−	16.6111i	−0.514840	−	0.891728i	−0.999852	−	0.0172210i	$-0.994518\pi$
$347$	−9.59040	−	16.6111i	−0.514840	−	0.891728i	0.485012	−	0.874507i	$-0.338815\pi$
$348$		0			0
$349$	10.1028	+	17.4985i	0.540789	+	0.936675i	0.998859	+	0.0477584i	$0.0152078\pi$
$349$	10.1028	+	17.4985i	0.540789	+	0.936675i	−0.458069	+	0.888916i	$0.651459\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	28.4999			1.51690			0.758448	−	0.651733i	$-0.225958\pi$
$353$	28.4999			1.51690			0.758448	+	0.651733i	$0.225958\pi$
$354$		0			0
$355$	−49.1361			−2.60787
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−15.4572	−	26.7727i	−0.815802	−	1.41301i	−0.908751	−	0.417339i	$-0.862963\pi$
$359$	−15.4572	−	26.7727i	−0.815802	−	1.41301i	0.0929489	−	0.995671i	$-0.470371\pi$
$360$		0			0
$361$	−17.7638	+	30.7677i	−0.934934	+	1.61935i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−13.9486	+	24.1597i	−0.730103	+	1.26458i
$366$		0			0
$367$	−6.83095			−0.356573			−0.178286	−	0.983979i	$-0.557055\pi$
$367$	−6.83095			−0.356573			−0.178286	+	0.983979i	$0.557055\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−4.54199	+	11.8568i	−0.235809	+	0.615574i
$372$		0			0
$373$	6.76490			0.350273			0.175137	−	0.984544i	$-0.443963\pi$
$373$	6.76490			0.350273			0.175137	+	0.984544i	$0.443963\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−2.86673			−0.147644
$378$		0			0
$379$	−7.62967			−0.391910			−0.195955	−	0.980613i	$-0.562781\pi$
$379$	−7.62967			−0.391910			−0.195955	+	0.980613i	$0.562781\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	6.42264			0.328181			0.164091	−	0.986445i	$-0.447531\pi$
$383$	6.42264			0.328181			0.164091	+	0.986445i	$0.447531\pi$
$384$		0			0
$385$	−19.0571	+	3.03185i	−0.971240	+	0.154518i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	15.8535			0.803804			0.401902	−	0.915683i	$-0.368349\pi$
$389$	15.8535			0.803804			0.401902	+	0.915683i	$0.368349\pi$
$390$		0			0
$391$	−14.3253	+	24.8121i	−0.724460	+	1.25480i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−2.99707	+	5.19107i	−0.150799	+	0.261191i
$396$		0			0
$397$	−8.56287	−	14.8313i	−0.429758	−	0.744363i	0.567093	−	0.823654i	$-0.308068\pi$
$397$	−8.56287	−	14.8313i	−0.429758	−	0.744363i	−0.996852	+	0.0792903i	$0.974735\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−23.7691			−1.18697			−0.593486	−	0.804844i	$-0.702249\pi$
$401$	−23.7691			−1.18697			−0.593486	+	0.804844i	$0.702249\pi$
$402$		0			0
$403$	−0.853681			−0.0425249
$404$		0			0
$405$		0			0
$406$		0			0
$407$	4.40316	+	7.62649i	0.218256	+	0.378031i
$408$		0			0
$409$	−7.55946	−	13.0934i	−0.373791	−	0.647425i	0.616354	−	0.787469i	$-0.288609\pi$
$409$	−7.55946	−	13.0934i	−0.373791	−	0.647425i	−0.990145	+	0.140044i	$0.955276\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	10.3383	+	12.7488i	0.508717	+	0.627326i
$414$		0			0
$415$	−9.58945	−	16.6094i	−0.470728	−	0.815324i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−2.82673	+	4.89604i	−0.138095	+	0.239187i	−0.926775	−	0.375616i	$-0.877431\pi$
$419$	−2.82673	+	4.89604i	−0.138095	+	0.239187i	0.788681	+	0.614803i	$0.210764\pi$
$420$		0			0
$421$	−12.5088	−	21.6658i	−0.609640	−	1.05593i	−0.991300	−	0.131625i	$-0.957981\pi$
$421$	−12.5088	−	21.6658i	−0.609640	−	1.05593i	0.381660	−	0.924303i	$-0.375353\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−11.5318	+	19.9737i	−0.559375	+	0.968865i
$426$		0			0
$427$	8.43370	−	22.0160i	0.408135	−	1.06543i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−10.4514	+	18.1024i	−0.503428	+	0.871962i	0.496564	+	0.868000i	$0.334595\pi$
$431$	−10.4514	+	18.1024i	−0.503428	+	0.871962i	−0.999992	+	0.00396247i	$0.998739\pi$
$432$		0			0
$433$	−21.2708			−1.02221			−0.511104	−	0.859519i	$-0.670763\pi$
$433$	−21.2708			−1.02221			−0.511104	+	0.859519i	$0.670763\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−23.8866	−	41.3728i	−1.14265	−	1.97913i
$438$		0			0
$439$	−8.59087	+	14.8798i	−0.410020	+	0.710176i	−0.994891	−	0.100951i	$-0.967812\pi$
$439$	−8.59087	+	14.8798i	−0.410020	+	0.710176i	0.584871	+	0.811126i	$0.301145\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−6.37181	+	11.0363i	−0.302734	+	0.524350i	−0.976754	−	0.214363i	$-0.931233\pi$
$443$	−6.37181	+	11.0363i	−0.302734	+	0.524350i	0.674020	+	0.738713i	$0.264566\pi$
$444$		0			0
$445$	8.47919	+	14.6864i	0.401952	+	0.696202i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−31.5913			−1.49088			−0.745442	−	0.666570i	$-0.767762\pi$
$449$	−31.5913			−1.49088			−0.745442	+	0.666570i	$0.767762\pi$
$450$		0			0
$451$	11.5309	−	19.9721i	0.542969	−	0.940449i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	4.08256	−	10.6574i	0.191393	−	0.499628i
$456$		0			0
$457$	3.65243	−	6.32619i	0.170853	−	0.295927i	−0.767865	−	0.640612i	$-0.778681\pi$
$457$	3.65243	−	6.32619i	0.170853	−	0.295927i	0.938718	+	0.344685i	$0.112014\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	13.3651	+	23.1491i	0.622477	+	1.07816i	0.989023	+	0.147761i	$0.0472068\pi$
$461$	13.3651	+	23.1491i	0.622477	+	1.07816i	−0.366546	+	0.930400i	$0.619460\pi$
$462$		0			0
$463$	−1.75608	+	3.04161i	−0.0816117	+	0.141356i	−0.903942	−	0.427654i	$-0.859340\pi$
$463$	−1.75608	+	3.04161i	−0.0816117	+	0.141356i	0.822331	+	0.569010i	$0.192673\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	7.80239	+	13.5141i	0.361052	+	0.625360i	0.988134	−	0.153593i	$-0.0490845\pi$
$467$	7.80239	+	13.5141i	0.361052	+	0.625360i	−0.627083	+	0.778953i	$0.715751\pi$
$468$		0			0
$469$	5.02550	+	6.19721i	0.232056	+	0.286161i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	9.69501	+	16.7922i	0.445777	+	0.772108i
$474$		0			0
$475$	−19.2287	−	33.3050i	−0.882272	−	1.52814i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	17.0889			0.780811			0.390405	−	0.920643i	$-0.372335\pi$
$479$	17.0889			0.780811			0.390405	+	0.920643i	$0.372335\pi$
$480$		0			0
$481$	−5.20830			−0.237478
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−23.7880	−	41.2020i	−1.08016	−	1.87089i
$486$		0			0
$487$	−12.9335	+	22.4014i	−0.586072	+	1.01511i	0.408669	+	0.912683i	$0.365993\pi$
$487$	−12.9335	+	22.4014i	−0.586072	+	1.01511i	−0.994741	+	0.102423i	$0.967340\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	7.51452	−	13.0155i	0.339126	−	0.587383i	−0.645143	−	0.764062i	$-0.723202\pi$
$491$	7.51452	−	13.0155i	0.339126	−	0.587383i	0.984269	+	0.176679i	$0.0565355\pi$
$492$		0			0
$493$	−9.40321			−0.423499
$494$		0			0
$495$		0			0
$496$		0			0
$497$	40.1838	−	6.39297i	1.80249	−	0.286764i
$498$		0			0
$499$	15.2419			0.682321			0.341160	−	0.940005i	$-0.389180\pi$
$499$	15.2419			0.682321			0.341160	+	0.940005i	$0.389180\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−18.6284			−0.830599			−0.415299	−	0.909685i	$-0.636323\pi$
$503$	−18.6284			−0.830599			−0.415299	+	0.909685i	$0.636323\pi$
$504$		0			0
$505$	−44.7491			−1.99131
$506$		0			0
$507$		0			0
$508$		0			0
$509$	7.44665			0.330067			0.165034	−	0.986288i	$-0.447227\pi$
$509$	7.44665			0.330067			0.165034	+	0.986288i	$0.447227\pi$
$510$		0			0
$511$	8.26391	−	21.5728i	0.365574	−	0.954324i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−51.3152			−2.26122
$516$		0			0
$517$	7.45527	−	12.9129i	0.327882	−	0.567909i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	11.3853	−	19.7200i	0.498800	−	0.863947i	−0.501199	−	0.865332i	$-0.667107\pi$
$521$	11.3853	−	19.7200i	0.498800	−	0.863947i	0.999999	+	0.00138491i	$0.000440830\pi$
$522$		0			0
$523$	16.5092	+	28.5949i	0.721899	+	1.25037i	0.960238	+	0.279184i	$0.0900639\pi$
$523$	16.5092	+	28.5949i	0.721899	+	1.25037i	−0.238339	+	0.971182i	$0.576603\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−2.80017			−0.121977
$528$		0			0
$529$	18.8556			0.819808
$530$		0			0
$531$		0			0
$532$		0			0
$533$	6.81969	+	11.8120i	0.295393	+	0.511636i
$534$		0			0
$535$	4.05189	+	7.01808i	0.175179	+	0.303418i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	15.1906	−	4.95894i	0.654304	−	0.213597i
$540$		0			0
$541$	8.53464	+	14.7824i	0.366933	+	0.635546i	0.989084	−	0.147351i	$-0.0470745\pi$
$541$	8.53464	+	14.7824i	0.366933	+	0.635546i	−0.622151	+	0.782897i	$0.713741\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−25.9097	+	44.8769i	−1.10985	+	1.92232i
$546$		0			0
$547$	16.3574	+	28.3318i	0.699390	+	1.21138i	0.968678	+	0.248319i	$0.0798782\pi$
$547$	16.3574	+	28.3318i	0.699390	+	1.21138i	−0.269288	+	0.963060i	$0.586788\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	7.83968	−	13.5787i	0.333981	−	0.578473i
$552$		0			0
$553$	1.77563	−	4.63524i	0.0755073	−	0.197110i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−17.0783	+	29.5806i	−0.723633	+	1.25337i	0.235902	+	0.971777i	$0.424196\pi$
$557$	−17.0783	+	29.5806i	−0.723633	+	1.25337i	−0.959534	+	0.281592i	$0.909138\pi$
$558$		0			0
$559$	−11.4678			−0.485036
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−4.83537	−	8.37510i	−0.203786	−	0.352969i	0.745959	−	0.665992i	$-0.231991\pi$
$563$	−4.83537	−	8.37510i	−0.203786	−	0.352969i	−0.949745	+	0.313023i	$0.898658\pi$
$564$		0			0
$565$	5.15989	−	8.93720i	0.217078	−	0.375991i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	5.56369	−	9.63659i	0.233242	−	0.403987i	−0.725518	−	0.688203i	$-0.758400\pi$
$569$	5.56369	−	9.63659i	0.233242	−	0.403987i	0.958760	+	0.284216i	$0.0917333\pi$
$570$		0			0
$571$	−0.364653	−	0.631597i	−0.0152602	−	0.0264315i	0.858294	−	0.513158i	$-0.171524\pi$
$571$	−0.364653	−	0.631597i	−0.0152602	−	0.0264315i	−0.873555	+	0.486726i	$0.838191\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	33.6937			1.40512
$576$		0			0
$577$	9.49359	−	16.4434i	0.395223	−	0.684547i	−0.597906	−	0.801566i	$-0.704001\pi$
$577$	9.49359	−	16.4434i	0.395223	−	0.684547i	0.993130	+	0.117019i	$0.0373338\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	10.0033	+	12.3356i	0.415008	+	0.511769i
$582$		0			0
$583$	−5.47755	+	9.48740i	−0.226857	+	0.392928i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	1.30535	+	2.26093i	0.0538775	+	0.0933185i	0.891706	−	0.452615i	$-0.149509\pi$
$587$	1.30535	+	2.26093i	0.0538775	+	0.0933185i	−0.837829	+	0.545933i	$0.816175\pi$
$588$		0			0
$589$	2.33457	−	4.04359i	0.0961942	−	0.166613i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	7.92622	+	13.7286i	0.325491	+	0.563767i	0.981612	−	0.190889i	$-0.0611371\pi$
$593$	7.92622	+	13.7286i	0.325491	+	0.563767i	−0.656121	+	0.754656i	$0.727804\pi$
$594$		0			0
$595$	13.3913	−	34.9576i	0.548988	−	1.43312i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	7.93051	+	13.7360i	0.324032	+	0.561239i	0.981316	−	0.192403i	$-0.0616282\pi$
$599$	7.93051	+	13.7360i	0.324032	+	0.561239i	−0.657284	+	0.753643i	$0.728295\pi$
$600$		0			0
$601$	0.834141	+	1.44477i	0.0340253	+	0.0589336i	0.882537	−	0.470244i	$-0.155834\pi$
$601$	0.834141	+	1.44477i	0.0340253	+	0.0589336i	−0.848511	+	0.529177i	$0.822501\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	18.4955			0.751949
$606$		0			0
$607$	−36.5110			−1.48194			−0.740968	−	0.671541i	$-0.765633\pi$
$607$	−36.5110			−1.48194			−0.740968	+	0.671541i	$0.765633\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	4.40925	+	7.63705i	0.178379	+	0.308962i
$612$		0			0
$613$	18.2957	−	31.6891i	0.738958	−	1.27991i	−0.214007	−	0.976832i	$-0.568652\pi$
$613$	18.2957	−	31.6891i	0.738958	−	1.27991i	0.952965	−	0.303080i	$-0.0980150\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	5.10936	−	8.84967i	0.205695	−	0.356274i	−0.744659	−	0.667445i	$-0.767388\pi$
$617$	5.10936	−	8.84967i	0.205695	−	0.356274i	0.950354	+	0.311171i	$0.100721\pi$
$618$		0			0
$619$	−24.7329			−0.994098			−0.497049	−	0.867723i	$-0.665583\pi$
$619$	−24.7329			−0.994098			−0.497049	+	0.867723i	$0.665583\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−8.84515	−	10.9074i	−0.354374	−	0.436997i
$624$		0			0
$625$	−23.9167			−0.956668
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−17.0838			−0.681177
$630$		0			0
$631$	42.1420			1.67765			0.838823	−	0.544404i	$-0.183244\pi$
$631$	42.1420			1.67765			0.838823	+	0.544404i	$0.183244\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	40.3939			1.60298
$636$		0			0
$637$	−1.95213	+	9.24690i	−0.0773463	+	0.366375i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	2.33038			0.0920444			0.0460222	−	0.998940i	$-0.485346\pi$
$641$	2.33038			0.0920444			0.0460222	+	0.998940i	$0.485346\pi$
$642$		0			0
$643$	16.5035	−	28.5850i	0.650836	−	1.12728i	−0.332085	−	0.943250i	$-0.607752\pi$
$643$	16.5035	−	28.5850i	0.650836	−	1.12728i	0.982920	−	0.184031i	$-0.0589147\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	10.4187	−	18.0458i	0.409603	−	0.709452i	−0.585243	−	0.810858i	$-0.699001\pi$
$647$	10.4187	−	18.0458i	0.409603	−	0.709452i	0.994845	+	0.101406i	$0.0323341\pi$
$648$		0			0
$649$	7.08101	+	12.2647i	0.277954	+	0.481430i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	48.8352			1.91107			0.955534	−	0.294882i	$-0.0952805\pi$
$653$	48.8352			1.91107			0.955534	+	0.294882i	$0.0952805\pi$
$654$		0			0
$655$	60.9241			2.38050
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−0.272662	−	0.472265i	−0.0106214	−	0.0183968i	0.860666	−	0.509170i	$-0.170048\pi$
$659$	−0.272662	−	0.472265i	−0.0106214	−	0.0183968i	−0.871287	+	0.490773i	$0.836714\pi$
$660$		0			0
$661$	23.2125	+	40.2052i	0.902861	+	1.56380i	0.823763	+	0.566934i	$0.191871\pi$
$661$	23.2125	+	40.2052i	0.902861	+	1.56380i	0.0790978	+	0.996867i	$0.474796\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	39.3160	+	48.4827i	1.52461	+	1.88008i
$666$		0			0
$667$	6.86858	+	11.8967i	0.265953	+	0.460643i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	10.1709	−	17.6165i	0.392642	−	0.680076i
$672$		0			0
$673$	−16.9838	−	29.4168i	−0.654677	−	1.13393i	−0.981975	−	0.189013i	$-0.939471\pi$
$673$	−16.9838	−	29.4168i	−0.654677	−	1.13393i	0.327298	−	0.944921i	$-0.393862\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	15.6425	−	27.0936i	0.601191	−	1.04129i	−0.391450	−	0.920199i	$-0.628026\pi$
$677$	15.6425	−	27.0936i	0.601191	−	1.04129i	0.992641	−	0.121094i	$-0.0386403\pi$
$678$		0			0
$679$	24.8147	+	30.6003i	0.952300	+	1.17433i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−0.289712	+	0.501795i	−0.0110855	+	0.0192007i	−0.871515	−	0.490369i	$-0.836862\pi$
$683$	−0.289712	+	0.501795i	−0.0110855	+	0.0192007i	0.860429	+	0.509570i	$0.170195\pi$
$684$		0			0
$685$	21.6133			0.825801
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−3.23957	−	5.61111i	−0.123418	−	0.213766i
$690$		0			0
$691$	−1.10782	+	1.91881i	−0.0421436	+	0.0729948i	−0.886328	−	0.463058i	$-0.846752\pi$
$691$	−1.10782	+	1.91881i	−0.0421436	+	0.0729948i	0.844184	+	0.536053i	$0.180085\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	20.9981	−	36.3698i	0.796504	−	1.37958i
$696$		0			0
$697$	22.3694	+	38.7449i	0.847300	+	1.46757i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−4.74299			−0.179140			−0.0895702	−	0.995981i	$-0.528549\pi$
$701$	−4.74299			−0.179140			−0.0895702	+	0.995981i	$0.528549\pi$
$702$		0			0
$703$	14.2432	−	24.6699i	0.537192	−	0.930444i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	36.5961	−	5.82219i	1.37634	−	0.218966i
$708$		0			0
$709$	11.6883	−	20.2446i	0.438962	−	0.760304i	−0.558648	−	0.829405i	$-0.688680\pi$
$709$	11.6883	−	20.2446i	0.438962	−	0.760304i	0.997610	+	0.0691011i	$0.0220131\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	2.04539	+	3.54272i	0.0766004	+	0.132676i
$714$		0			0
$715$	4.92348	−	8.52771i	0.184128	−	0.318918i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−13.0256	−	22.5610i	−0.485772	−	0.841382i	0.514094	−	0.857734i	$-0.328128\pi$
$719$	−13.0256	−	22.5610i	−0.485772	−	0.841382i	−0.999866	+	0.0163516i	$0.994795\pi$
$720$		0			0
$721$	41.9659	−	6.67649i	1.56289	−	0.248645i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	5.52919	+	9.57684i	0.205349	+	0.355675i
$726$		0			0
$727$	5.79712	+	10.0409i	0.215003	+	0.372396i	0.953274	−	0.302108i	$-0.0976905\pi$
$727$	5.79712	+	10.0409i	0.215003	+	0.372396i	−0.738270	+	0.674505i	$0.764357\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−37.6157			−1.39127
$732$		0			0
$733$	−35.3487			−1.30563			−0.652816	−	0.757516i	$-0.726413\pi$
$733$	−35.3487			−1.30563			−0.652816	+	0.757516i	$0.726413\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	3.44210	+	5.96189i	0.126791	+	0.219609i
$738$		0			0
$739$	4.66968	−	8.08812i	0.171777	−	0.297526i	−0.767264	−	0.641331i	$-0.778383\pi$
$739$	4.66968	−	8.08812i	0.171777	−	0.297526i	0.939041	+	0.343805i	$0.111716\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	14.6308	−	25.3412i	0.536750	−	0.929679i	−0.462326	−	0.886710i	$-0.652985\pi$
$743$	14.6308	−	25.3412i	0.536750	−	0.929679i	0.999076	−	0.0429687i	$-0.0136816\pi$
$744$		0			0
$745$	0.896240			0.0328357
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−4.22677	−	5.21225i	−0.154443	−	0.190452i
$750$		0			0
$751$	26.6213			0.971424			0.485712	−	0.874119i	$-0.338560\pi$
$751$	26.6213			0.971424			0.485712	+	0.874119i	$0.338560\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−28.3012			−1.02999
$756$		0			0
$757$	−35.3183			−1.28367			−0.641833	−	0.766845i	$-0.721826\pi$
$757$	−35.3183			−1.28367			−0.641833	+	0.766845i	$0.721826\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−31.5648			−1.14422			−0.572112	−	0.820175i	$-0.693876\pi$
$761$	−31.5648			−1.14422			−0.572112	+	0.820175i	$0.693876\pi$
$762$		0			0
$763$	15.3503	−	40.0717i	0.555719	−	1.45069i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−8.37580			−0.302433
$768$		0			0
$769$	−23.8477	+	41.3055i	−0.859972	+	1.48951i	0.0119829	+	0.999928i	$0.496186\pi$
$769$	−23.8477	+	41.3055i	−0.859972	+	1.48951i	−0.871955	+	0.489587i	$0.837148\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−20.7219	+	35.8914i	−0.745314	+	1.29092i	0.204733	+	0.978818i	$0.434367\pi$
$773$	−20.7219	+	35.8914i	−0.745314	+	1.29092i	−0.950048	+	0.312105i	$0.898966\pi$
$774$		0			0
$775$	1.64653	+	2.85188i	0.0591452	+	0.102442i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−74.5995			−2.67280
$780$		0			0
$781$	35.1071			1.25623
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−3.08148	−	5.33728i	−0.109983	−	0.190496i
$786$		0			0
$787$	13.1589	+	22.7918i	0.469063	+	0.812440i	0.999375	−	0.0353624i	$-0.0112585\pi$
$787$	13.1589	+	22.7918i	0.469063	+	0.812440i	−0.530312	+	0.847803i	$0.677925\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−3.05700	+	7.98024i	−0.108694	+	0.283745i
$792$		0			0
$793$	6.01533	+	10.4189i	0.213611	+	0.369984i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−8.42109	+	14.5858i	−0.298290	+	0.516654i	−0.975745	−	0.218911i	$-0.929750\pi$
$797$	−8.42109	+	14.5858i	−0.298290	+	0.516654i	0.677455	+	0.735565i	$0.263083\pi$
$798$		0			0
$799$	14.4629	+	25.0504i	0.511659	+	0.886220i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	9.96611	−	17.2618i	0.351696	−	0.609156i
$804$		0			0
$805$	−54.0093	+	8.59251i	−1.90358	+	0.302846i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	11.8734	−	20.5653i	0.417445	−	0.723036i	−0.578237	−	0.815869i	$-0.696259\pi$
$809$	11.8734	−	20.5653i	0.417445	−	0.723036i	0.995682	+	0.0928330i	$0.0295923\pi$
$810$		0			0
$811$	21.9596			0.771107			0.385553	−	0.922686i	$-0.374011\pi$
$811$	21.9596			0.771107			0.385553	+	0.922686i	$0.374011\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	38.9736	+	67.5042i	1.36518	+	2.36457i
$816$		0			0
$817$	31.3611	−	54.3190i	1.09718	−	1.90038i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−10.6104	+	18.3777i	−0.370305	+	0.641387i	−0.989612	−	0.143762i	$-0.954080\pi$
$821$	−10.6104	+	18.3777i	−0.370305	+	0.641387i	0.619307	+	0.785149i	$0.287413\pi$
$822$		0			0
$823$	−6.53927	−	11.3264i	−0.227945	−	0.394812i	0.729254	−	0.684243i	$-0.239867\pi$
$823$	−6.53927	−	11.3264i	−0.227945	−	0.394812i	−0.957199	+	0.289431i	$0.906534\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	25.8079			0.897427			0.448714	−	0.893676i	$-0.351882\pi$
$827$	25.8079			0.897427			0.448714	+	0.893676i	$0.351882\pi$
$828$		0			0
$829$	−6.21392	+	10.7628i	−0.215818	+	0.373808i	−0.953525	−	0.301313i	$-0.902575\pi$
$829$	−6.21392	+	10.7628i	−0.215818	+	0.373808i	0.737707	+	0.675121i	$0.235909\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−6.40322	+	30.3309i	−0.221858	+	1.05090i
$834$		0			0
$835$	8.80725	−	15.2546i	0.304788	−	0.527908i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−0.492155	−	0.852437i	−0.0169911	−	0.0294294i	0.857405	−	0.514643i	$-0.172075\pi$
$839$	−0.492155	−	0.852437i	−0.0169911	−	0.0294294i	−0.874396	+	0.485213i	$0.838742\pi$
$840$		0			0
$841$	12.2457	−	21.2102i	0.422266	−	0.731386i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−17.8556	−	30.9268i	−0.614251	−	1.06391i
$846$		0			0
$847$	−15.1257	+	2.40640i	−0.519727	+	0.0826849i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	12.4789	+	21.6141i	0.427771	+	0.740921i
$852$		0			0
$853$	−4.66990	−	8.08850i	−0.159894	−	0.276945i	0.774936	−	0.632040i	$-0.217782\pi$
$853$	−4.66990	−	8.08850i	−0.159894	−	0.276945i	−0.934830	+	0.355095i	$0.884449\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	11.5798			0.395559			0.197779	−	0.980247i	$-0.436627\pi$
$857$	11.5798			0.395559			0.197779	+	0.980247i	$0.436627\pi$
$858$		0			0
$859$	−53.6428			−1.83027			−0.915134	−	0.403150i	$-0.867915\pi$
$859$	−53.6428			−1.83027			−0.915134	+	0.403150i	$0.867915\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	4.80485	+	8.32225i	0.163559	+	0.283293i	0.936143	−	0.351620i	$-0.114369\pi$
$863$	4.80485	+	8.32225i	0.163559	+	0.283293i	−0.772584	+	0.634913i	$0.781036\pi$
$864$		0			0
$865$	−20.1368	+	34.8779i	−0.684671	+	1.18588i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	2.14137	−	3.70896i	0.0726409	−	0.125818i
$870$		0			0
$871$	−4.07150			−0.137958
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−1.73646	+	0.276259i	−0.0587031	+	0.00933926i
$876$		0			0
$877$	−1.06483			−0.0359568			−0.0179784	−	0.999838i	$-0.505723\pi$
$877$	−1.06483			−0.0359568			−0.0179784	+	0.999838i	$0.505723\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	20.7526			0.699171			0.349586	−	0.936904i	$-0.386322\pi$
$881$	20.7526			0.699171			0.349586	+	0.936904i	$0.386322\pi$
$882$		0			0
$883$	−8.80560			−0.296332			−0.148166	−	0.988963i	$-0.547337\pi$
$883$	−8.80560			−0.296332			−0.148166	+	0.988963i	$0.547337\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−20.0149			−0.672033			−0.336017	−	0.941856i	$-0.609080\pi$
$887$	−20.0149			−0.672033			−0.336017	+	0.941856i	$0.609080\pi$
$888$		0			0
$889$	−33.0344	+	5.25554i	−1.10794	+	0.176265i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−48.2321			−1.61403
$894$		0			0
$895$	16.3096	−	28.2490i	0.545169	−	0.944260i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−0.671304	+	1.16273i	−0.0223892	+	0.0387793i
$900$		0			0
$901$	−10.6262	−	18.4051i	−0.354009	−	0.613162i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	51.8861			1.72475
$906$		0			0
$907$	25.0615			0.832152			0.416076	−	0.909330i	$-0.363405\pi$
$907$	25.0615			0.832152			0.416076	+	0.909330i	$0.363405\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−4.86265	−	8.42236i	−0.161107	−	0.279045i	0.774159	−	0.632991i	$-0.218173\pi$
$911$	−4.86265	−	8.42236i	−0.161107	−	0.279045i	−0.935266	+	0.353946i	$0.884840\pi$
$912$		0			0
$913$	6.85154	+	11.8672i	0.226753	+	0.392748i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−49.8241	+	7.92668i	−1.64534	+	0.261762i
$918$		0			0
$919$	−23.2582	−	40.2844i	−0.767217	−	1.32886i	−0.939066	−	0.343736i	$-0.888308\pi$
$919$	−23.2582	−	40.2844i	−0.767217	−	1.32886i	0.171849	−	0.985123i	$-0.445026\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−10.3817	+	17.9815i	−0.341716	+	0.591870i
$924$		0			0
$925$	10.0455	+	17.3993i	0.330293	+	0.572085i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	17.2340	−	29.8501i	0.565429	−	0.979351i	−0.431581	−	0.902074i	$-0.642044\pi$
$929$	17.2340	−	29.8501i	0.565429	−	0.979351i	0.997010	−	0.0772768i	$-0.0246225\pi$
$930$		0			0
$931$	−38.4609	−	34.5342i	−1.26050	−	1.13181i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	16.1496	−	27.9719i	0.528148	−	0.914779i
$936$		0			0
$937$	27.1376			0.886547			0.443274	−	0.896386i	$-0.353817\pi$
$937$	27.1376			0.886547			0.443274	+	0.896386i	$0.353817\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−5.01950	−	8.69403i	−0.163631	−	0.283417i	0.772537	−	0.634969i	$-0.218987\pi$
$941$	−5.01950	−	8.69403i	−0.163631	−	0.283417i	−0.936168	+	0.351552i	$0.885654\pi$
$942$		0			0
$943$	32.6794	−	56.6025i	1.06419	−	1.84323i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−8.54883	+	14.8070i	−0.277800	+	0.481163i	−0.970838	−	0.239738i	$-0.922938\pi$
$947$	−8.54883	+	14.8070i	−0.277800	+	0.481163i	0.693038	+	0.720901i	$0.256272\pi$
$948$		0			0
$949$	5.89423	+	10.2091i	0.191335	+	0.331401i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	2.79843			0.0906500			0.0453250	−	0.998972i	$-0.485568\pi$
$953$	2.79843			0.0906500			0.0453250	+	0.998972i	$0.485568\pi$
$954$		0			0
$955$	6.29605	−	10.9051i	0.203736	−	0.352880i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−17.6755	+	2.81205i	−0.570771	+	0.0908058i
$960$		0			0
$961$	15.3001	−	26.5005i	0.493551	−	0.854856i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−9.17143	−	15.8854i	−0.295239	−	0.511369i
$966$		0			0
$967$	4.97799	−	8.62213i	0.160081	−	0.277269i	−0.774816	−	0.632186i	$-0.782158\pi$
$967$	4.97799	−	8.62213i	0.160081	−	0.277269i	0.934898	+	0.354917i	$0.115491\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	1.13634	+	1.96819i	0.0364668	+	0.0631623i	0.883683	−	0.468086i	$-0.155056\pi$
$971$	1.13634	+	1.96819i	0.0364668	+	0.0631623i	−0.847216	+	0.531249i	$0.821723\pi$
$972$		0			0
$973$	−12.4404	+	32.4755i	−0.398822	+	1.04112i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	8.42330	+	14.5896i	0.269485	+	0.466762i	0.968729	−	0.248121i	$-0.0798131\pi$
$977$	8.42330	+	14.5896i	0.269485	+	0.466762i	−0.699244	+	0.714883i	$0.746480\pi$
$978$		0			0
$979$	−6.05828	−	10.4932i	−0.193623	−	0.335366i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	21.5322			0.686772			0.343386	−	0.939194i	$-0.388426\pi$
$983$	21.5322			0.686772			0.343386	+	0.939194i	$0.388426\pi$
$984$		0			0
$985$	−24.5210			−0.781303
$986$		0			0
$987$		0			0
$988$		0			0
$989$	27.4764	+	47.5905i	0.873699	+	1.51329i
$990$		0			0
$991$	−16.8227	+	29.1378i	−0.534392	+	0.925594i	0.464801	+	0.885415i	$0.346126\pi$
$991$	−16.8227	+	29.1378i	−0.534392	+	0.925594i	−0.999193	+	0.0401785i	$0.987207\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	7.25033	−	12.5579i	0.229851	−	0.398113i
$996$		0			0
$997$	13.9881			0.443008			0.221504	−	0.975159i	$-0.428903\pi$
$997$	13.9881			0.443008			0.221504	+	0.975159i	$0.428903\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.t.c.361.2		22
3.2	odd	2		504.2.t.c.193.9	yes	22
4.3	odd	2		3024.2.t.k.1873.2		22
7.2	even	3		1512.2.q.d.793.10		22
9.2	odd	6		504.2.q.c.25.2	✓	22
9.7	even	3		1512.2.q.d.1369.10		22
12.11	even	2		1008.2.t.l.193.3		22
21.2	odd	6		504.2.q.c.121.2	yes	22
28.23	odd	6		3024.2.q.l.2305.10		22
36.7	odd	6		3024.2.q.l.2881.10		22
36.11	even	6		1008.2.q.l.529.10		22
63.2	odd	6		504.2.t.c.457.9	yes	22
63.16	even	3	inner	1512.2.t.c.289.2		22
84.23	even	6		1008.2.q.l.625.10		22
252.79	odd	6		3024.2.t.k.289.2		22
252.191	even	6		1008.2.t.l.961.3		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.c.25.2	✓	22	9.2	odd	6
504.2.q.c.121.2	yes	22	21.2	odd	6
504.2.t.c.193.9	yes	22	3.2	odd	2
504.2.t.c.457.9	yes	22	63.2	odd	6
1008.2.q.l.529.10		22	36.11	even	6
1008.2.q.l.625.10		22	84.23	even	6
1008.2.t.l.193.3		22	12.11	even	2
1008.2.t.l.961.3		22	252.191	even	6
1512.2.q.d.793.10		22	7.2	even	3
1512.2.q.d.1369.10		22	9.7	even	3
1512.2.t.c.289.2		22	63.16	even	3	inner
1512.2.t.c.361.2		22	1.1	even	1	trivial
3024.2.q.l.2305.10		22	28.23	odd	6
3024.2.q.l.2881.10		22	36.7	odd	6
3024.2.t.k.289.2		22	252.79	odd	6
3024.2.t.k.1873.2		22	4.3	odd	2

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Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1512.t (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-3.19500 q^{5} +(2.61289 - 0.415693i) q^{7} +O(q^{10})\)	\(q-3.19500 q^{5} +(2.61289 - 0.415693i) q^{7} +2.28279 q^{11} +(-0.675051 + 1.16922i) q^{13} +(-2.21425 + 3.83519i) q^{17} +(-3.69214 - 6.39497i) q^{19} +6.46959 q^{23} +5.20800 q^{25} +(1.06167 + 1.83887i) q^{29} +(0.316154 + 0.547595i) q^{31} +(-8.34818 + 1.32814i) q^{35} +(1.92885 + 3.34087i) q^{37} +(5.05124 - 8.74900i) q^{41} +(4.24701 + 7.35603i) q^{43} +(3.26587 - 5.65664i) q^{47} +(6.65440 - 2.17232i) q^{49} +(-2.39950 + 4.15606i) q^{53} -7.29349 q^{55} +(3.10191 + 5.37267i) q^{59} +(4.45546 - 7.71709i) q^{61} +(2.15679 - 3.73566i) q^{65} +(1.50785 + 2.61167i) q^{67} +15.3791 q^{71} +(4.36577 - 7.56173i) q^{73} +(5.96467 - 0.948938i) q^{77} +(0.938050 - 1.62475i) q^{79} +(3.00140 + 5.19857i) q^{83} +(7.07451 - 12.2534i) q^{85} +(-2.65390 - 4.59668i) q^{89} +(-1.27780 + 3.33566i) q^{91} +(11.7964 + 20.4319i) q^{95} +(7.44539 + 12.8958i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 2 q^{5} - q^{7}+O(q^{10}) \) 22 * q + 2 * q^5 - q^7	\( 22 q + 2 q^{5} - q^{7} + 6 q^{11} + 7 q^{13} + q^{17} + 13 q^{19} + 44 q^{25} + 7 q^{29} + 6 q^{31} - 2 q^{35} + 6 q^{37} - 4 q^{41} + 2 q^{43} - 17 q^{47} + 29 q^{49} - q^{53} + 2 q^{55} + 21 q^{59} + 31 q^{61} + 3 q^{65} - 26 q^{67} + 32 q^{71} + 17 q^{73} + 4 q^{77} - 16 q^{79} + 36 q^{83} + 28 q^{85} + 2 q^{89} + 15 q^{91} + 24 q^{95} + 19 q^{97}+O(q^{100}) \) 22 * q + 2 * q^5 - q^7 + 6 * q^11 + 7 * q^13 + q^17 + 13 * q^19 + 44 * q^25 + 7 * q^29 + 6 * q^31 - 2 * q^35 + 6 * q^37 - 4 * q^41 + 2 * q^43 - 17 * q^47 + 29 * q^49 - q^53 + 2 * q^55 + 21 * q^59 + 31 * q^61 + 3 * q^65 - 26 * q^67 + 32 * q^71 + 17 * q^73 + 4 * q^77 - 16 * q^79 + 36 * q^83 + 28 * q^85 + 2 * q^89 + 15 * q^91 + 24 * q^95 + 19 * q^97

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