LMFDB - Embedded newform 756.2.l.b.361.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [756,2,Mod(289,756)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("756.289"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(756, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.l (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [14] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 5x^{12} - 3x^{11} + 7x^{10} + 30x^{9} - 117x^{7} + 270x^{5} + 189x^{4} - 243x^{3} - 1215x^{2} + 2187 $ x^14 - 5x^12 - 3x^11 + 7x^10 + 30x^9 - 117x^7 + 270x^5 + 189x^4 - 243x^3 - 1215*x^2 + 2187
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{7} $
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.7
Root			$-1.58203 - 0.705117i$ of defining polynomial
Character	$\chi$	$=$	756.361
Dual form			756.2.l.b.289.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+2.52026 q^{5} +(1.98143 + 1.75326i) q^{7} +1.37408 q^{11} +(-2.80008 + 4.84989i) q^{13} +(2.69613 - 4.66983i) q^{17} +(2.44717 + 4.23863i) q^{19} -4.17529 q^{23} +1.35173 q^{25} +(1.56761 + 2.71518i) q^{29} +(-2.40060 - 4.15797i) q^{31} +(4.99373 + 4.41869i) q^{35} +(-2.69839 - 4.67374i) q^{37} +(3.02991 - 5.24797i) q^{41} +(2.44717 + 4.23863i) q^{43} +(-2.82774 + 4.89779i) q^{47} +(0.852135 + 6.94794i) q^{49} +(7.00281 - 12.1292i) q^{53} +3.46305 q^{55} +(7.13442 + 12.3572i) q^{59} +(3.42860 - 5.93852i) q^{61} +(-7.05695 + 12.2230i) q^{65} +(4.05678 + 7.02655i) q^{67} +2.25704 q^{71} +(3.51456 - 6.08739i) q^{73} +(2.72265 + 2.40913i) q^{77} +(-1.37843 + 2.38750i) q^{79} +(-7.48876 - 12.9709i) q^{83} +(6.79495 - 11.7692i) q^{85} +(-2.75804 - 4.77707i) q^{89} +(-14.0513 + 4.70043i) q^{91} +(6.16752 + 10.6825i) q^{95} +(0.894003 + 1.54846i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 4 q^{5} - 3 q^{7} + 4 q^{11} + 2 q^{13} - 2 q^{17} + 7 q^{19} + 22 q^{23} + 18 q^{25} - q^{29} - q^{31} + 19 q^{35} + 10 q^{37} + 33 q^{41} + 7 q^{43} + 3 q^{47} - 13 q^{49} + 15 q^{53} - 28 q^{55}+ \cdots - 18 q^{97}+O(q^{100}) $ 14 * q - 4 * q^5 - 3 * q^7 + 4 * q^11 + 2 * q^13 - 2 * q^17 + 7 * q^19 + 22 * q^23 + 18 * q^25 - q^29 - q^31 + 19 * q^35 + 10 * q^37 + 33 * q^41 + 7 * q^43 + 3 * q^47 - 13 * q^49 + 15 * q^53 - 28 * q^55 + 14 * q^59 - 10 * q^61 - 15 * q^65 + 6 * q^67 - 2 * q^71 + 21 * q^73 - 19 * q^77 - 10 * q^79 + 25 * q^83 + 8 * q^85 + 6 * q^89 + 2 * q^91 + 28 * q^95 - 18 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$

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
$5$	2.52026			1.12710			0.563548	−	0.826083i	$-0.309436\pi$
$5$	2.52026			1.12710			0.563548	+	0.826083i	$0.309436\pi$
$6$		0			0
$7$	1.98143	+	1.75326i	0.748910	+	0.662671i
$7$	1.98143	+	1.75326i	0.748910	+	0.662671i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.37408			0.414302			0.207151	−	0.978309i	$-0.433581\pi$
$11$	1.37408			0.414302			0.207151	+	0.978309i	$0.433581\pi$
$12$		0			0
$13$	−2.80008	+	4.84989i	−0.776603	+	1.34512i	0.157285	+	0.987553i	$0.449726\pi$
$13$	−2.80008	+	4.84989i	−0.776603	+	1.34512i	−0.933889	+	0.357563i	$0.883608\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	2.69613	−	4.66983i	0.653907	−	1.13260i	−0.328260	−	0.944588i	$-0.606462\pi$
$17$	2.69613	−	4.66983i	0.653907	−	1.13260i	0.982167	−	0.188013i	$-0.0602046\pi$
$18$		0			0
$19$	2.44717	+	4.23863i	0.561420	+	0.972408i	0.997373	+	0.0724385i	$0.0230781\pi$
$19$	2.44717	+	4.23863i	0.561420	+	0.972408i	−0.435953	+	0.899969i	$0.643589\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−4.17529			−0.870609			−0.435304	−	0.900283i	$-0.643359\pi$
$23$	−4.17529			−0.870609			−0.435304	+	0.900283i	$0.643359\pi$
$24$		0			0
$25$	1.35173			0.270346
$26$		0			0
$27$		0			0
$28$		0			0
$29$	1.56761	+	2.71518i	0.291097	+	0.504195i	0.974069	−	0.226249i	$-0.0726463\pi$
$29$	1.56761	+	2.71518i	0.291097	+	0.504195i	−0.682972	+	0.730444i	$0.739313\pi$
$30$		0			0
$31$	−2.40060	−	4.15797i	−0.431161	−	0.746793i	0.565812	−	0.824534i	$-0.308563\pi$
$31$	−2.40060	−	4.15797i	−0.431161	−	0.746793i	−0.996974	+	0.0777407i	$0.975229\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	4.99373	+	4.41869i	0.844094	+	0.746894i
$36$		0			0
$37$	−2.69839	−	4.67374i	−0.443612	−	0.768359i	0.554342	−	0.832289i	$-0.312970\pi$
$37$	−2.69839	−	4.67374i	−0.443612	−	0.768359i	−0.997954	+	0.0639302i	$0.979637\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	3.02991	−	5.24797i	0.473193	−	0.819595i	−0.526336	−	0.850277i	$-0.676435\pi$
$41$	3.02991	−	5.24797i	0.473193	−	0.819595i	0.999529	+	0.0306820i	$0.00976793\pi$
$42$		0			0
$43$	2.44717	+	4.23863i	0.373190	+	0.646385i	0.990054	−	0.140685i	$-0.0449305\pi$
$43$	2.44717	+	4.23863i	0.373190	+	0.646385i	−0.616864	+	0.787070i	$0.711597\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−2.82774	+	4.89779i	−0.412468	+	0.714416i	−0.995159	−	0.0982782i	$-0.968667\pi$
$47$	−2.82774	+	4.89779i	−0.412468	+	0.714416i	0.582691	+	0.812694i	$0.302000\pi$
$48$		0			0
$49$	0.852135	+	6.94794i	0.121734	+	0.992563i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	7.00281	−	12.1292i	0.961910	−	1.66608i	0.244214	−	0.969721i	$-0.421470\pi$
$53$	7.00281	−	12.1292i	0.961910	−	1.66608i	0.717696	−	0.696356i	$-0.245197\pi$
$54$		0			0
$55$	3.46305			0.466958
$56$		0			0
$57$		0			0
$58$		0			0
$59$	7.13442	+	12.3572i	0.928823	+	1.60877i	0.785294	+	0.619122i	$0.212512\pi$
$59$	7.13442	+	12.3572i	0.928823	+	1.60877i	0.143529	+	0.989646i	$0.454155\pi$
$60$		0			0
$61$	3.42860	−	5.93852i	0.438988	−	0.760349i	−0.558624	−	0.829421i	$-0.688670\pi$
$61$	3.42860	−	5.93852i	0.438988	−	0.760349i	0.997612	+	0.0690720i	$0.0220038\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−7.05695	+	12.2230i	−0.875307	+	1.51608i
$66$		0			0
$67$	4.05678	+	7.02655i	0.495615	+	0.858430i	0.999987	−	0.00505643i	$-0.00160952\pi$
$67$	4.05678	+	7.02655i	0.495615	+	0.858430i	−0.504373	+	0.863486i	$0.668276\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	2.25704			0.267861			0.133931	−	0.990991i	$-0.457240\pi$
$71$	2.25704			0.267861			0.133931	+	0.990991i	$0.457240\pi$
$72$		0			0
$73$	3.51456	−	6.08739i	0.411348	−	0.712475i	−0.583690	−	0.811977i	$-0.698392\pi$
$73$	3.51456	−	6.08739i	0.411348	−	0.712475i	0.995037	+	0.0995017i	$0.0317249\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	2.72265	+	2.40913i	0.310275	+	0.274546i
$78$		0			0
$79$	−1.37843	+	2.38750i	−0.155085	+	0.268615i	−0.933090	−	0.359643i	$-0.882898\pi$
$79$	−1.37843	+	2.38750i	−0.155085	+	0.268615i	0.778005	+	0.628258i	$0.216232\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−7.48876	−	12.9709i	−0.821998	−	1.42374i	−0.904192	−	0.427127i	$-0.859526\pi$
$83$	−7.48876	−	12.9709i	−0.821998	−	1.42374i	0.0821933	−	0.996616i	$-0.473808\pi$
$84$		0			0
$85$	6.79495	−	11.7692i	0.737016	−	1.27655i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−2.75804	−	4.77707i	−0.292352	−	0.506368i	0.682014	−	0.731339i	$-0.261104\pi$
$89$	−2.75804	−	4.77707i	−0.292352	−	0.506368i	−0.974365	+	0.224971i	$0.927771\pi$
$90$		0			0
$91$	−14.0513	+	4.70043i	−1.47298	+	0.492739i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	6.16752	+	10.6825i	0.632774	+	1.09600i
$96$		0			0
$97$	0.894003	+	1.54846i	0.0907722	+	0.157222i	0.907836	−	0.419325i	$-0.137733\pi$
$97$	0.894003	+	1.54846i	0.0907722	+	0.157222i	−0.817064	+	0.576547i	$0.804400\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−13.3907			−1.33242			−0.666211	−	0.745763i	$-0.732085\pi$
$101$	−13.3907			−1.33242			−0.666211	+	0.745763i	$0.732085\pi$
$102$		0			0
$103$	2.20328			0.217096			0.108548	−	0.994091i	$-0.465380\pi$
$103$	2.20328			0.217096			0.108548	+	0.994091i	$0.465380\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−4.93284	−	8.54392i	−0.476875	−	0.825972i	0.522774	−	0.852472i	$-0.324897\pi$
$107$	−4.93284	−	8.54392i	−0.476875	−	0.825972i	−0.999649	+	0.0264995i	$0.991564\pi$
$108$		0			0
$109$	1.54340	−	2.67325i	0.147831	−	0.256051i	−0.782595	−	0.622532i	$-0.786104\pi$
$109$	1.54340	−	2.67325i	0.147831	−	0.256051i	0.930426	+	0.366481i	$0.119438\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−0.218815	+	0.378999i	−0.0205844	+	0.0356532i	−0.876134	−	0.482067i	$-0.839886\pi$
$113$	−0.218815	+	0.378999i	−0.0205844	+	0.0356532i	0.855550	+	0.517721i	$0.173219\pi$
$114$		0			0
$115$	−10.5228			−0.981260
$116$		0			0
$117$		0			0
$118$		0			0
$119$	13.5296	−	4.52592i	1.24026	−	0.414891i
$120$		0			0
$121$	−9.11190			−0.828354
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−9.19461			−0.822391
$126$		0			0
$127$	−5.75958			−0.511080			−0.255540	−	0.966798i	$-0.582253\pi$
$127$	−5.75958			−0.511080			−0.255540	+	0.966798i	$0.582253\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	1.42973			0.124916			0.0624580	−	0.998048i	$-0.480106\pi$
$131$	1.42973			0.124916			0.0624580	+	0.998048i	$0.480106\pi$
$132$		0			0
$133$	−2.58253	+	12.6891i	−0.223934	+	1.10028i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−11.1867			−0.955744			−0.477872	−	0.878430i	$-0.658592\pi$
$137$	−11.1867			−0.955744			−0.477872	+	0.878430i	$0.658592\pi$
$138$		0			0
$139$	7.87024	−	13.6317i	0.667545	−	1.15622i	−0.311044	−	0.950396i	$-0.600679\pi$
$139$	7.87024	−	13.6317i	0.667545	−	1.15622i	0.978589	−	0.205826i	$-0.0659881\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−3.84755	+	6.66415i	−0.321748	+	0.557284i
$144$		0			0
$145$	3.95078	+	6.84296i	0.328095	+	0.568277i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−7.93026			−0.649672			−0.324836	−	0.945770i	$-0.605309\pi$
$149$	−7.93026			−0.649672			−0.324836	+	0.945770i	$0.605309\pi$
$150$		0			0
$151$	−10.7937			−0.878376			−0.439188	−	0.898395i	$-0.644734\pi$
$151$	−10.7937			−0.878376			−0.439188	+	0.898395i	$0.644734\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−6.05016	−	10.4792i	−0.485960	−	0.841708i
$156$		0			0
$157$	−10.5884	−	18.3396i	−0.845045	−	1.46366i	−0.885582	−	0.464483i	$-0.846240\pi$
$157$	−10.5884	−	18.3396i	−0.845045	−	1.46366i	0.0405373	−	0.999178i	$-0.487093\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−8.27305	−	7.32039i	−0.652008	−	0.576927i
$162$		0			0
$163$	0.536552	+	0.929336i	0.0420260	+	0.0727912i	0.886273	−	0.463163i	$-0.153285\pi$
$163$	0.536552	+	0.929336i	0.0420260	+	0.0727912i	−0.844247	+	0.535954i	$0.819952\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	7.71638	−	13.3652i	0.597112	−	1.03423i	−0.396133	−	0.918193i	$-0.629648\pi$
$167$	7.71638	−	13.3652i	0.597112	−	1.03423i	0.993245	−	0.116035i	$-0.0370185\pi$
$168$		0			0
$169$	−9.18094	−	15.9018i	−0.706226	−	1.22322i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	10.1810	−	17.6340i	0.774046	−	1.34069i	−0.161283	−	0.986908i	$-0.551563\pi$
$173$	10.1810	−	17.6340i	0.774046	−	1.34069i	0.935329	−	0.353779i	$-0.115103\pi$
$174$		0			0
$175$	2.67835	+	2.36993i	0.202465	+	0.179150i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−3.04960	+	5.28206i	−0.227938	+	0.394800i	−0.957197	−	0.289438i	$-0.906532\pi$
$179$	−3.04960	+	5.28206i	−0.227938	+	0.394800i	0.729259	+	0.684238i	$0.239865\pi$
$180$		0			0
$181$	10.0056			0.743714			0.371857	−	0.928290i	$-0.378721\pi$
$181$	10.0056			0.743714			0.371857	+	0.928290i	$0.378721\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−6.80065	−	11.7791i	−0.499993	−	0.866014i
$186$		0			0
$187$	3.70470	−	6.41673i	0.270915	−	0.469238i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−11.0993	+	19.2246i	−0.803120	+	1.39104i	0.114433	+	0.993431i	$0.463495\pi$
$191$	−11.0993	+	19.2246i	−0.803120	+	1.39104i	−0.917553	+	0.397613i	$0.869839\pi$
$192$		0			0
$193$	13.3080	+	23.0501i	0.957930	+	1.65918i	0.727516	+	0.686091i	$0.240675\pi$
$193$	13.3080	+	23.0501i	0.957930	+	1.65918i	0.230414	+	0.973093i	$0.425992\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−10.1696			−0.724551			−0.362276	−	0.932071i	$-0.618000\pi$
$197$	−10.1696			−0.724551			−0.362276	+	0.932071i	$0.618000\pi$
$198$		0			0
$199$	−1.66243	+	2.87941i	−0.117846	+	0.204116i	−0.918914	−	0.394458i	$-0.870932\pi$
$199$	−1.66243	+	2.87941i	−0.117846	+	0.204116i	0.801068	+	0.598574i	$0.204266\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−1.65431	+	8.12836i	−0.116110	+	0.570499i
$204$		0			0
$205$	7.63618	−	13.2263i	0.533334	−	0.923762i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	3.36262	+	5.82423i	0.232597	+	0.402870i
$210$		0			0
$211$	−1.29535	+	2.24361i	−0.0891755	+	0.154456i	−0.907163	−	0.420780i	$-0.861757\pi$
$211$	−1.29535	+	2.24361i	−0.0891755	+	0.154456i	0.817987	+	0.575236i	$0.195090\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	6.16752	+	10.6825i	0.420621	+	0.728538i
$216$		0			0
$217$	2.53338	−	12.4476i	0.171977	−	0.845000i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	15.0988	+	26.1518i	1.01565	+	1.75916i
$222$		0			0
$223$	−12.4029	−	21.4824i	−0.830556	−	1.43857i	−0.897598	−	0.440816i	$-0.854689\pi$
$223$	−12.4029	−	21.4824i	−0.830556	−	1.43857i	0.0670411	−	0.997750i	$-0.478644\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−7.10251			−0.471410			−0.235705	−	0.971825i	$-0.575740\pi$
$227$	−7.10251			−0.471410			−0.235705	+	0.971825i	$0.575740\pi$
$228$		0			0
$229$	−6.46504			−0.427222			−0.213611	−	0.976919i	$-0.568522\pi$
$229$	−6.46504			−0.427222			−0.213611	+	0.976919i	$0.568522\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	4.42950	+	7.67212i	0.290186	+	0.502617i	0.973854	−	0.227177i	$-0.0729495\pi$
$233$	4.42950	+	7.67212i	0.290186	+	0.502617i	−0.683667	+	0.729794i	$0.739616\pi$
$234$		0			0
$235$	−7.12665	+	12.3437i	−0.464891	+	0.805215i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−8.60836	+	14.9101i	−0.556828	+	0.964455i	0.440930	+	0.897541i	$0.354649\pi$
$239$	−8.60836	+	14.9101i	−0.556828	+	0.964455i	−0.997759	+	0.0669138i	$0.978685\pi$
$240$		0			0
$241$	20.2211			1.30256			0.651279	−	0.758839i	$-0.274233\pi$
$241$	20.2211			1.30256			0.651279	+	0.758839i	$0.274233\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	2.14760	+	17.5106i	0.137205	+	1.11871i
$246$		0			0
$247$	−27.4092			−1.74400
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−7.32214			−0.462169			−0.231085	−	0.972934i	$-0.574227\pi$
$251$	−7.32214			−0.462169			−0.231085	+	0.972934i	$0.574227\pi$
$252$		0			0
$253$	−5.73720			−0.360695
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−6.14617			−0.383387			−0.191694	−	0.981455i	$-0.561398\pi$
$257$	−6.14617			−0.383387			−0.191694	+	0.981455i	$0.561398\pi$
$258$		0			0
$259$	2.84764	−	13.9917i	0.176944	−	0.869401i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	0.164927			0.0101698			0.00508491	−	0.999987i	$-0.498381\pi$
$263$	0.164927			0.0101698			0.00508491	+	0.999987i	$0.498381\pi$
$264$		0			0
$265$	17.6489	−	30.5689i	1.08417	−	1.87783i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	1.86477	−	3.22988i	0.113697	−	0.196929i	−0.803561	−	0.595222i	$-0.797064\pi$
$269$	1.86477	−	3.22988i	0.113697	−	0.196929i	0.917258	+	0.398293i	$0.130397\pi$
$270$		0			0
$271$	−0.393652	−	0.681825i	−0.0239127	−	0.0414179i	0.853821	−	0.520566i	$-0.174279\pi$
$271$	−0.393652	−	0.681825i	−0.0239127	−	0.0414179i	−0.877734	+	0.479148i	$0.840946\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	1.85739			0.112005
$276$		0			0
$277$	−3.25908			−0.195819			−0.0979096	−	0.995195i	$-0.531216\pi$
$277$	−3.25908			−0.195819			−0.0979096	+	0.995195i	$0.531216\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−9.39147	−	16.2665i	−0.560248	−	0.970379i	−0.997474	−	0.0710269i	$-0.977372\pi$
$281$	−9.39147	−	16.2665i	−0.560248	−	0.970379i	0.437226	−	0.899352i	$-0.355961\pi$
$282$		0			0
$283$	6.41848	+	11.1171i	0.381539	+	0.660845i	0.991282	−	0.131754i	$-0.0420608\pi$
$283$	6.41848	+	11.1171i	0.381539	+	0.660845i	−0.609743	+	0.792599i	$0.708727\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	15.2046	−	5.08624i	0.897501	−	0.300231i
$288$		0			0
$289$	−6.03821	−	10.4585i	−0.355189	−	0.615205i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	13.6293	−	23.6066i	0.796230	−	1.37911i	−0.125825	−	0.992052i	$-0.540158\pi$
$293$	13.6293	−	23.6066i	0.796230	−	1.37911i	0.922055	−	0.387058i	$-0.126509\pi$
$294$		0			0
$295$	17.9806	+	31.1434i	1.04687	+	1.81324i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	11.6912	−	20.2497i	0.676118	−	1.17107i
$300$		0			0
$301$	−2.58253	+	12.6891i	−0.148854	+	0.731387i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	8.64098	−	14.9666i	0.494781	−	0.856986i
$306$		0			0
$307$	24.4623			1.39614			0.698069	−	0.716030i	$-0.254043\pi$
$307$	24.4623			1.39614			0.698069	+	0.716030i	$0.254043\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−8.58916	−	14.8769i	−0.487047	−	0.843590i	0.512842	−	0.858483i	$-0.328593\pi$
$311$	−8.58916	−	14.8769i	−0.487047	−	0.843590i	−0.999889	+	0.0148930i	$0.995259\pi$
$312$		0			0
$313$	−7.93226	+	13.7391i	−0.448358	+	0.776578i	−0.998279	−	0.0586380i	$-0.981324\pi$
$313$	−7.93226	+	13.7391i	−0.448358	+	0.776578i	0.549922	+	0.835216i	$0.314658\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−11.3626	+	19.6806i	−0.638188	+	1.10537i	0.347642	+	0.937627i	$0.386983\pi$
$317$	−11.3626	+	19.6806i	−0.638188	+	1.10537i	−0.985830	+	0.167747i	$0.946351\pi$
$318$		0			0
$319$	2.15402	+	3.73088i	0.120602	+	0.208889i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	26.3916			1.46847
$324$		0			0
$325$	−3.78495	+	6.55573i	−0.209951	+	0.363646i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−14.1901	+	4.74686i	−0.782324	+	0.261703i
$330$		0			0
$331$	−12.1140	+	20.9821i	−0.665848	+	1.15328i	0.313207	+	0.949685i	$0.398597\pi$
$331$	−12.1140	+	20.9821i	−0.665848	+	1.15328i	−0.979055	+	0.203597i	$0.934737\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	10.2242	+	17.7088i	0.558605	+	0.967533i
$336$		0			0
$337$	−2.20181	+	3.81365i	−0.119940	+	0.207743i	−0.919744	−	0.392519i	$-0.871604\pi$
$337$	−2.20181	+	3.81365i	−0.119940	+	0.207743i	0.799803	+	0.600262i	$0.204937\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−3.29863	−	5.71339i	−0.178631	−	0.309398i
$342$		0			0
$343$	−10.4931	+	15.2609i	−0.566575	+	0.824010i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−6.12528	−	10.6093i	−0.328823	−	0.569537i	0.653456	−	0.756965i	$-0.273318\pi$
$347$	−6.12528	−	10.6093i	−0.328823	−	0.569537i	−0.982278	+	0.187427i	$0.939985\pi$
$348$		0			0
$349$	7.19444	+	12.4611i	0.385110	+	0.667030i	0.991784	−	0.127921i	$-0.0408303\pi$
$349$	7.19444	+	12.4611i	0.385110	+	0.667030i	−0.606675	+	0.794950i	$0.707497\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	8.81670			0.469266			0.234633	−	0.972084i	$-0.424611\pi$
$353$	8.81670			0.469266			0.234633	+	0.972084i	$0.424611\pi$
$354$		0			0
$355$	5.68834			0.301906
$356$		0			0
$357$		0			0
$358$		0			0
$359$	3.04909	+	5.28118i	0.160925	+	0.278730i	0.935201	−	0.354118i	$-0.115219\pi$
$359$	3.04909	+	5.28118i	0.160925	+	0.278730i	−0.774276	+	0.632848i	$0.781886\pi$
$360$		0			0
$361$	−2.47731	+	4.29083i	−0.130385	+	0.225833i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	8.85761	−	15.3418i	0.463628	−	0.803028i
$366$		0			0
$367$	−6.91628			−0.361027			−0.180513	−	0.983573i	$-0.557776\pi$
$367$	−6.91628			−0.361027			−0.180513	+	0.983573i	$0.557776\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	35.1413	−	11.7554i	1.82445	−	0.610312i
$372$		0			0
$373$	−23.8978			−1.23738			−0.618691	−	0.785634i	$-0.712337\pi$
$373$	−23.8978			−1.23738			−0.618691	+	0.785634i	$0.712337\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−17.5577			−0.904269
$378$		0			0
$379$	34.6719			1.78097			0.890487	−	0.455008i	$-0.150364\pi$
$379$	34.6719			1.78097			0.890487	+	0.455008i	$0.150364\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−19.4301			−0.992834			−0.496417	−	0.868084i	$-0.665351\pi$
$383$	−19.4301			−0.992834			−0.496417	+	0.868084i	$0.665351\pi$
$384$		0			0
$385$	6.86179	+	6.07164i	0.349709	+	0.309439i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	32.6345			1.65463			0.827317	−	0.561736i	$-0.189866\pi$
$389$	32.6345			1.65463			0.827317	+	0.561736i	$0.189866\pi$
$390$		0			0
$391$	−11.2571	+	19.4979i	−0.569297	+	0.986051i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−3.47400	+	6.01714i	−0.174796	+	0.302755i
$396$		0			0
$397$	−3.11807	−	5.40065i	−0.156491	−	0.271051i	0.777110	−	0.629365i	$-0.216685\pi$
$397$	−3.11807	−	5.40065i	−0.156491	−	0.271051i	−0.933601	+	0.358314i	$0.883352\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	24.7345			1.23518			0.617591	−	0.786500i	$-0.288109\pi$
$401$	24.7345			1.23518			0.617591	+	0.786500i	$0.288109\pi$
$402$		0			0
$403$	26.8876			1.33937
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−3.70781	−	6.42211i	−0.183789	−	0.318332i
$408$		0			0
$409$	11.5749	+	20.0484i	0.572344	+	0.991329i	0.996325	+	0.0856575i	$0.0272991\pi$
$409$	11.5749	+	20.0484i	0.572344	+	0.991329i	−0.423981	+	0.905671i	$0.639368\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−7.52903	+	36.9934i	−0.370480	+	1.82033i
$414$		0			0
$415$	−18.8737	−	32.6901i	−0.926471	−	1.60470i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	0.703260	−	1.21808i	0.0343565	−	0.0595072i	−0.848336	−	0.529458i	$-0.822395\pi$
$419$	0.703260	−	1.21808i	0.0343565	−	0.0595072i	0.882692	+	0.469951i	$0.155729\pi$
$420$		0			0
$421$	−0.663904	−	1.14992i	−0.0323567	−	0.0560435i	0.849394	−	0.527760i	$-0.176968\pi$
$421$	−0.663904	−	1.14992i	−0.0323567	−	0.0560435i	−0.881750	+	0.471716i	$0.843635\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	3.64443	−	6.31234i	0.176781	−	0.306193i
$426$		0			0
$427$	17.2053	−	5.75551i	0.832624	−	0.278529i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	2.83378	−	4.90825i	0.136498	−	0.236422i	−0.789670	−	0.613531i	$-0.789748\pi$
$431$	2.83378	−	4.90825i	0.136498	−	0.236422i	0.926169	+	0.377109i	$0.123082\pi$
$432$		0			0
$433$	1.60371			0.0770696			0.0385348	−	0.999257i	$-0.487731\pi$
$433$	1.60371			0.0770696			0.0385348	+	0.999257i	$0.487731\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−10.2177	−	17.6975i	−0.488777	−	0.846587i
$438$		0			0
$439$	0.227323	−	0.393735i	0.0108495	−	0.0187919i	−0.860550	−	0.509367i	$-0.829880\pi$
$439$	0.227323	−	0.393735i	0.0108495	−	0.0187919i	0.871399	+	0.490575i	$0.163213\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	9.31442	−	16.1331i	0.442542	−	0.766505i	−0.555336	−	0.831626i	$-0.687410\pi$
$443$	9.31442	−	16.1331i	0.442542	−	0.766505i	0.997877	+	0.0651217i	$0.0207436\pi$
$444$		0			0
$445$	−6.95099	−	12.0395i	−0.329508	−	0.570725i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	14.2330			0.671696			0.335848	−	0.941916i	$-0.390977\pi$
$449$	14.2330			0.671696			0.335848	+	0.941916i	$0.390977\pi$
$450$		0			0
$451$	4.16335	−	7.21114i	0.196045	−	0.339559i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−35.4130	+	11.8463i	−1.66019	+	0.555364i
$456$		0			0
$457$	−14.6729	+	25.4142i	−0.686370	+	1.18883i	0.286634	+	0.958040i	$0.407464\pi$
$457$	−14.6729	+	25.4142i	−0.686370	+	1.18883i	−0.973004	+	0.230788i	$0.925870\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	12.6587	+	21.9254i	0.589572	+	1.02117i	0.994288	+	0.106727i	$0.0340371\pi$
$461$	12.6587	+	21.9254i	0.589572	+	1.02117i	−0.404716	+	0.914442i	$0.632630\pi$
$462$		0			0
$463$	−11.6503	+	20.1789i	−0.541435	+	0.937793i	0.457387	+	0.889268i	$0.348785\pi$
$463$	−11.6503	+	20.1789i	−0.541435	+	0.937793i	−0.998822	+	0.0485250i	$0.984548\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	20.8409	+	36.0976i	0.964403	+	1.67040i	0.711210	+	0.702980i	$0.248148\pi$
$467$	20.8409	+	36.0976i	0.964403	+	1.67040i	0.253194	+	0.967416i	$0.418519\pi$
$468$		0			0
$469$	−4.28116	+	21.0352i	−0.197686	+	0.971316i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	3.36262	+	5.82423i	0.154613	+	0.267798i
$474$		0			0
$475$	3.30791	+	5.72947i	0.151777	+	0.262886i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−5.53891			−0.253079			−0.126540	−	0.991962i	$-0.540387\pi$
$479$	−5.53891			−0.253079			−0.126540	+	0.991962i	$0.540387\pi$
$480$		0			0
$481$	30.2228			1.37804
$482$		0			0
$483$		0			0
$484$		0			0
$485$	2.25312	+	3.90252i	0.102309	+	0.177204i
$486$		0			0
$487$	12.3357	−	21.3661i	0.558985	−	0.968190i	−0.438597	−	0.898684i	$-0.644524\pi$
$487$	12.3357	−	21.3661i	0.558985	−	0.968190i	0.997582	−	0.0695061i	$-0.0221423\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	10.0509	−	17.4087i	0.453590	−	0.785642i	−0.545015	−	0.838426i	$-0.683476\pi$
$491$	10.0509	−	17.4087i	0.453590	−	0.785642i	0.998606	+	0.0527842i	$0.0168096\pi$
$492$		0			0
$493$	16.9059			0.761402
$494$		0			0
$495$		0			0
$496$		0			0
$497$	4.47217	+	3.95719i	0.200604	+	0.177504i
$498$		0			0
$499$	35.5173			1.58997			0.794987	−	0.606627i	$-0.207478\pi$
$499$	35.5173			1.58997			0.794987	+	0.606627i	$0.207478\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−24.2236			−1.08008			−0.540039	−	0.841640i	$-0.681590\pi$
$503$	−24.2236			−1.08008			−0.540039	+	0.841640i	$0.681590\pi$
$504$		0			0
$505$	−33.7480			−1.50177
$506$		0			0
$507$		0			0
$508$		0			0
$509$	7.73446			0.342824			0.171412	−	0.985199i	$-0.445167\pi$
$509$	7.73446			0.342824			0.171412	+	0.985199i	$0.445167\pi$
$510$		0			0
$511$	17.6366	−	5.89980i	0.780199	−	0.260992i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	5.55285			0.244688
$516$		0			0
$517$	−3.88555	+	6.72997i	−0.170886	+	0.295984i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	14.9050	−	25.8161i	0.652998	−	1.13103i	−0.329394	−	0.944193i	$-0.606844\pi$
$521$	14.9050	−	25.8161i	0.652998	−	1.13103i	0.982392	−	0.186833i	$-0.0598223\pi$
$522$		0			0
$523$	−1.76218	−	3.05219i	−0.0770547	−	0.133463i	0.824923	−	0.565245i	$-0.191218\pi$
$523$	−1.76218	−	3.05219i	−0.0770547	−	0.133463i	−0.901978	+	0.431782i	$0.857885\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−25.8893			−1.12776
$528$		0			0
$529$	−5.56693			−0.242040
$530$		0			0
$531$		0			0
$532$		0			0
$533$	16.9680	+	29.3895i	0.734967	+	1.27300i
$534$		0			0
$535$	−12.4320	−	21.5329i	−0.537484	−	0.930950i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	1.17090	+	9.54704i	0.0504344	+	0.411220i
$540$		0			0
$541$	13.8435	+	23.9777i	0.595180	+	1.03088i	0.993521	+	0.113645i	$0.0362525\pi$
$541$	13.8435	+	23.9777i	0.595180	+	1.03088i	−0.398342	+	0.917237i	$0.630414\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	3.88977	−	6.73729i	0.166620	−	0.288594i
$546$		0			0
$547$	−16.6136	−	28.7756i	−0.710347	−	1.23036i	−0.964727	−	0.263253i	$-0.915205\pi$
$547$	−16.6136	−	28.7756i	−0.710347	−	1.23036i	0.254380	−	0.967104i	$-0.418129\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−7.67241	+	13.2890i	−0.326856	+	0.566131i
$552$		0			0
$553$	−6.91718	+	2.31393i	−0.294148	+	0.0983983i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−7.80873	+	13.5251i	−0.330866	+	0.573078i	−0.982682	−	0.185300i	$-0.940674\pi$
$557$	−7.80873	+	13.5251i	−0.330866	+	0.573078i	0.651816	+	0.758378i	$0.274008\pi$
$558$		0			0
$559$	−27.4092			−1.15928
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−9.75592	−	16.8977i	−0.411163	−	0.712155i	0.583854	−	0.811858i	$-0.301544\pi$
$563$	−9.75592	−	16.8977i	−0.411163	−	0.712155i	−0.995017	+	0.0997034i	$0.968211\pi$
$564$		0			0
$565$	−0.551472	+	0.955177i	−0.0232006	+	0.0401846i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	3.59181	−	6.22119i	0.150576	−	0.260806i	−0.780863	−	0.624702i	$-0.785220\pi$
$569$	3.59181	−	6.22119i	0.150576	−	0.260806i	0.931439	+	0.363896i	$0.118554\pi$
$570$		0			0
$571$	−14.7886	−	25.6147i	−0.618886	−	1.07194i	−0.989689	−	0.143230i	$-0.954251\pi$
$571$	−14.7886	−	25.6147i	−0.618886	−	1.07194i	0.370804	−	0.928711i	$-0.379082\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−5.64386			−0.235365
$576$		0			0
$577$	5.18911	−	8.98780i	0.216025	−	0.374167i	−0.737564	−	0.675277i	$-0.764024\pi$
$577$	5.18911	−	8.98780i	0.216025	−	0.374167i	0.953589	+	0.301110i	$0.0973573\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	7.90297	−	38.8307i	0.327870	−	1.61097i
$582$		0			0
$583$	9.62244	−	16.6666i	0.398521	−	0.690259i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−14.4563	−	25.0391i	−0.596677	−	1.03348i	−0.993308	−	0.115497i	$-0.963154\pi$
$587$	−14.4563	−	25.0391i	−0.596677	−	1.03348i	0.396630	−	0.917978i	$-0.370179\pi$
$588$		0			0
$589$	11.7494	−	20.3505i	0.484125	−	0.838530i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	10.2645	+	17.7786i	0.421512	+	0.730080i	0.996088	−	0.0883714i	$-0.0281662\pi$
$593$	10.2645	+	17.7786i	0.421512	+	0.730080i	−0.574576	+	0.818451i	$0.694833\pi$
$594$		0			0
$595$	34.0982	−	11.4065i	1.39789	−	0.467622i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	3.91652	+	6.78361i	0.160025	+	0.277171i	0.934877	−	0.354971i	$-0.115509\pi$
$599$	3.91652	+	6.78361i	0.160025	+	0.277171i	−0.774853	+	0.632142i	$0.782176\pi$
$600$		0			0
$601$	−7.27021	−	12.5924i	−0.296558	−	0.513654i	0.678788	−	0.734334i	$-0.262505\pi$
$601$	−7.27021	−	12.5924i	−0.296558	−	0.513654i	−0.975346	+	0.220681i	$0.929172\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−22.9644			−0.933635
$606$		0			0
$607$	−30.5510			−1.24003			−0.620013	−	0.784592i	$-0.712873\pi$
$607$	−30.5510			−1.24003			−0.620013	+	0.784592i	$0.712873\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−15.8358	−	27.4284i	−0.640648	−	1.10964i
$612$		0			0
$613$	−14.4646	+	25.0534i	−0.584220	+	1.01190i	0.410752	+	0.911747i	$0.365266\pi$
$613$	−14.4646	+	25.0534i	−0.584220	+	1.01190i	−0.994972	+	0.100152i	$0.968067\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−20.2106	+	35.0059i	−0.813650	+	1.40928i	0.0966430	+	0.995319i	$0.469189\pi$
$617$	−20.2106	+	35.0059i	−0.813650	+	1.40928i	−0.910293	+	0.413964i	$0.864144\pi$
$618$		0			0
$619$	−18.1171			−0.728190			−0.364095	−	0.931362i	$-0.618622\pi$
$619$	−18.1171			−0.728190			−0.364095	+	0.931362i	$0.618622\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	2.91059	−	14.3010i	0.116610	−	0.572957i
$624$		0			0
$625$	−29.9315			−1.19726
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−29.1008			−1.16032
$630$		0			0
$631$	8.50373			0.338528			0.169264	−	0.985571i	$-0.445861\pi$
$631$	8.50373			0.338528			0.169264	+	0.985571i	$0.445861\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−14.5157			−0.576036
$636$		0			0
$637$	−36.0828	−	15.3221i	−1.42965	−	0.607082i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−22.0040			−0.869108			−0.434554	−	0.900646i	$-0.643094\pi$
$641$	−22.0040			−0.869108			−0.434554	+	0.900646i	$0.643094\pi$
$642$		0			0
$643$	13.1156	−	22.7170i	0.517230	−	0.895869i	−0.482569	−	0.875858i	$-0.660296\pi$
$643$	13.1156	−	22.7170i	0.517230	−	0.895869i	0.999800	−	0.0200115i	$-0.00637029\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−19.5845	+	33.9214i	−0.769946	+	1.33359i	0.167645	+	0.985847i	$0.446384\pi$
$647$	−19.5845	+	33.9214i	−0.769946	+	1.33359i	−0.937591	+	0.347739i	$0.886950\pi$
$648$		0			0
$649$	9.80329	+	16.9798i	0.384813	+	0.666515i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−13.6693			−0.534923			−0.267461	−	0.963569i	$-0.586185\pi$
$653$	−13.6693			−0.534923			−0.267461	+	0.963569i	$0.586185\pi$
$654$		0			0
$655$	3.60329			0.140792
$656$		0			0
$657$		0			0
$658$		0			0
$659$	3.06683	+	5.31191i	0.119467	+	0.206923i	0.919557	−	0.392958i	$-0.128548\pi$
$659$	3.06683	+	5.31191i	0.119467	+	0.206923i	−0.800090	+	0.599880i	$0.795215\pi$
$660$		0			0
$661$	22.3118	+	38.6451i	0.867828	+	1.50312i	0.864212	+	0.503128i	$0.167818\pi$
$661$	22.3118	+	38.6451i	0.867828	+	1.50312i	0.00361604	+	0.999993i	$0.498849\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−6.50865	+	31.9798i	−0.252395	+	1.24013i
$666$		0			0
$667$	−6.54522	−	11.3367i	−0.253432	−	0.438957i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	4.71119	−	8.16001i	0.181873	−	0.315014i
$672$		0			0
$673$	−16.3833	−	28.3767i	−0.631531	−	1.09384i	−0.987239	−	0.159246i	$-0.949094\pi$
$673$	−16.3833	−	28.3767i	−0.631531	−	1.09384i	0.355708	−	0.934597i	$-0.384240\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	13.5764	−	23.5150i	0.521782	−	0.903753i	−0.477897	−	0.878416i	$-0.658601\pi$
$677$	13.5764	−	23.5150i	0.521782	−	0.903753i	0.999679	−	0.0253373i	$-0.00806596\pi$
$678$		0			0
$679$	−0.943451	+	4.63558i	−0.0362063	+	0.177897i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	19.0334	−	32.9668i	0.728293	−	1.26144i	−0.229312	−	0.973353i	$-0.573647\pi$
$683$	19.0334	−	32.9668i	0.728293	−	1.26144i	0.957604	−	0.288087i	$-0.0930192\pi$
$684$		0			0
$685$	−28.1934			−1.07721
$686$		0			0
$687$		0			0
$688$		0			0
$689$	39.2169	+	67.9257i	1.49405	+	2.58776i
$690$		0			0
$691$	6.37848	−	11.0478i	0.242649	−	0.420280i	−0.718819	−	0.695197i	$-0.755317\pi$
$691$	6.37848	−	11.0478i	0.242649	−	0.420280i	0.961468	+	0.274917i	$0.0886504\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	19.8351	−	34.3554i	0.752387	−	1.30317i
$696$		0			0
$697$	−16.3381	−	28.2984i	−0.618849	−	1.07188i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−40.6428			−1.53506			−0.767528	−	0.641015i	$-0.778514\pi$
$701$	−40.6428			−1.53506			−0.767528	+	0.641015i	$0.778514\pi$
$702$		0			0
$703$	13.2068	−	22.8749i	0.498105	−	0.862744i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−26.5327	−	23.4774i	−0.997865	−	0.882958i
$708$		0			0
$709$	3.74552	−	6.48743i	0.140666	−	0.243640i	−0.787082	−	0.616849i	$-0.788409\pi$
$709$	3.74552	−	6.48743i	0.140666	−	0.243640i	0.927748	+	0.373208i	$0.121742\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	10.0232	+	17.3607i	0.375373	+	0.650165i
$714$		0			0
$715$	−9.69683	+	16.7954i	−0.362641	+	0.628112i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	1.64056	+	2.84154i	0.0611827	+	0.105972i	0.894994	−	0.446078i	$-0.147179\pi$
$719$	1.64056	+	2.84154i	0.0611827	+	0.105972i	−0.833812	+	0.552049i	$0.813846\pi$
$720$		0			0
$721$	4.36565	+	3.86293i	0.162585	+	0.143863i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	2.11898	+	3.67018i	0.0786969	+	0.136307i
$726$		0			0
$727$	8.01088	+	13.8753i	0.297107	+	0.514605i	0.975473	−	0.220120i	$-0.0706448\pi$
$727$	8.01088	+	13.8753i	0.297107	+	0.514605i	−0.678366	+	0.734724i	$0.737311\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	26.3916			0.976127
$732$		0			0
$733$	29.6245			1.09421			0.547104	−	0.837065i	$-0.315730\pi$
$733$	29.6245			1.09421			0.547104	+	0.837065i	$0.315730\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	5.57435	+	9.65506i	0.205334	+	0.355649i
$738$		0			0
$739$	−22.2867	+	38.6017i	−0.819829	+	1.41998i	0.0859797	+	0.996297i	$0.472598\pi$
$739$	−22.2867	+	38.6017i	−0.819829	+	1.41998i	−0.905808	+	0.423688i	$0.860735\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	5.67364	−	9.82704i	0.208146	−	0.360519i	−0.742985	−	0.669308i	$-0.766590\pi$
$743$	5.67364	−	9.82704i	0.208146	−	0.360519i	0.951130	+	0.308789i	$0.0999238\pi$
$744$		0			0
$745$	−19.9863			−0.732243
$746$		0			0
$747$		0			0
$748$		0			0
$749$	5.20567	−	25.5777i	0.190211	−	0.934591i
$750$		0			0
$751$	35.1856			1.28394			0.641970	−	0.766730i	$-0.278117\pi$
$751$	35.1856			1.28394			0.641970	+	0.766730i	$0.278117\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−27.2029			−0.990014
$756$		0			0
$757$	40.9186			1.48721			0.743605	−	0.668619i	$-0.233114\pi$
$757$	40.9186			1.48721			0.743605	+	0.668619i	$0.233114\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−11.4449			−0.414876			−0.207438	−	0.978248i	$-0.566513\pi$
$761$	−11.4449			−0.414876			−0.207438	+	0.978248i	$0.566513\pi$
$762$		0			0
$763$	7.74505	−	2.59087i	0.280390	−	0.0937957i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−79.9079			−2.88531
$768$		0			0
$769$	−14.9723	+	25.9328i	−0.539916	+	0.935162i	0.458992	+	0.888440i	$0.348211\pi$
$769$	−14.9723	+	25.9328i	−0.539916	+	0.935162i	−0.998908	+	0.0467217i	$0.985123\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	3.96578	−	6.86893i	0.142639	−	0.247058i	−0.785851	−	0.618416i	$-0.787775\pi$
$773$	3.96578	−	6.86893i	0.142639	−	0.247058i	0.928490	+	0.371358i	$0.121108\pi$
$774$		0			0
$775$	−3.24496	−	5.62044i	−0.116563	−	0.201892i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	29.6589			1.06264
$780$		0			0
$781$	3.10136			0.110975
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−26.6855	−	46.2207i	−0.952447	−	1.64969i
$786$		0			0
$787$	−21.6037	−	37.4187i	−0.770089	−	1.33383i	−0.937514	−	0.347949i	$-0.886878\pi$
$787$	−21.6037	−	37.4187i	−0.770089	−	1.33383i	0.167425	−	0.985885i	$-0.446455\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−1.09805	+	0.367320i	−0.0390422	+	0.0130604i
$792$		0			0
$793$	19.2008	+	33.2567i	0.681839	+	1.18098i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	8.34385	−	14.4520i	0.295554	−	0.511915i	−0.679559	−	0.733620i	$-0.737829\pi$
$797$	8.34385	−	14.4520i	0.295554	−	0.511915i	0.975114	+	0.221706i	$0.0711624\pi$
$798$		0			0
$799$	15.2479	+	26.4101i	0.539432	+	0.934323i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	4.82929	−	8.36458i	0.170422	−	0.295180i
$804$		0			0
$805$	−20.8503	−	18.4493i	−0.734876	−	0.650253i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	2.54846	−	4.41407i	0.0895992	−	0.155190i	−0.817743	−	0.575584i	$-0.804775\pi$
$809$	2.54846	−	4.41407i	0.0895992	−	0.155190i	0.907342	+	0.420394i	$0.138108\pi$
$810$		0			0
$811$	10.2996			0.361666			0.180833	−	0.983514i	$-0.442121\pi$
$811$	10.2996			0.361666			0.180833	+	0.983514i	$0.442121\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	1.35225	+	2.34217i	0.0473674	+	0.0820427i
$816$		0			0
$817$	−11.9773	+	20.7453i	−0.419033	+	0.725787i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−12.6369	+	21.8878i	−0.441031	+	0.763889i	−0.997766	−	0.0668013i	$-0.978721\pi$
$821$	−12.6369	+	21.8878i	−0.441031	+	0.763889i	0.556735	+	0.830690i	$0.312054\pi$
$822$		0			0
$823$	−4.44391	−	7.69707i	−0.154905	−	0.268303i	0.778120	−	0.628116i	$-0.216174\pi$
$823$	−4.44391	−	7.69707i	−0.154905	−	0.268303i	−0.933024	+	0.359813i	$0.882840\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	13.1680			0.457895			0.228947	−	0.973439i	$-0.426472\pi$
$827$	13.1680			0.457895			0.228947	+	0.973439i	$0.426472\pi$
$828$		0			0
$829$	−11.3459	+	19.6516i	−0.394058	+	0.682529i	−0.992981	−	0.118278i	$-0.962263\pi$
$829$	−11.3459	+	19.6516i	−0.394058	+	0.682529i	0.598922	+	0.800807i	$0.295596\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	34.7432	+	14.7532i	1.20378	+	0.511168i
$834$		0			0
$835$	19.4473	−	33.6838i	0.673002	−	1.16567i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	14.9632	+	25.9171i	0.516588	+	0.894757i	0.999814	+	0.0192618i	$0.00613161\pi$
$839$	14.9632	+	25.9171i	0.516588	+	0.894757i	−0.483226	+	0.875496i	$0.660535\pi$
$840$		0			0
$841$	9.58522	−	16.6021i	0.330525	−	0.572486i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−23.1384	−	40.0768i	−0.795984	−	1.37869i
$846$		0			0
$847$	−18.0546	−	15.9756i	−0.620363	−	0.548927i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	11.2666	+	19.5142i	0.386213	+	0.668940i
$852$		0			0
$853$	6.46929	+	11.2051i	0.221504	+	0.383657i	0.955265	−	0.295751i	$-0.0955699\pi$
$853$	6.46929	+	11.2051i	0.221504	+	0.383657i	−0.733761	+	0.679408i	$0.762237\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	8.24505			0.281645			0.140823	−	0.990035i	$-0.455025\pi$
$857$	8.24505			0.281645			0.140823	+	0.990035i	$0.455025\pi$
$858$		0			0
$859$	3.46798			0.118326			0.0591630	−	0.998248i	$-0.481157\pi$
$859$	3.46798			0.118326			0.0591630	+	0.998248i	$0.481157\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	0.256394	+	0.444087i	0.00872775	+	0.0151169i	0.870356	−	0.492423i	$-0.163889\pi$
$863$	0.256394	+	0.444087i	0.00872775	+	0.0151169i	−0.861629	+	0.507539i	$0.830555\pi$
$864$		0			0
$865$	25.6588	−	44.4423i	0.872424	−	1.51108i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−1.89407	+	3.28063i	−0.0642519	+	0.111288i
$870$		0			0
$871$	−45.4373			−1.53958
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−18.2185	−	16.1206i	−0.615897	−	0.544975i
$876$		0			0
$877$	36.3760			1.22833			0.614166	−	0.789177i	$-0.289493\pi$
$877$	36.3760			1.22833			0.614166	+	0.789177i	$0.289493\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	23.3999			0.788363			0.394181	−	0.919033i	$-0.371028\pi$
$881$	23.3999			0.788363			0.394181	+	0.919033i	$0.371028\pi$
$882$		0			0
$883$	−22.8345			−0.768442			−0.384221	−	0.923241i	$-0.625530\pi$
$883$	−22.8345			−0.768442			−0.384221	+	0.923241i	$0.625530\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−44.1582			−1.48269			−0.741344	−	0.671125i	$-0.765811\pi$
$887$	−44.1582			−1.48269			−0.741344	+	0.671125i	$0.765811\pi$
$888$		0			0
$889$	−11.4122	−	10.0981i	−0.382753	−	0.338678i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−27.6799			−0.926271
$894$		0			0
$895$	−7.68579	+	13.3122i	−0.256908	+	0.444977i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	7.52641	−	13.0361i	0.251020	−	0.434779i
$900$		0			0
$901$	−37.7610	−	65.4039i	−1.25800	−	2.17892i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	25.2169			0.838237
$906$		0			0
$907$	7.07769			0.235011			0.117505	−	0.993072i	$-0.462510\pi$
$907$	7.07769			0.235011			0.117505	+	0.993072i	$0.462510\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	23.6764	+	41.0088i	0.784435	+	1.35868i	0.929336	+	0.369235i	$0.120380\pi$
$911$	23.6764	+	41.0088i	0.784435	+	1.35868i	−0.144901	+	0.989446i	$0.546286\pi$
$912$		0			0
$913$	−10.2902	−	17.8231i	−0.340555	−	0.589859i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	2.83291	+	2.50669i	0.0935509	+	0.0827783i
$918$		0			0
$919$	12.9752	+	22.4736i	0.428011	+	0.741337i	0.996696	−	0.0812182i	$-0.0258811\pi$
$919$	12.9752	+	22.4736i	0.428011	+	0.741337i	−0.568685	+	0.822555i	$0.692548\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−6.31990	+	10.9464i	−0.208022	+	0.360305i
$924$		0			0
$925$	−3.64748	−	6.31763i	−0.119929	−	0.207722i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−2.66110	+	4.60917i	−0.0873080	+	0.151222i	−0.906372	−	0.422480i	$-0.861160\pi$
$929$	−2.66110	+	4.60917i	−0.0873080	+	0.151222i	0.819064	+	0.573702i	$0.194493\pi$
$930$		0			0
$931$	−27.3644	+	20.6147i	−0.896832	+	0.675619i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	9.33682	−	16.1719i	0.305347	−	0.528876i
$936$		0			0
$937$	−30.4266			−0.993994			−0.496997	−	0.867752i	$-0.665564\pi$
$937$	−30.4266			−0.993994			−0.496997	+	0.867752i	$0.665564\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	10.8818	+	18.8479i	0.354738	+	0.614424i	0.987073	−	0.160271i	$-0.0512368\pi$
$941$	10.8818	+	18.8479i	0.354738	+	0.614424i	−0.632335	+	0.774695i	$0.717903\pi$
$942$		0			0
$943$	−12.6508	+	21.9118i	−0.411966	+	0.713546i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−17.4392	+	30.2055i	−0.566697	+	0.981548i	0.430192	+	0.902737i	$0.358446\pi$
$947$	−17.4392	+	30.2055i	−0.566697	+	0.981548i	−0.996890	+	0.0788112i	$0.974888\pi$
$948$		0			0
$949$	19.6821	+	34.0904i	0.638908	+	1.10662i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−27.3744			−0.886742			−0.443371	−	0.896338i	$-0.646218\pi$
$953$	−27.3744			−0.886742			−0.443371	+	0.896338i	$0.646218\pi$
$954$		0			0
$955$	−27.9732	+	48.4511i	−0.905193	+	1.56784i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−22.1657	−	19.6132i	−0.715766	−	0.633344i
$960$		0			0
$961$	3.97419	−	6.88350i	0.128200	−	0.222048i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	33.5396	+	58.0924i	1.07968	+	1.87006i
$966$		0			0
$967$	7.21327	−	12.4937i	0.231963	−	0.401772i	−0.726423	−	0.687248i	$-0.758819\pi$
$967$	7.21327	−	12.4937i	0.231963	−	0.401772i	0.958386	+	0.285476i	$0.0921518\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	13.2592	+	22.9657i	0.425509	+	0.737004i	0.996468	−	0.0839752i	$-0.0267617\pi$
$971$	13.2592	+	22.9657i	0.425509	+	0.737004i	−0.570959	+	0.820979i	$0.693428\pi$
$972$		0			0
$973$	39.4942	−	13.2116i	1.26613	−	0.423544i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−20.1867	−	34.9643i	−0.645829	−	1.11861i	−0.984109	−	0.177563i	$-0.943179\pi$
$977$	−20.1867	−	34.9643i	−0.645829	−	1.11861i	0.338281	−	0.941045i	$-0.390155\pi$
$978$		0			0
$979$	−3.78978	−	6.56408i	−0.121122	−	0.209789i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	21.4597			0.684459			0.342230	−	0.939616i	$-0.388818\pi$
$983$	21.4597			0.684459			0.342230	+	0.939616i	$0.388818\pi$
$984$		0			0
$985$	−25.6300			−0.816639
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−10.2177	−	17.6975i	−0.324903	−	0.562748i
$990$		0			0
$991$	7.25341	−	12.5633i	0.230412	−	0.399085i	−0.727517	−	0.686089i	$-0.759326\pi$
$991$	7.25341	−	12.5633i	0.230412	−	0.399085i	0.957929	+	0.287004i	$0.0926593\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−4.18975	+	7.25687i	−0.132824	+	0.230058i
$996$		0			0
$997$	36.4409			1.15409			0.577047	−	0.816711i	$-0.304205\pi$
$997$	36.4409			1.15409			0.577047	+	0.816711i	$0.304205\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.l.b.361.7		14
3.2	odd	2		252.2.l.b.193.2	yes	14
4.3	odd	2		3024.2.t.j.1873.7		14
7.2	even	3		756.2.i.b.37.1		14
7.3	odd	6		5292.2.j.g.1765.7		14
7.4	even	3		5292.2.j.h.1765.1		14
7.5	odd	6		5292.2.i.i.1549.7		14
7.6	odd	2		5292.2.l.i.361.1		14
9.2	odd	6		252.2.i.b.25.6	✓	14
9.4	even	3		2268.2.k.f.1621.1		14
9.5	odd	6		2268.2.k.e.1621.7		14
9.7	even	3		756.2.i.b.613.1		14
12.11	even	2		1008.2.t.j.193.6		14
21.2	odd	6		252.2.i.b.121.6	yes	14
21.5	even	6		1764.2.i.i.373.2		14
21.11	odd	6		1764.2.j.g.589.5		14
21.17	even	6		1764.2.j.h.589.3		14
21.20	even	2		1764.2.l.i.949.6		14
28.23	odd	6		3024.2.q.j.2305.1		14
36.7	odd	6		3024.2.q.j.2881.1		14
36.11	even	6		1008.2.q.j.529.2		14
63.2	odd	6		252.2.l.b.205.2	yes	14
63.11	odd	6		1764.2.j.g.1177.5		14
63.16	even	3	inner	756.2.l.b.289.7		14
63.20	even	6		1764.2.i.i.1537.2		14
63.23	odd	6		2268.2.k.e.1297.7		14
63.25	even	3		5292.2.j.h.3529.1		14
63.34	odd	6		5292.2.i.i.2125.7		14
63.38	even	6		1764.2.j.h.1177.3		14
63.47	even	6		1764.2.l.i.961.6		14
63.52	odd	6		5292.2.j.g.3529.7		14
63.58	even	3		2268.2.k.f.1297.1		14
63.61	odd	6		5292.2.l.i.3313.1		14
84.23	even	6		1008.2.q.j.625.2		14
252.79	odd	6		3024.2.t.j.289.7		14
252.191	even	6		1008.2.t.j.961.6		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.i.b.25.6	✓	14	9.2	odd	6
252.2.i.b.121.6	yes	14	21.2	odd	6
252.2.l.b.193.2	yes	14	3.2	odd	2
252.2.l.b.205.2	yes	14	63.2	odd	6
756.2.i.b.37.1		14	7.2	even	3
756.2.i.b.613.1		14	9.7	even	3
756.2.l.b.289.7		14	63.16	even	3	inner
756.2.l.b.361.7		14	1.1	even	1	trivial
1008.2.q.j.529.2		14	36.11	even	6
1008.2.q.j.625.2		14	84.23	even	6
1008.2.t.j.193.6		14	12.11	even	2
1008.2.t.j.961.6		14	252.191	even	6
1764.2.i.i.373.2		14	21.5	even	6
1764.2.i.i.1537.2		14	63.20	even	6
1764.2.j.g.589.5		14	21.11	odd	6
1764.2.j.g.1177.5		14	63.11	odd	6
1764.2.j.h.589.3		14	21.17	even	6
1764.2.j.h.1177.3		14	63.38	even	6
1764.2.l.i.949.6		14	21.20	even	2
1764.2.l.i.961.6		14	63.47	even	6
2268.2.k.e.1297.7		14	63.23	odd	6
2268.2.k.e.1621.7		14	9.5	odd	6
2268.2.k.f.1297.1		14	63.58	even	3
2268.2.k.f.1621.1		14	9.4	even	3
3024.2.q.j.2305.1		14	28.23	odd	6
3024.2.q.j.2881.1		14	36.7	odd	6
3024.2.t.j.289.7		14	252.79	odd	6
3024.2.t.j.1873.7		14	4.3	odd	2
5292.2.i.i.1549.7		14	7.5	odd	6
5292.2.i.i.2125.7		14	63.34	odd	6
5292.2.j.g.1765.7		14	7.3	odd	6
5292.2.j.g.3529.7		14	63.52	odd	6
5292.2.j.h.1765.1		14	7.4	even	3
5292.2.j.h.3529.1		14	63.25	even	3
5292.2.l.i.361.1		14	7.6	odd	2
5292.2.l.i.3313.1		14	63.61	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.l (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+2.52026 q^{5} +(1.98143 + 1.75326i) q^{7} +1.37408 q^{11} +(-2.80008 + 4.84989i) q^{13} +(2.69613 - 4.66983i) q^{17} +(2.44717 + 4.23863i) q^{19} -4.17529 q^{23} +1.35173 q^{25} +(1.56761 + 2.71518i) q^{29} +(-2.40060 - 4.15797i) q^{31} +(4.99373 + 4.41869i) q^{35} +(-2.69839 - 4.67374i) q^{37} +(3.02991 - 5.24797i) q^{41} +(2.44717 + 4.23863i) q^{43} +(-2.82774 + 4.89779i) q^{47} +(0.852135 + 6.94794i) q^{49} +(7.00281 - 12.1292i) q^{53} +3.46305 q^{55} +(7.13442 + 12.3572i) q^{59} +(3.42860 - 5.93852i) q^{61} +(-7.05695 + 12.2230i) q^{65} +(4.05678 + 7.02655i) q^{67} +2.25704 q^{71} +(3.51456 - 6.08739i) q^{73} +(2.72265 + 2.40913i) q^{77} +(-1.37843 + 2.38750i) q^{79} +(-7.48876 - 12.9709i) q^{83} +(6.79495 - 11.7692i) q^{85} +(-2.75804 - 4.77707i) q^{89} +(-14.0513 + 4.70043i) q^{91} +(6.16752 + 10.6825i) q^{95} +(0.894003 + 1.54846i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 4 q^{5} - 3 q^{7} + 4 q^{11} + 2 q^{13} - 2 q^{17} + 7 q^{19} + 22 q^{23} + 18 q^{25} - q^{29} - q^{31} + 19 q^{35} + 10 q^{37} + 33 q^{41} + 7 q^{43} + 3 q^{47} - 13 q^{49} + 15 q^{53} - 28 q^{55}+ \cdots - 18 q^{97}+O(q^{100}) \) 14 * q - 4 * q^5 - 3 * q^7 + 4 * q^11 + 2 * q^13 - 2 * q^17 + 7 * q^19 + 22 * q^23 + 18 * q^25 - q^29 - q^31 + 19 * q^35 + 10 * q^37 + 33 * q^41 + 7 * q^43 + 3 * q^47 - 13 * q^49 + 15 * q^53 - 28 * q^55 + 14 * q^59 - 10 * q^61 - 15 * q^65 + 6 * q^67 - 2 * q^71 + 21 * q^73 - 19 * q^77 - 10 * q^79 + 25 * q^83 + 8 * q^85 + 6 * q^89 + 2 * q^91 + 28 * q^95 - 18 * q^97

Introduction

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