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lfunc_lfunctions • Show schema
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{'Lhash': '2901664977722849422733235545145', 'a10': [0.0, 0.0], 'a2': [-0.19420565730394976, -1.1013950135347974], 'a3': [1.4727383611133478, -1.235774215630842], 'a4': [-0.2356625177245492, 0.08577414178396724], 'a5': [0.0, 0.0], 'a6': [-1.6470896804074442, -1.3820723433457904], 'a7': [0.03489949670250097, -0.06044770144731418], 'a8': [-0.4189546972630588, -0.7256508217292555], 'a9': [0.4681721906098765, -2.6551364330563896], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.3559596393238675, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[11, [[1.0, 0], [-0.5, -0.8660254037844386]]], [13, [[1.0, 0], [0.766044443118978, 0.6427876096865394]]], [19, [[1.0, 0], [-0.24192189559966773, -0.9702957262759965]]]], 'bad_primes': [11, 13, 19], 'central_character': '2717.142', 'coefficient_field': 'CDF', 'conductor': 2717, 'conductor_radical': 2717, 'conjugate': '1417920763422314785323425844254', 'degree': 2, 'euler_factors': [[[1.0, 0], 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[0.766044443118978, 0.6427876096865394]], [[1.0, 0], [1.9951281005196484, 0], [1.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 9, 'label': '2-2717-2717.142-c0-0-9', 'leading_term': '1.876448894164795621922319889648', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/2717/1/db/c/142/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.8764488941647957, 2.003493277902113, 2.1573766120660385, 2.339910241398783, 2.5513351375794504, 2.790472705193662, 3.0549675038153947, 3.34153319647455, 3.646153632507767, 3.9642285123162515, 4.290674476233733, 4.619999440260775, 4.946366904891824, 5.26366289624475, 5.56557384859554, 5.845680081349917, 6.097566703135884, 6.314951641740457, 6.491828859428811, 6.622623519228992, 6.702354825159861, 6.726801420106293, 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'5.50242616414117599136028149165911', '6.47520011682501569567774256200315', '7.30402332889262598778853581459350', '8.078127166882226598108360620992183', '8.562360921398147252494351113936883', '9.130101761298355576040516781973918'], 'prelabel': '2-2717-2717.142-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1644568001106212, 'root_angle': 0.9727466913586346, 'root_number': '-0.99633694954884071544579734799553 + 0.085514226674342503056451966785004*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.4863733456793173', 'prec': 60}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.28901006097455405022257786459', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.82243939605949383917738065214', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.98537709382718455452957929333', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.3559596393238675, 'bad_primes': [11, 13, 19], 'central_character': '2717.142', 'conductor': 2717, 'conductor_radical': 2717, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2717/1/db/c/142/2'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-2717-2717.142-c0-0-9', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-2717-2717.142-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1644568001106212, 'root_angle': 0.4863733456793173, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.28901006097455405022257786459', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2901664977722849422733235545145', 'Lhash_array': ['2901664977722849422733235545145'], 'label': '2-2717-2717.142-c0-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2717/1/db/c/142/2'}