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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 0, 'Lhash': '2168413720289930975', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 1408.5610916553867, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1]], [7, [1]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '176400.1', 'coefficient_field': '1.1.1.1', 'conductor': 176400, 'conductor_radical': 210, 'degree': 2, 'euler_factors': [[1], [1], [1], [1], [1, 0, 11], [1, 6, 13], [1, 2, 17], [1, 8, 19], [1, 8, 23], [1, -2, 29], [1, -4, 31], [1, -2, 37], [1, 6, 41], [1, -4, 43], [1, -8, 47], [1, -10, 53], [1, 4, 59], [1, -2, 61], [1, -4, 67], [1, 12, 71], [1, 2, 73], [1, 8, 79], [1, 4, 83], [1, 6, 89], [1, 18, 97]], 'gamma_factors': [[], [0]], 'index': 495, 'label': '2-420e2-1.1-c1-0-495', 'leading_term': '12.5651199543', 'load_key': 'Cremona', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 2, 'origin': 'EllipticCurve/Q/176400/id', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, -0.737028209915268, -2.374667028355472, -3.392177345258676, -2.360127567562332, 0.4217896225088985, 2.66179981508231, 2.347392622400357, 0.2755605203572145, -0.7821704865029628, 0.1014645810087431, 0.4142911708385024, -2.146081067523419, -5.59447467494811, -5.795848429209614, -2.490704077509152, 0.06998758243918984, -0.4512117147291954, -1.068242190282266, 0.9869209057372239, 2.990843440329772, 1.314580173811537, -1.68262088680239, -1.141953802465767, 1.819213082301247, 1.974750710041932, -0.5963853484144095, -0.7973481220379693, 1.723341256062579, 1.827241944616457, -1.032346957132314, -1.426981152667896, 1.510097457124502, 2.260536159727305, -0.09650518907259811, 0.0251224018091732, 3.167692770691812, 3.125173189224378, -0.7689210024828858, -2.121389229601158, -0.05282460706354287, -0.03474941789495376, -1.598946059764415, 0.5131003057530099, 3.840441455979787, 1.89671567351173, -2.363849208061515, -1.936485815921239, 0.664972155465009, -0.01173095214706454, -0.6488032913190197, 2.070875913884828, 2.636038093806107, -1.22426146011184, -2.314432074039116, 1.093667577760591, 1.531996408456959, -1.481970308051199, -0.9847620404872428, 1.686821269066363, 0.6851606104553608, -0.5344741328687604, 2.058179730933008, 2.38178995045601, -2.032932463208432, -3.022463727941133, 0.8974244235275604, 1.577683065506631, -0.7969091917261918, 0.1275259527083679, 1.374416587238397, -0.8905133010331513, -0.4809007491573004, 3.953111648435372, 3.582196358625277, -1.358277012165461, -1.891379425741385, 0.1995407859490075, -1.382972808948431, -2.313913869661215, 0.03974472873597883, -0.8764006267635419, -3.631360598296565, -0.3800114816999407, 3.924524201258479, 1.406429641138418, -1.681087198479284, -0.2830773267052162, -0.2786340097691389, -1.112556565512702, 2.676821824166178, 4.985413528130738, 0.9582997427378441, -0.6443712109137701, 2.497946839545735, 1.698263784805245, -1.360937124134304, -0.1599193803784537, -0.0517260082660786, -3.43749433817262, -2.549327840750239, 0.4560315705093023, -1.984308516057929, -3.728552028749959, -0.01701995862692566, 0.847870118911626, -1.402106334957114, 0.9057795159809742, 3.012684988325038, -0.08974971392324635, -0.8835969037265755, 0.8200040365544904, -2.181965870968185, -4.18608111433479, -0.1568390603155203, 0.7554737413324304, -2.376741661206437, -0.7170194967262803, 1.75823721990274, -0.4285193065045914, -0.5527292897591868], 'positive_zeros': ['1.214946165904799', '2.036028346215775', '2.479014035366735', '2.819095466228097', '3.983171754618743', '4.156372566304164', '4.659968196458529', '5.346325400956165', '5.845471756201932', '6.439033325130713', '6.836598055696052', '7.411374929703662', '7.880361096255469', '8.488519166928601', '8.747374463524334', '9.450801990624473', '10.00743338222712', '10.24475309912066', '10.71667645902272', '11.34861732103148', '11.91363096314277', '12.24837390209479', '12.58153813909968', '13.17693758324475', '13.67346843961417', '14.12453481944869', '14.57998870192898', '15.07358812047792', '15.32900693327387', '15.89307210897936', '16.44251879383737', '16.90092790870583', '17.23645655641200', '17.66587195316040', '18.03158393744689', '18.67482420966839', '19.19960357745056', '19.34885288798422', '19.99450348916585'], 'prelabel': '2-420e2-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 37.53080190530688, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 2168413720289930975, 'z1': {'__RealLiteral__': 0, 'data': '1.214946165904799', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '2.036028346215775', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.479014035366735', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1408.5610916553867, 'bad_primes': [2, 3, 5, 7], 'central_character': '1.1', 'conductor': 176400, 'conductor_radical': 210, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, -2, 0, -8, 0, 0, 0, -8, 0, 0, 0, 0, 0, 2, 0, 4, 0, 0, 0, 0, 0, 2, 0, 0, 0, -6, 0, 4, 0, 0, 0, 8, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, -4, 0, 2, 0, 0, 0, 0, 0, 4, 0, 0, 0, -12, 0, -2, 0, 0, 0, 0, 0, -8, 0, 0, 0, -4, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, -18, 0, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, 6, 13], 'euler17': [1, 2, 17], 'euler19': [1, 8, 19], 'euler2': [1, 0, 0], 'euler23': [1, 8, 23], 'euler29': [1, -2, 29], 'euler3': [1, 0, 0], 'euler31': [1, -4, 31], 'euler37': [1, -2, 37], 'euler41': [1, 6, 41], 'euler43': [1, -4, 43], 'euler47': [1, -8, 47], 'euler5': [1, 0, 0], 'euler53': [1, -10, 53], 'euler59': [1, 4, 59], 'euler61': [1, -2, 61], 'euler67': [1, -4, 67], 'euler7': [1, 0, 0], 'euler71': [1, 12, 71], 'euler73': [1, 2, 73], 'euler79': [1, 8, 79], 'euler83': [1, 4, 83], 'euler89': [1, 6, 89], 'euler97': [1, 18, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 0, 0], [1, 0, 0], [1, 0, 11], [1, 6, 13], [1, 2, 17], [1, 8, 19], [1, 8, 23], [1, -2, 29], [1, -4, 31], [1, -2, 37], [1, 6, 41], [1, -4, 43], [1, -8, 47], [1, -10, 53], [1, 4, 59], [1, -2, 61], [1, -4, 67], [1, 12, 71], [1, 2, 73], [1, 8, 79], [1, 4, 83], [1, 6, 89], [1, 18, 97]], 'index': 495, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/176400/id'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-420e2-1.1-c1-0-495', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 2, 'prelabel': '2-420e2-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 37.53080190530688, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 2168413720289930975, 'z1': {'__RealLiteral__': 0, 'data': '1.214946165904799', 'prec': 57}}
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lfunc_instances • Show schema
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{'Lhash': '2168413720289930975', 'Lhash_array': ['2168413720289930975'], 'label': '2-420e2-1.1-c1-0-495', 'type': 'ECQ', 'url': 'EllipticCurve/Q/176400/id'}