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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -1, 'A4': 0, 'A5': 1, 'A6': 0, 'A7': -2, 'A8': 0, 'A9': 1, 'Lhash': '419986542305242989', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [-0.7559289460184544, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 1694.1061292834854, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [5, [1, -1]], [13, [1, -1]], [17, [1, -1]]], 'bad_primes': [2, 3, 5, 13, 17], 'central_character': '212160.1', 'coefficient_field': '1.1.1.1', 'conductor': 212160, 'conductor_radical': 6630, 'degree': 2, 'euler_factors': [[1], [1, 1], [1, -1], [1, 2, 7], [1, -2, 11], [1, -1], [1, -1], [1, -2, 19], [1, 2, 23], [1, -1, 29], [1, -5, 31], [1, 0, 37], [1, 10, 41], [1, 6, 43], [1, 8, 47], [1, -5, 53], [1, -3, 59], [1, 14, 61], [1, 5, 67], [1, 2, 71], [1, 2, 73], [1, 12, 79], [1, -14, 83], [1, -13, 89], [1, -6, 97]], 'gamma_factors': [[], [0]], 'index': 105, 'label': '2-212160-1.1-c1-0-105', 'leading_term': '6.36172106012', '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': 1, 'origin': 'EllipticCurve/Q/212160/cr', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.362464617681502, 1.520348662512952, 0.1577501303438867, -1.519991804786754, -1.662430449384036, -0.04961646748561423, 1.019760527938069, -0.6809499622892705, -3.905833772352332, -4.82419180326774, -2.095730490128746, 0.8346715118613321, 0.4456153848157588, -1.523992273672587, -0.7101844641241076, 2.699645646628139, 3.882256653538875, 1.197094660064439, -0.9561646117727004, 0.5064053872166173, 2.255970629182431, 0.7117691131203167, -1.626502140881674, -1.155625418148876, 0.2407280417740957, -0.3050389616187152, -0.3874808828826782, 2.302084389800322, 3.587980052781305, 0.1331691607178925, -2.562393728142039, 0.907031452925252, 5.189708008036672, 3.24909945544996, -0.8227995203139423, 0.1177547490303315, 3.004907166417108, 1.734967530378719, -0.8544333088657584, -0.24980497882561, 0.2171357250492995, -1.902223834245667, -1.461811679348026, 2.95466514449557, 4.448636462209047, 1.327977982063607, -0.04859909551348984, 0.8003383938542235, -1.35038811298608, -4.129903686110642, -2.125927788533056, 0.5693223899746688, -0.9048672557826457, -1.546616627923253, 1.137290081940535, 0.3788880109396935, -3.752463525923182, -2.461433072906442, 2.43173738147756, 1.27604741596285, -2.841843352607402, -1.093315890096901, 2.268938847312062, 0.6122478144657029, -0.9470541294216146, 0.999713748695942, 1.034421389125639, -0.5119965271168107, 1.327693355356026, 2.691439979360476, -0.1217211449802696, -0.9580786579303936, 1.394421870572652, 0.1052890176711645, -2.290689905283005, 0.5691902421039914, 2.453610382021957, -1.280525119647011, -2.063285018608913, 1.31757000024185, -0.5820857759775777, -4.478377141962942, -1.028226107234406, 3.229810529977763, 0.9614924468748659, -0.2825483013176342, 2.413389961541854, 1.821879946238348, -0.4916944599179839, 0.4148772895545011, -0.02072442633197046, -2.332238435870552, -0.8117204645770459, 0.1057843598811727, -3.998741405881252, -4.519896308757276, 0.08447194419082836, -0.03243362383086408, -2.534114069922439, -0.10304146479501, 0.7189457969065225, -2.642525391647876, -1.315749135449468, 2.051214874255588, 0.0847178144966027, 0.2432064531818868, 5.210521812524164, 4.245468658860141, -0.5182735198007004, 0.7252391020817446, 2.041325774369437, -1.425987357091902, -1.574114632332883, 1.041588435057012, -0.008559219006207238, -0.3881739858279071, 0.9917443396473489, -1.337467927602787, -2.520043813687824, 0.6399610768312248], 'positive_zeros': ['0.7712776096796075', '1.506708345119917', '1.938368379182356', '2.904525343265716', '3.303224610037178', '3.808296074775034', '4.596671501232553', '4.948361008288904', '5.562700226737648', '6.179441726875300', '6.428170193989252', '6.803292188678253', '7.507348663314552', '7.957955952283416', '8.678934907699866', '8.990858556629126', '9.640556877432695', '10.04214626197160', '10.28767615520016', '10.84275418354196', '11.65104421951223', '11.76767900397470', '12.14613477130651', '12.90716228302175', '13.15322626513276', '13.64739449819296', '14.02409810692704', '14.61406707087817', '15.06632317579229', '15.56192372883436', '16.05213978099545', '16.38974285232290', '16.88100818703752', '17.12597485551488', '17.74036884719495', '18.10090558271521', '18.50774216057079', '18.96653192487652', '19.42622395189816', '19.89206490776714'], 'prelabel': '2-212160-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 41.159520518143616, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 419986542305242989, 'z1': {'__RealLiteral__': 0, 'data': '0.7712776096796075', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.506708345119917', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.938368379182356', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1694.1061292834854, 'bad_primes': [2, 3, 5, 13, 17], 'central_character': '1.1', 'conductor': 212160, 'conductor_radical': 6630, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, 1, 0, -2, 0, 1, 0, 2, 0, 1, 0, -1, 0, 1, 0, 2, 0, 2, 0, -2, 0, 1, 0, -1, 0, 1, 0, 5, 0, -2, 0, -2, 0, 0, 0, -1, 0, -10, 0, -6, 0, 1, 0, -8, 0, -3, 0, -1, 0, 5, 0, 2, 0, -2, 0, 3, 0, -14, 0, -2, 0, 1, 0, -5, 0, 2, 0, -2, 0, -2, 0, -1, 0, -4, 0, -12, 0, 1, 0, 14, 0, 1, 0, -1, 0, 13, 0, -2, 0, -5, 0, 2, 0, 6, 0, 2, 0], 'euler11': [1, -2, 11], 'euler13': [1, -1, 0], 'euler17': [1, -1, 0], 'euler19': [1, -2, 19], 'euler2': [1, 0, 0], 'euler23': [1, 2, 23], 'euler29': [1, -1, 29], 'euler3': [1, 1, 0], 'euler31': [1, -5, 31], 'euler37': [1, 0, 37], 'euler41': [1, 10, 41], 'euler43': [1, 6, 43], 'euler47': [1, 8, 47], 'euler5': [1, -1, 0], 'euler53': [1, -5, 53], 'euler59': [1, -3, 59], 'euler61': [1, 14, 61], 'euler67': [1, 5, 67], 'euler7': [1, 2, 7], 'euler71': [1, 2, 71], 'euler73': [1, 2, 73], 'euler79': [1, 12, 79], 'euler83': [1, -14, 83], 'euler89': [1, -13, 89], 'euler97': [1, -6, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, -1, 0], [1, 2, 7], [1, -2, 11], [1, -1, 0], [1, -1, 0], [1, -2, 19], [1, 2, 23], [1, -1, 29], [1, -5, 31], [1, 0, 37], [1, 10, 41], [1, 6, 43], [1, 8, 47], [1, -5, 53], [1, -3, 59], [1, 14, 61], [1, 5, 67], [1, 2, 71], [1, 2, 73], [1, 12, 79], [1, -14, 83], [1, -13, 89], [1, -6, 97]], 'index': 105, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/212160/cr'], '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': '2-212160-1.1-c1-0-105', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-212160-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 41.159520518143616, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 419986542305242989, 'z1': {'__RealLiteral__': 0, 'data': '0.7712776096796075', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '419986542305242989', 'Lhash_array': ['419986542305242989'], 'label': '2-212160-1.1-c1-0-105', 'type': 'ECQ', 'url': 'EllipticCurve/Q/212160/cr'}