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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': -2, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 0, 'Lhash': '707375091622609478', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [-1.0, 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': 88.03506822846167, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [5, [1]], [7, [1]]], 'bad_primes': [3, 5, 7], 'central_character': '11025.1', 'coefficient_field': '1.1.1.1', 'conductor': 11025, 'conductor_radical': 105, 'degree': 2, 'euler_factors': [[1, 0, 2], [1], [1], [1], [1, 0, 11], [1, 7, 13], [1, 0, 17], [1, -7, 19], [1, 0, 23], [1, 0, 29], [1, -7, 31], [1, -1, 37], [1, 0, 41], [1, 5, 43], [1, 0, 47], [1, 0, 53], [1, 0, 59], [1, 14, 61], [1, 11, 67], [1, 0, 71], [1, 7, 73], [1, 13, 79], [1, 0, 83], [1, 0, 89], [1, -14, 97]], 'gamma_factors': [[], [0]], 'index': 4, 'label': '2-105e2-1.1-c1-0-4', 'leading_term': '1.08152111323', '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': 0, 'origin': 'EllipticCurve/Q/11025/r', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [1.081521113234368, 0.7950906752086371, -0.01025628840550666, -1.085945428937143, -1.898998357978186, -1.8036754228356, -0.4863769501580057, 1.623031555572255, 3.399397233942844, 3.6984212821738, 2.279035459173505, 0.1917091399287464, -0.8962711766370639, -0.0711186046713383, 1.934448893092689, 3.297152879207798, 2.781961332460935, 0.9661251728820477, -0.3433944388255084, -0.05424546799897236, 0.9676081740133768, 0.893872681527628, -0.7572789952830725, -2.188177905694069, -1.17790195730492, 2.139804343545938, 4.929231574661275, 4.555768024232838, 1.58633719737792, -0.7817371722650055, -0.429412140862579, 1.258167756230617, 1.318951884362571, -0.8812026364882809, -2.815175459912034, -2.174202091773666, 0.04546911714234119, 0.9753041479657526, -0.1434150129653757, -1.091749632152722, -0.2691063856615281, 0.494482535944822, -1.590621631660188, -5.692350625873195, -7.521643650897012, -4.748561236681554, -0.330448528771036, 1.223814412773676, -0.317556089419897, -1.176908144458747, 0.597294747393869, 2.387418546704293, 1.303784366362675, -1.22880033433895, -1.709708642838358, -0.02405477055291237, 0.5917189628354148, -0.9971328325915437, -1.915907555965597, -0.2678088248470785, 1.167961110701734, -0.8295213827320006, -4.137204413882639, -3.748210179375693, 0.5728871522029803, 3.437229568968648, 1.601131915336032, -1.548924557185747, -1.643088701031381, 0.1553420746075185, 0.01240629719824133, -1.780901897559258, -1.704189935720696, 0.3607531232798793, 0.6848020405483023, -1.611437156677964, -2.655578320978037, -0.5075389833158793, 1.235479774653986, -0.2489538279265103, -1.599363688197979, 1.141206993583268, 5.027230608679619, 4.207269988855427, -0.5645764501684346, -2.897645978581299, -0.7458047161907704, 1.251403228014271, 0.2358670792816907, -0.8056379760466759, 0.3125532522751769, 0.7674762592365054, -1.228084143091553, -2.077272237439601, 0.8316194101623929, 3.613323474019223, 2.207182235135754, -0.4517231184827437, 0.1218650922197746, 1.527012917192294, -1.060982937892062, -5.183621982003403, -4.305337923002747, 0.9692768303057993, 3.587603355448339, 1.47311738372852, -0.4090629649510497, 0.2672171014599646, 0.2655911207255784, -1.238092074184485, -0.6149821638630626, 2.190307258610229, 2.245479359190523, -1.158350492255436, -2.507063122096062, -0.1977172824833721, 0.3306887724294273, -2.842254392421439, -3.847426424322951, 0.1071568351565817, 3.015502615842891], 'positive_zeros': ['0.4974465266779612', '1.562264018334010', '2.776775483143016', '3.260457125717232', '4.402141274703869', '4.763923625670569', '5.402551153050883', '6.100722498393278', '7.137679194840246', '7.564214068400154', '8.165360561047153', '8.994350389100878', '9.476358465367494', '10.05066267034014', '10.35940226029709', '11.52468544963293', '11.95908325149761', '12.43814889379538', '13.12279074842885', '13.75354103870537', '14.11791316820387', '14.77938123448080', '15.18580870696054', '15.96957203593803', '16.61258139223701', '17.22233497571305', '17.50206624153659', '18.20442921032661', '18.59160639736568', '19.29661689152665', '19.72370939495870'], 'prelabel': '2-105e2-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 9.38270047632672, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'N(U(1))', 'trace_hash': 707375091622609478, 'z1': {'__RealLiteral__': 0, 'data': '0.4974465266779612', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.562264018334010', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.776775483143016', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 88.03506822846167, 'bad_primes': [3, 5, 7], 'central_character': '1.1', 'conductor': 11025, 'conductor_radical': 105, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -7, 0, 0, 4, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -5, 0, 0, 0, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 0, 0, 0, -14, 0, 0, -8, 0, 0, -11, 0, 0, 0, 0, 0, -7, 0, 0, -14, 0, 0, -13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 0, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, 7, 13], 'euler17': [1, 0, 17], 'euler19': [1, -7, 19], 'euler2': [1, 0, 2], 'euler23': [1, 0, 23], 'euler29': [1, 0, 29], 'euler3': [1, 0, 0], 'euler31': [1, -7, 31], 'euler37': [1, -1, 37], 'euler41': [1, 0, 41], 'euler43': [1, 5, 43], 'euler47': [1, 0, 47], 'euler5': [1, 0, 0], 'euler53': [1, 0, 53], 'euler59': [1, 0, 59], 'euler61': [1, 14, 61], 'euler67': [1, 11, 67], 'euler7': [1, 0, 0], 'euler71': [1, 0, 71], 'euler73': [1, 7, 73], 'euler79': [1, 13, 79], 'euler83': [1, 0, 83], 'euler89': [1, 0, 89], 'euler97': [1, -14, 97], 'euler_factors': [[1, 0, 2], [1, 0, 0], [1, 0, 0], [1, 0, 0], [1, 0, 11], [1, 7, 13], [1, 0, 17], [1, -7, 19], [1, 0, 23], [1, 0, 29], [1, -7, 31], [1, -1, 37], [1, 0, 41], [1, 5, 43], [1, 0, 47], [1, 0, 53], [1, 0, 59], [1, 14, 61], [1, 11, 67], [1, 0, 71], [1, 7, 73], [1, 13, 79], [1, 0, 83], [1, 0, 89], [1, -14, 97]], 'index': 4, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/11025/r'], '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': '2-105e2-1.1-c1-0-4', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-105e2-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 9.38270047632672, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 707375091622609478, 'z1': {'__RealLiteral__': 0, 'data': '0.4974465266779612', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '707375091622609478', 'Lhash_array': ['707375091622609478'], 'factors': ['2-105e2-1.1-c1-0-4'], 'label': '2-105e2-1.1-c1-0-4', 'type': 'ECQ', 'url': 'EllipticCurve/Q/11025/r'}