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lfunc_lfunctions • Show schema
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{'Lhash': '2291643223414316076060193169920', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': -5, 'a6': 0, 'a7': 2, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 21.240687602066632, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1, 5]]], 'bad_primes': [2, 3, 5], 'central_character': '360.1', 'coefficient_field': '1.1.1.1', 'conductor': 360, 'conductor_radical': 30, 'degree': 2, 'euler_factors': [[1], [1], [1, 5], [1, -2, 343], [1, -34, 1331], [1, 68, 2197], [1, -38, 4913], [1, -4, 6859], [1, 152, 12167], [1, -46, 24389], [1, 260, 29791], [1, 312, 50653], [1, 48, 68921], [1, 200, 79507], [1, 104, 103823], [1, -414, 148877], [1, -2, 205379], [1, 38, 226981], [1, 244, 300763], [1, 708, 357911], [1, 378, 389017], [1, 852, 493039], [1, 844, 571787], [1, -1380, 704969], [1, -514, 912673], [1, -702, 1030301], [1, -898, 1092727], [1, 876, 1225043], [1, -602, 1295029], [1, 1350, 1442897]], 'euler_factors_factorization': [[1], [1], [[[1, 5], 1]], [[[1, -2, 343], 1]], [[[1, -34, 1331], 1]], [[[1, 68, 2197], 1]], [[[1, -38, 4913], 1]], [[[1, -4, 6859], 1]], [[[1, 152, 12167], 1]], [[[1, -46, 24389], 1]], [[[1, 260, 29791], 1]], [[[1, 312, 50653], 1]], [[[1, 48, 68921], 1]], [[[1, 200, 79507], 1]], [[[1, 104, 103823], 1]], [[[1, -414, 148877], 1]], [[[1, -2, 205379], 1]], [[[1, 38, 226981], 1]], [[[1, 244, 300763], 1]], [[[1, 708, 357911], 1]], [[[1, 378, 389017], 1]], [[[1, 852, 493039], 1]], [[[1, 844, 571787], 1]], [[[1, -1380, 704969], 1]], [[[1, -514, 912673], 1]], [[[1, -702, 1030301], 1]], [[[1, -898, 1092727], 1]], [[[1, 876, 1225043], 1]], [[[1, -602, 1295029], 1]], [[[1, 1350, 1442897], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 10, 'label': '2-360-1.1-c3-0-10', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 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0.7245282526706947, 1.083188210555825, 1.4639295336564682, 1.841092539688041, 2.1889310024108606, 2.4831124849276063, 2.702150547409389, 2.828685789996892, 2.8505402742176327, 2.7614819194572457, 2.5616513774672804, 2.2576227940550173, 1.8620907278390146, 1.3931971313689322, 0.8735334614763924, 0.3288724280416229, -0.21329955558978853, -0.7253655136666352, -1.1811850122662848, -1.5576309481470616, -1.8359646125908387], 'positive_zeros': ['1.80778774766621477588324405382489', '3.36815809286081251988201683508843', '4.47024900874516878066698791039492', '5.59389864145631127028182876766218', '6.87000851106384288932643139817715', '7.64479870567527075430293645350968', '8.692933439812842681244189459039540', '9.687095346202039244043082137026614', '10.46731450202322132070595315024757'], 'prelabel': '2-360-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.608762046587634, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'trace_hash': 1784342816705640337, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.80778774766621477588324405382', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.36815809286081251988201683509', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.47024900874516878066698791039', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 21.240687602066632, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 360, 'conductor_radical': 30, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, -5, 0, 2, 0, 0, 0, 34, 0, -68, 0, 0, 0, 38, 0, 4, 0, 0, 0, -152, 0, 25, 0, 0, 0, 46, 0, -260, 0, 0, 0, -10, 0, -312, 0, 0, 0, -48, 0, -200, 0, 0, 0, -104, 0, -339, 0, 0, 0, 414, 0, -170, 0, 0, 0, 2, 0, -38, 0, 0, 0, 340, 0, -244, 0, 0, 0, -708, 0, -378, 0, 0, 0, 68, 0, -852, 0, 0, 0, -844, 0, -190, 0, 0, 0, 1380, 0, -136, 0, 0, 0, -20, 0, 514, 0, 0, 0], 'euler11': [1, -34, 1331], 'euler13': [1, 68, 2197], 'euler17': [1, -38, 4913], 'euler19': [1, -4, 6859], 'euler2': [1, 0, 0], 'euler23': [1, 152, 12167], 'euler29': [1, -46, 24389], 'euler3': [1, 0, 0], 'euler31': [1, 260, 29791], 'euler37': [1, 312, 50653], 'euler41': [1, 48, 68921], 'euler43': [1, 200, 79507], 'euler47': [1, 104, 103823], 'euler5': [1, 5, 0], 'euler53': [1, -414, 148877], 'euler59': [1, -2, 205379], 'euler61': [1, 38, 226981], 'euler67': [1, 244, 300763], 'euler7': [1, -2, 343], 'euler71': [1, 708, 357911], 'euler73': [1, 378, 389017], 'euler79': [1, 852, 493039], 'euler83': [1, 844, 571787], 'euler89': [1, -1380, 704969], 'euler97': [1, -514, 912673], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 5, 0], [1, -2, 343], [1, -34, 1331], [1, 68, 2197], [1, -38, 4913], [1, -4, 6859], [1, 152, 12167], [1, -46, 24389], [1, 260, 29791], [1, 312, 50653], [1, 48, 68921], [1, 200, 79507], [1, 104, 103823], [1, -414, 148877], [1, -2, 205379], [1, 38, 226981], [1, 244, 300763], [1, 708, 357911], [1, 378, 389017], [1, 852, 493039], [1, 844, 571787], [1, -1380, 704969], [1, -514, 912673]], 'index': 10, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/360/4/a/d/1/1', 'ModularForm/GL2/Q/holomorphic/360/4/a/d'], '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': '2-360-1.1-c3-0-10', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-360-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.608762046587634, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 1784342816705640337, 'z1': {'__RealLiteral__': 0, 'data': '1.80778774766621477588324405382', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20620080
{'Lhash': '2291643223414316076060193169920', 'Lhash_array': ['2291643223414316076060193169920'], 'label': '2-360-1.1-c3-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/360/4/a/d'}
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id: 24558189
{'Lhash': '2291643223414316076060193169920', 'Lhash_array': ['2291643223414316076060193169920'], 'label': '2-360-1.1-c3-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/360/4/a/d/1/1'}