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lfunc_lfunctions • Show schema
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{'Lhash': '3285862969306777018961384344348,4628250645246249240879341019525', 'a10': 9, 'a2': -3, 'a3': -2, 'a4': 4, 'a5': -3, 'a6': 6, 'a7': -2, 'a8': -3, 'a9': -3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.6764390383170376, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[103, [1, 2, 1]]], 'bad_primes': [103], 'central_character': '103.1', 'coefficient_field': '1.1.1.1', 'conductor': 10609, 'conductor_radical': 103, 'degree': 4, 'euler_factors': [[1, 3, 5, 6, 4], [1, 2, 7, 6, 9], [1, 3, 11, 15, 25], [1, 2, 15, 14, 49], [1, 3, 23, 33, 121], [1, 3, 17, 39, 169], [1, 9, 53, 153, 289], [1, -5, 33, -95, 361], [1, 0, 26, 0, 529], [1, 6, 62, 174, 841], [1, 0, 17, 0, 961], [1, 0, 29, 0, 1369], [1, 0, 2, 0, 1681], [1, 4, 45, 172, 1849], [1, 3, 65, 141, 2209], [1, 9, 95, 477, 2809], [1, -15, 173, -885, 3481], [1, -15, 167, -915, 3721], [1, -2, -45, -134, 4489], [1, -3, 113, -213, 5041], [1, 15, 191, 1095, 5329], [1, -7, 69, -553, 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3.3066854247217745, 6.754046619964141, 10.807990032201221], 'positive_zeros': ['2.59208883639954584899311384769688', '3.65104599359868815501951116460910', '4.91231967485079938577327554470200', '5.49393216015653352470861077787309', '6.41211906014764542616529081381339', '6.94244585770451458914106171343461', '7.80272369775436991917087217809256', '8.005816357257536141624131095436584', '8.738425004717429255596542261961924', '9.102211533828713010939301018280824', '9.888856913147113375102993549611673', '10.12933463243780987152001893330632', '11.08722419550826236265644041302846', '11.25361490978760122892096508652136', '11.60864535731955206900512239723139', '12.11379478170206293955745407269797', '12.94840009397894493978095356197959', '13.23610994267001705954558373175052'], 'prelabel': '4-103e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.9068953306855143, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e2-0', 'trace_hash': 1936178672590621224, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.59208883639954584899311384770', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.65104599359868815501951116461', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.91231967485079938577327554470', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.6764390383170376, 'bad_primes': [103], 'central_character': '1.1', 'conductor': 10609, 'conductor_radical': 103, 'degree': 4, 'dirichlet_coefficients': [1, -3, -2, 4, -3, 6, -2, -3, -3, 9, -3, -8, -3, 6, 6, 3, -9, 9, 5, -12, 4, 9, 0, 6, -2, 9, 14, -8, -6, -18, 0, -6, 6, 27, 6, -12, 0, -15, 6, 9, 0, -12, -4, -12, 9, 0, -3, -6, -11, 6, 18, -12, -9, -42, 9, 6, -10, 18, 15, 24, 15, 0, 6, 5, 9, -18, 2, -36, 0, -18, 3, 9, -15, 0, 4, 20, 6, -18, 7, -9, -4, 0, 3, 16, 27, 12, 12, 9, -18, -27, 6, 0, 0, 9, -15, 12, 10, 33, 9, -8], 'euler11': [1, 3, 23, 33, 121], 'euler13': [1, 3, 17, 39, 169], 'euler17': [1, 9, 53, 153, 289], 'euler19': [1, -5, 33, -95, 361], 'euler2': [1, 3, 5, 6, 4], 'euler23': [1, 0, 26, 0, 529], 'euler29': [1, 6, 62, 174, 841], 'euler3': [1, 2, 7, 6, 9], 'euler31': [1, 0, 17, 0, 961], 'euler37': [1, 0, 29, 0, 1369], 'euler41': [1, 0, 2, 0, 1681], 'euler43': [1, 4, 45, 172, 1849], 'euler47': [1, 3, 65, 141, 2209], 'euler5': [1, 3, 11, 15, 25], 'euler53': [1, 9, 95, 477, 2809], 'euler59': [1, -15, 173, -885, 3481], 'euler61': [1, -15, 167, -915, 3721], 'euler67': [1, -2, -45, -134, 4489], 'euler7': [1, 2, 15, 14, 49], 'euler71': [1, -3, 113, -213, 5041], 'euler73': [1, 15, 191, 1095, 5329], 'euler79': [1, -7, 69, -553, 6241], 'euler83': [1, -3, 107, -249, 6889], 'euler89': [1, 18, 214, 1602, 7921], 'euler97': [1, -10, 174, -970, 9409], 'euler_factors': [[1, 3, 5, 6, 4], [1, 2, 7, 6, 9], [1, 3, 11, 15, 25], [1, 2, 15, 14, 49], [1, 3, 23, 33, 121], [1, 3, 17, 39, 169], [1, 9, 53, 153, 289], [1, -5, 33, -95, 361], [1, 0, 26, 0, 529], [1, 6, 62, 174, 841], [1, 0, 17, 0, 961], [1, 0, 29, 0, 1369], [1, 0, 2, 0, 1681], [1, 4, 45, 172, 1849], [1, 3, 65, 141, 2209], [1, 9, 95, 477, 2809], [1, -15, 173, -885, 3481], [1, -15, 167, -915, 3721], [1, -2, -45, -134, 4489], [1, -3, 113, -213, 5041], [1, 15, 191, 1095, 5329], [1, -7, 69, -553, 6241], [1, -3, 107, -249, 6889], [1, 18, 214, 1602, 7921], [1, -10, 174, -970, 9409]], 'index': 1, 'instance_types': ['G2Q', 'CMF'], 'instance_urls': ['Genus2Curve/Q/10609/a', 'ModularForm/GL2/Q/holomorphic/103/2/a/a'], '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': True, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-103e2-1.1-c1e2-0-1', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 2, 'prelabel': '4-103e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.9068953306855143, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1936178672590621224, 'z1': {'__RealLiteral__': 0, 'data': '2.59208883639954584899311384770', 'prec': 103}}
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id: 9965281
{'Lhash': '3285862969306777018961384344348,4628250645246249240879341019525', 'Lhash_array': ['3285862969306777018961384344348', '4628250645246249240879341019525'], 'label': '4-103e2-1.1-c1e2-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/103/2/a/a'}
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id: 1224598
{'Lhash': '1936178672590621224', 'Lhash_array': ['1936178672590621224'], 'label': '4-103e2-1.1-c1e2-0-1', 'type': 'G2Q', 'url': 'Genus2Curve/Q/10609/a'}