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lfunc_lfunctions • Show schema
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{'Lhash': '2031246329970003702807997190347', 'a10': [0.0, 0.0], 'a2': [0.7071067811865476, -0.7071067811865476], 'a3': [0.0, 0.0], 'a4': [0.0, 1.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [2.0, 2.0], 'a8': [2.1213203435596424, 2.1213203435596424], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.7966340454788094, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5], 'central_character': '225.107', 'coefficient_field': 'CDF', 'conductor': 225, 'conductor_radical': 15, 'conjugate': '2727238806703946839506513509719', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.7071067811865476, 0.7071067811865476], [0, -2.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.0, -2.0], [0, 7.0]], [[1.0, 0], [0, 2.8284271247461903], [-11.0, 0]], [[1.0, 0], [1.0, -1.0], [0, -13.0]], [[1.0, 0], [-2.8284271247461903, 2.8284271247461903], [0, -17.0]], [[1.0, 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0]], [[1.0, 0], [-9.899494936611665, -9.899494936611665], [0, 113.0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 2, 'label': '2-15e2-15.2-c1-0-2', 'load_key': 'CMFs-workshop', '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': 'ModularForm/GL2/Q/holomorphic/225/2/f/a/107/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.6654177347502492, 1.6449179870291593, 1.6319018004286294, 1.6210599497455904, 1.6051033339091088, 1.5754893810130173, 1.5231401744369912, 1.4390922411798739, 1.3150874306612985, 1.1441389114344376, 0.9210962214960904, 0.6432088070875567, 0.31066251511049886, -0.07295586250983577, -0.5003229378450609, -0.9602333787508779, -1.437703104479161, -1.9143683926042778, -2.3692097926304734, -2.7796042483149326, -3.1226776061647707, -3.3768948722772887, -3.523790174747454, -3.54970612593014, 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'7.22408914352540503292374627313583', '7.87402606288572129739644673692874', '9.509366422982229982987214642022342', '10.32011556253008692366435768900651', '11.16369469681601332877654522516279', '12.44350411956089834311056661805203'], 'prelabel': '2-15e2-15.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3403857823323886, 'root_angle': -0.019705084840520273, 'root_number': '0.9980844756861901 - 0.06186581765581943*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.00985254242026', 'prec': 57}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.60237081858699516247308595620', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.92599680435465843769319585591', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.92528642053359984071928104512', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.7966340454788094, 'bad_primes': [3, 5], 'central_character': '15.2', 'conductor': 225, 'conductor_radical': 15, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/225/2/f/a/107/2'], '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': '2-15e2-15.2-c1-0-2', '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': '2-15e2-15.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3403857823323886, 'root_angle': -0.009852542420260136, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.60237081858699516247308595620', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2031246329970003702807997190347', 'Lhash_array': ['2031246329970003702807997190347'], 'label': '2-15e2-15.2-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/225/2/f/a/107/2'}