Formats: - HTML - YAML - JSON - 2026-07-28T04:40:53.065567
  • lfunc_lfunctions • Show schema
    {'Lhash': '840677398940026410991954198354', 'a10': [38129.85673911815, -92445.1947104571], 'a2': [-29.282203484258602, 12.905524363871207], 'a3': [0, -135.73337936388918], 'a4': [690.8948817870534, -755.8043809878675], 'a5': [-2255.449156756942, 2163.00117921475], 'a6': [1751.7104343712454, 3974.5724341394707], 'a7': [7878.523456551663, 7878.523456551663], 'a8': [-10476.872661561769, 31047.978408157585], 'a9': [40625.44972645854, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 50.82858021389796, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '5.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [29.282203484258602, -12.905524363871207]]], [5, [[1.0, 0], [2255.449156756942, -2163.00117921475]]]], 'bad_primes': [2, 5], 'central_character': '80.13', 'coefficient_field': 'CDF', 'conductor': 80, 'conductor_radical': 10, 'conjugate': '1126176083238211832357297626723', 'degree': 2, 'euler_factors': [[[1.0, 0], [29.282203484258602, -12.905524363871207]], [[1.0, 0], 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-15567285367.277454], [0, 339456738992222300000]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 53, 'label': '2-80-80.13-c10-0-53', 'load_key': 'CMFs-workshop', 'motivic_weight': 10, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [10], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/80/11/i/a/13/16', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.3234768876244307, 1.1940893271320434, 0.989351684792057, 0.7247030193010278, 0.41994678778926664, 0.09800384604509106, -0.21653300936572747, -0.4989655619798369, -0.7260922597873393, -0.8777557976721571, -0.9382455535959886, -0.8974680121126647, -0.7518066909189893, -0.5046061467511037, -0.16623222597886714, 0.24631757819111028, 0.7102547229322483, 1.1982648211959648, 1.6801427381845895, 2.1247151741094665, 2.5019431825395055, 2.7850764387896567, 2.952716897619385, 2.9906435365222346, 2.893253596446788, 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'8.986077013319683548664227850485244', '9.949819090245765899180918818464902', '10.90829223496125070477608618862780', '12.12792240005435389725745426435843'], 'prelabel': '2-80-80.13-c10-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.129416540916792, 'root_angle': -0.1103385000447106, 'root_number': '0.7691557904443523 - 0.6390613194568449*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.11033850004471062', 'prec': 67}, 'spectral_label': 'c10-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.66317753392667490500758615980433', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '1.80274546972024689881627685634981', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '3.84161966293461757145195082688665', 'prec': 113}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 50.82858021389796, 'bad_primes': [2, 5], 'central_character': '80.13', 'conductor': 80, 'conductor_radical': 10, 'degree': 2, 'index': 53, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/80/11/i/a/13/16'], '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': '2-80-80.13-c10-0-53', 'motivic_weight': 10, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [10], 'order_of_vanishing': 0, 'prelabel': '2-80-80.13-c10-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.129416540916792, 'root_angle': -0.1103385000447106, 'self_dual': False, 'spectral_label': 'c10-0', 'z1': {'__RealLiteral__': 0, 'data': '0.66317753392667490500758615980433', 'prec': 113}}
  • lfunc_instances • Show schema
    {'Lhash': '840677398940026410991954198354', 'Lhash_array': ['840677398940026410991954198354'], 'factors': ['2-80-80.13-c10-0-53'], 'label': '2-80-80.13-c10-0-53', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/80/11/i/a/13/16'}