Formats: - HTML - YAML - JSON - 2026-10-12T16:14:13.370590
  • lfunc_lfunctions • Show schema
    {'Lhash': '1118321330673460820836496831048', 'a10': [0.29069719175516373, 0.0], 'a2': [0.29069719175516373, 0.0], 'a3': [1.0, 0.0], 'a4': [-1.9154951427056617, 0.0], 'a5': [1.0, 0.0], 'a6': [0.29069719175516373, 0.0], 'a7': [-0.4865745086349781, 0.0], 'a8': [-1.1382234423155198, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 43.23899269452335, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[3, [[1.0, 0], [-1.0, 0]]], [5, [[1.0, 0], [-1.0, 0]]], [19, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5, 19], 'central_character': '5415.1', 'coefficient_field': 'CDF', 'conductor': 5415, 'conductor_radical': 285, 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.29069719175516373, 0], [2.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0.4865745086349781, 0], [7.0, 0]], [[1.0, 0], [-5.347638177700662, 0], [11.0, 0]], [[1.0, 0], [-2.486574508634978, 0], [13.0, 0]], [[1.0, 0], [3.4156070698459677, 0], 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[-15.729949462967951, 0], [109.0, 0]], [[1.0, 0], [14.801140756037574, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 86, 'label': '2-5415-1.1-c1-0-86', 'leading_term': '2.65727638848999183888216689720', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/5415/2/a/z/1/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 24}, 'plot_values': [2.6572763884899917, 2.6481950354068062, 2.6208940394449054, 2.575212142308748, 2.510911730353073, 2.427723224447398, 2.3254028165858154, 2.2037997008861803, 2.062928520263847, 1.9030426561786, 1.7247041701359298, 1.5288465846418733, 1.3168271901950508, 1.0904661194005325, 0.8520699954791471, 0.60443851693029, 0.35085287599047604, 0.09504542953990962, -0.15884944424540962, -0.4063628533449528, -0.6427762888065269, -0.8632224038282321, -1.062799631888716, -1.2366980720624483, 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'4.33571019733651494623673640432181', '5.18343317752888293396534787999474', '6.06521841688150259079659945990319', '6.66312812110099162460583336117647', '7.43954882266416155270524430340767', '8.528787460004892007838794396527088'], 'prelabel': '2-5415-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.575636295790952, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.882199977243032778929710025783', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '1.81964552155927779464209960618', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.04625630065028179613573610342', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 43.23899269452335, 'bad_primes': [3, 5, 19], 'central_character': '1.1', 'conductor': 5415, 'conductor_radical': 285, 'degree': 2, 'index': 86, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5415/2/a/z/1/3'], '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': '2-5415-1.1-c1-0-86', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-5415-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.575636295790952, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.882199977243032778929710025783', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1118321330673460820836496831048', 'Lhash_array': ['1118321330673460820836496831048'], 'factors': ['2-5415-1.1-c1-0-86'], 'label': '2-5415-1.1-c1-0-86', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5415/2/a/z/1/3'}