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  • lfunc_lfunctions • Show schema
    {'Lhash': '1938241923772745640511977420617', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.0, 0.0], 'a4': [0.0, 0.0], 'a5': [3.832211654587249, 0.0], 'a6': [0.0, 0.0], 'a7': [3.1965575937442616, 0.0], 'a8': [0.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 56.72572559591761, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [1.0, 0]]], [37, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 3, 37], 'central_character': '7104.1', 'coefficient_field': 'CDF', 'conductor': 7104, 'conductor_radical': 222, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-3.832211654587249, 0], [5.0, 0]], [[1.0, 0], [-3.1965575937442616, 0], [7.0, 0]], [[1.0, 0], [3.4892885718100786, 0], [11.0, 0]], [[1.0, 0], [5.489288571810079, 0], [13.0, 0]], [[1.0, 0], [7.321500226397328, 0], [17.0, 0]], [[1.0, 0], [-3.4892885718100786, 0], [19.0, 0]], [[1.0, 0], 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[113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 135, 'label': '2-7104-1.1-c1-0-135', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/7104/2/a/bq/1/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 17}, 'plot_values': [-7.31690468217267e-61, 0.21564125001752082, 0.43021596323118494, 0.642617592495656, 0.8516626836079934, 1.0560599771979287, 1.254387965914067, 1.4450827873182184, 1.6264376722798384, 1.7966144874426988, 1.9536672623924085, 2.095577015484479, 2.220296707497237, 2.325804764734063, 2.4101653174553856, 2.4715930842511105, 2.5085206853610935, 2.519666076838534, 2.5040977549931673, 2.461295382744786, 2.391203535810585, 2.294276359046934, 2.1715110652226843, 2.0244684038114245, 1.8552784791967047, 1.666630607666917, 1.4617462703391975, 1.2443346418034218, 1.0185306461910153, 0.7888160051065393, 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'7.68493487190545796537702814833999'], 'prelabel': '2-7104-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.531648265547031, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.52900327852468348720679966163', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.17570478264005327907290010858', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '2.73564968450473580351448534656', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 56.72572559591761, 'bad_primes': [2, 3, 37], 'central_character': '1.1', 'conductor': 7104, 'conductor_radical': 222, 'degree': 2, 'index': 135, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/7104/2/a/bq/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': '2-7104-1.1-c1-0-135', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-7104-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.531648265547031, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.52900327852468348720679966163', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1938241923772745640511977420617', 'Lhash_array': ['1938241923772745640511977420617'], 'factors': ['2-7104-1.1-c1-0-135'], 'label': '2-7104-1.1-c1-0-135', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7104/2/a/bq/1/3'}