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lfunc_lfunctions • Show schema
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{'Lhash': '1227535645598005957305535252933', 'a10': [0.0, 0.0], 'a2': [1.0, 0.0], 'a3': [0.0, 0.0], 'a4': [1.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-3.303003187441775, 0.0], 'a8': [1.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 17.966340454788096, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 5], 'central_character': '2250.1', 'coefficient_field': 'CDF', 'conductor': 2250, 'conductor_radical': 30, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [3.303003187441775, 0], [7.0, 0]], [[1.0, 0], [-5.344371422230032, 0], [11.0, 0]], [[1.0, 0], [5.344371422230032, 0], [13.0, 0]], [[1.0, 0], [1.2360679774997898, 0], [17.0, 0]], [[1.0, 0], [-2.381966011250105, 0], [19.0, 0]], [[1.0, 0], [-5.854101966249685, 0], [23.0, 0]], [[1.0, 0], 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'group': 'GL2', 'index': 12, 'label': '2-2250-1.1-c1-0-12', 'leading_term': '2.60851333651343045652637502668', '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/2250/2/a/r/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [2.6085133365134303, 2.6007309088809194, 2.577207794522047, 2.5374314038024552, 2.4805958986309493, 2.405670885818116, 2.311490177347632, 2.196854512670184, 2.060641868544392, 1.9019192972462584, 1.7200509230498373, 1.5147975739769783, 1.2864043627826842, 1.035673259754747, 0.7640182884898854, 0.47350144127264926, 0.16684779667800886, -0.15256131979520746, -0.4807179140139265, -0.8130399909987013, -1.1444471565198457, -1.4694584090760836, -1.7823107156218476, -2.077096242197186, -2.3479153541550764, -2.589041740954736, -2.795095292776085, 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'6.99484532353494687902932575732318', '8.232425258705726765917828830124347', '9.276343281714208623780051811519731'], 'prelabel': '2-2250-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.238672015477029, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.968354880577502114916302992359', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.54979719062032121946869467550', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.20170191994318645603667872750', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 17.966340454788096, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 2250, 'conductor_radical': 30, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2250/2/a/r/1/2'], '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': '2-2250-1.1-c1-0-12', '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': '2-2250-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.238672015477029, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.968354880577502114916302992359', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1227535645598005957305535252933', 'Lhash_array': ['1227535645598005957305535252933'], 'factors': ['2-2250-1.1-c1-0-12'], 'label': '2-2250-1.1-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2250/2/a/r/1/2'}