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lfunc_lfunctions • Show schema
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{'Lhash': '2291413987453726307537080956064,2366482668235461650031921754346', 'a10': -4, 'a2': 2, 'a3': 2, 'a4': 3, 'a5': -2, 'a6': 4, 'a7': 0, 'a8': 4, 'a9': 3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 931.3985971344308, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -2, 1]], [3, [1, -2, 1]], [7, [1]], [13, [1, 2, 1]]], 'bad_primes': [2, 3, 7, 13], 'central_character': '3822.1', 'coefficient_field': '1.1.1.1', 'conductor': 14607684, 'conductor_radical': 546, 'degree': 4, 'euler_factors': [[1, -2, 1], [1, -2, 1], [1, 2, 11, 10, 25], [1], [1, 10, 45, 110, 121], [1, 2, 1], [1, 2, 17, 34, 289], [1, -2, 7, -38, 361], [1, 10, 63, 230, 529], [1, 2, -13, 58, 841], [1, 0, 60, 0, 961], [1, 14, 121, 518, 1369], [1, 16, 138, 656, 1681], [1, 6, 63, 258, 1849], [1, -12, 130, -564, 2209], [1, 0, 74, 0, 2809], [1, 8, 84, 472, 3481], [1, -18, 201, -1098, 3721], [1, 0, -108, 0, 4489], [1, 20, 224, 1420, 5041], [1, -22, 267, -1606, 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1]], [[[1, 4, -24, 428, 11449], 1]]], 'gamma_factors': [[], [0, 0]], 'group': 'GL2', 'index': 17, 'label': '4-3822e2-1.1-c1e2-0-17', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 2, 'origin': 'ModularForm/GL2/Q/holomorphic/3822/2/a/br', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.025390625', 'prec': 37}, 'plot_values': [2.8738734220581824e-118, 0.020074465425114804, 0.08027039035729756, 0.18050388921305877, 0.32062785950278533, 0.5004245664297986, 0.7195893912319248, 0.9777194116901389, 1.2742888218973956, 1.6086344310667615, 1.9799259890000904, 2.3871491855022478, 2.8290748117811573, 3.3042410502243533, 3.8109241133378244, 4.3471242933107845, 4.910538383457148, 5.4985560366195045, 6.108233415496729, 6.736305631853117, 7.379162787854368, 8.032880927162447, 8.693204702288002, 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'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e2-0', 'trace_hash': 1527831855430498001, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.80760691237883472289884600279', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.86682565985406163731925913206', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.54760596510965282736806492296', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 931.3985971344308, 'bad_primes': [2, 3, 7, 13], 'central_character': '1.1', 'conductor': 14607684, 'conductor_radical': 546, 'degree': 4, 'dirichlet_coefficients': [1, 2, 2, 3, -2, 4, 0, 4, 3, -4, -10, 6, -2, 0, -4, 5, -2, 6, 2, -6, 0, -20, -10, 8, -7, -4, 4, 0, -2, -8, 0, 6, -20, -4, 0, 9, -14, 4, -4, -8, -16, 0, -6, -30, -6, -20, 12, 10, 0, -14, -4, -6, 0, 8, 20, 0, 4, -4, -8, -12, 18, 0, 0, 7, 4, -40, 0, -6, -20, 0, -20, 12, 22, -28, -14, 6, 0, -8, -4, -10, 5, -32, 4, 0, 4, -12, -4, -40, -20, -12, 0, -30, 0, 24, -4, 12, -8, 0, -30, -21], 'euler11': [1, 10, 45, 110, 121], 'euler13': [1, 2, 1, 0, 0], 'euler17': [1, 2, 17, 34, 289], 'euler19': [1, -2, 7, -38, 361], 'euler2': [1, -2, 1, 0, 0], 'euler23': [1, 10, 63, 230, 529], 'euler29': [1, 2, -13, 58, 841], 'euler3': [1, -2, 1, 0, 0], 'euler31': [1, 0, 60, 0, 961], 'euler37': [1, 14, 121, 518, 1369], 'euler41': [1, 16, 138, 656, 1681], 'euler43': [1, 6, 63, 258, 1849], 'euler47': [1, -12, 130, -564, 2209], 'euler5': [1, 2, 11, 10, 25], 'euler53': [1, 0, 74, 0, 2809], 'euler59': [1, 8, 84, 472, 3481], 'euler61': [1, -18, 201, -1098, 3721], 'euler67': [1, 0, -108, 0, 4489], 'euler7': [1, 0, 0, 0, 0], 'euler71': [1, 20, 224, 1420, 5041], 'euler73': [1, -22, 267, -1606, 5329], 'euler79': [1, 4, 144, 316, 6241], 'euler83': [1, -4, 138, -332, 6889], 'euler89': [1, 20, 260, 1780, 7921], 'euler97': [1, 8, 82, 776, 9409], 'euler_factors': [[1, -2, 1, 0, 0], [1, -2, 1, 0, 0], [1, 2, 11, 10, 25], [1, 0, 0, 0, 0], [1, 10, 45, 110, 121], [1, 2, 1, 0, 0], [1, 2, 17, 34, 289], [1, -2, 7, -38, 361], [1, 10, 63, 230, 529], [1, 2, -13, 58, 841], [1, 0, 60, 0, 961], [1, 14, 121, 518, 1369], [1, 16, 138, 656, 1681], [1, 6, 63, 258, 1849], [1, -12, 130, -564, 2209], [1, 0, 74, 0, 2809], [1, 8, 84, 472, 3481], [1, -18, 201, -1098, 3721], [1, 0, -108, 0, 4489], [1, 20, 224, 1420, 5041], [1, -22, 267, -1606, 5329], [1, 4, 144, 316, 6241], [1, -4, 138, -332, 6889], [1, 20, 260, 1780, 7921], [1, 8, 82, 776, 9409]], 'index': 17, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3822/2/a/br'], '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': '4-3822e2-1.1-c1e2-0-17', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 2, 'prelabel': '4-3822e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.5243844591531985, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1527831855430498001, 'z1': {'__RealLiteral__': 0, 'data': '1.80760691237883472289884600279', 'prec': 103}}
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{'Lhash': '2291413987453726307537080956064,2366482668235461650031921754346', 'Lhash_array': ['2291413987453726307537080956064', '2366482668235461650031921754346'], 'label': '4-3822e2-1.1-c1e2-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3822/2/a/br'}