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lfunc_lfunctions • Show schema
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{'Lhash': '1131633392591838978222986901163', 'a10': [-3.5130428348674685, 0.0], 'a2': [1.0, 0.0], 'a3': [1.0, 0.0], 'a4': [1.0, 0.0], 'a5': [-3.5130428348674685, 0.0], 'a6': [1.0, 0.0], 'a7': [0.0, 0.0], 'a8': [1.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 30.518823652533378, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [3, [[1.0, 0], [-1.0, 0]]], [7, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 3, 7, 13], 'central_character': '3822.1', 'coefficient_field': 'CDF', 'conductor': 3822, 'conductor_radical': 546, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [3.5130428348674685, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-3.455149987399731, 0], [11.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [1.4551499873997307, 0], [17.0, 0]], [[1.0, 0], [3.5130428348674685, 0], [19.0, 0]], [[1.0, 0], [-5.513042834867468, 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[-0.023980002585533802, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 25, 'label': '2-3822-1.1-c1-0-25', 'leading_term': '2.97849963976432228876477588211', '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/3822/2/a/ca/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [2.978499639764322, 2.969666119071991, 2.943065556499846, 2.898407070292541, 2.8352356590618952, 2.7529748821126927, 2.650982803166004, 2.528617887614548, 2.385311197552298, 2.220641171811978, 2.0344074532372294, 1.8267005579079267, 1.5979645974578023, 1.3490507064728112, 1.0812592529582767, 0.7963693019960785, 0.4966541582941437, 0.18488214039366543, -0.13569794893684164, -0.46138688119193033, -0.7880804939433862, -1.1113301820263677, -1.4264175952281666, 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'4.41831847213850327578222551332007', '5.27321299585697701137006245217625', '6.60349872942954370879200054069401', '6.86932311850730409196035929672971', '7.73458949160604605443764297798387', '8.512198484401419580142140877795170'], 'prelabel': '2-3822-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.5243844591531985, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.892701342458322731136182492659', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.23713187825935637898895269363', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.31716120465234644502125048628', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 30.518823652533378, 'bad_primes': [2, 3, 7, 13], 'central_character': '1.1', 'conductor': 3822, 'conductor_radical': 546, 'degree': 2, 'index': 25, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3822/2/a/ca/1/1'], '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': '2-3822-1.1-c1-0-25', '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': '2-3822-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.5243844591531985, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.892701342458322731136182492659', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1131633392591838978222986901163', 'Lhash_array': ['1131633392591838978222986901163'], 'label': '2-3822-1.1-c1-0-25', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3822/2/a/ca/1/1'}