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lfunc_lfunctions • Show schema
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{'Lhash': '230719616314259158518325646386', 'a10': [-59.126511915656295, -1.0834582710304014e-60], 'a2': [2.4606716494588343, 4.262008317607015], 'a3': [-9.267679482194522, 0.0], 'a4': [-8.10980993290092, 14.04660284351114], 'a5': [-6.007151739308631, 10.404692021258299], 'a6': [-22.80471615810739, -39.498927038028924], 'a7': [15.444782473658911, -26.75114795622656], 'a8': [-40.45157114621443, 0.0], 'a9': [58.88988298468932, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.077196730591286, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[103, [[1.0, 0], [-379.9064889029995, -973.8573097170832]]]], 'bad_primes': [103], 'central_character': '103.46', 'coefficient_field': 'CDF', 'conductor': 103, 'conductor_radical': 103, 'conjugate': '5509470157452571218359216778329', 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.4606716494588343, -4.262008317607015], [-4.0, 6.928203230275509]], [[1.0, 0], [9.267679482194522, 0], [27.0, 0]], 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[-647514.5, 1121528.0126375577]], [[1.0, 0], [1186.8193547507904, 0], [1442897.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 2, 'label': '2-103-103.46-c3-0-2', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/103/4/c/a/46/23', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.3501926407260198, 0.1038004408858996, -0.11676251036625616, -0.3111734942678712, -0.47866472107344876, -0.6179859467977545, -0.7274355734790952, -0.8049591140019535, -0.8483101318784193, -0.8552654224712067, -0.8238831996444401, -0.7527902461152208, -0.641481283242315, -0.4906112490250649, -0.3022589249612583, -0.08013873865242332, 0.17026300915506523, 0.4416503601649652, 0.7249984882212551, 1.0097683184668287, 1.2842630824966699, 1.536125568079464, 1.7529635921191946, 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'5.83134153204581178912610652705064', '8.278860593024999451376963495290688', '9.903786113978799397310962505319659', '10.91056713075727565543602075975335', '11.90012637534983406751038158417704', '12.13393859162555994081995405116213'], 'prelabel': '2-103-103.46-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.46519709771679, 'root_angle': 0.47451957840941683, 'root_number': '0.07996364209904418 + 0.9967977808674415*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.237259789205', 'prec': 47}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.18200568537791100313882054896', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.91640825358006317271747691324', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.30232456108700925712687296834', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.077196730591286, 'bad_primes': [103], 'central_character': '103.46', 'conductor': 103, 'conductor_radical': 103, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/103/4/c/a/46/23'], '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': '2-103-103.46-c3-0-2', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-103-103.46-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.46519709771679, 'root_angle': 0.23725978920470842, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.18200568537791100313882054896', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '230719616314259158518325646386', 'Lhash_array': ['230719616314259158518325646386'], 'label': '2-103-103.46-c3-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/103/4/c/a/46/23'}