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lfunc_lfunctions • Show schema
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{'Lhash': '1011354187897780162651887225246', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.4338837391175581, -0.9009688679024191], 'a4': [0.9009688679024191, 0.4338837391175581], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-0.5568293831692092, 0.2681548979405432], 'a8': [0.0, 0.0], 'a9': [-0.6234898018587335, 0.7818314824680298], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.2591410268730652, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.4338837391175581, 0.9009688679024191]]], [29, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 29], 'central_character': '2523.236', 'coefficient_field': 'CDF', 'conductor': 2523, 'conductor_radical': 87, 'conjugate': '1977351203648710065539043767692', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [-0.9009688679024191, -0.4338837391175581]], [[1.0, 0], [0.4338837391175581, 0.9009688679024191]], [[1.0, 0], [0, 0], [0.9009688679024191, 0.4338837391175581]], [[1.0, 0], 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[-0.6234898018587335, 0.7818314824680298]], [[1.0, 0], [-1.0088276910463683, 1.2650299121079898], [-0.2225209339563144, -0.9749279121818236]], [[1.0, 0], [0, 0], [0.2225209339563144, -0.9749279121818236]], [[1.0, 0], [-1.5774664984911633, 0.3600464343496873], [0.9009688679024191, -0.4338837391175581]], [[1.0, 0], [1.2650299121079898, 1.0088276910463683], [0.2225209339563144, 0.9749279121818236]], [[1.0, 0], [0, 0], [-0.6234898018587335, -0.7818314824680298]], [[1.0, 0], [0, 0], [-0.9009688679024191, -0.4338837391175581]], [[1.0, 0], [0.2681548979405432, -0.5568293831692092], [-0.6234898018587335, -0.7818314824680298]], [[1.0, 0], [0, 0], [-0.9009688679024191, 0.4338837391175581]], [[1.0, 0], [-0.3853378891876347, -0.48319842963995996], [-0.2225209339563144, 0.9749279121818236]], [[1.0, 0], [0, 0], [0.2225209339563144, 0.9749279121818236]], [[1.0, 0], [-0.5568293831692092, 0.2681548979405432], [0.6234898018587335, -0.7818314824680298]], [[1.0, 0], [0, 0], [0.6234898018587335, -0.7818314824680298]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-2523-87.62-c0-0-0', 'leading_term': '1.14554278685011422475299189398', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/2523/1/h/c/236/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.1455427868501142, 1.1069651683311288, 1.0743388864724526, 1.0445305180257274, 1.0137654831422211, 0.978001405079726, 0.9332497149813761, 0.87581174500406, 0.8024330469165325, 0.7103977781391109, 0.5975868335526849, 0.4625174242538087, 0.3043743743193544, 0.12303739295711118, -0.08089541293401598, -0.3060898171407119, -0.5504666870557611, -0.8112056248114052, -1.0847644008717596, -1.3669171065659842, -1.6528133049933034, -1.9370596616350244, -2.2138246248539324, -2.4769657322537655, 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'5.85729793888005566789182911659446', '6.54399052222372118006773460093297', '7.34454685301721989199556781571176', '8.335748486746748755914117474707127', '9.218278967967678883869697808398749'], 'prelabel': '2-2523-87.62-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1221145337589498, 'root_angle': -0.19580058132975997, 'root_number': '0.81670093530061286575565831098988 - 0.57706115991210512056517124359824*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.09790029066487999', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.797817780164104121578615914482', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.47036986056455500924864118256', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.34220847010021300115302694318', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.2591410268730652, 'bad_primes': [3, 29], 'central_character': '87.62', 'conductor': 2523, 'conductor_radical': 87, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2523/1/h/c/236/1'], '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': '2-2523-87.62-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-2523-87.62-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1221145337589498, 'root_angle': -0.09790029066487999, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.797817780164104121578615914482', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1011354187897780162651887225246', 'Lhash_array': ['1011354187897780162651887225246'], 'label': '2-2523-87.62-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2523/1/h/c/236/1'}