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lfunc_lfunctions • Show schema
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{'Lhash': '129757205769572084015226369102', 'a10': [0.8873197338773515, 1.536882861634068], 'a2': [-1.7358593375517808, -0.3689682923328088], 'a3': [0.3244925192972402, -3.0873400912627984], 'a4': [1.049979123733516, 0.4674808248612822], 'a5': [-0.6691306063588582, -0.7431448254773942], 'a6': [-1.7024039709116687, 5.2394606748966215], 'a7': [0.4272645736397437, 2.611023742540931], 'a8': [1.2212965120842725, 0.8873238553338372], 'a9': [-6.491930641837297, -1.3799024558291957], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.074240477819296, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0.6691306063588582, 0.7431448254773942]]], [7, [[1.0, 0], [-0.4272645736397437, -2.611023742540931]]], [11, [[1.0, 0], [2.85107837203667, -1.6945064521874003]]]], 'bad_primes': [5, 7, 11], 'central_character': '385.16', 'coefficient_field': 'CDF', 'conductor': 385, 'conductor_radical': 385, 'conjugate': 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[-5.484551505441612, 16.8797138770874], [-67.14841053312064, -48.78617594027527]], [[1.0, 0], [0.44744707637491715, -0.7750010699795084], [-44.5, -77.07626093681505]], [[1.0, 0], [1.3921530877425443, 4.2846066393729245], [-78.4746484543699, 57.01516947236989]], [[1.0, 0], [6.3566801882109045, -7.0598085697938195], [-10.557374790033, -100.44671143219561]], [[1.0, 0], [-1.452259527582291, -13.817326427535033], [-100.74920287558199, 21.414904154229212]], [[1.0, 0], [1.1020401378339226, -0.49065988172503533], [71.59697488039782, -79.51649632608118]], [[1.0, 0], [5.825896273418051, 10.090748345186247], [-54.5, 94.39676901250381]], [[1.0, 0], [7.594310376761584, 5.517589459589706], [34.91892036436906, 107.46938634135235]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-385-77.16-c1-0-0', '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/385/2/bg/a/16/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.11034572780125743, -0.0261991460588271, -0.18468848362398035, -0.370683992439093, -0.5893178038730622, -0.8443135167026752, -1.1371382944553061, -1.46631437971873, -1.826896083596754, -2.210130905614065, -2.6033464065507976, -2.9901198476273514, -3.3507880012129325, -3.663338952198922, -3.9046978693023093, -4.052377499307321, -4.086415313037237, -3.9914676772460185, -3.758883127991158, -3.3885386275443836, -2.8902017353963423, -2.2841844933394264, -1.6010865131734873, -0.8804876118258449, -0.16854310740975603, 0.48544794982603273, 1.0332997688662162, 1.4326882485944292, 1.6519417501657536, 1.674344612560338, 1.5013951774037129, 1.1544965823596782, 0.6746670348339393, 0.12003486008266588, -0.438879541771561, -0.9258196643650037, -1.2668333202014441, -1.3988973168416596, -1.2781494151917858, -0.886678405862282, 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1.753351213482141, 'root_angle': -0.39459664564063746, 'root_number': '0.3251160136167164 - 0.9456741392731299*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.19729832282', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.10236038680233372997130179584', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.03081972507102954418803258200', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.15136052062025672088436454976', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.074240477819296, 'bad_primes': [5, 7, 11], 'central_character': '77.16', 'conductor': 385, 'conductor_radical': 385, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/385/2/bg/a/16/4'], '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': '2-385-77.16-c1-0-0', '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': '2-385-77.16-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.753351213482141, 'root_angle': -0.19729832282031873, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.10236038680233372997130179584', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '129757205769572084015226369102', 'Lhash_array': ['129757205769572084015226369102'], 'label': '2-385-77.16-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/385/2/bg/a/16/4'}