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lfunc_lfunctions • Show schema
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{'Lhash': '243311626162369973871322205687', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [-10.925260001610862, 18.92310540869005], 'a6': [0, 0], 'a7': [-12.136680722436113, 13.989316675293601], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 29.736962642893282, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [12.136680722436113, -13.989316675293601]]]], 'bad_primes': [2, 3, 7], 'central_character': '504.89', 'coefficient_field': 'CDF', 'conductor': 504, 'conductor_radical': 42, 'conjugate': '3064123844856794207460425742243', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [10.925260001610862, -18.92310540869005], [-62.5, -108.25317547305482]], [[1.0, 0], [12.136680722436113, -13.989316675293601]], [[1.0, 0], [45.17336892172759, -26.080856707161697], [665.5, -1152.6798124370878]], [[1.0, 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975.3445291241873], [-1442897.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-504-21.5-c3-0-0', 'leading_term': '0.478355853970989263919717265313890874840031937032070156', '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/504/4/bl/a/89/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [0.4783558539709893, 0.3164498923348242, 0.1679113280827809, 0.034123386684645714, -0.08361677594344585, -0.18410363583945674, -0.2662308643892829, -0.329001036096274, -0.3715375109535514, -0.3930984046087544, -0.3930924422840641, -0.37109637855524985, -0.3268735579218777, -0.260393093633357, -0.1718490571529372, -0.06167900028347354, 0.06941892164439102, 0.22047099230548334, 0.3902159247480669, 0.5770965760432704, 0.7792561351372468, 0.9945394828758929, 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'5.05480432992413963237287170336635', '5.95562586174755076358092426786026', '7.58393400379676839265086818275924', '8.000480983495628686351342288008703', '8.859714356626364372033037801185183', '9.897172587085828915390749504481661'], 'prelabel': '2-504-21.5-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.453160793786782, 'root_angle': 0.6303917095223622, 'root_number': '-0.39827697091615519853431982942948927104217539213330757603 + 0.91726520398293320745892683586344421925470127265455015629*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.31519585476118117', 'prec': 64}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.19193902966524359630876654648', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.907618145121484527006637433688', 'prec': 107}, 'z3': {'__RealLiteral__': 0, 'data': '3.04812069813546936954760968725', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 29.736962642893282, 'bad_primes': [2, 3, 7], 'central_character': '21.5', 'conductor': 504, 'conductor_radical': 42, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/504/4/bl/a/89/1'], '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': '2-504-21.5-c3-0-0', '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': '2-504-21.5-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.453160793786782, 'root_angle': 0.3151958547611811, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.19193902966524359630876654648', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '243311626162369973871322205687', 'Lhash_array': ['243311626162369973871322205687'], 'label': '2-504-21.5-c3-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/504/4/bl/a/89/1'}