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lfunc_lfunctions • Show schema
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{'Lhash': '1021828609918875904758009176860', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.5615528128088303, 0.0], 'a4': [0.0, 0.0], 'a5': [-1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [2.5615528128088303, 0.0], 'a8': [0.0, 0.0], 'a9': [-0.5615528128088303, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 58.76989588766239, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [1.0, 0]]], [23, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 5, 23], 'central_character': '7360.1', 'coefficient_field': 'CDF', 'conductor': 7360, 'conductor_radical': 230, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.5615528128088303, 0], [3.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-2.5615528128088303, 0], [7.0, 0]], [[1.0, 0], [2.0, 0], [11.0, 0]], [[1.0, 0], [-3.5615528128088303, 0], [13.0, 0]], [[1.0, 0], [-2.5615528128088303, 0], [17.0, 0]], [[1.0, 0], [6.0, 0], [19.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 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'group': 'GL2', 'index': 62, 'label': '2-7360-1.1-c1-0-62', 'leading_term': '2.78358644370771063186795893893', '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/7360/2/a/bi/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [2.7835864437077107, 2.7721398163800113, 2.737750086755114, 2.680278995529197, 2.599532855579705, 2.495314731480224, 2.3674919425595653, 2.2160740405502803, 2.04129587771361, 1.8437002707332797, 1.6242150118356478, 1.3842194878641305, 1.1255968448459233, 0.8507683996403059, 0.5627077948151405, 0.26493318521814374, -0.03852347871153382, -0.3431702462717593, -0.6441314692649398, -0.9362453037213858, -1.2141803744658128, -1.4725688547679188, -1.7061525304306973, -1.9099377821851031, -2.0793548554324657, -2.210416318430813, -2.2998692663205937, 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'5.77083966711572480116835402838775', '6.55149312304631036741604650052911', '7.53646783731309843545785946743043', '8.096683657834363950212778636405914'], 'prelabel': '2-7360-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.66615261312103, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.806080642201332608709624620064', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.99846768591812328884215442760', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.63418107170488340334633108605', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 58.76989588766239, 'bad_primes': [2, 5, 23], 'central_character': '1.1', 'conductor': 7360, 'conductor_radical': 230, 'degree': 2, 'index': 62, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/7360/2/a/bi/1/2'], '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': '2-7360-1.1-c1-0-62', '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': '2-7360-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.66615261312103, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.806080642201332608709624620064', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1021828609918875904758009176860', 'Lhash_array': ['1021828609918875904758009176860'], 'label': '2-7360-1.1-c1-0-62', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7360/2/a/bi/1/2'}