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lfunc_lfunctions • Show schema
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{'Lhash': '1317185052224859772107337974467', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-1.5, -0.8660254037844386], 'a4': [0, 0], 'a5': [-2.1390167643610623, 1.2349619047049816], 'a6': [0, 0], 'a7': [-3.793763125418392, 5.882802168033162], 'a8': [0, 0], 'a9': [1.5, 2.598076211353316], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 18.310673765011956, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [1.5, 0.8660254037844386]]], [7, [[1.0, 0], [3.793763125418392, -5.882802168033162]]]], 'bad_primes': [2, 3, 7], 'central_character': '672.577', 'coefficient_field': 'CDF', 'conductor': 672, 'conductor_radical': 42, 'conjugate': '404261394781242248084003164815', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.5, 0.8660254037844386]], [[1.0, 0], [2.1390167643610623, -1.2349619047049816], [12.5, -21.650635094610966]], [[1.0, 0], [3.793763125418392, -5.882802168033162]], [[1.0, 0], 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'leading_term': '0.6899296891276497763373087419770456800986200697867447707', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/672/3/bh/b/577/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [0.6899296891276497, 0.7885708755862239, 0.8731908014599893, 0.9429305596412582, 0.9969116937617107, 1.034236729667972, 1.0539973350960516, 1.0552901012261648, 1.0372395978351279, 0.9990280406837738, 0.9399306360077926, 0.8593554377002709, 0.7568863687752758, 0.6323279178201987, 0.485749919851402, 0.31753076579899503, 0.12839735333335967, -0.08053990693624376, -0.3077586808949422, -0.5513044761769113, -0.8087800536942936, -1.0773458039146881, -1.3537322092230422, -1.634265269491127, -1.9149054762958384, -2.191300583607043, -2.458852042952034, -2.712794555186228, 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'9.997560071540097683860878873404758', '10.31802251407968941467493675096401'], 'prelabel': '2-672-7.3-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.279097307261423, 'root_angle': 0.23765367053408643, 'root_number': '0.0774964953019748996892088490694380755401345544904169309 + 0.9969926244541185081499695178595460687117764194297993065*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.23765367053408643', 'prec': 64}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.03907579264168858977624662755', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.02708827877209863847816925604', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.06804143754045729498932658968', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 18.310673765011956, 'bad_primes': [2, 3, 7], 'central_character': '7.3', 'conductor': 672, 'conductor_radical': 42, 'degree': 2, 'index': 18, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/672/3/bh/b/577/4'], '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': '2-672-7.3-c2-0-18', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-672-7.3-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.279097307261423, 'root_angle': 0.23765367053408643, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.03907579264168858977624662755', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1317185052224859772107337974467', 'Lhash_array': ['1317185052224859772107337974467'], 'factors': ['2-672-7.3-c2-0-18'], 'label': '2-672-7.3-c2-0-18', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/672/3/bh/b/577/4'}