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lfunc_lfunctions • Show schema
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{'Lhash': '1645142078443302552363980741877', 'a10': [-1.0, -3.657796605117526e-61], 'a2': [-0.8090169943749475, 0.5877852522924731], 'a3': [-0.06522709157352852, -0.2007483459136714], 'a4': [0.30901699437494745, -0.9510565162951535], 'a5': [0.8090169943749475, 0.5877852522924731], 'a6': [0.1707667427267995, 0.12406930095997], 'a7': [-0.30901699437494745, 0.9510565162951535], 'a8': [0.30901699437494745, 0.9510565162951535], 'a9': [2.391005658212909, -1.7371672953931285], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.148480955638592, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.8090169943749475, -0.5877852522924731]]], [5, [[1.0, 0], [-0.8090169943749475, -0.5877852522924731]]], [7, [[1.0, 0], [0.30901699437494745, -0.9510565162951535]]], [11, [[1.0, 0], [0.544486006631153, 3.271625740909687]]]], 'bad_primes': [2, 5, 7, 11], 'central_character': '770.421', 'coefficient_field': 'CDF', 'conductor': 770, 'conductor_radical': 770, 'conjugate': '1161098088375879757052728497472', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [0.06522709157352852, 0.2007483459136714], [-2.4270509831248424, 1.7633557568774194]], [[1.0, 0], [-0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [0.30901699437494745, -0.9510565162951535]], [[1.0, 0], [0.544486006631153, 3.271625740909687]], [[1.0, 0], [-0.3107050719574942, 0.2257404484440854], [4.017220926874317, -12.363734711836996]], [[1.0, 0], [-2.7114251632738235, -1.9699656926223124], [5.253288904374106, 16.167960777017612]], [[1.0, 0], [1.4894681723254366, 4.58411167311251], [-15.371322893124, 11.16791979355699]], [[1.0, 0], [-0.683066970907198, 0], [23.0, 0]], [[1.0, 0], [-0.49654541754855336, 1.528209657048995], [-23.461492836873475, -17.04577231648172]], [[1.0, 0], [-1.0175168563710961, 0.7392692691159238], [9.57952682562337, -29.48275200514976]], [[1.0, 0], [-0.2647933873483257, 0.814950248994812], [-29.933628791873055, -21.748054334821507]], [[1.0, 0], [-2.9730825257684006, -9.150207144220827], [-33.16969676937284, 24.099195343991397]], [[1.0, 0], [-9.55155400904785, 0], [43.0, 0]], [[1.0, 0], [2.333238200518852, 7.180968798045283], [-38.02379873562253, 27.625906857746237]], [[1.0, 0], [-10.95298737669119, 7.957811137872023], [16.377900701872214, -50.405995363643136]], [[1.0, 0], [-2.246320630480059, 6.913464023645614], [-47.7320026681219, -34.67932988525592]], [[1.0, 0], [3.1481390785163867, 2.287256924617763], [18.850036656871794, 58.014447494004365]], [[1.0, 0], [-4.97372174828498, 0], [67.0, 0]], [[1.0, 0], [0.6799265309491243, 0.493995540653692], [21.940206600621266, 67.52501265695591]], [[1.0, 0], [3.1978718194003424, -9.842037452565108], [-59.05824058937116, -42.90832341735054]], [[1.0, 0], [2.7245383937560996, -1.979493012247222], [24.412342555620846, -75.13346478731714]], [[1.0, 0], [-8.510480227002976, -6.183225818666379], [25.648410533120636, 78.93769085249775]], [[1.0, 0], [-15.036462441038843, 0], [89.0, 0]], [[1.0, 0], [9.115281194096589, -6.62263944223866], [29.974648454369902, -92.2524820806299]], [[1.0, 0], [0.5727774458644069, -0.41614717350277997], [31.210716431869688, -96.05670814581052]], [[1.0, 0], [-0.18604087663425267, 0.5725749432588917], [-83.32875042061958, -60.54188098612473]], [[1.0, 0], [-3.1767381673815747, -9.776994759666557], [-86.56481839811937, 62.893021995294625]], [[1.0, 0], [2.655296787305429, 0], [109.0, 0]], [[1.0, 0], [-3.1601224795442, -9.725856930750625], [-91.41892036436906, 66.41973350904946]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 9, 'label': '2-770-11.3-c1-0-9', '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/770/2/n/k/421/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': 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'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.29778826921796046356221761234', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.41642179482555713401762499222', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.89961038935394825154033375027', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.148480955638592, 'bad_primes': [2, 5, 7, 11], 'central_character': '11.3', 'conductor': 770, 'conductor_radical': 770, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/770/2/n/k/421/3'], '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': '2-770-11.3-c1-0-9', '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': '2-770-11.3-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4796130657097675, 'root_angle': 0.027536663662108617, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.29778826921796046356221761234', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1645142078443302552363980741877', 'Lhash_array': ['1645142078443302552363980741877'], 'factors': ['2-770-11.3-c1-0-9'], 'label': '2-770-11.3-c1-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/770/2/n/k/421/3'}