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lfunc_lfunctions • Show schema
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{'Lhash': '1868146881869324040444168634197', 'a10': [0.14275922718982786, -2.231506173653159], 'a2': [-0.35836794954530027, -0.9335804264972017], 'a3': [1.7530150314506006, 2.699406427971099], 'a4': [-0.7431448254773942, 0.6691306063588582], 'a5': [2.0321301538035645, 0.9329775120560518], 'a6': [1.8918886019715047, -2.6039612672990633], 'a7': [2.640593505787343, 0.1651240055040756], 'a8': [0.8910065241883679, 0.4539904997395468], 'a9': [-2.993523433652537, 6.723563715527616], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.148480955638592, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.35836794954530027, 0.9335804264972017]]], [5, [[1.0, 0], [-2.0321301538035645, -0.9329775120560518]]], [7, [[1.0, 0], [-2.640593505787343, -0.1651240055040756]]], [11, [[1.0, 0], [1.0881258026222367, 3.1330467978738703]]]], 'bad_primes': [2, 5, 7, 11], 'central_character': '770.157', 'coefficient_field': 'CDF', 'conductor': 770, 'conductor_radical': 770, 'conjugate': '2346053614171976504788292770101', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.35836794954530027, 0.9335804264972017]], [[1.0, 0], [-1.7530150314506006, -2.699406427971099], [-1.2202099292274007, 2.7406363729278027]], [[1.0, 0], [-2.0321301538035645, -0.9329775120560518]], [[1.0, 0], [-2.640593505787343, -0.1651240055040756]], [[1.0, 0], [1.0881258026222367, 3.1330467978738703]], [[1.0, 0], [-2.8397927339991407, -0.44977898281213863], [12.363734711836996, 4.017220926874317]], [[1.0, 0], [-1.8210037613879484, 4.743876985558025], [-12.633462033115702, -11.37522030810059]], [[1.0, 0], [-2.3093476881582253, 2.5647904435603897], [-1.986040802085416, -18.895916011997194]], [[1.0, 0], [-5.327051543811253, -1.4273791592031906], [19.91858428704209, 11.5]], [[1.0, 0], [6.196030912284016, 2.0132124818690196], [23.461492836873475, 17.04577231648172]], [[1.0, 0], [10.520312670870817, -1.1057294180276833], [30.322575622747976, -6.445262415350539]], [[1.0, 0], 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[[1.0, 0], [-0.04260896292064416, -0.2690224041789498], [-78.93769085249775, 25.648410533120636]], [[1.0, 0], [0.9775853022422515, 1.6932274122161568], [-44.5, 77.07626093681505]], [[1.0, 0], [1.6540995190238477, -10.443573343660077], [-92.2524820806299, -29.974648454369902]], [[1.0, 0], [8.060727882217444, -0.8472166397451802], [98.79290767411437, -20.999080772593693]], [[1.0, 0], [-8.579613121801636, -5.57166590799498], [41.89387423680742, 94.09518213718789]], [[1.0, 0], [-3.69176890682248, 0.19347741003274682], [106.41384280440525, -11.18454556963892]], [[1.0, 0], [-12.790868016744657, -7.384811092636502], [54.5, 94.39676901250381]], [[1.0, 0], [2.4295753429201916, 1.2379304686819916], [66.41973350904946, 91.41892036436906]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 31, 'label': '2-770-385.157-c1-0-31', '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/bv/a/157/24', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [2.3226344387344646, 2.206469118381719, 2.0834369762271914, 1.9470324495669988, 1.789852839918692, 1.605812945692792, 1.392081713548109, 1.1505188280589054, 0.888522791454705, 0.6192498103264663, 0.3611638458748644, 0.13688027836002314, -0.028704586706275945, -0.11094280145210793, -0.08847799306544536, 0.053444533493586965, 0.31974564459228605, 0.7027776833033228, 1.1805398917213645, 1.716272603148558, 2.259767573557285, 2.7505714661501695, 3.1230387776033246, 3.312929602060419, 3.264977586070583, 2.940613387192119, 2.3248615203258445, 1.4313734087907082, 0.3046464405296565, -0.9812795060576038, -2.3279701823696497, -3.621415847456565, -4.743800662060044, -5.586983329896616, -6.066044196888235, -6.13104343396458, -5.775181155024621, -5.037881778352632, -4.0019263076562615, -2.7845643117200973, -1.523445067611759, 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'root_angle': -0.27517402315465234, 'root_number': '0.6490322298513898 - 0.760760911597154*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.137587011577', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.47370804031724556941927398646', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.83913443318180385040932698360', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.53071409366836065357748803910', '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': '385.157', 'conductor': 770, 'conductor_radical': 770, 'degree': 2, 'index': 31, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/770/2/bv/a/157/24'], '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': '2-770-385.157-c1-0-31', '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': '2-770-385.157-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4796130657097675, 'root_angle': -0.13758701157732617, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.47370804031724556941927398646', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1868146881869324040444168634197', 'Lhash_array': ['1868146881869324040444168634197'], 'label': '2-770-385.157-c1-0-31', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/770/2/bv/a/157/24'}