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lfunc_lfunctions • Show schema
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{'Lhash': '1371366205135776306561567197231,4007862669372949899638369442992', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': -4, 'a5': 20, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 5, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 17.058004383195037, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 0, 4]], [5, [1, -20, 125]], [7, [1, 0, 49]]], 'bad_primes': [2, 5, 7], 'central_character': '70.1', 'coefficient_field': '1.1.1.1', 'conductor': 4900, 'conductor_radical': 70, 'degree': 4, 'euler_factors': [[1, 0, 4], [1, 0, -5, 0, 729], [1, -20, 125], [1, 0, 49], [1, 74, 4031, 98494, 1771561], [1, 0, -1793, 0, 4826809], [1, 0, -8145, 0, 24137569], [1, -216, 25382, -1481544, 47045881], [1, 0, -19434, 0, 148035889], [1, -498, 110779, -12145722, 594823321], [1, 268, 77538, 7983988, 887503681], [1, 0, 10250, 0, 2565726409], [1, -412, 180278, -28395452, 4750104241], [1, 0, -17638, 0, 6321363049], [1, 0, -125277, 0, 10779215329], [1, 0, -297718, 0, 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 17.058004383195037, 'bad_primes': [2, 5, 7], 'central_character': '1.1', 'conductor': 4900, 'conductor_radical': 70, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, -4, 20, 0, 0, 0, 5, 0, -74, 0, 0, 0, 0, 16, 0, 0, 216, -80, 0, 0, 0, 0, 275, 0, 0, 0, 498, 0, -268, 0, 0, 0, 0, -20, 0, 0, 0, 0, 412, 0, 0, 296, 100, 0, 0, 0, -49, 0, 0, 0, 0, 0, -1480, 0, 0, 0, 4, 0, -1880, 0, 0, -64, 0, 0, 0, 0, 0, 0, 912, 0, 0, 0, 0, -864, 0, 0, 2478, 320, -704, 0, 0, 0, 0, 0, 0, 0, 440, 0, 0, 0, 0, 0, 4320, 0, 0, 0, -370, -1100], 'euler11': [1, 74, 4031, 98494, 1771561], 'euler13': [1, 0, -1793, 0, 4826809], 'euler17': [1, 0, -8145, 0, 24137569], 'euler19': [1, -216, 25382, -1481544, 47045881], 'euler2': [1, 0, 4, 0, 0], 'euler23': [1, 0, -19434, 0, 148035889], 'euler29': [1, -498, 110779, -12145722, 594823321], 'euler3': [1, 0, -5, 0, 729], 'euler31': [1, 268, 77538, 7983988, 887503681], 'euler37': [1, 0, 10250, 0, 2565726409], 'euler41': [1, -412, 180278, -28395452, 4750104241], 'euler43': [1, 0, -17638, 0, 6321363049], 'euler47': [1, 0, -125277, 0, 10779215329], 'euler5': [1, -20, 125, 0, 0], 'euler53': [1, 0, -297718, 0, 22164361129], 'euler59': [1, -4, 410762, -821516, 42180533641], 'euler61': [1, 1880, 1337562, 426724280, 51520374361], 'euler67': [1, 0, -590290, 0, 90458382169], 'euler7': [1, 0, 49, 0, 0], 'euler71': [1, -912, 923758, -326414832, 128100283921], 'euler73': [1, 0, -355534, 0, 151334226289], 'euler79': [1, -2478, 2521199, -1221750642, 243087455521], 'euler83': [1, 0, -960390, 0, 326940373369], 'euler89': [1, -440, 1458338, -310186360, 496981290961], 'euler97': [1, 0, -712321, 0, 832972004929], 'euler_factors': [[1, 0, 4, 0, 0], [1, 0, -5, 0, 729], [1, -20, 125, 0, 0], [1, 0, 49, 0, 0], [1, 74, 4031, 98494, 1771561], [1, 0, -1793, 0, 4826809], [1, 0, -8145, 0, 24137569], [1, -216, 25382, -1481544, 47045881], [1, 0, -19434, 0, 148035889], [1, -498, 110779, -12145722, 594823321], [1, 268, 77538, 7983988, 887503681], [1, 0, 10250, 0, 2565726409], [1, -412, 180278, -28395452, 4750104241], [1, 0, -17638, 0, 6321363049], [1, 0, -125277, 0, 10779215329], [1, 0, -297718, 0, 22164361129], [1, -4, 410762, -821516, 42180533641], [1, 1880, 1337562, 426724280, 51520374361], [1, 0, -590290, 0, 90458382169], [1, -912, 923758, -326414832, 128100283921], [1, 0, -355534, 0, 151334226289], [1, -2478, 2521199, -1221750642, 243087455521], [1, 0, -960390, 0, 326940373369], [1, -440, 1458338, -310186360, 496981290961], [1, 0, -712321, 0, 832972004929]], 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/70/4/c/a'], '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': '4-70e2-1.1-c3e2-0-1', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3, 3], 'order_of_vanishing': 0, 'prelabel': '4-70e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.032273037857326, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e2-0', 'trace_hash': 1560179114445179381, 'z1': {'__RealLiteral__': 0, 'data': '1.08181718597291226594940416913', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1371366205135776306561567197231,4007862669372949899638369442992', 'Lhash_array': ['1371366205135776306561567197231', '4007862669372949899638369442992'], 'label': '4-70e2-1.1-c3e2-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/70/4/c/a'}