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lfunc_lfunctions • Show schema
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{'Lhash': '5021615502025887370595933477214,6726994036749113407839560496033', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': -4, 'a5': -10, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 50, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.34812253843255175, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 0, 4]], [5, [1, 10, 125]]], 'bad_primes': [2, 5], 'central_character': '10.1', 'coefficient_field': '1.1.1.1', 'conductor': 100, 'conductor_radical': 10, 'degree': 4, 'euler_factors': [[1, 0, 4], [1, 0, -50, 0, 729], [1, 10, 125], [1, 0, -10, 0, 117649], [1, 56, 3446, 74536, 1771561], [1, 0, -4250, 0, 4826809], [1, 0, -5730, 0, 24137569], [1, -120, 17318, -823080, 47045881], [1, 0, -20970, 0, 148035889], [1, 180, 56878, 4390020, 594823321], [1, 256, 75966, 7626496, 887503681], [1, 0, -45610, 0, 2565726409], [1, -484, 196406, -33357764, 4750104241], [1, 0, -27970, 0, 6321363049], [1, 0, -156570, 0, 10779215329], [1, 0, -286090, 0, 22164361129], [1, 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{'algebraic': True, 'analytic_conductor': 0.34812253843255175, 'bad_primes': [2, 5], 'central_character': '1.1', 'conductor': 100, 'conductor_radical': 10, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, -4, -10, 0, 0, 0, 50, 0, -56, 0, 0, 0, 0, 16, 0, 0, 120, 40, 0, 0, 0, 0, -25, 0, 0, 0, -180, 0, -256, 0, 0, 0, 0, -200, 0, 0, 0, 0, 484, 0, 0, 224, -500, 0, 0, 0, 10, 0, 0, 0, 0, 0, 560, 0, 0, 0, 40, 0, 1084, 0, 0, -64, 0, 0, 0, 0, 0, 0, -2256, 0, 0, 0, 0, -480, 0, 0, 1440, -160, 1771, 0, 0, 0, 0, 0, 0, 0, 980, 0, 0, 0, 0, 0, -1200, 0, 0, 0, -2800, 100], 'euler11': [1, 56, 3446, 74536, 1771561], 'euler13': [1, 0, -4250, 0, 4826809], 'euler17': [1, 0, -5730, 0, 24137569], 'euler19': [1, -120, 17318, -823080, 47045881], 'euler2': [1, 0, 4, 0, 0], 'euler23': [1, 0, -20970, 0, 148035889], 'euler29': [1, 180, 56878, 4390020, 594823321], 'euler3': [1, 0, -50, 0, 729], 'euler31': [1, 256, 75966, 7626496, 887503681], 'euler37': [1, 0, -45610, 0, 2565726409], 'euler41': [1, -484, 196406, -33357764, 4750104241], 'euler43': [1, 0, -27970, 0, 6321363049], 'euler47': [1, 0, -156570, 0, 10779215329], 'euler5': [1, 10, 125, 0, 0], 'euler53': [1, 0, -286090, 0, 22164361129], 'euler59': [1, -40, 411158, -8215160, 42180533641], 'euler61': [1, -1084, 747726, -246047404, 51520374361], 'euler67': [1, 0, -413170, 0, 90458382169], 'euler7': [1, 0, -10, 0, 117649], 'euler71': [1, 2256, 1988206, 807447216, 128100283921], 'euler73': [1, 0, -378610, 0, 151334226289], 'euler79': [1, -1440, 1504478, -709976160, 243087455521], 'euler83': [1, 0, -915090, 0, 326940373369], 'euler89': [1, -980, 1650038, -690869620, 496981290961], 'euler97': [1, 0, 294590, 0, 832972004929], 'euler_factors': [[1, 0, 4, 0, 0], [1, 0, -50, 0, 729], [1, 10, 125, 0, 0], [1, 0, -10, 0, 117649], [1, 56, 3446, 74536, 1771561], [1, 0, -4250, 0, 4826809], [1, 0, -5730, 0, 24137569], [1, -120, 17318, -823080, 47045881], [1, 0, -20970, 0, 148035889], [1, 180, 56878, 4390020, 594823321], [1, 256, 75966, 7626496, 887503681], [1, 0, -45610, 0, 2565726409], [1, -484, 196406, -33357764, 4750104241], [1, 0, -27970, 0, 6321363049], [1, 0, -156570, 0, 10779215329], [1, 0, -286090, 0, 22164361129], [1, -40, 411158, -8215160, 42180533641], [1, -1084, 747726, -246047404, 51520374361], [1, 0, -413170, 0, 90458382169], [1, 2256, 1988206, 807447216, 128100283921], [1, 0, -378610, 0, 151334226289], [1, -1440, 1504478, -709976160, 243087455521], [1, 0, -915090, 0, 326940373369], [1, -980, 1650038, -690869620, 496981290961], [1, 0, 294590, 0, 832972004929]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/10/4/b/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': '4-10e2-1.1-c3e2-0-0', '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': '4-10e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.7681270077646055, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e2-0', 'trace_hash': 1910513017018989661, 'z1': {'__RealLiteral__': 0, 'data': '3.96135615060000715278264354271', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '5021615502025887370595933477214,6726994036749113407839560496033', 'Lhash_array': ['5021615502025887370595933477214', '6726994036749113407839560496033'], 'label': '4-10e2-1.1-c3e2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/10/4/b/a'}