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lfunc_lfunctions • Show schema
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{'Lhash': '192881191892790673572500397711,2085158679206751753637614048716', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 7, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 5, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 628.7963350437966, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[5, [1]], [17, [1, 0, 289]]], 'bad_primes': [5, 17], 'central_character': '425.1', 'coefficient_field': '1.1.1.1', 'conductor': 180625, 'conductor_radical': 85, 'degree': 4, 'euler_factors': [[1, 0, -7, 0, 64], [1, 0, -5, 0, 729], [1], [1, 0, -202, 0, 117649], [1, 128, 6758, 170368, 1771561], [1, 0, 935, 0, 4826809], [1, 0, 289], [1, -98, 16119, -672182, 47045881], [1, 0, -12234, 0, 148035889], [1, 310, 72803, 7560590, 594823321], [1, 394, 98391, 11737654, 887503681], [1, 0, 37078, 0, 2565726409], [1, 524, 206486, 36114604, 4750104241], [1, 0, -92450, 0, 6321363049], [1, 0, -207477, 0, 10779215329], [1, 0, 128655, 0, 22164361129], [1, -666, 521647, -136782414, 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'8.721083287934512315851003840689276', '9.143450675301090011209132432819622', '9.969677708016068659007001447033374', '10.00895928951662892675725726914823', '10.67648762926406493718688872876017', '11.26686393124493063682663692121544'], 'prelabel': '4-425e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.00757543652013, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3e2-0', 'trace_hash': 1203952750702234286, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.15215643163665453418015397651', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.64490016320848755474632482515', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.20060047896779106553108096465', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 628.7963350437966, 'bad_primes': [5, 17], 'central_character': '1.1', 'conductor': 180625, 'conductor_radical': 85, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 7, 0, 0, 0, 0, 5, 0, -128, 0, 0, 0, 0, -15, 0, 0, 98, 0, 0, 0, 0, 0, 0, 0, 0, 0, -310, 0, -394, 0, 0, 0, 0, 35, 0, 0, 0, 0, -524, 0, 0, -896, 0, 0, 0, 0, 202, 0, 0, 0, 0, 0, 0, 0, 0, 0, 666, 0, -710, 0, 0, -553, 0, 0, 0, 0, 0, 0, 94, 0, 0, 0, 0, 686, 0, 0, 768, 0, -704, 0, 0, 0, 0, 0, 0, 0, -1022, 0, 0, 0, 0, 0, 0, 0, 0, 0, -640, 0], 'euler11': [1, 128, 6758, 170368, 1771561], 'euler13': [1, 0, 935, 0, 4826809], 'euler17': [1, 0, 289, 0, 0], 'euler19': [1, -98, 16119, -672182, 47045881], 'euler2': [1, 0, -7, 0, 64], 'euler23': [1, 0, -12234, 0, 148035889], 'euler29': [1, 310, 72803, 7560590, 594823321], 'euler3': [1, 0, -5, 0, 729], 'euler31': [1, 394, 98391, 11737654, 887503681], 'euler37': [1, 0, 37078, 0, 2565726409], 'euler41': [1, 524, 206486, 36114604, 4750104241], 'euler43': [1, 0, -92450, 0, 6321363049], 'euler47': [1, 0, -207477, 0, 10779215329], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, 0, 128655, 0, 22164361129], 'euler59': [1, -666, 521647, -136782414, 42180533641], 'euler61': [1, 710, 579987, 161156510, 51520374361], 'euler67': [1, 0, 61070, 0, 90458382169], 'euler7': [1, 0, -202, 0, 117649], 'euler71': [1, -94, 718031, -33643634, 128100283921], 'euler73': [1, 0, -587065, 0, 151334226289], 'euler79': [1, -768, 1133534, -378653952, 243087455521], 'euler83': [1, 0, -601878, 0, 326940373369], 'euler89': [1, 1022, 1671059, 720478318, 496981290961], 'euler97': [1, 0, -1536977, 0, 832972004929], 'euler_factors': [[1, 0, -7, 0, 64], [1, 0, -5, 0, 729], [1, 0, 0, 0, 0], [1, 0, -202, 0, 117649], [1, 128, 6758, 170368, 1771561], [1, 0, 935, 0, 4826809], [1, 0, 289, 0, 0], [1, -98, 16119, -672182, 47045881], [1, 0, -12234, 0, 148035889], [1, 310, 72803, 7560590, 594823321], [1, 394, 98391, 11737654, 887503681], [1, 0, 37078, 0, 2565726409], [1, 524, 206486, 36114604, 4750104241], [1, 0, -92450, 0, 6321363049], [1, 0, -207477, 0, 10779215329], [1, 0, 128655, 0, 22164361129], [1, -666, 521647, -136782414, 42180533641], [1, 710, 579987, 161156510, 51520374361], [1, 0, 61070, 0, 90458382169], [1, -94, 718031, -33643634, 128100283921], [1, 0, -587065, 0, 151334226289], [1, -768, 1133534, -378653952, 243087455521], [1, 0, -601878, 0, 326940373369], [1, 1022, 1671059, 720478318, 496981290961], [1, 0, -1536977, 0, 832972004929]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/425/4/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': '4-425e2-1.1-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': '4-425e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.00757543652013, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e2-0', 'trace_hash': 1203952750702234286, 'z1': {'__RealLiteral__': 0, 'data': '0.15215643163665453418015397651', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '192881191892790673572500397711,2085158679206751753637614048716', 'Lhash_array': ['192881191892790673572500397711', '2085158679206751753637614048716'], 'factors': ['2-425-5.4-c3-0-4', '2-425-5.4-c3-0-55'], 'label': '4-425e2-1.1-c3e2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/425/4/b/a'}