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lfunc_lfunctions • Show schema
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{'Lhash': '57861192337471718729834378322,1495419222707740671198144386191', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': -4, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6344.533262933256, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 0, 4]], [3, [1]], [5, [1]]], 'bad_primes': [2, 3, 5], 'central_character': '1350.1', 'coefficient_field': '1.1.1.1', 'conductor': 1822500, 'conductor_radical': 30, 'degree': 4, 'euler_factors': [[1, 0, 4], [1], [1], [1, 0, -517, 0, 117649], [1, 60, 3562, 79860, 1771561], [1, 0, -673, 0, 4826809], [1, 0, -9682, 0, 24137569], [1, -98, 16119, -672182, 47045881], [1, 0, -24010, 0, 148035889], [1, -372, 83374, -9072708, 594823321], [1, 320, 85182, 9533120, 887503681], [1, 0, -93025, 0, 2565726409], [1, -756, 280726, -52104276, 4750104241], [1, 0, -87190, 0, 6321363049], [1, 0, -186910, 0, 10779215329], [1, 0, 27146, 0, 22164361129], [1, 408, 452374, 83794632, 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'8.953832419026667716413265868581510', '9.564761769758543862653475748843948'], 'prelabel': '4-1350e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.924829326533358, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3e2-0', 'trace_hash': 1432978857852172823, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.04564443256450501203090249758', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.17967776171013015864471717909', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.40439505451726550675672085872', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6344.533262933256, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 1822500, 'conductor_radical': 30, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, -4, 0, 0, 0, 0, 0, 0, -60, 0, 0, 0, 0, 16, 0, 0, 98, 0, 0, 0, 0, 0, 0, 0, 0, 0, 372, 0, -320, 0, 0, 0, 0, 0, 0, 0, 0, 0, 756, 0, 0, 240, 0, 0, 0, 0, 517, 0, 0, 0, 0, 0, 0, 0, 0, 0, -408, 0, -1754, 0, 0, -64, 0, 0, 0, 0, 0, 0, -1212, 0, 0, 0, 0, -392, 0, 0, -2302, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1968, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler11': [1, 60, 3562, 79860, 1771561], 'euler13': [1, 0, -673, 0, 4826809], 'euler17': [1, 0, -9682, 0, 24137569], 'euler19': [1, -98, 16119, -672182, 47045881], 'euler2': [1, 0, 4, 0, 0], 'euler23': [1, 0, -24010, 0, 148035889], 'euler29': [1, -372, 83374, -9072708, 594823321], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 320, 85182, 9533120, 887503681], 'euler37': [1, 0, -93025, 0, 2565726409], 'euler41': [1, -756, 280726, -52104276, 4750104241], 'euler43': [1, 0, -87190, 0, 6321363049], 'euler47': [1, 0, -186910, 0, 10779215329], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, 0, 27146, 0, 22164361129], 'euler59': [1, 408, 452374, 83794632, 42180533641], 'euler61': [1, 1754, 1223091, 398124674, 51520374361], 'euler67': [1, 0, -566557, 0, 90458382169], 'euler7': [1, 0, -517, 0, 117649], 'euler71': [1, 1212, 1083058, 433788132, 128100283921], 'euler73': [1, 0, -592273, 0, 151334226289], 'euler79': [1, 2302, 2310879, 1134975778, 243087455521], 'euler83': [1, 0, -1133170, 0, 326940373369], 'euler89': [1, 1968, 2378194, 1387378992, 496981290961], 'euler97': [1, 0, -1755121, 0, 832972004929], 'euler_factors': [[1, 0, 4, 0, 0], [1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 0, -517, 0, 117649], [1, 60, 3562, 79860, 1771561], [1, 0, -673, 0, 4826809], [1, 0, -9682, 0, 24137569], [1, -98, 16119, -672182, 47045881], [1, 0, -24010, 0, 148035889], [1, -372, 83374, -9072708, 594823321], [1, 320, 85182, 9533120, 887503681], [1, 0, -93025, 0, 2565726409], [1, -756, 280726, -52104276, 4750104241], [1, 0, -87190, 0, 6321363049], [1, 0, -186910, 0, 10779215329], [1, 0, 27146, 0, 22164361129], [1, 408, 452374, 83794632, 42180533641], [1, 1754, 1223091, 398124674, 51520374361], [1, 0, -566557, 0, 90458382169], [1, 1212, 1083058, 433788132, 128100283921], [1, 0, -592273, 0, 151334226289], [1, 2302, 2310879, 1134975778, 243087455521], [1, 0, -1133170, 0, 326940373369], [1, 1968, 2378194, 1387378992, 496981290961], [1, 0, -1755121, 0, 832972004929]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1350/4/c/f'], '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': '4-1350e2-1.1-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': '4-1350e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.924829326533358, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e2-0', 'trace_hash': 1432978857852172823, 'z1': {'__RealLiteral__': 0, 'data': '0.04564443256450501203090249758', 'prec': 103}}
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{'Lhash': '57861192337471718729834378322,1495419222707740671198144386191', 'Lhash_array': ['57861192337471718729834378322', '1495419222707740671198144386191'], 'label': '4-1350e2-1.1-c3e2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1350/4/c/f'}