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lfunc_lfunctions • Show schema
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{'Lhash': '724158775032163022665881201944,1407327012925588140407416500685', 'a10': 0, 'a2': 1, 'a3': 0, 'a4': 9, 'a5': 0, 'a6': 0, 'a7': -24, 'a8': 25, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 21324.681244859, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [5, [1]], [11, [1, -22, 121]]], 'bad_primes': [3, 5, 11], 'central_character': '2475.1', 'coefficient_field': '1.1.1.1', 'conductor': 6125625, 'conductor_radical': 165, 'degree': 4, 'euler_factors': [[1, -1, -8, -8, 64], [1], [1], [1, 24, 442, 8232, 117649], [1, -22, 121], [1, 30, 4522, 65910, 4826809], [1, -106, 7882, -520778, 24137569], [1, -50, 14246, -342950, 47045881], [1, -134, 26398, -1630378, 148035889], [1, -198, 57706, -4829022, 594823321], [1, -360, 90430, -10724760, 887503681], [1, -328, 62630, -16614184, 2565726409], [1, -782, 285970, -53896222, 4750104241], [1, 386, 179870, 30689702, 6321363049], [1, -266, 92542, -27616918, 10779215329], 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False, 'rational': True, 'root_analytic_conductor': 12.084276033929715, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3e2-0', 'trace_hash': 1062205849442892564, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.57126054679561116444234669376', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.11018526135846204203044094696', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.27496928258631777666068177414', 'prec': 103}}
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{'algebraic': True, 'analytic_conductor': 21324.681244859, 'bad_primes': [3, 5, 11], 'central_character': '1.1', 'conductor': 6125625, 'conductor_radical': 165, 'degree': 4, 'dirichlet_coefficients': [1, 1, 0, 9, 0, 0, -24, 25, 0, 0, 22, 0, -30, -24, 0, 41, 106, 0, 50, 0, 0, 22, 134, 0, 0, -30, 0, -216, 198, 0, 360, 249, 0, 106, 0, 0, 328, 50, 0, 0, 782, 0, -386, 198, 0, 134, 266, 0, 134, 0, 0, -270, -522, 0, 0, -600, 0, 198, 172, 0, -778, 360, 0, 201, 0, 0, 776, 954, 0, 0, -630, 0, -1296, 328, 0, 450, -528, 0, 652, 0, 0, 782, -324, 0, 0, -386, 0, 550, 756, 0, 720, 1206, 0, 266, 0, 0, 452, 134, 0, 0], 'euler11': [1, -22, 121, 0, 0], 'euler13': [1, 30, 4522, 65910, 4826809], 'euler17': [1, -106, 7882, -520778, 24137569], 'euler19': [1, -50, 14246, -342950, 47045881], 'euler2': [1, -1, -8, -8, 64], 'euler23': [1, -134, 26398, -1630378, 148035889], 'euler29': [1, -198, 57706, -4829022, 594823321], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, -360, 90430, -10724760, 887503681], 'euler37': [1, -328, 62630, -16614184, 2565726409], 'euler41': [1, -782, 285970, -53896222, 4750104241], 'euler43': [1, 386, 179870, 30689702, 6321363049], 'euler47': [1, -266, 92542, -27616918, 10779215329], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, 522, 295162, 77713794, 22164361129], 'euler59': [1, -172, 175654, -35325188, 42180533641], 'euler61': [1, 778, 577250, 176591218, 51520374361], 'euler67': [1, -776, 528582, -233392088, 90458382169], 'euler7': [1, 24, 442, 8232, 117649], 'euler71': [1, 630, 744334, 225483930, 128100283921], 'euler73': [1, 1296, 1178926, 504166032, 151334226289], 'euler79': [1, -652, 589506, -321461428, 243087455521], 'euler83': [1, 324, 579670, 185258988, 326940373369], 'euler89': [1, -756, 1427110, -532956564, 496981290961], 'euler97': [1, -452, 982470, -412528196, 832972004929], 'euler_factors': [[1, -1, -8, -8, 64], [1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 24, 442, 8232, 117649], [1, -22, 121, 0, 0], [1, 30, 4522, 65910, 4826809], [1, -106, 7882, -520778, 24137569], [1, -50, 14246, -342950, 47045881], [1, -134, 26398, -1630378, 148035889], [1, -198, 57706, -4829022, 594823321], [1, -360, 90430, -10724760, 887503681], [1, -328, 62630, -16614184, 2565726409], [1, -782, 285970, -53896222, 4750104241], [1, 386, 179870, 30689702, 6321363049], [1, -266, 92542, -27616918, 10779215329], [1, 522, 295162, 77713794, 22164361129], [1, -172, 175654, -35325188, 42180533641], [1, 778, 577250, 176591218, 51520374361], [1, -776, 528582, -233392088, 90458382169], [1, 630, 744334, 225483930, 128100283921], [1, 1296, 1178926, 504166032, 151334226289], [1, -652, 589506, -321461428, 243087455521], [1, 324, 579670, 185258988, 326940373369], [1, -756, 1427110, -532956564, 496981290961], [1, -452, 982470, -412528196, 832972004929]], 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2475/4/a/p'], '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': '4-2475e2-1.1-c3e2-0-4', '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': '4-2475e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 12.084276033929715, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e2-0', 'trace_hash': 1062205849442892564, 'z1': {'__RealLiteral__': 0, 'data': '0.57126054679561116444234669376', 'prec': 103}}
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{'Lhash': '724158775032163022665881201944,1407327012925588140407416500685', 'Lhash_array': ['724158775032163022665881201944', '1407327012925588140407416500685'], 'label': '4-2475e2-1.1-c3e2-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2475/4/a/p'}