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lfunc_lfunctions • Show schema
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{'Lhash': '1360236014284849745754606778837,2390305014856235481849228306412', 'a10': 20, 'a2': 2, 'a3': 10, 'a4': -2, 'a5': 10, 'a6': 20, 'a7': 0, 'a8': 0, 'a9': 21, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 208.9605536941392, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[5, [1, -10, 25]], [7, [1]]], 'bad_primes': [5, 7], 'central_character': '245.1', 'coefficient_field': '1.1.1.1', 'conductor': 60025, 'conductor_radical': 35, 'degree': 4, 'euler_factors': [[1, -2, 6, -16, 64], [1, -10, 79, -270, 729], [1, -10, 25], [1], [1, -66, 3575, -87846, 1771561], [1, -10, 19, -21970, 4826809], [1, -70, 6651, -343910, 24137569], [1, -140, 14218, -960260, 47045881], [1, 16, 15774, 194672, 148035889], [1, 258, 40075, 6292362, 594823321], [1, 20, 20082, 595820, 887503681], [1, -328, 106906, -16614184, 2565726409], [1, -300, 50342, -20676300, 4750104241], [1, 116, 160794, 9222812, 6321363049], [1, 30, 190271, 3114690, 10779215329], [1, 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'trace_hash': 1340805550264410612, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.07303701354296771552814746054', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.88561817777381399392277858905', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.62346085043667259630895313482', 'prec': 103}}
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{'algebraic': True, 'analytic_conductor': 208.9605536941392, 'bad_primes': [5, 7], 'central_character': '1.1', 'conductor': 60025, 'conductor_radical': 35, 'degree': 4, 'dirichlet_coefficients': [1, 2, 10, -2, 10, 20, 0, 0, 21, 20, 66, -20, 10, 0, 100, -20, 70, 42, 140, -20, 0, 132, -16, 0, 75, 20, -310, 0, -258, 200, -20, -200, 660, 140, 0, -42, 328, 280, 100, 0, 300, 0, -116, -132, 210, -32, -30, -200, 0, 150, 700, -20, 540, -620, 660, 0, 1400, -516, 380, -200, 1080, -40, 0, -152, 100, 1320, 468, -140, -160, 0, -1056, 0, -860, 656, 750, -280, 0, 200, 158, -200, -2788, 600, 40, 0, 700, -232, -2580, 0, -240, 420, 0, 32, -200, -60, 1400, -2000, 1630, 0, 1386, -150], 'euler11': [1, -66, 3575, -87846, 1771561], 'euler13': [1, -10, 19, -21970, 4826809], 'euler17': [1, -70, 6651, -343910, 24137569], 'euler19': [1, -140, 14218, -960260, 47045881], 'euler2': [1, -2, 6, -16, 64], 'euler23': [1, 16, 15774, 194672, 148035889], 'euler29': [1, 258, 40075, 6292362, 594823321], 'euler3': [1, -10, 79, -270, 729], 'euler31': [1, 20, 20082, 595820, 887503681], 'euler37': [1, -328, 106906, -16614184, 2565726409], 'euler41': [1, -300, 50342, -20676300, 4750104241], 'euler43': [1, 116, 160794, 9222812, 6321363049], 'euler47': [1, 30, 190271, 3114690, 10779215329], 'euler5': [1, -10, 25, 0, 0], 'euler53': [1, -540, 212254, -80393580, 22164361129], 'euler59': [1, -380, 429258, -78044020, 42180533641], 'euler61': [1, -1080, 705962, -245139480, 51520374361], 'euler67': [1, -468, 554906, -140757084, 90458382169], 'euler7': [1, 0, 0, 0, 0], 'euler71': [1, 1056, 949550, 377954016, 128100283921], 'euler73': [1, 860, 522934, 334554620, 151334226289], 'euler79': [1, -158, -339825, -77900162, 243087455521], 'euler83': [1, -40, 703974, -22871480, 326940373369], 'euler89': [1, 240, -164062, 169192560, 496981290961], 'euler97': [1, -1630, 2133171, -1487656990, 832972004929], 'euler_factors': [[1, -2, 6, -16, 64], [1, -10, 79, -270, 729], [1, -10, 25, 0, 0], [1, 0, 0, 0, 0], [1, -66, 3575, -87846, 1771561], [1, -10, 19, -21970, 4826809], [1, -70, 6651, -343910, 24137569], [1, -140, 14218, -960260, 47045881], [1, 16, 15774, 194672, 148035889], [1, 258, 40075, 6292362, 594823321], [1, 20, 20082, 595820, 887503681], [1, -328, 106906, -16614184, 2565726409], [1, -300, 50342, -20676300, 4750104241], [1, 116, 160794, 9222812, 6321363049], [1, 30, 190271, 3114690, 10779215329], [1, -540, 212254, -80393580, 22164361129], [1, -380, 429258, -78044020, 42180533641], [1, -1080, 705962, -245139480, 51520374361], [1, -468, 554906, -140757084, 90458382169], [1, 1056, 949550, 377954016, 128100283921], [1, 860, 522934, 334554620, 151334226289], [1, -158, -339825, -77900162, 243087455521], [1, -40, 703974, -22871480, 326940373369], [1, 240, -164062, 169192560, 496981290961], [1, -1630, 2133171, -1487656990, 832972004929]], 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/245/4/a/j'], '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': '4-245e2-1.1-c3e2-0-8', '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': '4-245e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.802034712020191, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e2-0', 'trace_hash': 1340805550264410612, 'z1': {'__RealLiteral__': 0, 'data': '1.07303701354296771552814746054', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1360236014284849745754606778837,2390305014856235481849228306412', 'Lhash_array': ['1360236014284849745754606778837', '2390305014856235481849228306412'], 'label': '4-245e2-1.1-c3e2-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/245/4/a/j'}