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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -1, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 1, 'Lhash': '1489564189767141199,1731115709754361337', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-0.5773502691896257, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 68.86173639196915, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [5, [1]]], 'bad_primes': [2, 3, 5], 'central_character': '1080000.1', 'coefficient_field': '1.1.1.1', 'conductor': 1080000, 'conductor_radical': 30, 'degree': 4, 'euler_factors': [[1], [1, 1], [1], [1, 0, 14, 0, 49], [1, 0, 6, 0, 121], [1, 12, 62, 156, 169], [1, 0, -2, 0, 289], [1, 8, 54, 152, 361], [1, 0, 46, 0, 529], [1, 0, 54, 0, 841], [1, 16, 126, 496, 961], [1, -4, 78, -148, 1369], [1, 0, 46, 0, 1681], [1, 24, 230, 1032, 1849], [1, 0, 30, 0, 2209], [1, 0, 70, 0, 2809], [1, 0, -26, 0, 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-0.1679781285981768, 0.03105977794245446, 0.42620015092538444], 'positive_zeros': ['1.76966313536701547243535553598981', '2.07933314479152275364533906757678', '2.69982664061727220731686131413420', '3.42683606015106566673715003849075', '4.03205568616657235432062033061064', '4.60954800977677454684167974744270', '4.95639818252911756604562729940319', '5.36683559095823513937522588288546', '5.65229906256087841325445637568929', '6.65963768785974737826480192145103', '6.71920497811244846696035723021189', '7.06475469847576410250018540799256', '7.55727707153378484774141976096546'], 'prelabel': '4-1080000-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.88067651747632, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 914836890307808585, 'z1': {'__RealLiteral__': 0, 'data': '1.76966313536701547243535553598981', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.07933314479152275364533906757678', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.69982664061727220731686131413420', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 68.86173639196915, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 1080000, 'conductor_radical': 30, 'degree': 4, 'dirichlet_coefficients': [1, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, -12, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -16, 0, 0, 0, 0, 0, 4, 0, 12, 0, 0, 0, -24, 0, 0, 0, 0, 0, -14, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 28, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, -16, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, -4, 0, 0, 0], 'euler11': [1, 0, 6, 0, 121], 'euler13': [1, 12, 62, 156, 169], 'euler17': [1, 0, -2, 0, 289], 'euler19': [1, 8, 54, 152, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, 46, 0, 529], 'euler29': [1, 0, 54, 0, 841], 'euler3': [1, 1, 0, 0, 0], 'euler31': [1, 16, 126, 496, 961], 'euler37': [1, -4, 78, -148, 1369], 'euler41': [1, 0, 46, 0, 1681], 'euler43': [1, 24, 230, 1032, 1849], 'euler47': [1, 0, 30, 0, 2209], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, 0, 70, 0, 2809], 'euler59': [1, 0, -26, 0, 3481], 'euler61': [1, -28, 318, -1708, 3721], 'euler67': [1, 8, 150, 536, 4489], 'euler7': [1, 0, 14, 0, 49], 'euler71': [1, 0, 78, 0, 5041], 'euler73': [1, -12, 182, -876, 5329], 'euler79': [1, 16, 222, 1264, 6241], 'euler83': [1, 0, 22, 0, 6889], 'euler89': [1, 0, 78, 0, 7921], 'euler97': [1, 4, 198, 388, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 1, 0, 0, 0], [1, 0, 0, 0, 0], [1, 0, 14, 0, 49], [1, 0, 6, 0, 121], [1, 12, 62, 156, 169], [1, 0, -2, 0, 289], [1, 8, 54, 152, 361], [1, 0, 46, 0, 529], [1, 0, 54, 0, 841], [1, 16, 126, 496, 961], [1, -4, 78, -148, 1369], [1, 0, 46, 0, 1681], [1, 24, 230, 1032, 1849], [1, 0, 30, 0, 2209], [1, 0, 70, 0, 2809], [1, 0, -26, 0, 3481], [1, -28, 318, -1708, 3721], [1, 8, 150, 536, 4489], [1, 0, 78, 0, 5041], [1, -12, 182, -876, 5329], [1, 16, 222, 1264, 6241], [1, 0, 22, 0, 6889], [1, 0, 78, 0, 7921], [1, 4, 198, 388, 9409]], 'index': 16, 'instance_types': ['BMF', 'ECNF'], 'instance_urls': ['ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/120000.1/c', 'EllipticCurve/2.0.3.1/120000.1/c'], 'is_instance_Artin': False, 'is_instance_BMF': True, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': True, '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': '4-1080000-1.1-c1e2-0-16', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 2, 'prelabel': '4-1080000-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.88067651747632, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 914836890307808585, 'z1': {'__RealLiteral__': 0, 'data': '1.76966313536701547243535553598981', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9694757
{'Lhash': '1489564189767141199,1731115709754361337', 'Lhash_array': ['1489564189767141199', '1731115709754361337'], 'label': '4-1080000-1.1-c1e2-0-16', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.3.1/120000.1/c'}
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id: 9694870
{'Lhash': '1489564189767141199,1731115709754361337', 'Lhash_array': ['1489564189767141199', '1731115709754361337'], 'label': '4-1080000-1.1-c1e2-0-16', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/120000.1/c'}