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lfunc_lfunctions • Show schema
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{'Lhash': '746213779822805651228681623714', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': -5, 'a6': 0, 'a7': -32, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 42.481375204133265, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1, 5]]], 'bad_primes': [2, 3, 5], 'central_character': '720.1', 'coefficient_field': '1.1.1.1', 'conductor': 720, 'conductor_radical': 30, 'degree': 2, 'euler_factors': [[1], [1], [1, 5], [1, 32, 343], [1, -36, 1331], [1, 10, 2197], [1, -78, 4913], [1, 140, 6859], [1, 192, 12167], [1, 6, 24389], [1, -16, 29791], [1, 34, 50653], [1, -390, 68921], [1, -52, 79507], [1, -408, 103823], [1, -114, 148877], [1, -516, 205379], [1, 58, 226981], [1, -892, 300763], [1, 120, 357911], [1, 646, 389017], [1, -1168, 493039], [1, 732, 571787], [1, -1590, 704969], [1, -194, 912673], [1, 798, 1030301], [1, 272, 1092727], [1, -156, 1225043], [1, -1622, 1295029], [1, 1074, 1442897]], 'euler_factors_factorization': [[1], [1], [[[1, 5], 1]], [[[1, 32, 343], 1]], [[[1, -36, 1331], 1]], [[[1, 10, 2197], 1]], [[[1, -78, 4913], 1]], [[[1, 140, 6859], 1]], [[[1, 192, 12167], 1]], [[[1, 6, 24389], 1]], [[[1, -16, 29791], 1]], [[[1, 34, 50653], 1]], [[[1, -390, 68921], 1]], [[[1, -52, 79507], 1]], [[[1, -408, 103823], 1]], [[[1, -114, 148877], 1]], [[[1, -516, 205379], 1]], [[[1, 58, 226981], 1]], [[[1, -892, 300763], 1]], [[[1, 120, 357911], 1]], [[[1, 646, 389017], 1]], [[[1, -1168, 493039], 1]], [[[1, 732, 571787], 1]], [[[1, -1590, 704969], 1]], [[[1, -194, 912673], 1]], [[[1, 798, 1030301], 1]], [[[1, 272, 1092727], 1]], [[[1, -156, 1225043], 1]], [[[1, -1622, 1295029], 1]], [[[1, 1074, 1442897], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 2, 'label': '2-720-1.1-c3-0-2', 'leading_term': '1.135901801147528016572960935833000000000000000000000000000000000000000000000000000000000000', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/720/4/a/c', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.135901801147528, 1.1236911300539525, 1.0871721082926304, 1.026684417368334, 0.9427964664674081, 0.8363085149230898, 0.7082564808265955, 0.5599159010038632, 0.3928053934873811, 0.20868888625548196, 0.009575819008145794, -0.20228149939197493, -0.42439418506571847, -0.6540474873954262, -0.8883165953415119, -1.1240881146906814, -1.3580876480980835, -1.5869137418191177, -1.807078271864253, -2.0150531323022682, -2.2073228645084577, -2.38044263377269, -2.531100724824185, -2.656184496932107, -2.7528485191305307, -2.8185834039127786, -2.8512836807264175, -2.8493129060591933, -2.811564101925184, -2.737513555806987, -2.6272660085847686, -2.4815893077590867, -2.301936715228953, -2.090455234440768, -1.8499785615984603, 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2.861468671754799, 3.131503121369532, 3.2924769516046153, 3.3339257354792204, 3.2515647553915685, 3.0476410610028086, 2.730923688597665, 2.3163271764151614, 1.8241843331458356, 1.2792044676743626, 0.7091717909994498, 0.14345435793951597, -0.38859422783701825, -0.8592508190774474, -1.2439646663211106, -1.5227365453762358, -1.6812545303403235, -1.7117188747735692, -1.6133055808199175, -1.3922385335686167, -1.061462417951562, -0.6399317391759303, -0.15155378817625037, 0.3761560056794468, 0.9136304578651009, 1.430929683362253, 1.8994456637831374, 2.2935327250991664], 'positive_zeros': ['0.58865887783941126036912053374284', '2.34996550677371331764509638286102', '3.61923333518334604060585225870407', '4.16243700642419100532598394699082', '5.83717832399257337782806826056670', '6.41117117781216744707866810814905', '7.30205102656031344667386087786947', '8.347613759734358918530732483072121', '9.277064500079016034987917324072711', '9.948943151524774269076606562535824'], 'prelabel': '2-720-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.517773792034613, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'trace_hash': 406468585459467938, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.58865887783941126036912053374', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.34996550677371331764509638286', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.61923333518334604060585225870', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 42.481375204133265, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 720, 'conductor_radical': 30, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, -5, 0, -32, 0, 0, 0, 36, 0, -10, 0, 0, 0, 78, 0, -140, 0, 0, 0, -192, 0, 25, 0, 0, 0, -6, 0, 16, 0, 0, 0, 160, 0, -34, 0, 0, 0, 390, 0, 52, 0, 0, 0, 408, 0, 681, 0, 0, 0, 114, 0, -180, 0, 0, 0, 516, 0, -58, 0, 0, 0, 50, 0, 892, 0, 0, 0, -120, 0, -646, 0, 0, 0, -1152, 0, 1168, 0, 0, 0, -732, 0, -390, 0, 0, 0, 1590, 0, 320, 0, 0, 0, 700, 0, 194, 0, 0, 0], 'euler11': [1, -36, 1331], 'euler13': [1, 10, 2197], 'euler17': [1, -78, 4913], 'euler19': [1, 140, 6859], 'euler2': [1, 0, 0], 'euler23': [1, 192, 12167], 'euler29': [1, 6, 24389], 'euler3': [1, 0, 0], 'euler31': [1, -16, 29791], 'euler37': [1, 34, 50653], 'euler41': [1, -390, 68921], 'euler43': [1, -52, 79507], 'euler47': [1, -408, 103823], 'euler5': [1, 5, 0], 'euler53': [1, -114, 148877], 'euler59': [1, -516, 205379], 'euler61': [1, 58, 226981], 'euler67': [1, -892, 300763], 'euler7': [1, 32, 343], 'euler71': [1, 120, 357911], 'euler73': [1, 646, 389017], 'euler79': [1, -1168, 493039], 'euler83': [1, 732, 571787], 'euler89': [1, -1590, 704969], 'euler97': [1, -194, 912673], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 5, 0], [1, 32, 343], [1, -36, 1331], [1, 10, 2197], [1, -78, 4913], [1, 140, 6859], [1, 192, 12167], [1, 6, 24389], [1, -16, 29791], [1, 34, 50653], [1, -390, 68921], [1, -52, 79507], [1, -408, 103823], [1, -114, 148877], [1, -516, 205379], [1, 58, 226981], [1, -892, 300763], [1, 120, 357911], [1, 646, 389017], [1, -1168, 493039], [1, 732, 571787], [1, -1590, 704969], [1, -194, 912673]], 'index': 2, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/720/4/a/c/1/1', 'ModularForm/GL2/Q/holomorphic/720/4/a/c'], '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': '2-720-1.1-c3-0-2', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-720-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.517773792034613, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 406468585459467938, 'z1': {'__RealLiteral__': 0, 'data': '0.58865887783941126036912053374', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20472468
{'Lhash': '746213779822805651228681623714', 'Lhash_array': ['746213779822805651228681623714'], 'label': '2-720-1.1-c3-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/720/4/a/c'}
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id: 24569810
{'Lhash': '746213779822805651228681623714', 'Lhash_array': ['746213779822805651228681623714'], 'label': '2-720-1.1-c3-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/720/4/a/c/1/1'}