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lfunc_lfunctions • Show schema
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{'Lhash': '1728436804220786008602026111874,2376897341515099811729140739785', 'a10': -4, 'a2': -2, 'a3': 2, 'a4': 3, 'a5': 2, 'a6': -4, 'a7': -2, 'a8': -4, 'a9': 2, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.611670552024722, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 2, 1]], [7, [1, 2, 1]], [17, [1, -2, 1]]], 'bad_primes': [2, 7, 17], 'central_character': '238.1', 'coefficient_field': '1.1.1.1', 'conductor': 56644, 'conductor_radical': 238, 'degree': 4, 'euler_factors': [[1, 2, 1], [1, -2, 2, -6, 9], [1, -2, 6, -10, 25], [1, 2, 1], [1, -6, 26, -66, 121], [1, -4, 10, -52, 169], [1, -2, 1], [1, 8, 34, 152, 361], [1, -16, 110, -368, 529], [1, -2, 14, -58, 841], [1, 12, 78, 372, 961], [1, 2, 70, 74, 1369], [1, 16, 126, 656, 1681], [1, 4, 70, 172, 1849], [1, -4, 78, -188, 2209], [1, 0, 86, 0, 2809], [1, 12, 154, 708, 3481], [1, 2, 118, 122, 3721], [1, 12, 150, 804, 4489], [1, -4, 126, -284, 5041], [1, 0, -34, 0, 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1.7123701009789793, -1.7339339367639184, -4.7330330446975015], 'positive_zeros': ['1.36349622199492200919804644331022', '1.87504138844501808137256975525106', '3.13391409231110049395176238943731', '3.28061967569918783190091349428573', '4.23178491420962269647117850282062', '5.31932687459869695779278148644316', '6.11347826531456823537239071133961', '6.66062702753093859465403758477351', '6.83921001446596737633967757559817', '7.41093439925521310147741227555143', '8.451991930124608559593159911554968', '8.610264838777983408651887538746993', '9.103938484655653492425357032400581', '9.173706923637329481742301738429066', '9.752887239297725819796461544628111', '10.36006400201378464173297109921340', '10.90494291763676779852377629712820', '10.98017512674928301187353752954436', '11.92612142471837471706435068419078', '12.28832103067981868195069364998984'], 'prelabel': '4-238e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.37856431409872, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e2-0', 'trace_hash': 1543583302828871488, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.36349622199492200919804644331', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.87504138844501808137256975525', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.13391409231110049395176238944', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.611670552024722, 'bad_primes': [2, 7, 17], 'central_character': '1.1', 'conductor': 56644, 'conductor_radical': 238, 'degree': 4, 'dirichlet_coefficients': [1, -2, 2, 3, 2, -4, -2, -4, 2, -4, 6, 6, 4, 4, 4, 5, 2, -4, -8, 6, -4, -12, 16, -8, -2, -8, 6, -6, 2, -8, -12, -6, 12, -4, -4, 6, -2, 16, 8, -8, -16, 8, -4, 18, 4, -32, 4, 10, 3, 4, 4, 12, 0, -12, 12, 8, -16, -4, -12, 12, -2, 24, -4, 7, 8, -24, -12, 6, 32, 8, 4, -8, 0, 4, -4, -24, -12, -16, -12, 10, 11, 32, 4, -12, 4, 8, 4, -24, 4, -8, -8, 48, -24, -8, -16, -12, -8, -6, 12, -6], 'euler11': [1, -6, 26, -66, 121], 'euler13': [1, -4, 10, -52, 169], 'euler17': [1, -2, 1, 0, 0], 'euler19': [1, 8, 34, 152, 361], 'euler2': [1, 2, 1, 0, 0], 'euler23': [1, -16, 110, -368, 529], 'euler29': [1, -2, 14, -58, 841], 'euler3': [1, -2, 2, -6, 9], 'euler31': [1, 12, 78, 372, 961], 'euler37': [1, 2, 70, 74, 1369], 'euler41': [1, 16, 126, 656, 1681], 'euler43': [1, 4, 70, 172, 1849], 'euler47': [1, -4, 78, -188, 2209], 'euler5': [1, -2, 6, -10, 25], 'euler53': [1, 0, 86, 0, 2809], 'euler59': [1, 12, 154, 708, 3481], 'euler61': [1, 2, 118, 122, 3721], 'euler67': [1, 12, 150, 804, 4489], 'euler7': [1, 2, 1, 0, 0], 'euler71': [1, -4, 126, -284, 5041], 'euler73': [1, 0, -34, 0, 5329], 'euler79': [1, 12, 174, 948, 6241], 'euler83': [1, -4, 170, -332, 6889], 'euler89': [1, -4, 182, -356, 7921], 'euler97': [1, 8, 190, 776, 9409], 'euler_factors': [[1, 2, 1, 0, 0], [1, -2, 2, -6, 9], [1, -2, 6, -10, 25], [1, 2, 1, 0, 0], [1, -6, 26, -66, 121], [1, -4, 10, -52, 169], [1, -2, 1, 0, 0], [1, 8, 34, 152, 361], [1, -16, 110, -368, 529], [1, -2, 14, -58, 841], [1, 12, 78, 372, 961], [1, 2, 70, 74, 1369], [1, 16, 126, 656, 1681], [1, 4, 70, 172, 1849], [1, -4, 78, -188, 2209], [1, 0, 86, 0, 2809], [1, 12, 154, 708, 3481], [1, 2, 118, 122, 3721], [1, 12, 150, 804, 4489], [1, -4, 126, -284, 5041], [1, 0, -34, 0, 5329], [1, 12, 174, 948, 6241], [1, -4, 170, -332, 6889], [1, -4, 182, -356, 7921], [1, 8, 190, 776, 9409]], 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/238/2/a/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': '4-238e2-1.1-c1e2-0-6', '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': 0, 'prelabel': '4-238e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.37856431409872, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1543583302828871488, 'z1': {'__RealLiteral__': 0, 'data': '1.36349622199492200919804644331', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1728436804220786008602026111874,2376897341515099811729140739785', 'Lhash_array': ['1728436804220786008602026111874', '2376897341515099811729140739785'], 'label': '4-238e2-1.1-c1e2-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/238/2/a/f'}