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lfunc_lfunctions • Show schema
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{'Lhash': '663919480448718657201512804513,2857163350008453972922806509459', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': -1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 60.612674220014505, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, 0, 1]], [5, [1]], [13, [1, 0, 1]]], 'bad_primes': [3, 5, 13], 'central_character': '975.1', 'coefficient_field': '1.1.1.1', 'conductor': 950625, 'conductor_radical': 195, 'degree': 4, 'euler_factors': [[1, 0, 0, 0, 4], [1, 0, 1], [1], [1, 0, -5, 0, 49], [1, 2, 23, 22, 121], [1, 0, 1], [1, 0, -33, 0, 289], [1, -4, 42, -76, 361], [1, 0, -37, 0, 529], [1, -4, 62, -116, 841], [1, 12, 98, 372, 961], [1, 0, 47, 0, 1369], [1, 10, 107, 410, 1681], [1, 0, -70, 0, 1849], [1, 0, 6, 0, 2209], [1, 0, 15, 0, 2809], [1, 16, 182, 944, 3481], [1, -26, 291, -1586, 3721], [1, 0, 10, 0, 4489], [1, 10, 167, 710, 5041], [1, 0, -46, 0, 5329], [1, -6, 167, -474, 6241], [1, 0, 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['0.52374012234064004903235829385094', '1.64623953612891172505083644100105', '2.25390446665196758907232158288435', '2.81640120225307199592208901711000', '3.55769438444294647887380150435977', '3.74830190083547619016975775396301', '4.67094723650139846474220326037408', '5.02313578734529331417150860929662', '5.32396479233902370931894440031313', '5.98898085612776500076704849767595', '6.29844590597326332851426982424310', '7.09344020224328043004654971087162', '7.11358636170508588123127764353294', '7.70514096117492222865427021470992', '8.113749870469077080885296620988958', '8.735931152600397430769209815601344', '8.850491829005862190419234371682356', '9.422242296943292539054103396031095', '9.706071431802248887959096682322858', '10.31735317396824768809502703641931'], 'prelabel': '4-975e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.790235509249146, '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': 1541875681530010915, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.52374012234064004903235829385', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.64623953612891172505083644100', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.25390446665196758907232158288', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 60.612674220014505, 'bad_primes': [3, 5, 13], 'central_character': '1.1', 'conductor': 950625, 'conductor_radical': 195, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, -1, 0, -2, 0, 0, 0, 0, -4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, 26, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, 6, 0, 1, 0, 0, 0, 0, 0, 0, 0, 30, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0], 'euler11': [1, 2, 23, 22, 121], 'euler13': [1, 0, 1, 0, 0], 'euler17': [1, 0, -33, 0, 289], 'euler19': [1, -4, 42, -76, 361], 'euler2': [1, 0, 0, 0, 4], 'euler23': [1, 0, -37, 0, 529], 'euler29': [1, -4, 62, -116, 841], 'euler3': [1, 0, 1, 0, 0], 'euler31': [1, 12, 98, 372, 961], 'euler37': [1, 0, 47, 0, 1369], 'euler41': [1, 10, 107, 410, 1681], 'euler43': [1, 0, -70, 0, 1849], 'euler47': [1, 0, 6, 0, 2209], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, 0, 15, 0, 2809], 'euler59': [1, 16, 182, 944, 3481], 'euler61': [1, -26, 291, -1586, 3721], 'euler67': [1, 0, 10, 0, 4489], 'euler7': [1, 0, -5, 0, 49], 'euler71': [1, 10, 167, 710, 5041], 'euler73': [1, 0, -46, 0, 5329], 'euler79': [1, -6, 167, -474, 6241], 'euler83': [1, 0, -22, 0, 6889], 'euler89': [1, -30, 403, -2670, 7921], 'euler97': [1, 0, 95, 0, 9409], 'euler_factors': [[1, 0, 0, 0, 4], [1, 0, 1, 0, 0], [1, 0, 0, 0, 0], [1, 0, -5, 0, 49], [1, 2, 23, 22, 121], [1, 0, 1, 0, 0], [1, 0, -33, 0, 289], [1, -4, 42, -76, 361], [1, 0, -37, 0, 529], [1, -4, 62, -116, 841], [1, 12, 98, 372, 961], [1, 0, 47, 0, 1369], [1, 10, 107, 410, 1681], [1, 0, -70, 0, 1849], [1, 0, 6, 0, 2209], [1, 0, 15, 0, 2809], [1, 16, 182, 944, 3481], [1, -26, 291, -1586, 3721], [1, 0, 10, 0, 4489], [1, 10, 167, 710, 5041], [1, 0, -46, 0, 5329], [1, -6, 167, -474, 6241], [1, 0, -22, 0, 6889], [1, -30, 403, -2670, 7921], [1, 0, 95, 0, 9409]], 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/975/2/c/a'], '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': '4-975e2-1.1-c1e2-0-7', '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': '4-975e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.790235509249146, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1541875681530010915, 'z1': {'__RealLiteral__': 0, 'data': '0.52374012234064004903235829385', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '663919480448718657201512804513,2857163350008453972922806509459', 'Lhash_array': ['663919480448718657201512804513', '2857163350008453972922806509459'], 'label': '4-975e2-1.1-c1e2-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/975/2/c/a'}