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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 2, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 1, 'Lhash': '419279816181121911,1560038282679592288', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.894427190999916, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 58.76201505448033, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 0, -1]], [5, [1, -2, 1]]], 'bad_primes': [2, 3, 5], 'central_character': '921600.1', 'coefficient_field': '1.1.1.1', 'conductor': 921600, 'conductor_radical': 30, 'degree': 4, 'euler_factors': [[1], [1, 0, -1], [1, -2, 1], [1, 0, 14, 0, 49], [1, 0, 6, 0, 121], [1, 4, 30, 52, 169], [1, 4, 38, 68, 289], [1, 0, -26, 0, 361], [1, 0, 30, 0, 529], [1, -12, 94, -348, 841], [1, 0, 62, 0, 961], [1, 4, 78, 148, 1369], [1, 12, 118, 492, 1681], [1, 0, 70, 0, 1849], [1, 0, -50, 0, 2209], [1, -12, 142, -636, 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0.5215604562109463, 0.10603817371010633, -0.06131714892989326, -0.0626919449782346], 'positive_zeros': ['1.30789464322825876552451590970317', '1.90410956588849953091073290915852', '2.56100826409250417816310835163622', '3.01325599841700254495812174326707', '3.64257092304627787883654309435351', '4.59744237493557402533707286051552', '4.66281454287229345249472136353930', '5.10335741728591181213017059039250', '5.73892987388308473685173648012494', '6.25812475404630879226037514190479', '6.73746543691429154932020719884718', '6.84594392053537268258202260884291', '7.46133055491293853299357806270743', '7.985644465490789105614221217605191'], 'prelabel': '4-960e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.768688966648822, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 1979318098860714199, 'z1': {'__RealLiteral__': 0, 'data': '1.30789464322825876552451590970317', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '1.90410956588849953091073290915852', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.56100826409250417816310835163622', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 58.76201505448033, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 921600, 'conductor_radical': 30, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, -4, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, -12, 0, 0, 0, 2, 0, 0, 0, -14, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, -28, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -8, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -28, 0, 0, 0], 'euler11': [1, 0, 6, 0, 121], 'euler13': [1, 4, 30, 52, 169], 'euler17': [1, 4, 38, 68, 289], 'euler19': [1, 0, -26, 0, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, 30, 0, 529], 'euler29': [1, -12, 94, -348, 841], 'euler3': [1, 0, -1, 0, 0], 'euler31': [1, 0, 62, 0, 961], 'euler37': [1, 4, 78, 148, 1369], 'euler41': [1, 12, 118, 492, 1681], 'euler43': [1, 0, 70, 0, 1849], 'euler47': [1, 0, -50, 0, 2209], 'euler5': [1, -2, 1, 0, 0], 'euler53': [1, -12, 142, -636, 2809], 'euler59': [1, 0, -26, 0, 3481], 'euler61': [1, 28, 318, 1708, 3721], 'euler67': [1, 0, -10, 0, 4489], 'euler7': [1, 0, 14, 0, 49], 'euler71': [1, 0, 142, 0, 5041], 'euler73': [1, -4, 150, -292, 5329], 'euler79': [1, 0, 94, 0, 6241], 'euler83': [1, 0, 150, 0, 6889], 'euler89': [1, -4, 182, -356, 7921], 'euler97': [1, 28, 390, 2716, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, -1, 0, 0], [1, -2, 1, 0, 0], [1, 0, 14, 0, 49], [1, 0, 6, 0, 121], [1, 4, 30, 52, 169], [1, 4, 38, 68, 289], [1, 0, -26, 0, 361], [1, 0, 30, 0, 529], [1, -12, 94, -348, 841], [1, 0, 62, 0, 961], [1, 4, 78, 148, 1369], [1, 12, 118, 492, 1681], [1, 0, 70, 0, 1849], [1, 0, -50, 0, 2209], [1, -12, 142, -636, 2809], [1, 0, -26, 0, 3481], [1, 28, 318, 1708, 3721], [1, 0, -10, 0, 4489], [1, 0, 142, 0, 5041], [1, -4, 150, -292, 5329], [1, 0, 94, 0, 6241], [1, 0, 150, 0, 6889], [1, -4, 182, -356, 7921], [1, 28, 390, 2716, 9409]], 'index': 60, 'instance_types': ['ECNF', 'BMF'], 'instance_urls': ['EllipticCurve/2.0.4.1/57600.2/z', 'ModularForm/GL2/ImaginaryQuadratic/2.0.4.1/57600.2/z'], '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': '4-960e2-1.1-c1e2-0-60', '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': 1, 'prelabel': '4-960e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.768688966648822, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1979318098860714199, 'z1': {'__RealLiteral__': 0, 'data': '1.30789464322825876552451590970317', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9709833
{'Lhash': '419279816181121911,1560038282679592288', 'Lhash_array': ['419279816181121911', '1560038282679592288'], 'label': '4-960e2-1.1-c1e2-0-60', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.4.1/57600.2/z'}
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id: 9709972
{'Lhash': '419279816181121911,1560038282679592288', 'Lhash_array': ['419279816181121911', '1560038282679592288'], 'label': '4-960e2-1.1-c1e2-0-60', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.4.1/57600.2/z'}