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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -1, 'A4': 0, 'A5': 2, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 1, 'Lhash': '1322073695642866361', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [0.8944271909999159, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 793.4894149658678, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [7, [1]], [13, [1]]], 'bad_primes': [2, 3, 7, 13], 'central_character': '99372.1', 'coefficient_field': '1.1.1.1', 'conductor': 99372, 'conductor_radical': 546, 'degree': 2, 'euler_factors': [[1], [1, 1], [1, -2, 5], [1], [1, -1, 11], [1], [1, -5, 17], [1, -7, 19], [1, 6, 23], [1, -9, 29], [1, 8, 31], [1, 6, 37], [1, 2, 41], [1, -8, 43], [1, 1, 47], [1, 1, 53], [1, -9, 59], [1, -5, 61], [1, -3, 67], [1, -15, 71], [1, 10, 73], [1, 0, 79], [1, 0, 83], [1, 6, 89], [1, -2, 97]], 'gamma_factors': [[], [0]], 'index': 47, 'label': '2-99372-1.1-c1-0-47', 'leading_term': '7.55085808744', 'load_key': 'Cremona', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'EllipticCurve/Q/99372/x', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.721012567548661, 2.508097147849435, 1.88653073349287, 0.4348488006123884, -0.3572000858531465, 0.5040058455852029, 2.113291158866832, 2.297958676817542, 0.2369718293639733, -1.971180374465299, -1.426048253665486, 1.74407785480754, 3.980341485053753, 2.707118453297595, 0.02946134195966325, 0.1355568214477077, 3.401038030532603, 5.630652002756255, 3.948027547833662, 0.7423725182648112, -0.3039258262851391, 0.2833513450915933, -0.4221581588059956, -2.082719850216037, -1.750583084817078, 0.1694594872384652, -0.1653744546769978, -3.084179375818583, -3.947007587777654, -1.131449034766089, 0.3514527566782692, 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2.509040695490449, -1.112274441355777, 0.3531341161922558, 2.385167116005447, 0.2839230748028454, -0.7636852022451931, 0.946179931979161, 0.2320372499132949, -1.296278404330806, 0.8806499128588685, 1.873018841762822, -1.873087094982577, -3.235247646459861, -0.1955758265529245, -0.4372887398680693, -3.290319059925223, -1.509088575382215, 1.259006914103018, -0.9020851657015646, -2.159422789573645, 0.7268310147547375, 0.8098592721769096, -1.064499131023313, 2.594969012108983, 6.546206896931112, 2.819516244173141, -1.229144388177521, 0.7459082705195542, 1.23019476779098, -1.839482028264083, -0.8215028306755898, 2.378209249802736, 1.109326795815038, -0.4094004065864986, 1.377201282575064, 1.283422688536353, -0.142427093221587, 1.399614327479377, 1.127707228547124], 'positive_zeros': ['1.088115330071247', '1.406704442179513', '2.272019241669676', '2.874355872242822', '3.754077893589045', '3.983054216223103', '5.095735059748508', '5.379057278679409', '5.675033236489165', '6.472143100175402', '6.729472226508703', '7.603883983315213', '7.806858567582514', '8.583345189603044', '9.235437867735558', '9.646554093492100', '10.15775209918876', '10.33586824213547', '11.09502748911167', '11.77619073431914', '11.90408633102350', '12.54008863977370', '12.90997025995758', '13.71732749535495', '14.01802961070183', '14.25080567333918', '14.83164604422231', '15.73783727131007', '15.87343504542171', '16.40816818104161', '16.78695850321406', '17.49713217551937', '17.72655872943202', '18.01928284114005', '18.65117210051851', '18.97658606249835', '19.70220596024064'], 'prelabel': '2-99372-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 28.16894415781088, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1322073695642866361, 'z1': {'__RealLiteral__': 0, 'data': '1.088115330071247', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '1.406704442179513', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.272019241669676', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 793.4894149658678, 'bad_primes': [2, 3, 7, 13], 'central_character': '1.1', 'conductor': 99372, 'conductor_radical': 546, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, 2, 0, 0, 0, 1, 0, 1, 0, 0, 0, -2, 0, 5, 0, 7, 0, 0, 0, -6, 0, -1, 0, -1, 0, 9, 0, -8, 0, -1, 0, 0, 0, -6, 0, 0, 0, -2, 0, 8, 0, 2, 0, -1, 0, 0, 0, -5, 0, -1, 0, 2, 0, -7, 0, 9, 0, 5, 0, 0, 0, 0, 0, 3, 0, 6, 0, 15, 0, -10, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 10, 0, -9, 0, -6, 0, 0, 0, 8, 0, 14, 0, 2, 0, 1, 0], 'euler11': [1, -1, 11], 'euler13': [1, 0, 0], 'euler17': [1, -5, 17], 'euler19': [1, -7, 19], 'euler2': [1, 0, 0], 'euler23': [1, 6, 23], 'euler29': [1, -9, 29], 'euler3': [1, 1, 0], 'euler31': [1, 8, 31], 'euler37': [1, 6, 37], 'euler41': [1, 2, 41], 'euler43': [1, -8, 43], 'euler47': [1, 1, 47], 'euler5': [1, -2, 5], 'euler53': [1, 1, 53], 'euler59': [1, -9, 59], 'euler61': [1, -5, 61], 'euler67': [1, -3, 67], 'euler7': [1, 0, 0], 'euler71': [1, -15, 71], 'euler73': [1, 10, 73], 'euler79': [1, 0, 79], 'euler83': [1, 0, 83], 'euler89': [1, 6, 89], 'euler97': [1, -2, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, -2, 5], [1, 0, 0], [1, -1, 11], [1, 0, 0], [1, -5, 17], [1, -7, 19], [1, 6, 23], [1, -9, 29], [1, 8, 31], [1, 6, 37], [1, 2, 41], [1, -8, 43], [1, 1, 47], [1, 1, 53], [1, -9, 59], [1, -5, 61], [1, -3, 67], [1, -15, 71], [1, 10, 73], [1, 0, 79], [1, 0, 83], [1, 6, 89], [1, -2, 97]], 'index': 47, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/99372/x'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-99372-1.1-c1-0-47', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-99372-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 28.16894415781088, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1322073695642866361, 'z1': {'__RealLiteral__': 0, 'data': '1.088115330071247', 'prec': 57}}
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lfunc_instances • Show schema
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{'Lhash': '1322073695642866361', 'Lhash_array': ['1322073695642866361'], 'factors': ['2-99372-1.1-c1-0-47'], 'label': '2-99372-1.1-c1-0-47', 'type': 'ECQ', 'url': 'EllipticCurve/Q/99372/x'}