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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': -3, 'Lhash': '2152660544315067409', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [-1.0, 0], 'algebraic': True, 'analytic_conductor': 626.0271518468385, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1]], [7, [1]]], 'bad_primes': [2, 5, 7], 'central_character': '78400.1', 'coefficient_field': '1.1.1.1', 'conductor': 78400, 'conductor_radical': 70, 'degree': 2, 'euler_factors': [[1], [1, 0, 3], [1], [1], [1, -6, 11], [1, -4, 13], [1, -7, 17], [1, -4, 19], [1, -1, 23], [1, -6, 29], [1, 3, 31], [1, 4, 37], [1, 9, 41], [1, -8, 43], [1, 11, 47], [1, 4, 53], [1, -10, 59], [1, 2, 61], [1, -8, 67], [1, 3, 71], [1, -2, 73], [1, 17, 79], [1, -2, 83], [1, 7, 89], [1, 1, 97]], 'gamma_factors': [[], [0]], 'index': 139, 'label': '2-280e2-1.1-c1-0-139', 'leading_term': '3.51675462568', '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': 0, 'origin': 'EllipticCurve/Q/78400/gw', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [3.516754625680409, 2.888639810981805, 1.299582901386762, -0.3426261827034455, -0.8959615526860084, -0.02903122546910575, 1.062999977405647, 0.5315411316385735, -2.051991104601433, -4.714710823557372, -4.885292678001367, -2.377448261277781, 0.1723663119107175, 0.4842699251877949, -0.4367038371993766, 0.1530534632166208, 2.44941135361507, 3.293381117159686, 0.664893623401344, -2.804514139703728, -3.038843511983848, -0.2932559636328891, 1.271453872111771, -0.07259000040657838, -1.215859502459788, 0.2895500637776518, 1.896572781396137, 0.4964277008262615, -1.668648025182354, -0.2525332430474629, 3.585214534812176, 4.429977820577516, 1.339574018457455, -0.7556012253553629, 0.4474762686909096, 1.159846765951131, -0.9029290673972044, -2.076356477192933, 0.04319239901500038, 1.402191093456779, -1.089397359939478, -3.055438480358885, -0.1270674448114169, 3.771002858500549, 3.050158511252908, 0.0241281832032682, -0.2293044673394779, 0.768829112241543, -0.5571094621088566, -1.43127333206165, 1.544784422359647, 3.81701689058145, 0.2475683872526803, -4.586301637554814, -3.893298365190928, -0.3610963768009053, 0.0628832455506208, -0.9768461997583285, -0.05285018606747959, -0.3954717370101522, -4.072035441617337, -5.044436895075557, -0.1079224430442837, 3.712875393181542, 1.786776649152671, -0.1072529838858573, 1.806410084238525, 2.500506637097031, 0.1008562917741858, -0.2213460949290274, 1.470836923601462, -0.4845426217894288, -4.062227494012425, -2.489494422009812, 1.354569886110438, 0.3392414290707595, -2.397293184592272, -0.7120255459796802, 1.567481994560039, -0.1234373415906774, -1.055269736121116, 1.313154762361399, 1.118689743449138, -2.191436692423802, -1.871583430188006, 0.6920720314447717, -1.684476333930023, -5.715496058370087, -3.834074008573972, 0.1435993033429302, 0.006847361877123723, -0.29433135515455, 2.052218861921524, 1.738709235013084, -0.7870045065511119, 1.166771240031872, 4.342702325844372, 1.006637244855016, -3.893933926701802, -2.544701155964682, 0.2928313758289841, -0.4652599369290299, -0.1703842498117001, 1.794285935509872, 0.09405656542617936, -1.556443117820197, 2.968407191838819, 6.747733115177304, 3.043825531545794, -0.8872367639336775, -0.1433033933782185, -0.655233208991417, -2.567528622819137, -0.3687067805414257, 1.697309844699155, -1.256854575845436, -2.303069076069951, 1.356074623396013, 1.307229706121138, -2.448942177051258, -1.474381408975607], 'positive_zeros': ['0.6884952226076359', '1.255596077141062', '1.816758779656928', '2.974713274596224', '3.374015454423693', '3.727153954347551', '4.542763605011333', '5.276318676410443', '5.740787891103083', '6.218230481768580', '6.796362792577124', '7.267874562364245', '8.109509523787328', '8.438795987668519', '8.911102919790627', '9.496056978998235', '9.918585479666589', '10.50679443999762', '11.25294461525684', '11.54415629469872', '11.93093662675764', '12.39921864433202', '13.01080358187037', '13.79279846921650', '14.01273377545151', '14.51117257616312', '14.70014318843267', '15.50453212989757', '16.18095434754503', '16.28977327690535', '17.01173783582863', '17.28197317390339', '17.71875325525598', '18.39164145955908', '18.77504594848263', '19.30360274803477', '19.73785582227378'], 'prelabel': '2-280e2-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 25.02053460353792, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 2152660544315067409, 'z1': {'__RealLiteral__': 0, 'data': '0.6884952226076359', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.255596077141062', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.816758779656928', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 626.0271518468385, 'bad_primes': [2, 5, 7], 'central_character': '1.1', 'conductor': 78400, 'conductor_radical': 70, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, -3, 0, 6, 0, 4, 0, 0, 0, 7, 0, 4, 0, 0, 0, 1, 0, 0, 0, 0, 0, 6, 0, -3, 0, 0, 0, 0, 0, -4, 0, 0, 0, -9, 0, 8, 0, 0, 0, -11, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 10, 0, -2, 0, 0, 0, 0, 0, 8, 0, 0, 0, -3, 0, 2, 0, 0, 0, 0, 0, -17, 0, 9, 0, 2, 0, 0, 0, 0, 0, -7, 0, 0, 0, 0, 0, 0, 0, -1, 0, -18, 0], 'euler11': [1, -6, 11], 'euler13': [1, -4, 13], 'euler17': [1, -7, 17], 'euler19': [1, -4, 19], 'euler2': [1, 0, 0], 'euler23': [1, -1, 23], 'euler29': [1, -6, 29], 'euler3': [1, 0, 3], 'euler31': [1, 3, 31], 'euler37': [1, 4, 37], 'euler41': [1, 9, 41], 'euler43': [1, -8, 43], 'euler47': [1, 11, 47], 'euler5': [1, 0, 0], 'euler53': [1, 4, 53], 'euler59': [1, -10, 59], 'euler61': [1, 2, 61], 'euler67': [1, -8, 67], 'euler7': [1, 0, 0], 'euler71': [1, 3, 71], 'euler73': [1, -2, 73], 'euler79': [1, 17, 79], 'euler83': [1, -2, 83], 'euler89': [1, 7, 89], 'euler97': [1, 1, 97], 'euler_factors': [[1, 0, 0], [1, 0, 3], [1, 0, 0], [1, 0, 0], [1, -6, 11], [1, -4, 13], [1, -7, 17], [1, -4, 19], [1, -1, 23], [1, -6, 29], [1, 3, 31], [1, 4, 37], [1, 9, 41], [1, -8, 43], [1, 11, 47], [1, 4, 53], [1, -10, 59], [1, 2, 61], [1, -8, 67], [1, 3, 71], [1, -2, 73], [1, 17, 79], [1, -2, 83], [1, 7, 89], [1, 1, 97]], 'index': 139, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/78400/gw'], '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': '2-280e2-1.1-c1-0-139', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-280e2-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 25.02053460353792, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 2152660544315067409, 'z1': {'__RealLiteral__': 0, 'data': '0.6884952226076359', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '2152660544315067409', 'Lhash_array': ['2152660544315067409'], 'factors': ['2-280e2-1.1-c1-0-139'], 'label': '2-280e2-1.1-c1-0-139', 'type': 'ECQ', 'url': 'EllipticCurve/Q/78400/gw'}