-
lfunc_lfunctions • Show schema
Hide schema
{'A10': 0, 'A2': 0, 'A3': -1, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 1, 'Lhash': '543131308109902690', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 2582.362001368209, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [5, [1]], [7, [1]], [11, [1, 1]]], 'bad_primes': [2, 3, 5, 7, 11], 'central_character': '323400.1', 'coefficient_field': '1.1.1.1', 'conductor': 323400, 'conductor_radical': 2310, 'degree': 2, 'euler_factors': [[1], [1, 1], [1], [1], [1, 1], [1, 3, 13], [1, -4, 17], [1, 1, 19], [1, 2, 23], [1, 1, 29], [1, 4, 31], [1, -3, 37], [1, 4, 41], [1, 2, 43], [1, -5, 47], [1, 2, 53], [1, 9, 59], [1, -2, 61], [1, -3, 67], [1, -12, 71], [1, -7, 73], [1, 8, 79], [1, -12, 83], [1, -2, 89], [1, -10, 97]], 'gamma_factors': [[], [0]], 'index': 129, 'label': '2-323400-1.1-c1-0-129', 'leading_term': '5.5659391486', '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/323400/q', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.131977343208532, 0.9441409499213739, -0.6903444205522452, -2.126561562654208, -1.407300937312039, 1.040743836520775, 2.237193088753226, 0.4570428219164418, -1.781673852524109, -0.8212087659542375, 2.420890963852434, 3.161827258538807, 0.04895115670799828, -2.274518016313928, -0.4413928513429149, 1.996505581645832, 0.5318116678661605, -2.566487931977598, -2.433704904031505, -0.2175338904677645, -0.2589256567868814, -1.497626730547415, -0.04437575239877802, 2.259119657847848, 1.153537003329962, -0.9343465588507122, 0.7668653186634046, 3.427478021575741, 1.957634002101782, -0.5381728497980943, 0.6002569162251667, 1.262908985141126, -2.532401551729564, -4.431611379985288, 0.424688259084819, 4.625687286264224, 2.26961656172248, -0.2008988151054147, 1.888514844141514, 2.777817282425482, 0.2791873018082049, 0.1991223231699049, 2.202528395579655, 0.4912234784984111, -2.235906652114385, -0.4332468296860301, 1.724387751154411, 0.1301304840531253, -0.1991134325764115, 2.048555677763429, 1.326788857073065, -0.04234113870676684, 3.690269739443737, 6.389306495632453, 2.135776174176224, -0.8266046675501704, 2.002666202545385, 1.845327367927396, -2.347848981430993, -1.758139936554082, 1.070052055392549, -1.326764876470174, -3.209654774470446, 0.3725220007237822, 1.820484422109639, -0.7625836543232193, -0.503278007846982, 0.7885136876990939, -0.8237721081888612, 0.1495834961768, 3.848485564034035, 2.699661524327952, -0.2270079691211107, 1.087983789126577, 0.7684684960684455, -2.448566724863857, -0.3668401749629942, 2.961763456481, -0.7471249919218834, -3.414398945493252, 0.03370212411002307, -0.5070523937997444, -4.52980202850977, -1.895428721186955, 2.098577972942304, 0.0951949482031234, -0.9737605747626749, 0.143728800686116, -2.662054141467829, -4.177301843382375, -0.7273016118977081, -0.2088177948210208, -1.901973137784235, 0.2252905805164791, 0.6400182687979349, -2.0659716956104, -0.717111584404856, 0.02315841640288484, -4.355633498000528, -3.82479374413215, 1.276908298364365, 0.2985868409805153, -0.7409377500930951, 3.877049407681176, 3.068666644181923, -2.498172143421234, -1.405672513074069, 0.7303418504211786, -1.836525699892495, -1.104141325244115, 1.079994086396698, -1.321385694823751, -1.215530916638272, 1.733655144382134, -0.07206429787379366, -1.289055722174864, 1.13324112664949, -0.1050820029323638, -1.285584335686048, 1.558651791574559], 'positive_zeros': ['0.6591492494238998', '1.398186702256106', '2.041347515268345', '2.566825408769767', '3.253290473424743', '3.784470115687064', '4.289618833569675', '5.042416643833795', '5.195065485436791', '5.754009044959167', '6.357809613740229', '6.687927375722754', '7.413977950973864', '7.679313852737722', '8.108289805703019', '8.733425311095331', '9.430459956962298', '9.562777729781201', '10.28561149462192', '10.47247362340614', '11.03417319139294', '11.53260459120277', '12.01616731062932', '12.27623955902151', '12.90757332191871', '13.00914607955000', '13.86140874220751', '14.10278943294613', '14.60709920616067', '15.12116223550879', '15.41298419547708', '15.97775126964849', '16.42339009401235', '16.81085037385069', '17.14228039811346', '17.48918297425651', '18.20579977318398', '18.36580830365610', '18.80713278084443', '19.26893329826468', '19.71610621236896'], 'prelabel': '2-323400-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 50.816946005916265, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 543131308109902690, 'z1': {'__RealLiteral__': 0, 'data': '0.6591492494238998', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.398186702256106', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.041347515268345', 'prec': 57}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 2582.362001368209, 'bad_primes': [2, 3, 5, 7, 11], 'central_character': '1.1', 'conductor': 323400, 'conductor_radical': 2310, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, 0, 0, 0, 0, 1, 0, -1, 0, -3, 0, 0, 0, 4, 0, -1, 0, 0, 0, -2, 0, 0, 0, -1, 0, -1, 0, -4, 0, 1, 0, 0, 0, 3, 0, 3, 0, -4, 0, -2, 0, 0, 0, 5, 0, 0, 0, -4, 0, -2, 0, 0, 0, 1, 0, -9, 0, 2, 0, 0, 0, 0, 0, 3, 0, 2, 0, 12, 0, 7, 0, 0, 0, 0, 0, -8, 0, 1, 0, 12, 0, 0, 0, 1, 0, 2, 0, 0, 0, 4, 0, 0, 0, 10, 0, -1, 0], 'euler11': [1, 1, 0], 'euler13': [1, 3, 13], 'euler17': [1, -4, 17], 'euler19': [1, 1, 19], 'euler2': [1, 0, 0], 'euler23': [1, 2, 23], 'euler29': [1, 1, 29], 'euler3': [1, 1, 0], 'euler31': [1, 4, 31], 'euler37': [1, -3, 37], 'euler41': [1, 4, 41], 'euler43': [1, 2, 43], 'euler47': [1, -5, 47], 'euler5': [1, 0, 0], 'euler53': [1, 2, 53], 'euler59': [1, 9, 59], 'euler61': [1, -2, 61], 'euler67': [1, -3, 67], 'euler7': [1, 0, 0], 'euler71': [1, -12, 71], 'euler73': [1, -7, 73], 'euler79': [1, 8, 79], 'euler83': [1, -12, 83], 'euler89': [1, -2, 89], 'euler97': [1, -10, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, 0, 0], [1, 0, 0], [1, 1, 0], [1, 3, 13], [1, -4, 17], [1, 1, 19], [1, 2, 23], [1, 1, 29], [1, 4, 31], [1, -3, 37], [1, 4, 41], [1, 2, 43], [1, -5, 47], [1, 2, 53], [1, 9, 59], [1, -2, 61], [1, -3, 67], [1, -12, 71], [1, -7, 73], [1, 8, 79], [1, -12, 83], [1, -2, 89], [1, -10, 97]], 'index': 129, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/323400/q'], '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': '2-323400-1.1-c1-0-129', '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': '2-323400-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 50.816946005916265, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 543131308109902690, 'z1': {'__RealLiteral__': 0, 'data': '0.6591492494238998', 'prec': 60}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '543131308109902690', 'Lhash_array': ['543131308109902690'], 'label': '2-323400-1.1-c1-0-129', 'type': 'ECQ', 'url': 'EllipticCurve/Q/323400/q'}