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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -1, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': 3, 'A8': 0, 'A9': -2, 'Lhash': '1045313075019248910', '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': [1.1338934190276817, 0], 'a8': [0.0, 0], 'a9': [-0.6666666666666666, 0], 'algebraic': True, 'analytic_conductor': 242.7452221446925, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1]], [19, [1, -1]]], 'bad_primes': [2, 5, 19], 'central_character': '30400.1', 'coefficient_field': '1.1.1.1', 'conductor': 30400, 'conductor_radical': 190, 'degree': 2, 'euler_factors': [[1], [1, 1, 3], [1], [1, -3, 7], [1, -2, 11], [1, -1, 13], [1, -5, 17], [1, -1], [1, 1, 23], [1, -3, 29], [1, 4, 31], [1, -2, 37], [1, 8, 41], [1, -8, 43], [1, 8, 47], [1, -9, 53], [1, -1, 59], [1, 14, 61], [1, 13, 67], [1, 10, 71], [1, 9, 73], [1, -10, 79], [1, 10, 83], [1, 12, 89], [1, 14, 97]], 'gamma_factors': [[], [0]], 'index': 42, 'label': '2-30400-1.1-c1-0-42', 'leading_term': '5.44105654544', '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/30400/t', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.273315813996274, 2.026573548825481, 1.851847644325854, 0.8167323644397828, -0.2810111202477752, -0.3183020038662263, 1.141885810848639, 3.121883766230944, 3.778956895714921, 2.119043472435553, -0.7039337221774976, -2.153495316647349, -0.811337199214993, 1.924078938446993, 3.112625128359396, 1.475600792596018, -1.101991494178274, -1.78090701823072, -0.189539082686989, 1.260124376535438, 0.6818555961814085, -0.7542250791095787, -0.6690614067758792, 0.7990530731180647, 0.9228984594081866, -1.507361403079719, -3.832319038162451, -2.920978332841369, 0.1786290124136711, 1.399815663672021, -0.5520240440055395, -2.315033280447736, -1.051507044945976, 1.075265892771878, 0.3363176884824598, -2.295777491833541, -2.181138486800274, 1.693485646981801, 4.609608795342652, 3.002847804448266, -0.2497975908116501, -0.4936391185805717, 1.662768889752858, 2.149579079682428, 0.4422835635372721, -0.2510803803214349, 0.7225113395371168, 0.4974993681713604, -1.121502638007776, -0.2464264484862011, 3.903992672378054, 5.932217925637962, 2.290442962514977, -2.505746914625413, -2.722231337546303, -0.1972632266235505, -0.1839402625815782, -2.036722354515446, -1.468521147871357, 0.3482281416732529, -1.588142614571225, -6.210745566983755, -6.909072234841677, -2.548615530328049, 0.6636721119791087, -0.2113231850504095, -0.9951523199216906, 0.6826649978041047, 1.339025539115282, -0.5582329340475527, -1.346837475424365, -0.007485752250767206, -0.551703283192766, -3.200856761629286, -2.445536921913033, 2.325542869904657, 4.138083191640222, 0.6479649762943273, -1.356742170649326, 1.563159426550644, 3.443893906035237, 0.6805218196551455, -1.409580603731355, 0.4429373332189883, 1.279927580968683, -1.444208397610023, -2.471993142311955, 0.4265823729230853, 1.7567125592929, -0.6384219588498633, -1.553361328029461, 0.5952866457590046, 0.8621713168152053, -1.423202508156265, -1.472342549394704, 0.1225081979274942, -1.58993751268683, -4.551744733471693, -2.960572131518356, 0.4270504156448607, -0.6601673417953153, -3.02445444848662, -0.6268059901034648, 2.1569640136204, -1.107333182083669, -5.220383521248942, -2.784444443439717, 1.885451897592723, 1.880137894140298, 0.06059143746725024, 0.5873587146044956, 0.3118447013004366, -2.014832648713738, -1.485929140800312, 1.694293703457221, 1.370583215067263, -1.493327188510688, -0.624570368995307, 1.871470055024323, -0.02268571799859043], 'positive_zeros': ['1.171327912285865', '1.579414869593928', '2.685269580800644', '3.325560048849139', '4.134562883775517', '4.773652789057065', '5.359334091179485', '5.868747880892866', '6.368886740602586', '7.234409518936245', '7.697025375406851', '8.355077383778564', '8.783632882391516', '9.404644236761159', '10.22394363483280', '10.56514642698179', '11.32457313520712', '11.58212582485547', '12.07726228555158', '12.51949370281869', '13.35386987793128', '14.02998844386694', '14.21943863010100', '14.92382286677239', '15.12563816643701', '16.15871854677273', '16.46982814970688', '16.91595894238821', '17.43595443808415', '18.00173076673410', '18.17231447608727', '18.88445762567764', '19.54116094329098', '19.89549213243258'], 'prelabel': '2-30400-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 15.580283121454901, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1045313075019248910, 'z1': {'__RealLiteral__': 0, 'data': '1.171327912285865', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '1.579414869593928', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.685269580800644', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 242.7452221446925, 'bad_primes': [2, 5, 19], 'central_character': '1.1', 'conductor': 30400, 'conductor_radical': 190, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, 0, 0, 3, 0, -2, 0, 2, 0, 1, 0, 0, 0, 5, 0, 1, 0, -3, 0, -1, 0, 0, 0, 5, 0, 3, 0, -4, 0, -2, 0, 0, 0, 2, 0, -1, 0, -8, 0, 8, 0, 0, 0, -8, 0, 2, 0, -5, 0, 9, 0, 0, 0, -1, 0, 1, 0, -14, 0, -6, 0, 0, 0, -13, 0, 1, 0, -10, 0, -9, 0, 0, 0, 6, 0, 10, 0, 1, 0, -10, 0, 0, 0, -3, 0, -12, 0, 3, 0, 4, 0, 0, 0, -14, 0, -4, 0], 'euler11': [1, -2, 11], 'euler13': [1, -1, 13], 'euler17': [1, -5, 17], 'euler19': [1, -1, 0], 'euler2': [1, 0, 0], 'euler23': [1, 1, 23], 'euler29': [1, -3, 29], 'euler3': [1, 1, 3], 'euler31': [1, 4, 31], 'euler37': [1, -2, 37], 'euler41': [1, 8, 41], 'euler43': [1, -8, 43], 'euler47': [1, 8, 47], 'euler5': [1, 0, 0], 'euler53': [1, -9, 53], 'euler59': [1, -1, 59], 'euler61': [1, 14, 61], 'euler67': [1, 13, 67], 'euler7': [1, -3, 7], 'euler71': [1, 10, 71], 'euler73': [1, 9, 73], 'euler79': [1, -10, 79], 'euler83': [1, 10, 83], 'euler89': [1, 12, 89], 'euler97': [1, 14, 97], 'euler_factors': [[1, 0, 0], [1, 1, 3], [1, 0, 0], [1, -3, 7], [1, -2, 11], [1, -1, 13], [1, -5, 17], [1, -1, 0], [1, 1, 23], [1, -3, 29], [1, 4, 31], [1, -2, 37], [1, 8, 41], [1, -8, 43], [1, 8, 47], [1, -9, 53], [1, -1, 59], [1, 14, 61], [1, 13, 67], [1, 10, 71], [1, 9, 73], [1, -10, 79], [1, 10, 83], [1, 12, 89], [1, 14, 97]], 'index': 42, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/30400/t'], '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': '2-30400-1.1-c1-0-42', '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': '2-30400-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 15.580283121454901, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1045313075019248910, 'z1': {'__RealLiteral__': 0, 'data': '1.171327912285865', 'prec': 57}}
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lfunc_instances • Show schema
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{'Lhash': '1045313075019248910', 'Lhash_array': ['1045313075019248910'], 'label': '2-30400-1.1-c1-0-42', 'type': 'ECQ', 'url': 'EllipticCurve/Q/30400/t'}