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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': -1, 'A8': 0, 'A9': 0, 'Lhash': '1249309145433172290', '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': [-0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 201.22301309362666, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1]], [7, [1, 1]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '25200.1', 'coefficient_field': '1.1.1.1', 'conductor': 25200, 'conductor_radical': 210, 'degree': 2, 'euler_factors': [[1], [1], [1], [1, 1], [1, -4, 11], [1, -6, 13], [1, -2, 17], [1, 0, 19], [1, 0, 23], [1, 6, 29], [1, 8, 31], [1, -10, 37], [1, 2, 41], [1, -4, 43], [1, 8, 47], [1, 2, 53], [1, 8, 59], [1, 14, 61], [1, 12, 67], [1, 16, 71], [1, 2, 73], [1, -8, 79], [1, 8, 83], [1, 10, 89], [1, 2, 97]], 'gamma_factors': [[], [0]], 'index': 151, 'label': '2-25200-1.1-c1-0-151', 'leading_term': '6.02312097491', '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/25200/cw', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.425276051688547, 2.357914303558084, 2.36377434113752, 1.40461177587116, 0.1506392731557617, -0.2719003424939361, 0.8305985222468683, 2.885360485748745, 4.23248890402713, 3.500566831250098, 1.038106083218233, -1.184041952142454, -1.445653409573188, -0.1171611701464638, 0.7149713166013217, -0.2683645726678932, -1.818636811377983, -1.430248725460657, 1.456890457868782, 4.307180404496114, 4.230325516460889, 1.486776309615076, -0.8079669408473578, -0.6693309489259897, 0.2828646211005329, -0.6438892389853834, -3.085197694284648, -3.897648778017378, -1.782889233670706, 0.4002703477637991, -0.5608564435265423, -3.504354726260477, -4.337337574412306, -1.873410673695074, 0.5579468800667061, 0.2587610510282628, -0.8238484635125791, 0.4288590781452973, 2.825090761332291, 2.414801374135456, -1.025229792211922, -3.089539967390145, -1.355993981112054, 0.9663516738202274, 0.4219567443975468, -1.052696706198059, 0.3026870573305655, 3.25165034848218, 3.268351403733516, 0.1951170140915577, -1.267084933025665, 0.6185080773533662, 1.865951552040812, -0.05012664872871672, -1.644406300716592, 0.3177216801211678, 2.819061299062649, 1.815335652001722, -0.4625421493221968, 0.5263277502694316, 3.239350527673653, 2.531668129491561, -1.121104893889109, -2.315300122132156, -0.1388809130644064, 0.8702488780084825, -0.2892288825064845, 0.6866277611295643, 4.429864547782856, 5.470125841016825, 1.797947347447551, -1.201238506868888, -0.2109298335306549, 0.5993957593088584, -1.794020724560093, -3.27450731585818, -0.7640355191153408, 1.440040708339153, -0.2385616853171772, -1.823647852233422, 0.2633352335370313, 2.056722224697755, 0.02132377881691153, -1.551068046368647, 1.197684864498895, 3.782902898579485, 1.761139611553273, -0.8004696914121572, 0.5641487461134632, 2.209586927534104, 0.2618506483003129, -1.428039863002651, 0.5041002746821874, 1.677485044312616, -0.919731029802005, -2.082352292811873, 1.339645738055358, 3.469389042076034, 0.4316049652761587, -2.354499458462764, -1.019070148466208, 0.03981118005002907, -1.45687534590177, -0.8789703731057336, 2.319205055352894, 1.927459201082731, -2.322541025397664, -3.076404619281594, 0.656545992590353, 2.029850223199172, 0.08328463468776592, 0.2022130042925975, 1.507150933449032, -1.078066301366646, -4.623543612540577, -3.075860778201862, 0.1738766314505014, -1.005001757765189, -3.123747743073253, -0.9612505569833422], 'positive_zeros': ['1.289536795897307', '1.603751430783516', '2.849232259202210', '3.520408916186592', '3.958304595354019', '4.641112214827860', '5.633641894516340', '6.147463424058473', '6.404926253783660', '7.426673015063221', '7.687415713700300', '8.666270407425560', '9.046144138277398', '9.453342363461301', '10.18134088651184', '10.87082540907919', '11.30720593768393', '11.72259650091484', '12.51614036892032', '12.93732035748255', '13.49527811742600', '13.97453481354031', '14.67720168082641', '14.94644561349370', '15.67225083859428', '16.26501304803228', '16.68471912133106', '16.92899525087802', '17.86120095862963', '18.27790715682996', '18.59142620864023', '19.30715494396952', '19.72792904682034'], 'prelabel': '2-25200-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 14.185309763753017, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1249309145433172290, 'z1': {'__RealLiteral__': 0, 'data': '1.289536795897307', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '1.603751430783516', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.849232259202210', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 201.22301309362666, 'bad_primes': [2, 3, 5, 7], 'central_character': '1.1', 'conductor': 25200, 'conductor_radical': 210, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 4, 0, 6, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, -8, 0, 0, 0, 0, 0, 10, 0, 0, 0, -2, 0, 4, 0, 0, 0, -8, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, -8, 0, -14, 0, 0, 0, 0, 0, -12, 0, 0, 0, -16, 0, -2, 0, 0, 0, -4, 0, 8, 0, 0, 0, -8, 0, 0, 0, 0, 0, -10, 0, -6, 0, 0, 0, 0, 0, -2, 0, 0, 0], 'euler11': [1, -4, 11], 'euler13': [1, -6, 13], 'euler17': [1, -2, 17], 'euler19': [1, 0, 19], 'euler2': [1, 0, 0], 'euler23': [1, 0, 23], 'euler29': [1, 6, 29], 'euler3': [1, 0, 0], 'euler31': [1, 8, 31], 'euler37': [1, -10, 37], 'euler41': [1, 2, 41], 'euler43': [1, -4, 43], 'euler47': [1, 8, 47], 'euler5': [1, 0, 0], 'euler53': [1, 2, 53], 'euler59': [1, 8, 59], 'euler61': [1, 14, 61], 'euler67': [1, 12, 67], 'euler7': [1, 1, 0], 'euler71': [1, 16, 71], 'euler73': [1, 2, 73], 'euler79': [1, -8, 79], 'euler83': [1, 8, 83], 'euler89': [1, 10, 89], 'euler97': [1, 2, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 0, 0], [1, 1, 0], [1, -4, 11], [1, -6, 13], [1, -2, 17], [1, 0, 19], [1, 0, 23], [1, 6, 29], [1, 8, 31], [1, -10, 37], [1, 2, 41], [1, -4, 43], [1, 8, 47], [1, 2, 53], [1, 8, 59], [1, 14, 61], [1, 12, 67], [1, 16, 71], [1, 2, 73], [1, -8, 79], [1, 8, 83], [1, 10, 89], [1, 2, 97]], 'index': 151, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/25200/cw'], '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': '2-25200-1.1-c1-0-151', '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': '2-25200-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 14.185309763753017, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1249309145433172290, 'z1': {'__RealLiteral__': 0, 'data': '1.289536795897307', 'prec': 57}}
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lfunc_instances • Show schema
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{'Lhash': '1249309145433172290', 'Lhash_array': ['1249309145433172290'], 'label': '2-25200-1.1-c1-0-151', 'type': 'ECQ', 'url': 'EllipticCurve/Q/25200/cw'}