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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': -2, 'A8': 0, 'A9': -3, 'Lhash': '1145702099048296642', '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': [-0.7559289460184544, 0], 'a8': [0.0, 0], 'a9': [-1.0, 0], 'algebraic': True, 'analytic_conductor': 2925.7187300597147, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1]], [229, [1, -1]]], 'bad_primes': [2, 5, 229], 'central_character': '366400.1', 'coefficient_field': '1.1.1.1', 'conductor': 366400, 'conductor_radical': 2290, 'degree': 2, 'euler_factors': [[1], [1, 0, 3], [1], [1, 2, 7], [1, -4, 11], [1, -2, 13], [1, -2, 17], [1, -8, 19], [1, -2, 23], [1, 10, 29], [1, 2, 31], [1, -6, 37], [1, -10, 41], [1, -8, 43], [1, 2, 47], [1, -10, 53], [1, 6, 59], [1, 2, 61], [1, -2, 67], [1, 0, 71], [1, -14, 73], [1, 14, 79], [1, 0, 83], [1, 6, 89], [1, 6, 97]], 'gamma_factors': [[], [0]], 'index': 54, 'label': '2-366400-1.1-c1-0-54', 'leading_term': '8.7485644115', '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/366400/bf', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.893769786980695, 2.282656912565213, 0.9591935457474446, -0.339379596103997, 0.4720152645766709, 2.884872697705725, 3.659276094168059, 0.9677016579438067, -2.467762374046422, -2.673581748766132, -0.176688013869008, 0.8445016634792273, -0.7274675265265323, -1.487873423894977, -0.1906310311752529, -0.5320399233999037, -3.943793334857821, -5.334670561917906, -1.266806869323047, 3.199918626287618, 2.448353751254248, -0.5505394437067404, -0.6814104374307686, -0.04928356354158432, -2.088202383494363, -3.234366855815104, -0.2278598961761097, 2.025647960404851, -0.2005588298818327, -1.608244147586053, 1.001101650846086, 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-3.051988288955028, -1.122927248572286, 1.743176009525715, -2.602221236444189, -4.663720793162991, 1.316208399156116, 3.703442803850944, 0.5095053629554389, 0.06409160525883915, 0.1186567360495912, -0.4392107869584435, 3.105374814275246, 3.656365761368093, -2.986096695683246, -4.259811141059843, 1.07735629450034, 1.257627741250216, -0.001825606711493476, 3.115710717778006, 2.493556393183987, -0.9808121940551096, 0.2833333562853949, 0.8316367103174417, -0.726729578141914, 1.915542429165803, 1.673457485373584, -4.902189609297456, -5.17541936253178, -0.1636140856309339, -0.3695787450105417, 0.1756400385774486, 4.070538381001802, 2.499656449702352, -0.1241306461193306, 1.408043965388588, -0.355258424785454, -2.323430732393411, 1.179743827538499, 0.4779554899026361], 'positive_zeros': ['0.9029630994044640', '1.181293100029866', '2.062046385227663', '2.768800983415399', '3.154793492221391', '3.796056539048939', '3.916710681005216', '4.806494151939097', '5.440825418946503', '5.926372417215080', '5.975169104333870', '6.764785113044694', '7.233985224099858', '7.669559744138613', '8.094980054968222', '8.875537479512369', '9.153685265092603', '9.539929732309204', '9.736261242097180', '10.60604665672452', '11.04788376353747', '11.44952939437415', '11.68938468824213', '12.26951916728079', '12.75866035403334', '13.12134790816630', '13.66472988431488', '14.11362598653050', '14.44755114652368', '14.73269012265940', '15.40337359115465', '15.79020421903351', '16.33732929375773', '16.61183708013843', '16.95481160298710', '17.35206816344765', '18.08175296500861', '18.18138560867243', '18.74936729807558', '19.21570846405934', '19.68890614725907', '19.94479769402773'], 'prelabel': '2-366400-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 54.08991338558155, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1145702099048296642, 'z1': {'__RealLiteral__': 0, 'data': '0.9029630994044640', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.181293100029866', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.062046385227663', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2925.7187300597147, 'bad_primes': [2, 5, 229], 'central_character': '1.1', 'conductor': 366400, 'conductor_radical': 2290, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, -2, 0, -3, 0, 4, 0, 2, 0, 0, 0, 2, 0, 8, 0, 0, 0, 2, 0, 0, 0, 0, 0, -10, 0, -2, 0, 0, 0, 0, 0, 6, 0, 0, 0, 10, 0, 8, 0, 0, 0, -2, 0, -3, 0, 0, 0, 10, 0, 0, 0, 0, 0, -6, 0, -2, 0, 6, 0, 0, 0, 2, 0, 0, 0, 0, 0, 14, 0, 0, 0, -8, 0, -14, 0, 9, 0, 0, 0, 0, 0, 0, 0, -6, 0, -4, 0, 0, 0, 0, 0, -6, 0, -12, 0], 'euler11': [1, -4, 11], 'euler13': [1, -2, 13], 'euler17': [1, -2, 17], 'euler19': [1, -8, 19], 'euler2': [1, 0, 0], 'euler23': [1, -2, 23], 'euler29': [1, 10, 29], 'euler3': [1, 0, 3], 'euler31': [1, 2, 31], 'euler37': [1, -6, 37], 'euler41': [1, -10, 41], 'euler43': [1, -8, 43], 'euler47': [1, 2, 47], 'euler5': [1, 0, 0], 'euler53': [1, -10, 53], 'euler59': [1, 6, 59], 'euler61': [1, 2, 61], 'euler67': [1, -2, 67], 'euler7': [1, 2, 7], 'euler71': [1, 0, 71], 'euler73': [1, -14, 73], 'euler79': [1, 14, 79], 'euler83': [1, 0, 83], 'euler89': [1, 6, 89], 'euler97': [1, 6, 97], 'euler_factors': [[1, 0, 0], [1, 0, 3], [1, 0, 0], [1, 2, 7], [1, -4, 11], [1, -2, 13], [1, -2, 17], [1, -8, 19], [1, -2, 23], [1, 10, 29], [1, 2, 31], [1, -6, 37], [1, -10, 41], [1, -8, 43], [1, 2, 47], [1, -10, 53], [1, 6, 59], [1, 2, 61], [1, -2, 67], [1, 0, 71], [1, -14, 73], [1, 14, 79], [1, 0, 83], [1, 6, 89], [1, 6, 97]], 'index': 54, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/366400/bf'], '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': '2-366400-1.1-c1-0-54', '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': '2-366400-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 54.08991338558155, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1145702099048296642, 'z1': {'__RealLiteral__': 0, 'data': '0.9029630994044640', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1145702099048296642', 'Lhash_array': ['1145702099048296642'], 'factors': ['2-366400-1.1-c1-0-54'], 'label': '2-366400-1.1-c1-0-54', 'type': 'ECQ', 'url': 'EllipticCurve/Q/366400/bf'}