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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 2, 'A3': 1, 'A4': 2, 'A5': 0, 'A6': 2, 'A7': 3, 'A8': 0, 'A9': 1, 'Lhash': '844623571844123580', 'a10': [0.0, 0], 'a2': [1.414213562373095, 0], 'a3': [0.5773502691896258, 0], 'a4': [1.0, 0], 'a5': [0.0, 0], 'a6': [0.8164965809277261, 0], 'a7': [1.1338934190276817, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 2810.5345251440176, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, -1]], [5, [1]], [13, [1, -1]], [19, [1]]], 'bad_primes': [3, 5, 13, 19], 'central_character': '351975.1', 'coefficient_field': '1.1.1.1', 'conductor': 351975, 'conductor_radical': 3705, 'degree': 2, 'euler_factors': [[1, -2, 2], [1, -1], [1], [1, -3, 7], [1, 5, 11], [1, -1], [1, 5, 17], [1], [1, -1, 23], [1, 10, 29], [1, -2, 31], [1, 3, 37], [1, -9, 41], [1, -4, 43], [1, 10, 47], [1, -9, 53], [1, 0, 59], [1, 11, 61], [1, 4, 67], [1, 15, 71], [1, 6, 73], [1, -11, 79], [1, 8, 83], [1, -11, 89], [1, 9, 97]], 'gamma_factors': [[], [0]], 'index': 7, 'label': '2-351975-1.1-c1-0-7', 'leading_term': '3.85287980724', '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/351975/bz', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [3.852879807242002, 1.68005915737959, -3.54286280711937, -8.253506673431591, -8.737823047696619, -4.697569870507524, -0.06282013170630343, 1.187728490481786, -0.4589585079815917, -1.39832277401397, -0.3422569626402271, 0.316496725992613, -0.8552661730125123, -1.675381063481262, -0.3285891476776698, 1.207466550345468, 0.706228207801095, -0.3418503808882049, 0.1033557670398947, 0.642968563142661, -0.2613421030825872, -0.6512042039221754, 0.6157539786472214, 0.5519475149472608, -1.677069717914278, -1.313766191433995, 2.943343649973832, 4.437303807858844, 0.2797450586481695, -2.472898804302428, -0.1889973789895693, 0.4511768616616553, -2.942503529891324, -2.691084796220103, 2.216460848483582, 2.562141784095727, -1.248256022815294, 1.568912498438795, 8.392207566410184, 5.080996629937569, -5.937184120967444, -8.256344376057497, -1.340428621486339, 1.466391002923939, -0.6357320090559146, 0.4952452493279245, 2.161624164534424, -0.8706813010316278, -2.807739134833617, 0.3211070169466647, 2.175069355666917, 0.3513999644148789, -0.2437473307683368, 0.5283388573350213, 0.05073823389424943, 0.3029427210524827, 1.411397917458205, 0.2778478558881502, -1.152043351825484, -0.3058474809887484, -0.07852965423103452, -0.3233281771925812, 1.668224455566289, 1.657275791859944, -1.241823906152249, 1.201782405382165, 4.483704626754817, -5.550922967732884, -18.87921177317016, -14.50393060916481, -1.827251385190123, -0.08327137776449885, -1.141247804061572, 3.690374878052789, 2.525439754326491, -3.445588345119386, 1.035144592894322, 7.978235655994221, 2.164679184262526, -5.218653037790163, -2.282919752829363, 1.124365695442883, -0.3692436523718817, -0.4124917404624159, 0.3392229489700938, -0.1650113593364636, 0.957332112256633, 0.8467307205327488, -2.284960107923069, -2.168297933197668, 0.2281220693170926, -0.9988817071672669, -1.658920304255908, 0.6705680960673708, 0.1040804103821282, -1.709696721549911, -0.5113762952500802, -0.0984074605016736, -0.3712358529912534, 0.1951402023471732, -4.1425654856099, -8.57551909373223, -2.544661763368287, 3.584330109009672, 0.2918102972821193, -0.2556237417118346, 2.348488239648352, -2.490970162996239, -2.863482282661194, 7.054921037165584, 7.308848263123781, -0.2671627685238456, 2.629613440231195, 3.405990927904633, -8.365506176525848, -11.20117731460222, -1.694133320749807, 0.5202847017137422, -1.420059660042581, 2.028125181401789, 2.431685370883419], 'positive_zeros': ['0.3401992161952798', '1.504793387944356', '1.941105666721035', '2.567768803739728', '2.851795595267761', '3.540951563451646', '4.138487291594142', '4.472585906594823', '4.945076518905391', '5.391973860977773', '5.820668132570775', '6.339254881036309', '7.014258721085052', '7.516975409230467', '7.793937663111217', '8.388002576218213', '8.902596010412610', '9.187277946939322', '9.863790649545607', '10.55632447947197', '10.91689976552204', '11.20429238582209', '11.69674953181382', '12.22921897731782', '12.80112745052234', '13.06969977606374', '13.52165375280871', '13.66870874542394', '14.28324177718798', '14.83744490261421', '14.96628608719307', '15.31205804039477', '15.88047994950047', '16.19085607228257', '16.65341942585189', '17.57372485989258', '17.74244204977457', '18.07418040098296', '18.59015328455928', '18.97162745953989', '19.55333818371321'], 'prelabel': '2-351975-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 53.01447467573377, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 844623571844123580, 'z1': {'__RealLiteral__': 0, 'data': '0.3401992161952798', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.504793387944356', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.941105666721035', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2810.5345251440176, 'bad_primes': [3, 5, 13, 19], 'central_character': '1.1', 'conductor': 351975, 'conductor_radical': 3705, 'degree': 2, 'dirichlet_coefficients': [1, 2, 1, 2, 0, 2, 3, 0, 1, 0, -5, 2, 1, 6, 0, -4, -5, 2, 0, 0, 3, -10, 1, 0, 0, 2, 1, 6, -10, 0, 2, -8, -5, -10, 0, 2, -3, 0, 1, 0, 9, 6, 4, -10, 0, 2, -10, -4, 2, 0, -5, 2, 9, 2, 0, 0, 0, -20, 0, 0, -11, 4, 3, -8, 0, -10, -4, -10, 1, 0, -15, 0, -6, -6, 0, 0, -15, 2, 11, 0, 1, 18, -8, 6, 0, 8, -10, 0, 11, 0, 3, 2, 2, -20, 0, -8, -9, 4, -5, 0], 'euler11': [1, 5, 11], 'euler13': [1, -1, 0], 'euler17': [1, 5, 17], 'euler19': [1, 0, 0], 'euler2': [1, -2, 2], 'euler23': [1, -1, 23], 'euler29': [1, 10, 29], 'euler3': [1, -1, 0], 'euler31': [1, -2, 31], 'euler37': [1, 3, 37], 'euler41': [1, -9, 41], 'euler43': [1, -4, 43], 'euler47': [1, 10, 47], 'euler5': [1, 0, 0], 'euler53': [1, -9, 53], 'euler59': [1, 0, 59], 'euler61': [1, 11, 61], 'euler67': [1, 4, 67], 'euler7': [1, -3, 7], 'euler71': [1, 15, 71], 'euler73': [1, 6, 73], 'euler79': [1, -11, 79], 'euler83': [1, 8, 83], 'euler89': [1, -11, 89], 'euler97': [1, 9, 97], 'euler_factors': [[1, -2, 2], [1, -1, 0], [1, 0, 0], [1, -3, 7], [1, 5, 11], [1, -1, 0], [1, 5, 17], [1, 0, 0], [1, -1, 23], [1, 10, 29], [1, -2, 31], [1, 3, 37], [1, -9, 41], [1, -4, 43], [1, 10, 47], [1, -9, 53], [1, 0, 59], [1, 11, 61], [1, 4, 67], [1, 15, 71], [1, 6, 73], [1, -11, 79], [1, 8, 83], [1, -11, 89], [1, 9, 97]], 'index': 7, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/351975/bz'], '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': '2-351975-1.1-c1-0-7', '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': '2-351975-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 53.01447467573377, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 844623571844123580, 'z1': {'__RealLiteral__': 0, 'data': '0.3401992161952798', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '844623571844123580', 'Lhash_array': ['844623571844123580'], 'label': '2-351975-1.1-c1-0-7', 'type': 'ECQ', 'url': 'EllipticCurve/Q/351975/bz'}