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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -1, 'A4': 0, 'A5': -1, 'A6': 0, 'A7': -1, 'A8': 0, 'A9': 1, 'Lhash': '1127381665529345259', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [-0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [-0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 2623.56480881119, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [5, [1, 1]], [37, [1]]], 'bad_primes': [2, 3, 5, 37], 'central_character': '328560.1', 'coefficient_field': '1.1.1.1', 'conductor': 328560, 'conductor_radical': 1110, 'degree': 2, 'euler_factors': [[1], [1, 1], [1, 1], [1, 1, 7], [1, -6, 11], [1, -7, 13], [1, -2, 17], [1, -4, 19], [1, 4, 23], [1, 4, 29], [1, -9, 31], [1], [1, -4, 41], [1, -1, 43], [1, -4, 47], [1, -12, 53], [1, 6, 59], [1, -2, 61], [1, 7, 67], [1, -6, 71], [1, 1, 73], [1, -15, 79], [1, 6, 83], [1, -2, 89], [1, -11, 97]], 'gamma_factors': [[], [0]], 'index': 30, 'label': '2-328560-1.1-c1-0-30', 'leading_term': '3.10300590569', '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/328560/e', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [3.103005905685041, 2.278932556557031, 0.4545441110166902, -0.816979888917271, -0.5320979309231988, 0.2209918452941774, -0.770628804968131, -3.461644918119094, -4.388780514824221, -0.8474412807205322, 4.4659150183038, 5.912030373543544, 2.387630244882303, -1.13980898337419, -1.043488116808208, 0.1427095876705862, -0.6602645056379268, -1.17162387153931, 1.411486060473701, 3.73496259972562, 1.323832262785599, -2.897081776444375, -2.979733360614529, -0.02147004624224016, 0.7596566873471757, -0.1139279365953706, 0.9525989716022001, 1.850252810012829, -0.7182552307379862, -2.62495366855612, 0.408036362593231, 3.140539925817308, 0.3426589815408837, -2.392385459846342, 0.3577159668728633, 2.896889276488728, 0.5393394110681562, -0.7862648466493193, 1.992403008739094, 2.116018191680614, -1.805564500621504, -1.990380186845781, 1.87223323058709, 1.961057822654913, -1.118452241946634, -0.9172142481470044, 0.7049938979474063, -0.2075973591637275, -0.3307671291306804, 0.7957141968951397, -1.970946534685654, -5.394530912633017, -2.271216277259676, 2.100558927887742, 0.4714750326364649, -0.908269812354847, 2.140970954137888, 1.615325304918204, -2.682326074234374, -0.8637804071317273, 4.24203353312104, 2.520957768221158, -1.638561893720995, -0.7543234595089499, 0.09892397805266862, -1.682426226308605, -0.7465531632509422, 0.637834762194921, -1.622199346549987, -1.397759824678525, 2.512128007993761, 1.804617334248093, -1.44778058179958, 0.128088428779152, 1.201651151642635, -1.845111045395028, -1.166330046226855, 2.152616722191288, 0.3397962856440305, -1.123883393275455, 2.10184678858349, 1.142777495823966, -3.128138406927685, -0.9382012669499644, 1.889827582939834, -1.583374938072066, -1.68018580102964, 3.677388568257998, 3.504646091210134, -0.3836649532296081, -0.2701530019012694, 0.05093115833801357, -0.3486257721115246, 2.190661242386457, 2.021820452301742, -1.798177908671601, -0.4973832324495006, 2.339911283424458, -0.1787980561026045, -0.01276718604144211, 3.921912966119116, 1.707353767770882, -1.103028864630177, 2.55852511177762, 2.246596948827997, -2.715993424576029, -1.094347244907844, 1.0394488664831, -3.525965195209937, -4.447075968834914, -0.2015796615695731, 0.2956213194794305, -0.1569896643476231, 0.3391913725128336, -2.215963621814321, -1.570193045301321, 3.336722061244153, 1.490824871234867, -3.128866919521762, -1.010142940998657, 0.3566644469454158], 'positive_zeros': ['0.5656859034554707', '1.144905950403082', '1.382858567997714', '2.288580612381216', '3.143058698984054', '3.690097895326709', '3.866735753669468', '4.393261684885998', '5.071059838694153', '5.752184539855376', '6.189535226477134', '6.339197124737805', '6.948087822971325', '7.476642885080934', '8.019732738653172', '8.478677552724422', '9.043709926841056', '9.341481794798590', '9.887415796196616', '10.37850850782694', '10.89957304054112', '11.35968087478883', '11.71326872329888', '12.05696001833669', '12.37536313291075', '13.10124479329351', '13.53692010107904', '13.84259466239469', '14.33848966177822', '14.78767967808966', '15.37585291890230', '15.84597242927837', '16.01931839352638', '16.57849522798623', '16.84995228058732', '17.33981437392115', '17.86442090724486', '18.23940468480442', '18.60934026072453', '19.07393597085828', '19.52458057319069', '19.85187974741286'], 'prelabel': '2-328560-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 51.220745883003204, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1127381665529345259, 'z1': {'__RealLiteral__': 0, 'data': '0.5656859034554707', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.144905950403082', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.382858567997714', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2623.56480881119, 'bad_primes': [2, 3, 5, 37], 'central_character': '1.1', 'conductor': 328560, 'conductor_radical': 1110, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, -1, 0, -1, 0, 1, 0, 6, 0, 7, 0, 1, 0, 2, 0, 4, 0, 1, 0, -4, 0, 1, 0, -1, 0, -4, 0, 9, 0, -6, 0, 1, 0, 0, 0, -7, 0, 4, 0, 1, 0, -1, 0, 4, 0, -6, 0, -2, 0, 12, 0, -6, 0, -4, 0, -6, 0, 2, 0, -1, 0, -7, 0, -7, 0, 4, 0, 6, 0, -1, 0, -1, 0, -6, 0, 15, 0, 1, 0, -6, 0, -2, 0, 4, 0, 2, 0, -7, 0, -9, 0, -4, 0, 11, 0, 6, 0], 'euler11': [1, -6, 11], 'euler13': [1, -7, 13], 'euler17': [1, -2, 17], 'euler19': [1, -4, 19], 'euler2': [1, 0, 0], 'euler23': [1, 4, 23], 'euler29': [1, 4, 29], 'euler3': [1, 1, 0], 'euler31': [1, -9, 31], 'euler37': [1, 0, 0], 'euler41': [1, -4, 41], 'euler43': [1, -1, 43], 'euler47': [1, -4, 47], 'euler5': [1, 1, 0], 'euler53': [1, -12, 53], 'euler59': [1, 6, 59], 'euler61': [1, -2, 61], 'euler67': [1, 7, 67], 'euler7': [1, 1, 7], 'euler71': [1, -6, 71], 'euler73': [1, 1, 73], 'euler79': [1, -15, 79], 'euler83': [1, 6, 83], 'euler89': [1, -2, 89], 'euler97': [1, -11, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, 1, 0], [1, 1, 7], [1, -6, 11], [1, -7, 13], [1, -2, 17], [1, -4, 19], [1, 4, 23], [1, 4, 29], [1, -9, 31], [1, 0, 0], [1, -4, 41], [1, -1, 43], [1, -4, 47], [1, -12, 53], [1, 6, 59], [1, -2, 61], [1, 7, 67], [1, -6, 71], [1, 1, 73], [1, -15, 79], [1, 6, 83], [1, -2, 89], [1, -11, 97]], 'index': 30, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/328560/e'], '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': '2-328560-1.1-c1-0-30', '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': '2-328560-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 51.220745883003204, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1127381665529345259, 'z1': {'__RealLiteral__': 0, 'data': '0.5656859034554707', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1127381665529345259', 'Lhash_array': ['1127381665529345259'], 'label': '2-328560-1.1-c1-0-30', 'type': 'ECQ', 'url': 'EllipticCurve/Q/328560/e'}