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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -2, 'A4': 0, 'A5': -4, 'A6': 0, 'A7': -2, 'A8': 0, 'A9': 1, 'Lhash': '314457295871535336', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-1.1547005383792517, 0], 'a4': [0.0, 0], 'a5': [-1.7888543819998317, 0], 'a6': [0.0, 0], 'a7': [-0.7559289460184544, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 242.55358117984142, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3797, [1, 1]]], 'bad_primes': [2, 3797], 'central_character': '30376.1', 'coefficient_field': '1.1.1.1', 'conductor': 30376, 'conductor_radical': 7594, 'degree': 2, 'euler_factors': [[1], [1, 2, 3], [1, 4, 5], [1, 2, 7], [1, 6, 11], [1, 1, 13], [1, 8, 17], [1, 7, 19], [1, 9, 23], [1, 6, 29], [1, 6, 31], [1, 4, 37], [1, 2, 41], [1, -5, 43], [1, 0, 47], [1, 6, 53], [1, 0, 59], [1, 6, 61], [1, 4, 67], [1, 10, 71], [1, 1, 73], [1, -1, 79], [1, 14, 83], [1, 6, 89], [1, 8, 97]], 'gamma_factors': [[], [0]], 'index': 0, 'label': '2-30376-1.1-c1-0-0', 'leading_term': '6.18663781646', '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': 3, 'origin': 'EllipticCurve/Q/30376/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, -0.095648102103858, -0.7315125699941918, -2.20880730393077, -4.21249204306257, -5.659348127550072, -5.258982506452014, -2.655976873145239, 0.8134431658157658, 2.7883985681122, 1.827828909011186, -1.058272336691407, -3.081609298759498, -2.301854532216764, 0.3823700594267347, 2.218288372808991, 1.696234650947063, 0.1970397583876157, 0.07700354912322861, 1.49681526661769, 2.175578935684631, 0.5968758378493786, -1.630864935597722, -1.774434596597512, 0.1694522206000062, 1.295942867488987, -0.1082499504773808, -2.004009232395313, -1.596893170260445, 0.3356680065046917, 0.5041978342285577, -1.688686735678498, -2.915401875245164, -1.187490312965613, 0.3883284101387146, -1.967145254691815, -6.143599891129444, -6.038292884469267, -0.2215271316473471, 5.387677393724908, 5.326730094278707, 1.515785938475131, -0.6270810753558045, -0.06460031631866811, 0.1294683802018499, -0.8499468212688923, -0.6073428841226655, 1.135213742130876, 1.510242603974149, -0.1097671382380586, -0.7423613118069113, 0.3423366245416031, -0.2353552571556524, -2.896934111813606, -1.907235319938553, 5.629421102245638, 12.54868477630553, 10.34936021860827, 1.777430049620528, -3.06215343454397, -1.113978374049976, 1.481722265011224, 0.811625668397111, -0.2641558001689343, 0.1781072876926571, -0.2483688165197987, -1.773286183583731, -0.8885167918497447, 2.18309553228442, 2.439664313044417, -0.7938108101338047, -1.942081516261234, 0.7885670159508464, 2.209246658688331, 0.1942792808216788, -0.4217060642208439, 2.249245386444768, 3.148642056761575, 0.3833657460016714, -0.9002417413894978, 0.8332271541192953, 0.00564332998368965, -4.10016640334165, -3.793579764146635, 2.879109529285316, 6.691813726141148, 2.373622201610644, -2.859175158233981, -2.395037270800925, 0.0362026427661813, -0.0628052117508741, -0.257676971870069, 1.339593666692139, 1.780098034782709, 0.4092391550252426, 0.0225575195062515, -0.09114622707184332, -1.453482703400907, 0.8977211935896016, 10.19985984162889, 17.04031062414668, 11.4875512396829, 0.4232101080687606, -2.977327916504801, 0.1009993848163948, 0.3009768527125563, -1.663610592272938, 0.1910334320311151, 2.942134927256811, 1.142032329895786, -1.692477436361739, -0.8790589947452784, 0.4438417480215659, -0.3009242168701544, 0.2479060217413121, 2.25559839269277, 1.573847418444524, -0.0316208582902589, 1.895928829251013, 3.151568832102996, -1.59329301226967], 'positive_zeros': ['1.938045659864408', '2.663208327258735', '3.465613178018053', '4.303826073777747', '4.476114756748991', '5.310543461569214', '5.979993841803799', '6.487796721061515', '7.201200827403869', '7.573758829419918', '8.384022462641684', '8.595562855046562', '9.507890997338932', '10.37686057515731', '10.76860725672937', '11.04161857036807', '11.59378100753876', '12.23389790931235', '12.67243219943437', '12.97073328959031', '13.58199547138613', '14.55843154946923', '15.08083110328672', '15.64234861513119', '15.92595014189507', '16.20014430310327', '16.82478108523873', '17.44191120567265', '17.93886690382282', '18.52203406620998', '18.80559021609568', '19.53338796507155', '19.89006398661433'], 'prelabel': '2-30376-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 15.574131795379202, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 314457295871535336, 'z1': {'__RealLiteral__': 0, 'data': '1.938045659864408', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '2.663208327258735', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '3.465613178018053', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 242.55358117984142, 'bad_primes': [2, 3797], 'central_character': '1.1', 'conductor': 30376, 'conductor_radical': 7594, 'degree': 2, 'dirichlet_coefficients': [1, 0, -2, 0, -4, 0, -2, 0, 1, 0, -6, 0, -1, 0, 8, 0, -8, 0, -7, 0, 4, 0, -9, 0, 11, 0, 4, 0, -6, 0, -6, 0, 12, 0, 8, 0, -4, 0, 2, 0, -2, 0, 5, 0, -4, 0, 0, 0, -3, 0, 16, 0, -6, 0, 24, 0, 14, 0, 0, 0, -6, 0, -2, 0, 4, 0, -4, 0, 18, 0, -10, 0, -1, 0, -22, 0, 12, 0, 1, 0, -11, 0, -14, 0, 32, 0, 12, 0, -6, 0, 2, 0, 12, 0, 28, 0, -8, 0, -6, 0], 'euler11': [1, 6, 11], 'euler13': [1, 1, 13], 'euler17': [1, 8, 17], 'euler19': [1, 7, 19], 'euler2': [1, 0, 0], 'euler23': [1, 9, 23], 'euler29': [1, 6, 29], 'euler3': [1, 2, 3], 'euler31': [1, 6, 31], 'euler37': [1, 4, 37], 'euler41': [1, 2, 41], 'euler43': [1, -5, 43], 'euler47': [1, 0, 47], 'euler5': [1, 4, 5], 'euler53': [1, 6, 53], 'euler59': [1, 0, 59], 'euler61': [1, 6, 61], 'euler67': [1, 4, 67], 'euler7': [1, 2, 7], 'euler71': [1, 10, 71], 'euler73': [1, 1, 73], 'euler79': [1, -1, 79], 'euler83': [1, 14, 83], 'euler89': [1, 6, 89], 'euler97': [1, 8, 97], 'euler_factors': [[1, 0, 0], [1, 2, 3], [1, 4, 5], [1, 2, 7], [1, 6, 11], [1, 1, 13], [1, 8, 17], [1, 7, 19], [1, 9, 23], [1, 6, 29], [1, 6, 31], [1, 4, 37], [1, 2, 41], [1, -5, 43], [1, 0, 47], [1, 6, 53], [1, 0, 59], [1, 6, 61], [1, 4, 67], [1, 10, 71], [1, 1, 73], [1, -1, 79], [1, 14, 83], [1, 6, 89], [1, 8, 97]], 'index': 0, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/30376/a'], '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': '2-30376-1.1-c1-0-0', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 3, 'prelabel': '2-30376-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 15.574131795379202, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 314457295871535336, 'z1': {'__RealLiteral__': 0, 'data': '1.938045659864408', 'prec': 57}}
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lfunc_instances • Show schema
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{'Lhash': '314457295871535336', 'Lhash_array': ['314457295871535336'], 'label': '2-30376-1.1-c1-0-0', 'type': 'ECQ', 'url': 'EllipticCurve/Q/30376/a'}