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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': -2, 'A5': -2, 'A6': 0, 'A7': -3, 'A8': 0, 'A9': 0, 'Lhash': '744728441749494658', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [-1.0, 0], 'a5': [-0.8944271909999159, 0], 'a6': [0.0, 0], 'a7': [-1.1338934190276817, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 113.0442141415267, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [11, [1]], [13, [1, -1]]], 'bad_primes': [3, 11, 13], 'central_character': '14157.1', 'coefficient_field': '1.1.1.1', 'conductor': 14157, 'conductor_radical': 429, 'degree': 2, 'euler_factors': [[1, 0, 2], [1], [1, 2, 5], [1, 3, 7], [1], [1, -1], [1, -2, 17], [1, 7, 19], [1, 8, 23], [1, 6, 29], [1, -5, 31], [1, 3, 37], [1, -4, 41], [1, -4, 43], [1, 6, 47], [1, -4, 53], [1, 6, 59], [1, 11, 61], [1, 3, 67], [1, 4, 71], [1, 3, 73], [1, -5, 79], [1, 6, 83], [1, -2, 89], [1, 13, 97]], 'gamma_factors': [[], [0]], 'index': 19, 'label': '2-14157-1.1-c1-0-19', 'leading_term': '4.9384966981', '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': 2, 'origin': 'EllipticCurve/Q/14157/j', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, -0.3021480369334868, -1.114756125107725, -2.081659522100555, -2.54767799761999, -1.835144227108418, 0.2106199393418535, 2.824789371324421, 4.561873063835936, 4.234994631153896, 1.931861980683985, -0.8354557535953911, -2.221396907708628, -1.585997288853238, -0.03197918379978386, 0.7451961349082772, 0.2626646977247651, -0.2276908841917227, 0.7457965024983672, 2.891682186013774, 4.115218986124277, 2.812533066129853, -0.01614555604649234, -1.573890946963156, -0.4483852651976842, 1.537198821621875, 1.3466632347936, -1.507912892602572, -4.122441336468016, -3.614479966720992, -0.673429837456855, 1.349721739287374, 0.7410924849641503, -0.5519411845182911, 0.1039226289686566, 2.208742347020973, 2.911676896897735, 1.31537519909449, -0.04612029834879033, 1.034771610751442, 2.92871181301974, 2.461707747991665, -0.02586565469496923, -0.5944306809508557, 2.629790019733295, 6.192389548773414, 5.708736239676858, 1.892817758533559, -0.6158085503176728, 0.1062842490802544, 1.097367356851097, -0.2261059222248048, -1.973256713992678, -1.334009173222959, 0.3118795520989205, -0.5061840490212091, -3.283544771924937, -3.821083289499525, -0.975897290954785, 1.140647864276638, -0.4036728549183317, -2.605087401153067, -1.4558939953793, 1.446301816615086, 1.689278286637002, -0.4138342663194191, -0.4258395356588773, 2.36238034081473, 3.412445606754775, 0.7156741206960056, -1.421316619792205, 0.5863504880687344, 3.575122014654597, 2.932946246929015, 0.06434723259336274, -0.6396996925340586, 0.621340577701848, 0.4639103478570707, -0.6502565609498928, 0.4950995805399229, 2.500489007733635, 0.4042081697206104, -5.113173122439376, -7.056767413874304, -2.943412296669831, 0.9243589246673768, -0.4334288862073962, -3.185227546824688, -2.120120034326906, 0.7440372522007322, 0.9368950342827406, -0.476719190090907, -0.2791472620059374, 0.1530395977117514, -1.58464363793947, -2.860584224857128, -0.9274715627118709, 0.1561226622975682, -4.187625800262094, -9.426536131693862, -7.784305637045254, -1.034827615134417, 2.277328024488176, 0.4293156818188098, -0.8224309482915693, 0.1338545771012065, -0.8213376853716875, -3.734667126521196, -3.75962118484224, -0.674776369324983, 0.6750349890262302, -0.279032122660042, 0.1699604313561779, 1.053612521410579, -1.725302302199455, -5.453695201030854, -3.503208195191462, 2.215544554659385, 3.473170091602409, 0.04206679113056781, -0.5448878200729406], 'positive_zeros': ['1.479002360313681', '2.667884081482667', '3.505757316123722', '4.086773010138506', '4.364837967335280', '5.498484340593158', '6.051731380705423', '6.635377147259025', '7.558163541203709', '8.120428442113119', '8.484985666349242', '9.470482666927445', '9.568468241754712', '10.49712083564882', '10.82138112923136', '11.89767435264773', '12.23283106647308', '12.72333396840047', '13.43325929288581', '13.68791085057380', '14.57780352268707', '14.96232578529806', '15.61808223442100', '16.19741471483877', '16.54887360507324', '17.30419386859897', '17.70631532191601', '18.50711555100583', '18.87930801387366', '19.33742083932445', '19.69337883966340'], 'prelabel': '2-14157-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 10.63222526762515, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 744728441749494658, 'z1': {'__RealLiteral__': 0, 'data': '1.479002360313681', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '2.667884081482667', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '3.505757316123722', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 113.0442141415267, 'bad_primes': [3, 11, 13], 'central_character': '1.1', 'conductor': 14157, 'conductor_radical': 429, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, -2, -2, 0, -3, 0, 0, 0, 0, 0, 1, 0, 0, 4, 2, 0, -7, 4, 0, 0, -8, 0, -1, 0, 0, 6, -6, 0, 5, 0, 0, 0, 6, 0, -3, 0, 0, 0, 4, 0, 4, 0, 0, 0, -6, 0, 2, 0, 0, -2, 4, 0, 0, 0, 0, 0, -6, 0, -11, 0, 0, -8, -2, 0, -3, -4, 0, 0, -4, 0, -3, 0, 0, 14, 0, 0, 5, -8, 0, 0, -6, 0, -4, 0, 0, 0, 2, 0, -3, 16, 0, 0, 14, 0, -13, 0, 0, 2], 'euler11': [1, 0, 0], 'euler13': [1, -1, 0], 'euler17': [1, -2, 17], 'euler19': [1, 7, 19], 'euler2': [1, 0, 2], 'euler23': [1, 8, 23], 'euler29': [1, 6, 29], 'euler3': [1, 0, 0], 'euler31': [1, -5, 31], 'euler37': [1, 3, 37], 'euler41': [1, -4, 41], 'euler43': [1, -4, 43], 'euler47': [1, 6, 47], 'euler5': [1, 2, 5], 'euler53': [1, -4, 53], 'euler59': [1, 6, 59], 'euler61': [1, 11, 61], 'euler67': [1, 3, 67], 'euler7': [1, 3, 7], 'euler71': [1, 4, 71], 'euler73': [1, 3, 73], 'euler79': [1, -5, 79], 'euler83': [1, 6, 83], 'euler89': [1, -2, 89], 'euler97': [1, 13, 97], 'euler_factors': [[1, 0, 2], [1, 0, 0], [1, 2, 5], [1, 3, 7], [1, 0, 0], [1, -1, 0], [1, -2, 17], [1, 7, 19], [1, 8, 23], [1, 6, 29], [1, -5, 31], [1, 3, 37], [1, -4, 41], [1, -4, 43], [1, 6, 47], [1, -4, 53], [1, 6, 59], [1, 11, 61], [1, 3, 67], [1, 4, 71], [1, 3, 73], [1, -5, 79], [1, 6, 83], [1, -2, 89], [1, 13, 97]], 'index': 19, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/14157/j'], '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': '2-14157-1.1-c1-0-19', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 2, 'prelabel': '2-14157-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 10.63222526762515, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 744728441749494658, 'z1': {'__RealLiteral__': 0, 'data': '1.479002360313681', 'prec': 57}}
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lfunc_instances • Show schema
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{'Lhash': '744728441749494658', 'Lhash_array': ['744728441749494658'], 'label': '2-14157-1.1-c1-0-19', 'type': 'ECQ', 'url': 'EllipticCurve/Q/14157/j'}