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lfunc_lfunctions • Show schema
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{'A10': -2, 'A2': 1, 'A3': -2, 'A4': 1, 'A5': -2, 'A6': -2, 'A7': 1, 'A8': 1, 'A9': 1, 'Lhash': '1919067531732231675', 'a10': [-0.6324555320336759, 0], 'a2': [0.7071067811865475, 0], 'a3': [-1.1547005383792517, 0], 'a4': [0.5, 0], 'a5': [-0.8944271909999159, 0], 'a6': [-0.8164965809277261, 0], 'a7': [0.3779644730092272, 0], 'a8': [0.35355339059327373, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 2162.364856816678, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [7, [1, -1]], [23, [1, 1]], [29, [1]]], 'bad_primes': [2, 7, 23, 29], 'central_character': '270802.1', 'coefficient_field': '1.1.1.1', 'conductor': 270802, 'conductor_radical': 9338, 'degree': 2, 'euler_factors': [[1, -1], [1, 2, 3], [1, 2, 5], [1, -1], [1, 4, 11], [1, -2, 13], [1, 0, 17], [1, 2, 19], [1, 1], [1], [1, 10, 31], [1, -6, 37], [1, 12, 41], [1, 8, 43], [1, 2, 47], [1, 10, 53], [1, 8, 59], [1, -12, 61], [1, -12, 67], [1, 0, 71], [1, 8, 73], [1, -4, 79], [1, -12, 83], [1, 0, 89], [1, 8, 97]], 'gamma_factors': [[], [0]], 'index': 10, 'label': '2-270802-1.1-c1-0-10', 'leading_term': '4.44774921171', '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/270802/m', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 0.8315217839613758, 0.2234744612466938, -2.010739427954261, -4.076492211779129, -3.570026836130338, -0.5160766321879053, 1.734525451732897, 0.1706701068592206, -3.571217622717215, -4.672725129783385, -1.522055310603395, 1.844213999118824, 1.469692385465088, -0.8722994737862966, -0.9398639260356263, 1.089369884272788, 1.491587932285908, -0.2670935160366939, -1.000320610100431, 0.03578127467842519, 0.2290855930387459, -0.6242258567156206, 0.07257375996265727, 1.651141149343356, 0.7786986457681224, -1.321486951173276, -0.4525879686024449, 1.64246695496503, -0.2163574936118443, -3.76169272822203, -2.745099156231234, 0.2519531188938849, -1.10388249337304, -1.871749303405814, 6.216135429865588, 15.30578171157931, 11.11145745431215, -1.403425222626637, -4.92563779917934, 1.648350682959589, 4.868571339847942, 1.626886881956492, -0.2123599709453784, 0.5754513609063652, 0.04366117684001711, -0.3214685177120115, 1.022137675890122, 0.8276428962212711, -0.4547733568960723, 0.8912150180128958, 2.191560349353562, 0.1919316504918943, -0.3341960800433842, 2.094984955165551, 0.1354720712726157, -5.722784533652836, -5.588581763074561, -0.503697980252865, -0.1021083536979525, -2.440789289339872, -0.6243078430459132, 1.325485145088797, -0.3888573617886891, -0.5553806272138903, 1.013603436658391, -0.4366119770424841, -0.9658450608367385, 2.324180302730624, 1.656591933756334, -3.202090156221054, -2.308022384567009, 1.587991300265713, -0.5425797581758831, -2.457811595048767, 0.8230078225672918, -1.178083570363028, -8.246430388932042, -5.902481246447083, 2.55971237707085, 2.752533090181354, -0.6910452074966373, 0.7900831581401629, -0.09920961219856854, -5.094223754287201, -4.451395296671887, -0.1354415938212122, -0.005092788731394938, -0.2482146034022477, 1.596506383741526, 0.3183547079774894, -2.098735540915391, -1.056547454251115, 0.13531017450201, -0.05483944128147027, -0.009252104542022221, -1.266153940725027, -0.366450863674412, 5.866105109940808, 7.173635803770658, 0.6544642029149506, 0.7886263061191565, 6.21161563185043, 2.099739718287222, -2.715073281022172, 3.856585642471201, 6.497193908565017, -1.68341991238416, -3.571708402580159, 1.35014314771834, 0.2870911030070802, -1.162305097712712, 2.200283006948179, 1.897458693819885, -0.3997855136824157, 0.9923523365020988, 0.3672260202601825, -1.222744504197293, 1.985949168668774, 2.550107699911008, -1.524098672996796], 'positive_zeros': ['0.5333769338030790', '1.539283050996870', '2.012440881271181', '2.842642724209554', '3.398801132986382', '3.870182429342392', '4.464079366864442', '4.991558930639943', '5.317104411779455', '5.739138309073427', '6.330965459306657', '6.794279482285717', '7.235840723983273', '7.961653630213916', '8.144368911681048', '8.589975498159707', '9.467913543944251', '9.943951060687235', '10.65312000913336', '10.83592132573387', '11.25984146677067', '11.57394907143715', '12.12943602005689', '12.39494827634074', '13.02076658421919', '13.29050488419460', '13.75625726161419', '14.53796165545562', '14.73947316345619', '15.29855556753239', '15.70365849776474', '16.07384867239467', '16.45355823597357', '16.83588409697945', '17.33356986509960', '17.87211721904134', '18.21680397687078', '18.68722708998559', '18.95022147694556', '19.66173947323137'], 'prelabel': '2-270802-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 46.50123500313382, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1919067531732231675, 'z1': {'__RealLiteral__': 0, 'data': '0.5333769338030790', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.539283050996870', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.012440881271181', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2162.364856816678, 'bad_primes': [2, 7, 23, 29], 'central_character': '1.1', 'conductor': 270802, 'conductor_radical': 9338, 'degree': 2, 'dirichlet_coefficients': [1, 1, -2, 1, -2, -2, 1, 1, 1, -2, -4, -2, 2, 1, 4, 1, 0, 1, -2, -2, -2, -4, -1, -2, -1, 2, 4, 1, 0, 4, -10, 1, 8, 0, -2, 1, 6, -2, -4, -2, -12, -2, -8, -4, -2, -1, -2, -2, 1, -1, 0, 2, -10, 4, 8, 1, 4, 0, -8, 4, 12, -10, 1, 1, -4, 8, 12, 0, 2, -2, 0, 1, -8, 6, 2, -2, -4, -4, 4, -2, -11, -12, 12, -2, 0, -8, 0, -4, 0, -2, 2, -1, 20, -2, 4, -2, -8, 1, -4, -1], 'euler11': [1, 4, 11], 'euler13': [1, -2, 13], 'euler17': [1, 0, 17], 'euler19': [1, 2, 19], 'euler2': [1, -1, 0], 'euler23': [1, 1, 0], 'euler29': [1, 0, 0], 'euler3': [1, 2, 3], 'euler31': [1, 10, 31], 'euler37': [1, -6, 37], 'euler41': [1, 12, 41], 'euler43': [1, 8, 43], 'euler47': [1, 2, 47], 'euler5': [1, 2, 5], 'euler53': [1, 10, 53], 'euler59': [1, 8, 59], 'euler61': [1, -12, 61], 'euler67': [1, -12, 67], 'euler7': [1, -1, 0], 'euler71': [1, 0, 71], 'euler73': [1, 8, 73], 'euler79': [1, -4, 79], 'euler83': [1, -12, 83], 'euler89': [1, 0, 89], 'euler97': [1, 8, 97], 'euler_factors': [[1, -1, 0], [1, 2, 3], [1, 2, 5], [1, -1, 0], [1, 4, 11], [1, -2, 13], [1, 0, 17], [1, 2, 19], [1, 1, 0], [1, 0, 0], [1, 10, 31], [1, -6, 37], [1, 12, 41], [1, 8, 43], [1, 2, 47], [1, 10, 53], [1, 8, 59], [1, -12, 61], [1, -12, 67], [1, 0, 71], [1, 8, 73], [1, -4, 79], [1, -12, 83], [1, 0, 89], [1, 8, 97]], 'index': 10, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/270802/m'], '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': '2-270802-1.1-c1-0-10', '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': '2-270802-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 46.50123500313382, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1919067531732231675, 'z1': {'__RealLiteral__': 0, 'data': '0.5333769338030790', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1919067531732231675', 'Lhash_array': ['1919067531732231675'], 'label': '2-270802-1.1-c1-0-10', 'type': 'ECQ', 'url': 'EllipticCurve/Q/270802/m'}