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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -3, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': 2, 'A8': 0, 'A9': 6, 'Lhash': '1724741254376473404', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-1.7320508075688774, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.7559289460184544, 0], 'a8': [0.0, 0], 'a9': [2.0, 0], 'algebraic': True, 'analytic_conductor': 1545.903783131989, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1]], [11, [1]]], 'bad_primes': [2, 5, 11], 'central_character': '193600.1', 'coefficient_field': '1.1.1.1', 'conductor': 193600, 'conductor_radical': 110, 'degree': 2, 'euler_factors': [[1], [1, 3, 3], [1], [1, -2, 7], [1], [1, 4, 13], [1, -5, 17], [1, -1, 19], [1, -2, 23], [1, 8, 29], [1, -10, 31], [1, 6, 37], [1, -3, 41], [1, 4, 43], [1, 4, 47], [1, -6, 53], [1, 8, 59], [1, -10, 61], [1, 1, 67], [1, 12, 71], [1, -3, 73], [1, 6, 79], [1, -13, 83], [1, 9, 89], [1, -14, 97]], 'gamma_factors': [[], [0]], 'index': 51, 'label': '2-440e2-1.1-c1-0-51', 'leading_term': '1.07845909257', '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/193600/l', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [1.078459092570181, 0.563383841073268, -0.5257053175959864, -1.073068278242804, -0.3115782634106598, 0.9506594392444796, 0.7622175399985353, -1.40767516747045, -2.978615180279286, -0.7663555706175113, 4.310028356048422, 6.915844133808758, 3.534680377395194, -2.296369964959053, -3.838926994247707, 0.1090232547296512, 3.87802116645817, 3.12984904382133, 0.3057969309685811, -0.4672434484844814, 0.2107304256230753, -0.3112514999313119, -1.168245646972558, -0.2683935497246453, 0.6501761647417058, -0.890970859349318, -2.482484268752572, -0.7883038500936593, 1.60332057913421, 0.7678503244180362, -0.4327032879345697, 2.107180024834927, 3.950952312328504, -0.7853999586160701, -6.381392685790052, -3.10677534381062, 5.349106230079505, 7.025013093311941, 1.433481635643842, -1.608035341695283, 0.0597013010810054, 0.2848501972340157, -1.335274883389045, -0.2917886483129862, 1.927077657132543, 1.338331795068087, 0.006084810165676663, 0.387255102019986, -0.09272383801549008, -1.487759097766802, -0.292530285733423, 0.8875473015936993, -2.329543048930454, -4.001581521528078, 1.955943358311103, 6.784350706017084, 1.961555093179906, -3.409490010215622, -0.3495197957468649, 2.776563754205524, -0.8786158450718771, -2.842958114626073, 1.035509402911127, 1.998268106673464, -1.907491705381981, -2.670618031085027, -0.0718353021612168, 0.2006211570777968, -0.3766681058176235, 0.5629211887882225, 0.05198552661190592, -1.025930328184608, 0.4267485537621424, 0.4136969205799443, -2.610940424338242, -1.827726550821147, 1.573533366545151, -0.4873702809032993, -1.720680545392122, 7.383171962437104, 14.85163191974062, 7.838151503478695, -1.442494855076721, -0.5746649462309606, 1.726466326244707, -0.4322266582903158, 0.1339207102905833, 2.814792623814168, 1.321642827149337, -0.5410938261905937, 0.543063358326246, -0.04932773278475947, -1.489077328861462, -0.1640792141184485, -0.1824299443627357, -2.260224637726241, -1.004831490119998, 0.5976421434812048, -1.158427013444698, -0.5068750772103205, -0.1823806377643627, -9.263293959977563, -16.24551503989095, -6.741144786951414, 4.388458910996197, 1.712347998193275, -2.058923030095482, 1.971113283688414, 3.04247316680116, -0.3384381092129671, -0.2164309261992123, 0.6678386920284455, -0.3874317586145522, 0.5963173610120742, 0.9318433393020972, -1.565770372747928, -0.9024448664991268, 1.682451839880599, 0.6519841398697677, -0.1034613166913168, -0.2320702351170368], 'positive_zeros': ['0.3813280301358895', '1.057438757515623', '1.606097296547197', '2.292145315204809', '3.144238061221675', '3.744586736298942', '4.538837628780275', '4.907569761760039', '5.175401754116664', '5.794475752226039', '6.147825617360329', '6.815717067461508', '7.347287371833091', '7.581132895554293', '8.222069779588460', '8.839815914121758', '9.568534769782978', '9.992159190000727', '10.29359497918336', '10.77835099528788', '11.50423210437249', '11.58113955722064', '11.98419765451013', '12.53187733563193', '12.85414132886411', '13.43719400605365', '14.06492456876823', '14.51624537959826', '14.95518866564697', '15.44095589412184', '15.88477066142021', '16.50945529892635', '16.79873735869627', '17.11522021990949', '17.50823701355644', '17.94432604822913', '18.29021778817419', '18.86395457206260', '19.22026305993948', '19.57431386003443'], 'prelabel': '2-440e2-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 39.317982948416734, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1724741254376473404, 'z1': {'__RealLiteral__': 0, 'data': '0.3813280301358895', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.057438757515623', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.606097296547197', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1545.903783131989, 'bad_primes': [2, 5, 11], 'central_character': '1.1', 'conductor': 193600, 'conductor_radical': 110, 'degree': 2, 'dirichlet_coefficients': [1, 0, -3, 0, 0, 0, 2, 0, 6, 0, 0, 0, -4, 0, 0, 0, 5, 0, 1, 0, -6, 0, 2, 0, 0, 0, -9, 0, -8, 0, 10, 0, 0, 0, 0, 0, -6, 0, 12, 0, 3, 0, -4, 0, 0, 0, -4, 0, -3, 0, -15, 0, 6, 0, 0, 0, -3, 0, -8, 0, 10, 0, 12, 0, 0, 0, -1, 0, -6, 0, -12, 0, 3, 0, 0, 0, 0, 0, -6, 0, 9, 0, 13, 0, 0, 0, 24, 0, -9, 0, -8, 0, -30, 0, 0, 0, 14, 0, 0, 0], 'euler11': [1, 0, 0], 'euler13': [1, 4, 13], 'euler17': [1, -5, 17], 'euler19': [1, -1, 19], 'euler2': [1, 0, 0], 'euler23': [1, -2, 23], 'euler29': [1, 8, 29], 'euler3': [1, 3, 3], 'euler31': [1, -10, 31], 'euler37': [1, 6, 37], 'euler41': [1, -3, 41], 'euler43': [1, 4, 43], 'euler47': [1, 4, 47], 'euler5': [1, 0, 0], 'euler53': [1, -6, 53], 'euler59': [1, 8, 59], 'euler61': [1, -10, 61], 'euler67': [1, 1, 67], 'euler7': [1, -2, 7], 'euler71': [1, 12, 71], 'euler73': [1, -3, 73], 'euler79': [1, 6, 79], 'euler83': [1, -13, 83], 'euler89': [1, 9, 89], 'euler97': [1, -14, 97], 'euler_factors': [[1, 0, 0], [1, 3, 3], [1, 0, 0], [1, -2, 7], [1, 0, 0], [1, 4, 13], [1, -5, 17], [1, -1, 19], [1, -2, 23], [1, 8, 29], [1, -10, 31], [1, 6, 37], [1, -3, 41], [1, 4, 43], [1, 4, 47], [1, -6, 53], [1, 8, 59], [1, -10, 61], [1, 1, 67], [1, 12, 71], [1, -3, 73], [1, 6, 79], [1, -13, 83], [1, 9, 89], [1, -14, 97]], 'index': 51, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/193600/l'], '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': '2-440e2-1.1-c1-0-51', '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': '2-440e2-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 39.317982948416734, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1724741254376473404, 'z1': {'__RealLiteral__': 0, 'data': '0.3813280301358895', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1724741254376473404', 'Lhash_array': ['1724741254376473404'], 'label': '2-440e2-1.1-c1-0-51', 'type': 'ECQ', 'url': 'EllipticCurve/Q/193600/l'}