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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -2, 'A4': 0, 'A5': 1, 'A6': 0, 'A7': 1, 'A8': 0, 'A9': 1, 'Lhash': '895770132318626556', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-1.1547005383792517, 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': 1614.255727262205, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1, -1]], [7, [1, -1]], [19, [1]]], 'bad_primes': [2, 5, 7, 19], 'central_character': '202160.1', 'coefficient_field': '1.1.1.1', 'conductor': 202160, 'conductor_radical': 1330, 'degree': 2, 'euler_factors': [[1], [1, 2, 3], [1, -1], [1, -1], [1, 1, 11], [1, -3, 13], [1, 7, 17], [1], [1, 1, 23], [1, 1, 29], [1, 4, 31], [1, -4, 37], [1, -5, 41], [1, -8, 43], [1, -2, 47], [1, -4, 53], [1, -5, 59], [1, 1, 61], [1, 1, 67], [1, 11, 71], [1, 14, 73], [1, -11, 79], [1, -9, 83], [1, 6, 89], [1, 2, 97]], 'gamma_factors': [[], [0]], 'index': 41, 'label': '2-202160-1.1-c1-0-41', 'leading_term': '5.14240621672', '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/202160/o', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.084582684536542, 1.121496586672022, -0.09249892179077025, -1.360908808768989, -0.9733375836976962, 1.144281952133668, 2.690737566524012, 1.588263898741227, -0.7742636587222493, -0.6513719216286025, 2.805774626169031, 5.30579381990631, 2.677509748204971, -2.89081283744414, -5.230847762758085, -2.652022808072385, 0.08217772185145561, -0.5940130330023369, -2.016075410401208, -0.753291981498032, 1.380692165378383, 1.177570484537274, -0.01130959296312261, 0.4644795273218982, 0.9222080725168781, -0.891068735874543, -2.118835068935655, -0.01238402749563249, 1.27530864928927, -2.405742135565276, -6.021377079436367, -3.147221385805225, 1.873543411622131, 1.164970503568655, -2.480360466177876, -1.678616104746656, 0.9018024153236458, -1.68333417980711, -6.097123684748495, -4.752816222473321, -0.1581950969456535, 0.8225672287129844, -0.4166615094429486, 0.1631361535303014, 0.4048144748012308, -0.9966216900336144, -0.1259071018393033, 2.381987542644235, 0.9879198810841578, -2.348073988247964, -1.267895578972727, 1.311210877450574, -0.2229948607681282, -1.218965742686023, 2.335074493061403, 2.991183224924603, -2.199002069332653, -3.408402632887387, 1.659129096914777, 2.285620292480195, -2.773087327084396, -3.276557888982203, 0.6302317566717853, 0.6700390445682879, -1.150302125103372, 0.4382765748519663, 1.142030210236681, -1.564924979287744, -2.095876763666971, -0.02998514420675672, 0.1541173786429369, 0.1973560481046789, 1.058509763618169, -1.784269884417791, -4.67759758382123, -0.1230276259372462, 4.248849916545212, -0.8026125081764655, -5.171076830304038, -0.1720436802535795, 3.378798480101464, -0.06580882517497945, -0.501080209722954, 2.492961034772897, 0.1234357402282592, -3.571358904731068, -1.691449172558907, 0.3100124207422889, -0.2313490806932761, 1.554205325209218, 2.956608696859752, 0.3358820307845881, -0.4757679415297837, 1.327463032960433, -0.03435089429511075, -1.086115888231324, 1.432135930783012, 0.3170402648768773, -3.169710793790857, -0.145584240373525, 2.730546056073339, -2.611410214039456, -5.419500487661571, -0.943753668450543, -0.599052380423225, -2.990629897793547, 1.561924380829962, 5.356937062350456, 1.373506215683701, -0.5790990849987336, 1.927988757844565, 1.035929797374405, -0.7086854067497742, 0.4548440774754057, -0.1012778615363825, -1.033969755298472, 0.6633265313250944, 0.08784648109324995, -0.5931677892818217, 4.223221069579794], 'positive_zeros': ['0.7349952187574182', '1.378099399229301', '2.158183964594018', '2.562841602265312', '3.369474776970746', '4.233201693607921', '4.406807125047198', '5.075946566876566', '5.744612768371754', '5.868737163687948', '6.403867389921818', '7.001087234950906', '7.372443290204807', '8.137838038482099', '8.572974078213031', '9.129591859115609', '9.402828017373324', '10.26195841609479', '10.64549127817637', '10.96406658890750', '11.32865609808308', '11.76196667056693', '12.31470721379174', '12.84596368710635', '13.22960006974694', '13.60757478805051', '14.15276085380161', '14.67152743668268', '15.11755513497162', '15.70212461709221', '16.06970982626763', '16.45461538733716', '16.86901860131447', '17.50509483038968', '17.81681896672509', '17.93827327678302', '18.39040782356553', '19.00439865825432', '19.47347493616296'], 'prelabel': '2-202160-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 40.17780142394809, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 895770132318626556, 'z1': {'__RealLiteral__': 0, 'data': '0.7349952187574182', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.378099399229301', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.158183964594018', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1614.255727262205, 'bad_primes': [2, 5, 7, 19], 'central_character': '1.1', 'conductor': 202160, 'conductor_radical': 1330, 'degree': 2, 'dirichlet_coefficients': [1, 0, -2, 0, 1, 0, 1, 0, 1, 0, -1, 0, 3, 0, -2, 0, -7, 0, 0, 0, -2, 0, -1, 0, 1, 0, 4, 0, -1, 0, -4, 0, 2, 0, 1, 0, 4, 0, -6, 0, 5, 0, 8, 0, 1, 0, 2, 0, 1, 0, 14, 0, 4, 0, -1, 0, 0, 0, 5, 0, -1, 0, 1, 0, 3, 0, -1, 0, 2, 0, -11, 0, -14, 0, -2, 0, -1, 0, 11, 0, -11, 0, 9, 0, -7, 0, 2, 0, -6, 0, 3, 0, 8, 0, 0, 0, -2, 0, -1, 0], 'euler11': [1, 1, 11], 'euler13': [1, -3, 13], 'euler17': [1, 7, 17], 'euler19': [1, 0, 0], 'euler2': [1, 0, 0], 'euler23': [1, 1, 23], 'euler29': [1, 1, 29], 'euler3': [1, 2, 3], 'euler31': [1, 4, 31], 'euler37': [1, -4, 37], 'euler41': [1, -5, 41], 'euler43': [1, -8, 43], 'euler47': [1, -2, 47], 'euler5': [1, -1, 0], 'euler53': [1, -4, 53], 'euler59': [1, -5, 59], 'euler61': [1, 1, 61], 'euler67': [1, 1, 67], 'euler7': [1, -1, 0], 'euler71': [1, 11, 71], 'euler73': [1, 14, 73], 'euler79': [1, -11, 79], 'euler83': [1, -9, 83], 'euler89': [1, 6, 89], 'euler97': [1, 2, 97], 'euler_factors': [[1, 0, 0], [1, 2, 3], [1, -1, 0], [1, -1, 0], [1, 1, 11], [1, -3, 13], [1, 7, 17], [1, 0, 0], [1, 1, 23], [1, 1, 29], [1, 4, 31], [1, -4, 37], [1, -5, 41], [1, -8, 43], [1, -2, 47], [1, -4, 53], [1, -5, 59], [1, 1, 61], [1, 1, 67], [1, 11, 71], [1, 14, 73], [1, -11, 79], [1, -9, 83], [1, 6, 89], [1, 2, 97]], 'index': 41, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/202160/o'], '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': '2-202160-1.1-c1-0-41', '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': '2-202160-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 40.17780142394809, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 895770132318626556, 'z1': {'__RealLiteral__': 0, 'data': '0.7349952187574182', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '895770132318626556', 'Lhash_array': ['895770132318626556'], 'label': '2-202160-1.1-c1-0-41', 'type': 'ECQ', 'url': 'EllipticCurve/Q/202160/o'}