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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': 2, 'A8': 0, 'A9': 0, 'Lhash': '1966070613267335790', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.7559289460184544, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 1379.8149469277257, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1]]], 'bad_primes': [2, 3, 5], 'central_character': '172800.1', 'coefficient_field': '1.1.1.1', 'conductor': 172800, 'conductor_radical': 30, 'degree': 2, 'euler_factors': [[1], [1], [1], [1, -2, 7], [1, 5, 11], [1, 5, 13], [1, 1, 17], [1, -2, 19], [1, -1, 23], [1, -5, 29], [1, -1, 31], [1, -2, 37], [1, 6, 41], [1, -5, 43], [1, -7, 47], [1, -4, 53], [1, -12, 59], [1, 6, 61], [1, 12, 67], [1, 2, 71], [1, 12, 73], [1, 5, 79], [1, 2, 83], [1, 6, 89], [1, 16, 97]], 'gamma_factors': [[], [0]], 'index': 43, 'label': '2-172800-1.1-c1-0-43', 'leading_term': '6.45055184621', '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/172800/bw', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.379941423497115, 1.505360699261406, -0.05965158978059713, -2.200582501217378, -2.837045814424114, -1.081069575669925, 1.345637603025353, 1.814459027049276, 0.1156422501768106, -1.132485510551965, -0.2694654623503508, 0.5579189882171453, -1.640353277801883, -5.586873965943009, -6.619337882009225, -3.306190566798196, 0.1639268570430457, 0.1491429657915172, -1.260878207481556, -0.5547328069304475, 0.9098379972274921, -0.04918198091375593, -1.494833696982692, 0.950718418784366, 5.496526261133332, 5.766107544143794, 1.309678033165978, -1.499081561483568, -0.2853008120719815, 0.3112828617693988, -1.59614445636769, -1.901134411424094, 0.1854058636356271, -0.1958239267246703, -3.260935990674208, -2.849922110599911, 1.579409326073047, 2.920128208202442, -0.4314306348487607, -1.982664461404133, -0.1865762311100881, -0.4429222180934456, -2.622420297955326, -1.176977912899974, 2.257670828175639, 1.453839193368425, -1.367238256968497, -0.3044847622167807, 1.493006733416713, -1.03169050079278, -3.259180620920641, -0.7737250703746793, 0.721526038291338, -2.159329014946323, -2.923039621175181, 0.3964201334718622, 0.8583434387360851, -1.884618740789974, -1.13481957444142, 1.49955834328245, 0.1900479356133527, -1.394063049086036, 0.9113617365175349, 1.086170099520493, -3.245615935073894, -4.066729486075102, -0.4303120190877276, -0.7504204140442859, -4.135473472220131, -3.04914117871154, -0.1183218563548154, -0.2664527319778887, 1.103813690783179, 5.024077607282568, 4.129041093922524, -0.06275938686197692, 0.4448811300989303, 1.806509471709555, -2.246143126327982, -4.806313584440807, -1.252231755793231, 0.6852852538496957, -0.6704532986993199, 1.11350927544179, 3.180348084065109, 0.6720376280093758, -0.317539193719595, 2.096432024510604, 0.3654068641429087, -2.88291941279561, 0.5409065428286355, 4.421398512177546, 1.617076082781675, -0.4500738546449757, 1.64577183707577, 1.063494119080457, -0.5922247367270922, 1.397903117618392, 1.07409702406732, -2.559812507254794, -0.9467033523968543, 2.61102161958634, -0.4484755044876732, -3.221811946869495, 0.3623989801978819, 2.007328925735158, -0.007351238496400639, 0.915676330408095, 1.245800157098585, -1.47454822882572, 0.8148371992076172, 5.801671453197726, 3.463352571906984, -0.849644384287731, 0.2268964160638735, 0.4994346075696549, -0.4310969095131681, 3.420601827873033, 5.237597432301575, 0.517643086103487], 'positive_zeros': ['0.7431056482285218', '1.602494739021511', '2.264627271793694', '2.796380045721471', '3.112338606434310', '4.229955778038804', '4.524320288671999', '5.076210435512130', '5.493920940587879', '5.942543729014979', '6.825767787501677', '7.291405579576698', '7.556939162859706', '8.224232379674034', '8.479204242259917', '9.163247381755744', '9.720836686394370', '10.28316836303289', '10.43455810691510', '11.07651129887557', '11.61014422075987', '12.02763955195442', '12.43012399280473', '13.06139499751620', '13.33774333029815', '13.96934113984616', '14.32982616455478', '14.83967198669299', '15.26702283751137', '15.67109396620165', '16.07437691196709', '16.79693157200151', '16.92586957590733', '17.77595345484700', '17.90541062367328', '18.14808874855671', '18.99395211777879', '19.20518915160486', '19.64067996695914'], 'prelabel': '2-172800-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 37.14586042788248, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1966070613267335790, 'z1': {'__RealLiteral__': 0, 'data': '0.7431056482285218', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.602494739021511', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.264627271793694', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1379.8149469277257, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 172800, 'conductor_radical': 30, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 2, 0, 0, 0, -5, 0, -5, 0, 0, 0, -1, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 5, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, -6, 0, 5, 0, 0, 0, 7, 0, -3, 0, 0, 0, 4, 0, 0, 0, 0, 0, 12, 0, -6, 0, 0, 0, 0, 0, -12, 0, 0, 0, -2, 0, -12, 0, 0, 0, -10, 0, -5, 0, 0, 0, -2, 0, 0, 0, 0, 0, -6, 0, -10, 0, 0, 0, 0, 0, -16, 0, 0, 0], 'euler11': [1, 5, 11], 'euler13': [1, 5, 13], 'euler17': [1, 1, 17], 'euler19': [1, -2, 19], 'euler2': [1, 0, 0], 'euler23': [1, -1, 23], 'euler29': [1, -5, 29], 'euler3': [1, 0, 0], 'euler31': [1, -1, 31], 'euler37': [1, -2, 37], 'euler41': [1, 6, 41], 'euler43': [1, -5, 43], 'euler47': [1, -7, 47], 'euler5': [1, 0, 0], 'euler53': [1, -4, 53], 'euler59': [1, -12, 59], 'euler61': [1, 6, 61], 'euler67': [1, 12, 67], 'euler7': [1, -2, 7], 'euler71': [1, 2, 71], 'euler73': [1, 12, 73], 'euler79': [1, 5, 79], 'euler83': [1, 2, 83], 'euler89': [1, 6, 89], 'euler97': [1, 16, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 0, 0], [1, -2, 7], [1, 5, 11], [1, 5, 13], [1, 1, 17], [1, -2, 19], [1, -1, 23], [1, -5, 29], [1, -1, 31], [1, -2, 37], [1, 6, 41], [1, -5, 43], [1, -7, 47], [1, -4, 53], [1, -12, 59], [1, 6, 61], [1, 12, 67], [1, 2, 71], [1, 12, 73], [1, 5, 79], [1, 2, 83], [1, 6, 89], [1, 16, 97]], 'index': 43, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/172800/bw'], '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': '2-172800-1.1-c1-0-43', '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': '2-172800-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 37.14586042788248, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1966070613267335790, 'z1': {'__RealLiteral__': 0, 'data': '0.7431056482285218', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1966070613267335790', 'Lhash_array': ['1966070613267335790'], 'factors': ['2-172800-1.1-c1-0-43'], 'label': '2-172800-1.1-c1-0-43', 'type': 'ECQ', 'url': 'EllipticCurve/Q/172800/bw'}