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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -1, 'A4': 0, 'A5': -1, 'A6': 0, 'A7': 3, 'A8': 0, 'A9': 1, 'Lhash': '320749682849306354', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [-0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [1.1338934190276817, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 2623.56480881119, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [5, [1, 1]], [37, [1]]], 'bad_primes': [2, 3, 5, 37], 'central_character': '328560.1', 'coefficient_field': '1.1.1.1', 'conductor': 328560, 'conductor_radical': 1110, 'degree': 2, 'euler_factors': [[1], [1, 1], [1, 1], [1, -3, 7], [1, -2, 11], [1, -3, 13], [1, 2, 17], [1, -5, 19], [1, -4, 23], [1, 1, 29], [1, 0, 31], [1], [1, 12, 41], [1, 4, 43], [1, 6, 47], [1, -12, 53], [1, 0, 59], [1, -6, 61], [1, -10, 67], [1, 1, 71], [1, -4, 73], [1, -4, 79], [1, 9, 83], [1, -16, 89], [1, 16, 97]], 'gamma_factors': [[], [0]], 'index': 70, 'label': '2-328560-1.1-c1-0-70', 'leading_term': '8.44031314718', '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/328560/l', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.841471002670385, 2.289461674634034, 1.072800701682341, -0.3673584837758533, -0.2398028861030945, 1.051033923670647, 0.8688884149466863, -1.877336953399449, -4.064372461298256, -1.92156229426734, 3.057310422893133, 5.165341202973183, 2.408302441202034, -0.5434745878234869, 0.2749834069320864, 2.060272735981365, 0.689359985386092, -1.891460061715653, -1.585498728358103, 0.1339829753504396, -0.4244222921259986, -1.325117622249194, 1.193036789908324, 4.184114351656612, 2.600220677960701, -0.8768965898242548, -0.7675414598769131, 0.5924589389489702, -1.556231845961528, -3.821793735827489, -1.426030363406585, 1.397904181732061, -0.0477032933771563, -1.132250647844789, 1.507375567095078, 1.678484274559596, -2.896116999206688, -3.940663419767728, 0.8114715468604834, 2.200825338882227, -2.060670847289254, -3.424767389544155, -0.272902755714096, 0.711413231831032, -0.4835563718038426, 0.1843615084316605, 0.5143811904832425, -0.3426556178207709, 2.34591554581617, 6.092978923390784, 3.478298088127808, -0.9892042852585625, 0.9599705115463496, 3.635758310996158, 0.7357118089044923, -0.2322001609067762, 3.9616684565866, 4.081076508397627, -0.4585706279667623, -0.9526715307429087, 0.2565518978574531, -2.663675638514748, -3.608398900449511, 0.3607984968240345, 1.150118352456861, -1.160099782604894, 0.5380167108496304, 2.362980677421755, -0.4187552190299772, -1.447339784439127, 0.5149435546277603, -0.7642628957470671, -2.246791013545556, -0.2417298122622837, -1.245849618587411, -4.000200128938907, 0.3082133654197903, 5.232200051655409, 1.599113320493119, -1.655412935973455, 1.019545673353437, 0.7261094810572313, -1.563387241736597, 1.399403705402488, 2.885518485673634, -0.8816088644136194, -0.8713157406461741, 1.57395812427188, -1.135761094037745, -2.799559993310532, 0.3013708313143369, 0.3755829770146557, -1.122769385995543, 1.091504505180599, 0.9938656155672319, -1.965986136894748, -0.8508183428232551, 0.2102923952826732, -1.282681729467393, 1.810683938825242, 3.730783892831152, -3.254044708178897, -5.873783224352453, 1.204975252019964, 2.264973165663343, -2.849965819223067, -1.643707671248295, 1.038387969247665, -0.4179870283399813, -0.1014446025115595, -0.2065490553595514, -3.285669806564882, -2.26972497911377, 0.209589427852545, -1.169738066642663, 1.015668380130005, 4.988904294906382, 1.088674916662052, -2.349539135920563, 1.331877363602286], 'positive_zeros': ['0.9174267293619499', '1.301369814492647', '1.849191045097021', '2.598613913632997', '3.425789341442035', '3.717886975660092', '4.308837802804650', '4.967887885019537', '5.174018317198219', '5.666903032293594', '6.420686341389058', '6.849947417384736', '7.120124473634195', '7.843424580437769', '8.245317815222336', '8.627830476068031', '9.103940825914454', '9.709441539803488', '10.14101486683264', '10.77399149304292', '11.13270624809667', '11.46349840054988', '11.86346385038761', '12.08084416128072', '12.91567885921741', '13.19049237935990', '13.80445407873752', '14.02050167567887', '14.71983340156386', '15.12044412999547', '15.29611897590323', '15.97683160962248', '16.35940119729794', '16.70868338747964', '17.21905814602982', '17.66849866267727', '17.92531690702100', '18.54749176419213', '18.61641969454378', '19.23911513737238', '19.82289278981347'], 'prelabel': '2-328560-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 51.220745883003204, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 320749682849306354, 'z1': {'__RealLiteral__': 0, 'data': '0.9174267293619499', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.301369814492647', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.849191045097021', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2623.56480881119, 'bad_primes': [2, 3, 5, 37], 'central_character': '1.1', 'conductor': 328560, 'conductor_radical': 1110, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, -1, 0, 3, 0, 1, 0, 2, 0, 3, 0, 1, 0, -2, 0, 5, 0, -3, 0, 4, 0, 1, 0, -1, 0, -1, 0, 0, 0, -2, 0, -3, 0, 0, 0, -3, 0, -12, 0, -4, 0, -1, 0, -6, 0, 2, 0, 2, 0, 12, 0, -2, 0, -5, 0, 0, 0, 6, 0, 3, 0, -3, 0, 10, 0, -4, 0, -1, 0, 4, 0, -1, 0, 6, 0, 4, 0, 1, 0, -9, 0, 2, 0, 1, 0, 16, 0, 9, 0, 0, 0, -5, 0, -16, 0, 2, 0], 'euler11': [1, -2, 11], 'euler13': [1, -3, 13], 'euler17': [1, 2, 17], 'euler19': [1, -5, 19], 'euler2': [1, 0, 0], 'euler23': [1, -4, 23], 'euler29': [1, 1, 29], 'euler3': [1, 1, 0], 'euler31': [1, 0, 31], 'euler37': [1, 0, 0], 'euler41': [1, 12, 41], 'euler43': [1, 4, 43], 'euler47': [1, 6, 47], 'euler5': [1, 1, 0], 'euler53': [1, -12, 53], 'euler59': [1, 0, 59], 'euler61': [1, -6, 61], 'euler67': [1, -10, 67], 'euler7': [1, -3, 7], 'euler71': [1, 1, 71], 'euler73': [1, -4, 73], 'euler79': [1, -4, 79], 'euler83': [1, 9, 83], 'euler89': [1, -16, 89], 'euler97': [1, 16, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, 1, 0], [1, -3, 7], [1, -2, 11], [1, -3, 13], [1, 2, 17], [1, -5, 19], [1, -4, 23], [1, 1, 29], [1, 0, 31], [1, 0, 0], [1, 12, 41], [1, 4, 43], [1, 6, 47], [1, -12, 53], [1, 0, 59], [1, -6, 61], [1, -10, 67], [1, 1, 71], [1, -4, 73], [1, -4, 79], [1, 9, 83], [1, -16, 89], [1, 16, 97]], 'index': 70, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/328560/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': '2-328560-1.1-c1-0-70', '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': '2-328560-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 51.220745883003204, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 320749682849306354, 'z1': {'__RealLiteral__': 0, 'data': '0.9174267293619499', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '320749682849306354', 'Lhash_array': ['320749682849306354'], 'label': '2-328560-1.1-c1-0-70', 'type': 'ECQ', 'url': 'EllipticCurve/Q/328560/l'}