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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': -1, 'A8': 0, 'A9': 1, 'Lhash': '919115817130561577', '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': [-0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 1234.1678136409103, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]], [5, [1, -1]], [7, [1, 1]], [23, [1, 1]]], 'bad_primes': [2, 3, 5, 7, 23], 'central_character': '154560.1', 'coefficient_field': '1.1.1.1', 'conductor': 154560, 'conductor_radical': 4830, 'degree': 2, 'euler_factors': [[1], [1, -1], [1, -1], [1, 1], [1, -2, 11], [1, 4, 13], [1, 2, 17], [1, -4, 19], [1, 1], [1, 4, 29], [1, 0, 31], [1, -6, 37], [1, 10, 41], [1, -2, 43], [1, -8, 47], [1, 6, 53], [1, 0, 59], [1, -2, 61], [1, -2, 67], [1, -10, 71], [1, 2, 73], [1, -16, 79], [1, 0, 83], [1, 12, 89], [1, 12, 97]], 'gamma_factors': [[], [0]], 'index': 158, 'label': '2-154560-1.1-c1-0-158', 'leading_term': '9.35923342896', '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/154560/gy', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 2.094434178416097, 2.829264109507816, 1.565488336091592, -0.8048056981992695, -2.189137707846256, -1.287264109835999, 0.7466347369711712, 1.450767434262562, 0.1672046792527286, -0.9694253137391533, -0.05160615686843485, 1.566607684170367, 1.096438344349563, -1.166490759147691, -1.810122434685663, 0.3270083379074459, 1.734491312478672, -0.4380396196769999, -3.334516945239387, -2.595110767917671, 0.279851306470458, 0.0566713689372877, -3.322269648286641, -4.26437053378227, -0.9864350054240242, 1.411100342911503, -0.05599094422311341, -1.289587974845453, 0.770261839237879, 2.258970414760704, 0.08382979059386235, -1.59085483266645, 0.8965692362848966, 3.39561793716196, 1.567679718545995, -1.185541325349144, -0.7742092120817046, 0.1719414416854552, -0.7551254009411251, -0.09331671035174699, 2.979704480414765, 2.661849984482801, -1.888128336715463, -2.831403900927957, 1.791252101490619, 3.461318440601884, -0.7387475029513585, -2.868392788457916, -0.1671804341162295, 0.4229418787034462, -2.446774108291723, -2.199227696818682, 1.126109800789068, 1.35658888025522, -0.4088290669816542, 0.6394203807014446, 1.681044493507903, -0.6579072610530147, -1.767775266332507, 0.3217814416211197, -0.1134114194600022, -2.846586538588457, -0.9316322718875629, 3.275619356451743, 1.820479916695903, -1.770413391796353, -0.2328306477922495, 1.738117312390632, -0.8288730630774549, -1.312783843810209, 2.822727431032663, 3.258463878009337, -0.5657673288971261, -0.1917372267879506, 2.764270486633243, 1.079903485350796, -1.351082709201094, 0.67972163427582, 1.870789380472019, -0.1092392339689892, 0.0751837925650413, 0.8295054534446068, -2.30490956535374, -3.366708974766833, 1.412415236574376, 3.611944749951215, 0.592531743394228, -0.2530062912842958, 0.3296251601442223, -1.793701813798804, -0.09340307266959862, 6.804792913022315, 6.874493730766354, -0.4525583477744459, -1.967389993227948, 1.863130739323566, 1.077586867232687, -1.08586057738537, 0.8032850041496055, 1.288861696500245, -0.4556016267024377, 0.8236209290233131, 1.292680261192157, -2.324116049853245, -2.965641940801319, -0.1306615900472166, -0.557796910038057, -0.9217339871316913, 1.769822328213118, -0.4740028972588135, -5.931301768306721, -3.272368997619051, 2.367473317487581, 0.4276970176529428, -2.005112973405043, 0.5378636015182185, -0.1048619889893427, -3.018714592712906, -0.8066940413840622, 0.9218390387960441], 'positive_zeros': ['0.9153250889636469', '1.654581091161047', '2.274860653005750', '2.757249622925550', '3.374770205932431', '3.968637323759964', '4.467390900165786', '5.218774819447049', '5.505584016806205', '6.317283469926874', '6.744043978104551', '7.180493624615515', '7.756972052098475', '8.187172917521146', '8.868018946569222', '9.393195392604777', '9.579390405636218', '10.00919334432429', '10.65011843858285', '11.16277888232229', '11.71185608922696', '12.26496349773393', '12.54512280721138', '13.15938972463066', '13.66719320235550', '13.91870188375873', '14.44387879934032', '14.96031642092520', '15.23906771858426', '15.79842849449529', '16.35361574231185', '16.76727130153808', '17.18666959337709', '17.59065417060725', '18.20611848718957', '18.51483012208507', '19.07595572991998', '19.44283171979145', '19.98414196973454'], 'prelabel': '2-154560-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 35.13072463871063, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 919115817130561577, 'z1': {'__RealLiteral__': 0, 'data': '0.9153250889636469', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.654581091161047', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.274860653005750', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1234.1678136409103, 'bad_primes': [2, 3, 5, 7, 23], 'central_character': '1.1', 'conductor': 154560, 'conductor_radical': 4830, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, 1, 0, -1, 0, 1, 0, 2, 0, -4, 0, 1, 0, -2, 0, 4, 0, -1, 0, -1, 0, 1, 0, 1, 0, -4, 0, 0, 0, 2, 0, -1, 0, 6, 0, -4, 0, -10, 0, 2, 0, 1, 0, 8, 0, 1, 0, -2, 0, -6, 0, 2, 0, 4, 0, 0, 0, 2, 0, -1, 0, -4, 0, 2, 0, -1, 0, 10, 0, -2, 0, 1, 0, -2, 0, 16, 0, 1, 0, 0, 0, -2, 0, -4, 0, -12, 0, 4, 0, 0, 0, 4, 0, -12, 0, 2, 0], 'euler11': [1, -2, 11], 'euler13': [1, 4, 13], 'euler17': [1, 2, 17], 'euler19': [1, -4, 19], 'euler2': [1, 0, 0], 'euler23': [1, 1, 0], 'euler29': [1, 4, 29], 'euler3': [1, -1, 0], 'euler31': [1, 0, 31], 'euler37': [1, -6, 37], 'euler41': [1, 10, 41], 'euler43': [1, -2, 43], 'euler47': [1, -8, 47], 'euler5': [1, -1, 0], 'euler53': [1, 6, 53], 'euler59': [1, 0, 59], 'euler61': [1, -2, 61], 'euler67': [1, -2, 67], 'euler7': [1, 1, 0], 'euler71': [1, -10, 71], 'euler73': [1, 2, 73], 'euler79': [1, -16, 79], 'euler83': [1, 0, 83], 'euler89': [1, 12, 89], 'euler97': [1, 12, 97], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, -1, 0], [1, 1, 0], [1, -2, 11], [1, 4, 13], [1, 2, 17], [1, -4, 19], [1, 1, 0], [1, 4, 29], [1, 0, 31], [1, -6, 37], [1, 10, 41], [1, -2, 43], [1, -8, 47], [1, 6, 53], [1, 0, 59], [1, -2, 61], [1, -2, 67], [1, -10, 71], [1, 2, 73], [1, -16, 79], [1, 0, 83], [1, 12, 89], [1, 12, 97]], 'index': 158, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/154560/gy'], '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': '2-154560-1.1-c1-0-158', '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': '2-154560-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 35.13072463871063, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 919115817130561577, 'z1': {'__RealLiteral__': 0, 'data': '0.9153250889636469', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '919115817130561577', 'Lhash_array': ['919115817130561577'], 'label': '2-154560-1.1-c1-0-158', 'type': 'ECQ', 'url': 'EllipticCurve/Q/154560/gy'}