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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -1, 'A4': 0, 'A5': -2, 'A6': 0, 'A7': 4, 'A8': 0, 'A9': 1, 'Lhash': '34593828701224219', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [-0.8944271909999159, 0], 'a6': [0.0, 0], 'a7': [1.5118578920369088, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 788.4109293973144, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [11, [1]], [17, [1, 1]]], 'bad_primes': [2, 3, 11, 17], 'central_character': '98736.1', 'coefficient_field': '1.1.1.1', 'conductor': 98736, 'conductor_radical': 1122, 'degree': 2, 'euler_factors': [[1], [1, 1], [1, 2, 5], [1, -4, 7], [1], [1, 2, 13], [1, 1], [1, -8, 19], [1, -6, 23], [1, 2, 29], [1, -4, 31], [1, -6, 37], [1, 6, 41], [1, -4, 43], [1, -12, 47], [1, 0, 53], [1, 6, 59], [1, 12, 61], [1, -8, 67], [1, 10, 71], [1, -10, 73], [1, -12, 79], [1, -12, 83], [1, 10, 89], [1, -2, 97]], 'gamma_factors': [[], [0]], 'index': 31, 'label': '2-98736-1.1-c1-0-31', 'leading_term': '2.42214373333', '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/98736/t', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [2.422143733332505, 1.868929828743667, 0.5529386234254694, -0.5511087497611411, -0.3992671636598937, 0.9824647388761436, 2.024236970170368, 0.9869775558981446, -1.789542648683391, -3.573156154164219, -2.085260310313684, 1.406415945230811, 3.011371982611, 0.8405127435903015, -2.407211278809571, -2.799325845793909, -0.3204626377941457, 1.414203053057618, 0.5539412745540243, -0.6120793104904924, 0.06789949134365247, 0.8085190718572147, -0.7586111063479719, -2.570169229075683, -0.7362928354426052, 3.582536347872629, 4.874781196715065, 1.58535618371544, -1.447594924345471, -0.7991748556501364, 0.7081300561769788, 0.2243124600896786, 0.299315077997554, 3.15745807964557, 4.882237362496028, 1.867430125678264, -1.581674948157718, 0.103263805246759, 3.523145775698454, 1.714469823118668, -3.475113373727283, -4.408869432167345, -0.7147444357538434, 1.170556203143367, -0.2139347907350711, -0.6331968209469859, 0.3860430772791133, -0.1215785568943548, -0.9284728419320623, 0.3356423603868374, 0.02267905892432842, -4.927765394370543, -8.416151240371455, -4.69725245550594, 0.2908999820454798, -0.7582230763212701, -3.287040413207794, -0.650029670011255, 2.771458454905253, 1.090745618261014, -1.445953228424456, -0.2648046553938229, 0.4079392610893869, -1.713383079890646, -1.080002078620668, 3.119422087517061, 3.882818021226756, 0.5847223061607204, -0.1242855246096884, 1.492793686243427, 0.07108485047898172, -2.073747641990328, -0.4263659780811939, 1.025073715759904, -0.8171764987186367, -0.3205991659517677, 3.610016515950223, 3.131919013217287, -1.779840425178986, -2.208800188669007, 1.165711121323481, 0.2963962090519997, -2.44634832632062, -0.6792032808376227, 0.9263596250994899, -2.198863391091557, -3.236262815794009, 0.7556936521352449, 1.999739712884409, -0.5784321752908795, 0.2828691019482786, 3.025918171084258, 1.337292886227619, -1.16382509541143, 0.02732287611541253, 0.3502203698924991, -1.572646204777139, -0.9161853052537456, 0.2504575161915397, -1.692111661128878, -0.9161683875550923, 3.125729874165103, -1.017586886443488, -12.42383381185657, -14.54242161416423, -5.518220817851949, 0.164134544943958, -0.3661979857952853, 0.1719718363695328, 0.6147317472767798, -1.157317018990936, -0.6840252626586318, 0.4676288813228821, -2.513887406648059, -4.279092049454641, -1.076877831360391, -0.1822417274847331, -1.842986254924437, 2.108017880656757, 7.205658897290679, 4.256627819957822], 'positive_zeros': ['0.6036304735793320', '1.088054216380447', '1.847114047907338', '2.649538226065880', '3.309041030914029', '4.029763953712793', '4.588328427739178', '4.986681394399924', '5.416243913696604', '6.044958918628762', '6.850922184245809', '7.354974487349461', '7.820846040174275', '7.934544692603834', '8.856484816105479', '9.243328666827439', '9.831849457048590', '10.55104590848546', '10.96744164694695', '11.39438995762797', '11.72603241382482', '12.19801290509385', '12.50196901852671', '13.47303089118454', '13.68861779394940', '14.28556671767832', '14.82944043304891', '15.28401488943063', '15.56232270923274', '16.07055590166910', '16.80922722745191', '17.02031100204302', '17.50608669023449', '18.03978926451637', '18.40623145103942', '18.77388869633407', '19.40582550047583', '19.90254369887996'], 'prelabel': '2-98736-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 28.078656118078626, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 34593828701224219, 'z1': {'__RealLiteral__': 0, 'data': '0.6036304735793320', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.088054216380447', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.847114047907338', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 788.4109293973144, 'bad_primes': [2, 3, 11, 17], 'central_character': '1.1', 'conductor': 98736, 'conductor_radical': 1122, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, -2, 0, 4, 0, 1, 0, 0, 0, -2, 0, 2, 0, -1, 0, 8, 0, -4, 0, 6, 0, -1, 0, -1, 0, -2, 0, 4, 0, 0, 0, -8, 0, 6, 0, 2, 0, -6, 0, 4, 0, -2, 0, 12, 0, 9, 0, 1, 0, 0, 0, 0, 0, -8, 0, -6, 0, -12, 0, 4, 0, 4, 0, 8, 0, -6, 0, -10, 0, 10, 0, 1, 0, 0, 0, 12, 0, 1, 0, 12, 0, 2, 0, 2, 0, -10, 0, -8, 0, -4, 0, -16, 0, 2, 0, 0, 0], 'euler11': [1, 0, 0], 'euler13': [1, 2, 13], 'euler17': [1, 1, 0], 'euler19': [1, -8, 19], 'euler2': [1, 0, 0], 'euler23': [1, -6, 23], 'euler29': [1, 2, 29], 'euler3': [1, 1, 0], 'euler31': [1, -4, 31], 'euler37': [1, -6, 37], 'euler41': [1, 6, 41], 'euler43': [1, -4, 43], 'euler47': [1, -12, 47], 'euler5': [1, 2, 5], 'euler53': [1, 0, 53], 'euler59': [1, 6, 59], 'euler61': [1, 12, 61], 'euler67': [1, -8, 67], 'euler7': [1, -4, 7], 'euler71': [1, 10, 71], 'euler73': [1, -10, 73], 'euler79': [1, -12, 79], 'euler83': [1, -12, 83], 'euler89': [1, 10, 89], 'euler97': [1, -2, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, 2, 5], [1, -4, 7], [1, 0, 0], [1, 2, 13], [1, 1, 0], [1, -8, 19], [1, -6, 23], [1, 2, 29], [1, -4, 31], [1, -6, 37], [1, 6, 41], [1, -4, 43], [1, -12, 47], [1, 0, 53], [1, 6, 59], [1, 12, 61], [1, -8, 67], [1, 10, 71], [1, -10, 73], [1, -12, 79], [1, -12, 83], [1, 10, 89], [1, -2, 97]], 'index': 31, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/98736/t'], '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': '2-98736-1.1-c1-0-31', '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': '2-98736-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 28.078656118078626, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 34593828701224219, 'z1': {'__RealLiteral__': 0, 'data': '0.6036304735793320', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '34593828701224219', 'Lhash_array': ['34593828701224219'], 'label': '2-98736-1.1-c1-0-31', 'type': 'ECQ', 'url': 'EllipticCurve/Q/98736/t'}