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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -1, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': -1, 'A8': 0, 'A9': 1, 'Lhash': '1560103524742240551', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [-0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 2951.2708587065245, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [5, [1]], [7, [1, 1]], [11, [1, -1]]], 'bad_primes': [2, 3, 5, 7, 11], 'central_character': '369600.1', 'coefficient_field': '1.1.1.1', 'conductor': 369600, 'conductor_radical': 2310, 'degree': 2, 'euler_factors': [[1], [1, 1], [1], [1, 1], [1, -1], [1, -3, 13], [1, 1, 17], [1, 5, 19], [1, 4, 23], [1, 0, 29], [1, -10, 31], [1, -5, 37], [1, 3, 41], [1, 10, 43], [1, -2, 47], [1, -13, 53], [1, 6, 59], [1, 1, 61], [1, 1, 67], [1, -7, 71], [1, 9, 73], [1, -10, 79], [1, -12, 83], [1, 2, 89], [1, -10, 97]], 'gamma_factors': [[], [0]], 'index': 110, 'label': '2-369600-1.1-c1-0-110', 'leading_term': '1.74174637496', '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/369600/fp', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [1.741746374958416, 0.9886613380316468, -0.5391429304246425, -1.132942353012977, 0.212344759388966, 2.121359633396947, 1.964916343580848, -0.4997685062303197, -2.003872224178829, -0.08430192197467207, 2.674741957619133, 1.776494613396313, -2.177591614783822, -3.796598249043603, -1.190149183192034, 1.037680878837317, -0.3501160476447936, -1.879532220032486, -0.2309231999988429, 1.2349284886921, -1.091349878995417, -3.609987544701955, -1.83905718378119, 1.209594948630769, 0.9694822338390197, -0.3482173354583993, 0.2984021644265667, -0.1633673450682175, -3.20701325265484, -3.17068766322847, 1.689040769173883, 3.775918431389099, 0.168527749571075, -1.596520283478141, 1.043477664735667, 0.9250949103879009, -2.649115647847596, -1.805322600405892, 2.807353428370273, 2.897413044373548, -0.3574494069332062, -0.1499759296996486, 0.9497584563822871, -1.48799939982386, -2.562204191709333, 0.3544251944404548, 1.025488346838117, -1.266528830276186, -0.666146783663285, 0.5390711757054295, -2.404567328004387, -3.915702967345496, -0.4030341709002089, 1.0398763309551, -0.5448975536207468, 1.621972281889696, 3.464730738212154, -1.955348735396559, -6.120616955487867, -1.875586580430546, 1.240959965083057, -1.414626255989357, -1.433608048815995, 0.9068118661395089, -1.211999356574664, -3.13348165686023, -0.3953509176650704, 0.7238041868154818, -0.07454030165239939, 2.65032917762485, 4.025069912598938, 0.3473932210143548, -0.8501033160978948, 0.6201773316303087, -1.948303535853741, -3.421965430419296, 0.448105601130922, 1.045418799990485, -1.499987013669047, 1.389954801666865, 3.590389879632565, -1.071110608748011, -2.107463593499646, 2.290901764253148, 1.007747708168359, -2.535928637820347, -0.1745240088971719, 1.334764867910029, -0.1661195196799275, 2.380287561749282, 4.490056328880989, 1.128940754509188, -0.4964674586646724, 0.06554934429267176, -1.745074391685217, -0.3080077412199067, 3.705443384336432, 1.504534697744237, -0.8831849952607871, 2.75288396331964, 2.483267778057719, -1.537403836358529, 0.4436192354816929, 1.614508021805048, -2.681674550858673, -1.826599870502945, 1.707952674517506, -0.669844638387974, -0.1686644002342432, 5.338258709778149, 4.327222337707204, 0.2010847375939998, 0.3072661881064252, -1.009196752288893, -2.424983216434827, 0.4293837420087466, 0.2157508521967929, -1.953363162861294, 1.400719133256262, 2.948729785404739, -0.08665789126406259], 'positive_zeros': ['0.4099768395616594', '0.9737394619070005', '1.704425534860027', '2.256608502762887', '2.867484361331718', '3.593581326176381', '3.963069197010515', '4.522894865076789', '4.918399163723590', '5.630680432042815', '6.147962391536436', '6.426417017902574', '6.730484164214887', '7.420443377087953', '8.010261211844804', '8.411201804180931', '8.817516281666365', '9.345924593742208', '9.963287284430616', '10.26944957142833', '10.62886796528719', '11.22117508818726', '11.61024583358424', '12.07712420130287', '12.32819543881247', '13.02756795184422', '13.39302128828016', '13.62896067498165', '14.18186690320353', '14.83919341575612', '15.13910261887336', '15.62396544663610', '15.91211843540963', '16.53364079742661', '16.89968772483222', '17.02054400255043', '17.77397301837135', '18.11212253445453', '18.36009172851534', '18.97217203487550', '19.33477828058691', '19.67506473566549'], 'prelabel': '2-369600-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 54.32560039895118, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1560103524742240551, 'z1': {'__RealLiteral__': 0, 'data': '0.4099768395616594', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '0.9737394619070005', 'prec': 60}, 'z3': {'__RealLiteral__': 0, 'data': '1.704425534860027', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2951.2708587065245, 'bad_primes': [2, 3, 5, 7, 11], 'central_character': '1.1', 'conductor': 369600, 'conductor_radical': 2310, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, 0, 0, -1, 0, 1, 0, 1, 0, 3, 0, 0, 0, -1, 0, -5, 0, 1, 0, -4, 0, 0, 0, -1, 0, 0, 0, 10, 0, -1, 0, 0, 0, 5, 0, -3, 0, -3, 0, -10, 0, 0, 0, 2, 0, 1, 0, 1, 0, 13, 0, 0, 0, 5, 0, -6, 0, -1, 0, -1, 0, 0, 0, -1, 0, 4, 0, 7, 0, -9, 0, 0, 0, -1, 0, 10, 0, 1, 0, 12, 0, 0, 0, 0, 0, -2, 0, -3, 0, -10, 0, 0, 0, 10, 0, 1, 0], 'euler11': [1, -1, 0], 'euler13': [1, -3, 13], 'euler17': [1, 1, 17], 'euler19': [1, 5, 19], 'euler2': [1, 0, 0], 'euler23': [1, 4, 23], 'euler29': [1, 0, 29], 'euler3': [1, 1, 0], 'euler31': [1, -10, 31], 'euler37': [1, -5, 37], 'euler41': [1, 3, 41], 'euler43': [1, 10, 43], 'euler47': [1, -2, 47], 'euler5': [1, 0, 0], 'euler53': [1, -13, 53], 'euler59': [1, 6, 59], 'euler61': [1, 1, 61], 'euler67': [1, 1, 67], 'euler7': [1, 1, 0], 'euler71': [1, -7, 71], 'euler73': [1, 9, 73], 'euler79': [1, -10, 79], 'euler83': [1, -12, 83], 'euler89': [1, 2, 89], 'euler97': [1, -10, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, 0, 0], [1, 1, 0], [1, -1, 0], [1, -3, 13], [1, 1, 17], [1, 5, 19], [1, 4, 23], [1, 0, 29], [1, -10, 31], [1, -5, 37], [1, 3, 41], [1, 10, 43], [1, -2, 47], [1, -13, 53], [1, 6, 59], [1, 1, 61], [1, 1, 67], [1, -7, 71], [1, 9, 73], [1, -10, 79], [1, -12, 83], [1, 2, 89], [1, -10, 97]], 'index': 110, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/369600/fp'], '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': '2-369600-1.1-c1-0-110', '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': '2-369600-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 54.32560039895118, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1560103524742240551, 'z1': {'__RealLiteral__': 0, 'data': '0.4099768395616594', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1560103524742240551', 'Lhash_array': ['1560103524742240551'], 'label': '2-369600-1.1-c1-0-110', 'type': 'ECQ', 'url': 'EllipticCurve/Q/369600/fp'}