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lfunc_lfunctions • Show schema
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{'Lhash': '1617680258357398683406608352531,1869648794204215521203079319314,2056512131423519219622560863540,2514695685351068237964520367612,2518830051908370404194642583915', 'a10': -35, 'a2': 5, 'a3': -3, 'a4': 15, 'a5': -7, 'a6': -15, 'a7': 0, 'a8': 35, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6018744.436558225, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -5, 10, -10, 5, -1]], [7, [1]], [29, [1, 5, 10, 10, 5, 1]]], 'bad_primes': [2, 7, 29], 'central_character': '2842.1', 'coefficient_field': '1.1.1.1', 'conductor': 185404541473635232, 'conductor_radical': 406, 'degree': 10, 'euler_factors': [[1, -5, 10, -10, 5, -1], [1, 3, 8, 17, 33, 55, 99, 153, 216, 243, 243], [1, 7, 31, 105, 293, 691, 1465, 2625, 3875, 4375, 3125], [1], [1, 0, 22, -54, 109, -1179, 1199, -6534, 29282, 0, 161051], [1, 10, 93, 513, 2664, 9855, 34632, 86697, 204321, 285610, 371293], [1, 8, 94, 522, 3329, 13121, 56593, 150858, 461822, 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'3.12468921968438183811165060432775', '3.47659756898704189107202459999345', '3.57771181879290227296319645852654', '3.63859373649584479674640626054299', '3.78533211784464000497506071189234', '4.04321432478185671176907791488191', '4.30117814300836855188890856754748', '4.40341404326942714998195828219137', '4.40402726620414147595580142323401', '4.55402668345791104712431028734902', '4.88098556482957925673773739165657', '4.94637061191778016761641610989891', '5.18074850931924726154974558280003', '5.21487319081941694376704900603559', '5.26472880568909878577360395396328', '5.49309309228463545295925437026591', '5.75760327735358633243494712443925', '5.94432127309126770530840730405495', '6.05749251166054018855601490881204', '6.06089499247630166509504639385942', '6.19765393047081426532635150267455', '6.79154046246677045827208656811113', '6.79508534274820881473627590430463', '6.82651662222004008508547463026777', '7.01449603554066323796229114942939', '7.03303267801444372389968694794941', '7.20848040035940420312451754244854', '7.35664789906106393024784346265728', '7.37029426501220590225071278389072', '7.68274190144318904770596166033682', '7.71838180988731143123506778601527', '7.979512776218004828345084265058894', '8.314347335169829874266284637765361', '8.372645206223070456802750876793741', '8.407932515611875582067630547204935', '8.476975119599703023820426059951222'], 'prelabel': '10-2842e5-1.1-c1e5-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.7637678631990354, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1e5-0', 'trace_hash': 2104346948656402274, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.27612471296597777331642573794', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.47489284024131066636424286719', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.62230202159274976889338111277', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6018744.436558225, 'bad_primes': [2, 7, 29], 'central_character': '1.1', 'conductor': 185404541473635232, 'conductor_radical': 406, 'degree': 10, 'dirichlet_coefficients': [1, 5, -3, 15, -7, -15, 0, 35, 1, -35, 0, -45, -10, 0, 21, 70, -8, 5, -2, -105, 0, 0, 1, -105, 18, -50, 4, 0, -5, 105, -11, 126, 0, -40, 0, 15, -8, -10, 30, -245, -23, 0, -3, 0, -7, 5, -16, -210, 0, 90, 24, -150, 7, 20, 0, 0, 6, -25, 9, 315, -15, -55, 0, 210, 70, 0, -4, -120, -3, 0, -22, 35, 0, -40, -54, -30, 0, 150, -13, -490, -2, -115, -28, 0, 56, -15, 15, 0, -17, -35, 0, 15, 33, -80, 14, -378, -42, 0, 0, 270], 'euler11': [1, 0, 22, -54, 109, -1179, 1199, -6534, 29282, 0, 161051], 'euler13': [1, 10, 93, 513, 2664, 9855, 34632, 86697, 204321, 285610, 371293], 'euler17': [1, 8, 94, 522, 3329, 13121, 56593, 150858, 461822, 668168, 1419857], 'euler19': [1, 2, 32, 14, 757, 711, 14383, 5054, 219488, 260642, 2476099], 'euler2': [1, -5, 10, -10, 5, -1, 0, 0, 0, 0, 0], 'euler23': [1, -1, 76, -189, 2555, -7603, 58765, -99981, 924692, -279841, 6436343], 'euler29': [1, 5, 10, 10, 5, 1, 0, 0, 0, 0, 0], 'euler3': [1, 3, 8, 17, 33, 55, 99, 153, 216, 243, 243], 'euler31': [1, 11, 131, 1073, 8071, 44997, 250201, 1031153, 3902621, 10158731, 28629151], 'euler37': [1, 8, 138, 762, 8211, 34833, 303807, 1043178, 6990114, 14993288, 69343957], 'euler41': [1, 23, 337, 3477, 29189, 200675, 1196749, 5844837, 23226377, 64992503, 115856201], 'euler43': [1, 3, 52, 137, 3085, 17531, 132655, 253313, 4134364, 10256403, 147008443], 'euler47': [1, 16, 244, 2424, 22157, 157105, 1041379, 5354616, 25332812, 78074896, 229345007], 'euler5': [1, 7, 31, 105, 293, 691, 1465, 2625, 3875, 4375, 3125], 'euler53': [1, -7, 208, -1533, 19187, -122989, 1016911, -4306197, 30966416, -55233367, 418195493], 'euler59': [1, -9, 256, -1833, 28669, -154293, 1691471, -6380673, 52577024, -109056249, 714924299], 'euler61': [1, 15, 295, 3022, 35197, 262381, 2147017, 11244862, 66959395, 207687615, 844596301], 'euler67': [1, 4, 161, 367, 14278, 24747, 956626, 1647463, 48422843, 80604484, 1350125107], 'euler7': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler71': [1, 22, 406, 5106, 58901, 521437, 4181971, 25739346, 145311866, 559056982, 1804229351], 'euler73': [1, 0, 118, 226, 7843, 33337, 572539, 1204354, 45904006, 0, 2073071593], 'euler79': [1, 13, 362, 3727, 54655, 428163, 4317745, 23260207, 178480118, 506351053, 3077056399], 'euler83': [1, 28, 628, 8973, 112748, 1077883, 9358084, 61814997, 359082236, 1328832988, 3939040643], 'euler89': [1, 17, 250, 2316, 32888, 305705, 2927032, 18345036, 176242250, 1066618097, 5584059449], 'euler97': [1, 42, 1024, 18106, 247831, 2707201, 24039607, 170359354, 934577152, 3718229802, 8587340257], 'euler_factors': [[1, -5, 10, -10, 5, -1, 0, 0, 0, 0, 0], [1, 3, 8, 17, 33, 55, 99, 153, 216, 243, 243], [1, 7, 31, 105, 293, 691, 1465, 2625, 3875, 4375, 3125], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 22, -54, 109, -1179, 1199, -6534, 29282, 0, 161051], [1, 10, 93, 513, 2664, 9855, 34632, 86697, 204321, 285610, 371293], [1, 8, 94, 522, 3329, 13121, 56593, 150858, 461822, 668168, 1419857], [1, 2, 32, 14, 757, 711, 14383, 5054, 219488, 260642, 2476099], [1, -1, 76, -189, 2555, -7603, 58765, -99981, 924692, -279841, 6436343], [1, 5, 10, 10, 5, 1, 0, 0, 0, 0, 0], [1, 11, 131, 1073, 8071, 44997, 250201, 1031153, 3902621, 10158731, 28629151], [1, 8, 138, 762, 8211, 34833, 303807, 1043178, 6990114, 14993288, 69343957], [1, 23, 337, 3477, 29189, 200675, 1196749, 5844837, 23226377, 64992503, 115856201], [1, 3, 52, 137, 3085, 17531, 132655, 253313, 4134364, 10256403, 147008443], [1, 16, 244, 2424, 22157, 157105, 1041379, 5354616, 25332812, 78074896, 229345007], [1, -7, 208, -1533, 19187, -122989, 1016911, -4306197, 30966416, -55233367, 418195493], [1, -9, 256, -1833, 28669, -154293, 1691471, -6380673, 52577024, -109056249, 714924299], [1, 15, 295, 3022, 35197, 262381, 2147017, 11244862, 66959395, 207687615, 844596301], [1, 4, 161, 367, 14278, 24747, 956626, 1647463, 48422843, 80604484, 1350125107], [1, 22, 406, 5106, 58901, 521437, 4181971, 25739346, 145311866, 559056982, 1804229351], [1, 0, 118, 226, 7843, 33337, 572539, 1204354, 45904006, 0, 2073071593], [1, 13, 362, 3727, 54655, 428163, 4317745, 23260207, 178480118, 506351053, 3077056399], [1, 28, 628, 8973, 112748, 1077883, 9358084, 61814997, 359082236, 1328832988, 3939040643], [1, 17, 250, 2316, 32888, 305705, 2927032, 18345036, 176242250, 1066618097, 5584059449], [1, 42, 1024, 18106, 247831, 2707201, 24039607, 170359354, 934577152, 3718229802, 8587340257]], 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2842/2/a/x'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, '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': '10-2842e5-1.1-c1e5-0-7', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1, 1], 'order_of_vanishing': 5, 'prelabel': '10-2842e5-1.1-c1e5-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.7637678631990354, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e5-0', 'trace_hash': 2104346948656402274, 'z1': {'__RealLiteral__': 0, 'data': '1.27612471296597777331642573794', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1617680258357398683406608352531,1869648794204215521203079319314,2056512131423519219622560863540,2514695685351068237964520367612,2518830051908370404194642583915', 'Lhash_array': ['1617680258357398683406608352531', '1869648794204215521203079319314', '2056512131423519219622560863540', '2514695685351068237964520367612', '2518830051908370404194642583915'], 'label': '10-2842e5-1.1-c1e5-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2842/2/a/x'}