-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1438829542596275150258669590985', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': -34, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 106.20343801033316, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1]]], 'bad_primes': [2, 3, 5], 'central_character': '1800.1', 'coefficient_field': '1.1.1.1', 'conductor': 1800, 'conductor_radical': 30, 'degree': 2, 'euler_factors': [[1], [1], [1], [1, 34, 343], [1, -18, 1331], [1, 12, 2197], [1, -106, 4913], [1, 44, 6859], [1, 56, 12167], [1, -270, 24389], [1, -204, 29791], [1, 120, 50653], [1, -80, 68921], [1, 536, 79507], [1, -536, 103823], [1, 542, 148877], [1, 174, 205379], [1, -186, 226981], [1, 332, 300763], [1, 132, 357911], [1, -602, 389017], [1, 548, 493039], [1, -492, 571787], [1, 1052, 704969], [1, 482, 912673], [1, -1214, 1030301], [1, 898, 1092727], [1, 1364, 1225043], [1, -218, 1295029], [1, 1386, 1442897]], 'euler_factors_factorization': [[1], [1], [1], [[[1, 34, 343], 1]], [[[1, -18, 1331], 1]], [[[1, 12, 2197], 1]], [[[1, -106, 4913], 1]], [[[1, 44, 6859], 1]], [[[1, 56, 12167], 1]], [[[1, -270, 24389], 1]], [[[1, -204, 29791], 1]], [[[1, 120, 50653], 1]], [[[1, -80, 68921], 1]], [[[1, 536, 79507], 1]], [[[1, -536, 103823], 1]], [[[1, 542, 148877], 1]], [[[1, 174, 205379], 1]], [[[1, -186, 226981], 1]], [[[1, 332, 300763], 1]], [[[1, 132, 357911], 1]], [[[1, -602, 389017], 1]], [[[1, 548, 493039], 1]], [[[1, -492, 571787], 1]], [[[1, 1052, 704969], 1]], [[[1, 482, 912673], 1]], [[[1, -1214, 1030301], 1]], [[[1, 898, 1092727], 1]], [[[1, 1364, 1225043], 1]], [[[1, -218, 1295029], 1]], [[[1, 1386, 1442897], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 39, 'label': '2-1800-1.1-c3-0-39', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/1800/4/a/b', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [-6.611953732727463e-61, 0.2033954376427492, 0.4035377672874152, 0.5972057021835057, 0.7812417999116543, 0.9525848635056784, 1.108302846674985, 1.2456263167427368, 1.3619824373437648, 1.45502932625277, 1.5226905266361086, 1.5631892077255933, 1.575081588877731, 1.557288964778974, 1.5091276046658262, 1.4303357100596048, 1.3210965484574084, 1.1820568389010204, 1.0143394529140242, 0.8195495137271498, 0.5997730299163814, 0.3575672875447488, 0.09594234763551737, -0.1816668476964546, -0.47143806891410805, -0.7692091841489745, -1.0705351859931191, -1.3707544495434631, -1.6650635371808407, -1.948599585047514, -2.2165290268341233, -2.46414114049187, -2.6869446514367565, -2.8807654004870997, -3.0418428949044185, -3.1669234149198044, -3.2533472538759436, -3.2991276345941847, -3.303018873640098, -3.264571463246521, -3.1841719105224917, -3.063065416088185, -2.903359788194418, -2.7080093702387935, -2.4807782035883705, -2.22618214563385, -1.949410204626367, -1.6562259255341352, -1.3528502504228177, -1.0458278665991345, -0.7418796285936263, -0.4477441778183194, -0.1700123679431949, 0.08504148351739174, 0.31162717357339514, 0.5046004598620859, 0.6596145125811533, 0.7732563403990262, 0.8431637260364887, 0.8681185162508771, 0.8481125613026058, 0.7843831859914835, 0.6794157887198388, 0.5369119927986616, 0.36172269684036684, 0.15974636579530554, -0.06220605560032527, -0.29657716927027544, -0.535256613001642, -0.7697975460338211, -0.9916507598437058, -1.192410256136393, -1.3640634970791299, -1.4992390745199078, -1.5914442900235914, -1.6352851055177593, -1.6266611284231627, -1.5629287415399995, -1.4430261751455793, -1.2675552370679957, -1.0388155479683125, -0.7607884475394658, -0.4390692088905923, -0.08074778204987816, 0.3057600637426716, 0.7109276672615985, 1.1243733200702126, 1.5351503548349308, 1.9320634354665278, 2.3040018476699515, 2.640279685999687, 2.930972231034583, 3.1672375422747803, 3.3416123833049873, 3.4482720587454665, 3.4832445781352415, 3.4445707576240374, 3.332403400273827, 3.149040520841884, 2.8988896497075523, 2.5883625005534276, 2.225701645551312, 1.8207432309323361, 1.3846221010581952, 0.9294278947618936, 0.46782264936567514, 0.01263211544701308, -0.4235757232029569, -0.8289105765033465, -1.1925635064616207, -1.5051797521876422, -1.75918683968924, -1.9490653049063456, -2.071551071165706, -2.12576069256907, -2.1132332389077204, -2.037885474220476, -1.9058800736819423, -1.7254098236819686, -1.506403940916632, -1.2601657070182928, -0.9989534249679669, -0.7355191465253483, -0.4826215901786511, -0.2525310749365635, -0.05654506340091512, 0.09546701318723266, 0.19547161099187044, 0.23761492364848294, 0.21848807427643335, 0.13730166044506883, -0.004039129623491214, -0.20096396832442542, -0.446372596997902, -0.7308728720263747, -1.0431146186512235, -1.3702083132057705, -1.698213989241572, -2.012682616845852, -2.2992296782097283, -2.5441188767262455, -2.7348329660299227, -2.8606086330099796, -2.9129132439066834, -2.885843057071434, -2.7764251737679864, -2.5848089560210625, -2.3143367692323302, -1.9714885568170317, -1.56569974788637, -1.1090571406204706, -0.6158824848272256, -0.10221829479770256, 0.4147652495222404, 0.9174198023515406, 1.3882994346743815, 1.8108451593518167, 2.1700455245905776, 2.4530458154416848, 2.6496799769705595, 2.7529020701596063, 2.7590978066996192, 2.668261348919733, 2.4840279309092925, 2.213558744800969, 1.8672807024018756, 1.458489868456902, 1.0028333015081825, 0.5176894688329617, 0.02147207575091228, -0.46711415431967623, -0.9298346782590938, -1.3496710042311961, -1.711519077650906, -2.002809581127598, -2.214022475570745, -2.3390723108343545, -2.3755461506945563, -2.3247821770904284, -2.191783905186915, -1.9849721613382003, -1.7157842347135654, -1.3981365850133967, -1.04777385321708, -0.6815323792805422, -0.3165507137230808, 0.030537500258547446, 0.34439156216940126, 0.6116962678987231, 0.8218045638774226, 0.9672594780817049, 1.0441695799794344, 1.0524185760199942, 0.995697013944684, 0.8813521283487309, 0.7200602523266315, 0.5253345626884038, 0.31288882971686915, 0.09988492897641606, -0.09590220579149598, -0.25696405440141806, -0.3669415224138507, -0.41146972918045605, -0.3789438756783049, -0.26116850266868824, -0.05385729141888582, 0.2430429563056809, 0.6252226696949965, 1.0840838276321105, 1.6070183854466846, 2.177881275449264, 2.7776390505772817, 3.3851665773482345, 3.978156683595776, 4.5341017103073975, 5.031301820895105, 5.449852917669647, 5.77256723990276, 5.985782201127924, 6.0800176866319715, 6.050448689152379, 5.8971685244401115, 5.625227562377509, 5.244442985086773, 4.768986040307711, 4.216764067259018, 3.608624701356425, 2.967418605060547, 2.3169643653602168, 1.6809644574620635, 1.0819241062892289, 0.5401252996788583, 0.072706058516786, -0.3071095846910406, -0.5905924139857852, -0.7738701483139923, -0.8580518861797146, -0.8491075455233674, -0.7575071133541662, -0.5976365748452868, -0.3870187473042102, -0.1453773165022577, 0.10640936776117883, 0.34741217920262796, 0.5577568243392281, 0.7196746171481534, 0.8184441480255655, 0.843174666749406, 0.7873896753382773, 0.6493791315533571, 0.4323003197696736, 0.14402027714560242, -0.20329397681601208, -0.5938179544924361, -1.008913143709061, -1.4281287029189667, -1.830309953315686], 'positive_zeros': ['1.13503637543123197955099945813537', '2.67389012941901964485779336576356', '3.33768781813259207778091142682679', '4.22572386700575919813598731174312', '5.38424602421298264458701189353670', '6.36475773943266278649277295625140', '6.65113326413272609196858278754988', '7.72876181082921071888120306898011', '8.584232553168694314021033728584973'], 'prelabel': '2-1800-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 10.305505228291, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'trace_hash': 2194687426156041625, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.13503637543123197955099945814', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.67389012941901964485779336576', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.33768781813259207778091142683', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 106.20343801033316, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 1800, 'conductor_radical': 30, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, -34, 0, 0, 0, 18, 0, -12, 0, 0, 0, 106, 0, -44, 0, 0, 0, -56, 0, 0, 0, 0, 0, 270, 0, 204, 0, 0, 0, 0, 0, -120, 0, 0, 0, 80, 0, -536, 0, 0, 0, 536, 0, 813, 0, 0, 0, -542, 0, 0, 0, 0, 0, -174, 0, 186, 0, 0, 0, 0, 0, -332, 0, 0, 0, -132, 0, 602, 0, 0, 0, -612, 0, -548, 0, 0, 0, 492, 0, 0, 0, 0, 0, -1052, 0, 408, 0, 0, 0, 0, 0, -482, 0, 0, 0], 'euler11': [1, -18, 1331], 'euler13': [1, 12, 2197], 'euler17': [1, -106, 4913], 'euler19': [1, 44, 6859], 'euler2': [1, 0, 0], 'euler23': [1, 56, 12167], 'euler29': [1, -270, 24389], 'euler3': [1, 0, 0], 'euler31': [1, -204, 29791], 'euler37': [1, 120, 50653], 'euler41': [1, -80, 68921], 'euler43': [1, 536, 79507], 'euler47': [1, -536, 103823], 'euler5': [1, 0, 0], 'euler53': [1, 542, 148877], 'euler59': [1, 174, 205379], 'euler61': [1, -186, 226981], 'euler67': [1, 332, 300763], 'euler7': [1, 34, 343], 'euler71': [1, 132, 357911], 'euler73': [1, -602, 389017], 'euler79': [1, 548, 493039], 'euler83': [1, -492, 571787], 'euler89': [1, 1052, 704969], 'euler97': [1, 482, 912673], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 0, 0], [1, 34, 343], [1, -18, 1331], [1, 12, 2197], [1, -106, 4913], [1, 44, 6859], [1, 56, 12167], [1, -270, 24389], [1, -204, 29791], [1, 120, 50653], [1, -80, 68921], [1, 536, 79507], [1, -536, 103823], [1, 542, 148877], [1, 174, 205379], [1, -186, 226981], [1, 332, 300763], [1, 132, 357911], [1, -602, 389017], [1, 548, 493039], [1, -492, 571787], [1, 1052, 704969], [1, 482, 912673]], 'index': 39, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1800/4/a/b/1/1', 'ModularForm/GL2/Q/holomorphic/1800/4/a/b'], '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': '2-1800-1.1-c3-0-39', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-1800-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 10.305505228291, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 2194687426156041625, 'z1': {'__RealLiteral__': 0, 'data': '1.13503637543123197955099945814', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
-
id: 21146058
{'Lhash': '1438829542596275150258669590985', 'Lhash_array': ['1438829542596275150258669590985'], 'label': '2-1800-1.1-c3-0-39', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1800/4/a/b'}
-
id: 24592234
{'Lhash': '1438829542596275150258669590985', 'Lhash_array': ['1438829542596275150258669590985'], 'label': '2-1800-1.1-c3-0-39', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1800/4/a/b/1/1'}