-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2964027412036546644416021279009', 'a10': [-930.0472106276454, 0.0], 'a2': [9.32729307051191, 0.0], 'a3': [0.0, 0.0], 'a4': [54.9983960232195, 0.0], 'a5': [-99.71244642971229, 0.0], 'a6': [0.0, 0.0], 'a7': [125.98296343903635, 0.0], 'a8': [214.5127798602639, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 33.199450701287, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [23, [[1.0, 0], [-529.0, 0]]]], 'bad_primes': [3, 23], 'central_character': '207.1', 'coefficient_field': 'CDF', 'conductor': 207, 'conductor_radical': 69, 'degree': 2, 'euler_factors': [[[1.0, 0], [-9.32729307051191, 0], [32.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [99.71244642971229, 0], [3125.0, 0]], [[1.0, 0], [-125.98296343903635, 0], [16807.0, 0]], [[1.0, 0], [177.7149852464132, 0], [161051.0, 0]], [[1.0, 0], [919.6181656388223, 0], [371293.0, 0]], [[1.0, 0], [1568.2378946401957, 0], [1419857.0, 0]], [[1.0, 0], [-447.9596370138016, 0], [2476099.0, 0]], [[1.0, 0], [-529.0, 0]], [[1.0, 0], [-1298.7151254862897, 0], [20511149.0, 0]], [[1.0, 0], [6651.883278067368, 0], [28629151.0, 0]], [[1.0, 0], [8056.797001581015, 0], [69343957.0, 0]], [[1.0, 0], [17941.431900466137, 0], [115856201.0, 0]], [[1.0, 0], [-10710.681962338356, 0], [147008443.0, 0]], [[1.0, 0], [-17886.90314762443, 0], [229345007.0, 0]], [[1.0, 0], [-20343.902287561014, 0], [418195493.0, 0]], [[1.0, 0], [28488.547717416477, 0], [714924299.0, 0]], [[1.0, 0], [-16222.269560233415, 0], [844596301.0, 0]], [[1.0, 0], [-54127.99074122997, 0], [1350125107.0, 0]], [[1.0, 0], [42505.58937660582, 0], [1804229351.0, 0]], [[1.0, 0], [-40936.18965463408, 0], [2073071593.0, 0]], [[1.0, 0], [24760.645105667303, 0], [3077056399.0, 0]], [[1.0, 0], [-30825.24778407882, 0], [3939040643.0, 0]], [[1.0, 0], [-66531.57707707485, 0], [5584059449.0, 0]], [[1.0, 0], [104505.60440297263, 0], [8587340257.0, 0]], [[1.0, 0], [-203117.2934369329, 0], [10510100501.0, 0]], [[1.0, 0], [148131.96916369954, 0], [11592740743.0, 0]], [[1.0, 0], [-43750.852801084795, 0], [14025517307.0, 0]], [[1.0, 0], [-189051.88180794977, 0], [15386239549.0, 0]], [[1.0, 0], [-82382.32018398732, 0], [18424351793.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 44, 'label': '2-207-1.1-c5-0-44', 'load_key': 'CMFs-workshop', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/207/6/a/f/1/5', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0703125', 'prec': 30}, 'plot_values': [-3.676683831158194e-60, 0.4514087420607228, 0.898376490242529, 1.3364995097620311, 1.7614488255227252, 2.1690081788446296, 2.5551126022425668, 2.915887697474348, 3.2476896042490626, 3.547145531642861, 3.8111945957615694, 4.037128570461681, 4.222632018407621, 4.365821133143479, 4.465280495107414, 4.520096831552533, 4.529888777955047, 4.494831572182199, 4.415675577485736, 4.2937575306774365, 4.1310034512348786, 3.929922228230081, 3.6935890264215, 3.425617820911346, 3.1301225803937576, 2.81166686969381, 2.475201928983449, 2.1259936041602865, 1.769538843245281, 1.4114728286701625, 1.0574681749973867, 0.7131279747740771, 0.38387480975545935, 0.07483814789382434, -0.20925719474787471, -0.4641986465163001, -0.6863865145608206, -0.8729245973694476, -1.021697750881725, -1.1314335205745016, -1.2017451915302724, -1.2331539525544084, -1.227088317244979, -1.1858594891174685, -1.1126119900728022, -1.0112495782736919, -0.886337245517259, -0.7429808844047946, -0.5866870276460926, -0.423205858592445, -0.2583614444670746, -0.09787382154797605, 0.052821865525059436, 0.18875352931579675, 0.3055816912152239, 0.3997544069272822, 0.4686416633101114, 0.5106436695369034, 0.5252680125158743, 0.5131714128520009, 0.4761627926995955, 0.41716553112548116, 0.3401381076392694, 0.2499537833051164, 0.15224149636859105, 0.05319170381850159, -0.040667575411390794, -0.12271782653584927, -0.18651224495455315, -0.22604404684873222, -0.236011054838666, -0.2120662584792409, -0.1510439447133722, -0.051151286182366106, 0.08788401666475731, 0.26471831799853396, 0.4763555828810155, 0.7181747663091443, 0.9840236418550238, 1.2663792295851055, 1.5565723230527924, 1.8450708882322933, 2.1218144094312654, 2.37658870137801, 2.5994284082050463, 2.781032482084119, 2.913176482693522, 2.9891046570472763, 3.003884523692776, 2.954707150167104, 2.841117506241647, 2.665161197131081, 2.4314364985216357, 2.1470438648781727, 1.8214288682361608, 1.4661187210137259, 1.094356991332816, 0.7206456593732364, 0.3602080994082184, 0.02839070723376067, -0.25997547042087693, -0.49122879755507787, -0.6535204013660946, -0.7374193228709975, -0.7364519905805614, -0.6475497365428747, -0.47138046439875586, -0.2125441324974763, 0.12038365494415394, 0.5149700889891308, 0.9552094564366544, 1.421970301361401, 1.8935953839932083, 2.346637365604488, 2.7567065111729376, 3.099400749182923, 3.351283460463949, 3.490870657860428, 3.499586995949086, 3.362649489786022, 3.0698390319936095, 2.6161228112634642, 2.0020955044220896, 1.2342135073190366, 0.32480427430589415, -0.7081582363060163, -1.841511316900799, -3.0475837127063636, -4.295077540432295, -5.550121753340614, -6.777458537322093, -7.941716998551807, -9.008723279870752, -9.94679313035106, -10.727952173515632, -11.329030795418802, -11.73258471292641, -11.927598776081732, -11.909940180091898, -11.682537674774569, -11.25527512577285, -10.64460038454901, -9.872863286257322, -8.967409106800448, -7.959465360279686, -6.882869820793232, -5.772695581361317, -4.663834377836141, -3.589601979588898, -2.580428987267597, -1.6626968343707051, -0.8577722722391967, -0.18128439040389843, 0.35732330490871855, 0.7549465235514831, 1.0146747168061312, 1.1453564900924709, 1.1609003562395115, 1.079348629517023, 0.9217737806546855, 0.7110556310137639, 0.4706038418082118, 0.2230928821050891, -0.010724159704964837, -0.21306093087959072, -0.3699480906037861, -0.4718450036174361, -0.5139825373234428, -0.4964215929818957, -0.42382789378791674, -0.30497951629653974, -0.15203878880759503, 0.020366378213854536, 0.19619570871688988, 0.3591204965260712, 0.49365026804140305, 0.5861939542374328, 0.6259911350072442, 0.6058565438526162, 0.5226920968160043, 0.3777346309814115, 0.17652351756396317, -0.07141057431273062, -0.35311725913791914, -0.6530235565216006, -0.9539073827285445, -1.237986728700722, -1.4880559390399486, -1.6885967719416461, -1.826792664711712, -1.8933798946405014, -1.8832788717464901, -1.7959621160486892, -1.6355317963191374, -1.4104980698881868, -1.1332687405265118, -0.8193797328221109, -0.48651334249347533, -0.15336600222746555, 0.16156161903621585, 0.441172800884897, 0.6709003515040377, 0.839672479989186, 0.9406508335587457, 0.9716862959923193, 0.9354558506346438, 0.8392644533351733, 0.6945181642010911, 0.5158973284685613, 0.3202798901586359, 0.1254835138745138, -0.051090244973168955, -0.19381704835344168, -0.29011999345632283, -0.3315556545963179, -0.3146319610648437, -0.241289247013268, -0.11899635951840142, 0.039561689758817964, 0.21720088448815117, 0.3933285256480495, 0.5453480523100114, 0.6502955160354054, 0.6866052377923747, 0.6358885957293435, 0.4846035039278687, 0.22549366233438087, -0.14131369250181608, -0.6076453348246637, -1.1571242363721361, -1.765555618442875, -2.4018620763643566, -3.0295371387593506, -3.60855123218998, -4.097611418705934, -4.456648701278926, -4.649386146552648, -4.645829166638596, -4.424517137140337, -3.9743836161054755, -3.2960906261118614, -2.402729962662195, -1.319819855518608, -0.08456653316515617, 1.2555951269241803, 2.64512239193667, 4.023044383825786, 5.326060183588463, 6.491884465798181, 7.462649283153665, 8.188161528012351, 8.628818831080924, 8.758002344054532, 8.563792315329076, 8.049890145726998, 7.235676537037429, 6.155386669928332], 'positive_zeros': ['2.33820534735904312861278639632403', '3.63092596899130499872450297993143', '4.60936165108928591535315987969867', '5.16103936442287838475006853797102', '6.96736703447452818538092760264328', '7.56993171792478183357468199171986', '8.741713999613928393615283364822925', '10.70920981130083802671423911922950', '11.45753341952795246274899398902043'], 'prelabel': '2-207-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.761896450066332, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.33820534735904312861278639632', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.63092596899130499872450297993', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.60936165108928591535315987970', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 33.199450701287, 'bad_primes': [3, 23], 'central_character': '1.1', 'conductor': 207, 'conductor_radical': 69, 'degree': 2, 'index': 44, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/207/6/a/f/1/5'], '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': '2-207-1.1-c5-0-44', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 1, 'prelabel': '2-207-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.761896450066332, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '2.33820534735904312861278639632', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2964027412036546644416021279009', 'Lhash_array': ['2964027412036546644416021279009'], 'label': '2-207-1.1-c5-0-44', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/207/6/a/f/1/5'}