Query:
/api/lfunc_search/?_offset=0
Table lfunc_search
L-function search data
{'algebraic': True, 'analytic_conductor': 261610950031859.22, 'bad_primes': [2, 11, 19], 'central_character': '1.1', 'conductor': 15828474533481853782019206390016, 'conductor_radical': 418, 'degree': 16, 'dirichlet_coefficients': [1, 8, -5, 36, 1, -40, -4, 120, 8, 8, -8, -180, -3, -32, -5, 330, -6, 64, 0, 36, 20, -64, 9, -600, -19, -24, 2, -144, -4, -40, -11, 792, 40, -48, -4, 288, 10, 0, 15, 120, -29, 160, 2, -288, 8, 72, 0, -1650, -24, -152, 30, -108, -59, 16, -8, -480, 0, -32, -23, -180, -2, -88, -32, 1716, -3, 320, 3, -216, -45, -32, -1, 960, -6, 80, 95, 0, 32, 120, 0, 330, -21, -232, 15, 720, -6, 16, 20, -960, -4, 64, 12, 324, 55, 0, 0, -3960, -62, -192, -64, -684], 'euler11': [1, 8, 28, 56, 70, 56, 28, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler13': [1, 3, 32, 32, 458, -644, 2607, -29023, -625, -377299, 440583, -1414868, 13080938, 11881376, 154457888, 188245551, 815730721], 'euler17': [1, 6, 116, 587, 6153, 26305, 195117, 699036, 4050559, 11883612, 56388813, 129236465, 513904713, 833456059, 2799958004, 2462032038, 6975757441], 'euler19': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler2': [1, -8, 28, -56, 70, -56, 28, -8, 1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, -9, 122, -736, 5373, -26844, 144595, -725377, 3403722, -16683671, 76490755, -326610948, 1503585693, -4737148448, 18060378458, -30643429023, 78310985281], 'euler29': [1, 4, 132, 149, 7210, -8455, 261495, -702233, 7976455, -20364757, 219917295, -206208995, 5099496010, 3056161201, 78516678372, 68999505236, 500246412961], 'euler3': [1, 5, 17, 43, 90, 182, 378, 760, 1420, 2280, 3402, 4914, 7290, 10449, 12393, 10935, 6561], 'euler31': [1, 11, 222, 1765, 20656, 130021, 1137593, 5928155, 42218816, 183772805, 1093226873, 3873455611, 19076249776, 50530451515, 197025817182, 302638755221, 852891037441], 'euler37': [1, -10, 221, -1934, 23831, -175415, 1590889, -9764443, 71129081, -361284391, 2177927041, -8885295995, 44663130791, -134111212838, 567025536389, -949318771330, 3512479453921], 'euler41': [1, 29, 591, 8870, 109589, 1132509, 10137134, 78739477, 538618569, 3228318557, 17040522254, 78053652789, 309672322229, 1027644502870, 2807311606431, 5647873942549, 7984925229121], 'euler43': [1, -2, 236, -465, 27460, -51575, 2034075, -3419244, 104089696, -147027492, 3761004675, -4100573525, 93880275460, -68358925995, 1491841679564, -543637222214, 11688200277601], 'euler47': [1, 0, 117, 136, 7238, 18338, 426984, 1406698, 22678952, 66114806, 943207656, 1903906174, 35319131078, 31190920952, 1261168193493, 0, 23811286661761], 'euler5': [1, -1, 20, -12, 174, -56, 953, -141, 4561, -705, 23825, -7000, 108750, -37500, 312500, -78125, 390625], 'euler53': [1, 59, 1773, 35994, 555641, 6950535, 73081626, 659060411, 5148041929, 34930201783, 205286287434, 1034774799195, 4384274753321, 15052528575042, 39297412281717, 69307957250383, 62259690411361], 'euler59': [1, 23, 391, 5027, 56886, 553890, 5066388, 41897990, 333030964, 2471981410, 17636096628, 113757374310, 689308197846, 3593924451073, 16492588653631, 57238984150837, 146830437604321], 'euler61': [1, 2, 59, 36, 8639, 3895, 529997, -186683, 37362403, -11387663, 1972118837, 884090995, 119614220399, 30405466836, 3039702087299, 6285485672042, 191707312997281], 'euler67': [1, -3, 339, -841, 56502, -122764, 6176868, -11961514, 484321692, -801421438, 27727960452, -36922868932, 1138578638742, -1135455214987, 30665391555291, -18182134815969, 406067677556641], 'euler7': [1, 4, 40, 141, 746, 2383, 8841, 25082, 73288, 175574, 433209, 817369, 1791146, 2369787, 4705960, 3294172, 5764801], 'euler71': [1, 1, 200, 642, 22644, 133805, 1838211, 14593132, 133386112, 1036112372, 9266421651, 47890281355, 575422104564, 1158315243342, 25620056784200, 9095120158391, 645753531245761], 'euler73': [1, 6, 155, 1840, 23849, 267699, 2403405, 25891991, 218901495, 1890115343, 12807745245, 104139461883, 677269649609, 3814451731120, 23456805074795, 66284391114582, 806460091894081], 'euler79': [1, 0, 222, -1008, 23865, -199880, 2046977, -22369928, 157302126, -1767224312, 12775183457, -98548635320, 929543683065, -3101672850192, 53965415125662, 0, 1517108809906561], 'euler83': [1, -15, 425, -5251, 90501, -941833, 12398464, -111235053, 1207619210, -9232509399, 85413018496, -538527865571, 4295025508821, -20683902416393, 138949658681825, -407040764844405, 2252292232139041], 'euler89': [1, 4, 615, 2228, 173044, 549813, 29004737, 78354964, 3163082895, 6973591796, 229746521777, 387601120797, 10857168351604, 12441284452372, 305643493941015, 176925339582116, 3936588805702081], 'euler97': [1, 62, 2150, 52739, 1017422, 16273323, 222841507, 2658362297, 27886183171, 257861142809, 2096715739363, 14852222522379, 90071638133582, 452887737813923, 1790889810597350, 5009493637643006, 7837433594376961], 'euler_factors': [[1, -8, 28, -56, 70, -56, 28, -8, 1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 5, 17, 43, 90, 182, 378, 760, 1420, 2280, 3402, 4914, 7290, 10449, 12393, 10935, 6561], [1, -1, 20, -12, 174, -56, 953, -141, 4561, -705, 23825, -7000, 108750, -37500, 312500, -78125, 390625], [1, 4, 40, 141, 746, 2383, 8841, 25082, 73288, 175574, 433209, 817369, 1791146, 2369787, 4705960, 3294172, 5764801], [1, 8, 28, 56, 70, 56, 28, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 3, 32, 32, 458, -644, 2607, -29023, -625, -377299, 440583, -1414868, 13080938, 11881376, 154457888, 188245551, 815730721], [1, 6, 116, 587, 6153, 26305, 195117, 699036, 4050559, 11883612, 56388813, 129236465, 513904713, 833456059, 2799958004, 2462032038, 6975757441], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, -9, 122, -736, 5373, -26844, 144595, -725377, 3403722, -16683671, 76490755, -326610948, 1503585693, -4737148448, 18060378458, -30643429023, 78310985281], [1, 4, 132, 149, 7210, -8455, 261495, -702233, 7976455, -20364757, 219917295, -206208995, 5099496010, 3056161201, 78516678372, 68999505236, 500246412961], [1, 11, 222, 1765, 20656, 130021, 1137593, 5928155, 42218816, 183772805, 1093226873, 3873455611, 19076249776, 50530451515, 197025817182, 302638755221, 852891037441], [1, -10, 221, -1934, 23831, -175415, 1590889, -9764443, 71129081, -361284391, 2177927041, -8885295995, 44663130791, -134111212838, 567025536389, -949318771330, 3512479453921], [1, 29, 591, 8870, 109589, 1132509, 10137134, 78739477, 538618569, 3228318557, 17040522254, 78053652789, 309672322229, 1027644502870, 2807311606431, 5647873942549, 7984925229121], [1, -2, 236, -465, 27460, -51575, 2034075, -3419244, 104089696, -147027492, 3761004675, -4100573525, 93880275460, -68358925995, 1491841679564, -543637222214, 11688200277601], [1, 0, 117, 136, 7238, 18338, 426984, 1406698, 22678952, 66114806, 943207656, 1903906174, 35319131078, 31190920952, 1261168193493, 0, 23811286661761], [1, 59, 1773, 35994, 555641, 6950535, 73081626, 659060411, 5148041929, 34930201783, 205286287434, 1034774799195, 4384274753321, 15052528575042, 39297412281717, 69307957250383, 62259690411361], [1, 23, 391, 5027, 56886, 553890, 5066388, 41897990, 333030964, 2471981410, 17636096628, 113757374310, 689308197846, 3593924451073, 16492588653631, 57238984150837, 146830437604321], [1, 2, 59, 36, 8639, 3895, 529997, -186683, 37362403, -11387663, 1972118837, 884090995, 119614220399, 30405466836, 3039702087299, 6285485672042, 191707312997281], [1, -3, 339, -841, 56502, -122764, 6176868, -11961514, 484321692, -801421438, 27727960452, -36922868932, 1138578638742, -1135455214987, 30665391555291, -18182134815969, 406067677556641], [1, 1, 200, 642, 22644, 133805, 1838211, 14593132, 133386112, 1036112372, 9266421651, 47890281355, 575422104564, 1158315243342, 25620056784200, 9095120158391, 645753531245761], [1, 6, 155, 1840, 23849, 267699, 2403405, 25891991, 218901495, 1890115343, 12807745245, 104139461883, 677269649609, 3814451731120, 23456805074795, 66284391114582, 806460091894081], [1, 0, 222, -1008, 23865, -199880, 2046977, -22369928, 157302126, -1767224312, 12775183457, -98548635320, 929543683065, -3101672850192, 53965415125662, 0, 1517108809906561], [1, -15, 425, -5251, 90501, -941833, 12398464, -111235053, 1207619210, -9232509399, 85413018496, -538527865571, 4295025508821, -20683902416393, 138949658681825, -407040764844405, 2252292232139041], [1, 4, 615, 2228, 173044, 549813, 29004737, 78354964, 3163082895, 6973591796, 229746521777, 387601120797, 10857168351604, 12441284452372, 305643493941015, 176925339582116, 3936588805702081], [1, 62, 2150, 52739, 1017422, 16273323, 222841507, 2658362297, 27886183171, 257861142809, 2096715739363, 14852222522379, 90071638133582, 452887737813923, 1790889810597350, 5009493637643006, 7837433594376961]], 'id': 21865249, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/7942/2/a/bp'], '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': '16-7942e8-1.1-c1e8-0-5', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0, 0, 0, 0, 0, 0, 0], 'nu_real_doubled': [1, 1, 1, 1, 1, 1, 1, 1], 'order_of_vanishing': 8, 'prelabel': '16-7942e8-1.1-c1e8-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.9634910237471175, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e8-0', 'trace_hash': 488776419326682673, 'z1': {'__RealLiteral__': 0, 'data': '1.10876524187700719941787450513', 'prec': 100}}