Database - lfunc_search (L-function search data)

Formats: - HTML - YAML - JSON - 2026-07-28T01:54:42.242612

Query: /api/lfunc_search/?_offset=0

Column	Type
algebraic	boolean
analytic_conductor	double precision
bad_primes	bigint[]
central_character	text
conductor	numeric
conductor_radical	bigint
degree	smallint
dirichlet_coefficients	numeric[]
euler11	numeric[]
euler13	numeric[]
euler17	numeric[]
euler19	numeric[]
euler2	numeric[]
euler23	numeric[]
euler29	numeric[]
euler3	numeric[]
euler31	numeric[]
euler37	numeric[]
euler41	numeric[]
euler43	numeric[]
euler47	numeric[]
euler5	numeric[]
euler53	numeric[]
euler59	numeric[]
euler61	numeric[]
euler67	numeric[]
euler7	numeric[]
euler71	numeric[]
euler73	numeric[]
euler79	numeric[]
euler83	numeric[]
euler89	numeric[]
euler97	numeric[]
euler_factors	numeric[]
index	smallint
instance_types	text[]
instance_urls	text[]
is_instance_Artin	boolean
is_instance_BMF	boolean
is_instance_CMF	boolean
is_instance_DIR	boolean
is_instance_ECNF	boolean
is_instance_ECQ	boolean
is_instance_G2Q	boolean
is_instance_HMF	boolean
is_instance_MaassGL3	boolean
is_instance_MaassGL4	boolean
is_instance_MaassGSp4	boolean
is_instance_NF	boolean
label	text
motivic_weight	smallint
mu_imag	numeric[]
mu_real	smallint[]
nu_imag	numeric[]
nu_real_doubled	smallint[]
order_of_vanishing	smallint
prelabel	text
primitive	boolean
rational	boolean
root_analytic_conductor	double precision
root_angle	double precision
self_dual	boolean
spectral_label	text
trace_hash	bigint
z1	numeric

{'algebraic': True, 'analytic_conductor': 630.9591889234952, 'bad_primes': [3], 'central_character': '1.1', 'conductor': 59049, 'conductor_radical': 3, 'degree': 4, 'dirichlet_coefficients': [1, -9, 0, 38, 45, 0, -50, -99, 0, -405, -36, 0, -254, 450, 0, 297, 0, 0, 502, 1710, 0, 324, 585, 0, 725, 2286, 0, -1900, 1881, 0, -380, -1584, 0, 0, -2250, 0, -2648, -4518, 0, -4455, 5364, 0, 3586, -1368, 0, -5265, 2421, 0, 2401, -6525, 0, -9652, 0, 0, -1620, 4950, 0, -16929, -3114, 0, -1826, 3420, 0, 6013, -11430, 0, -5225, 0, 0, 20250, 0, 0, -6062, 23832, 0, 19076, 1800, 0, 4360, 13365, 0, -48276, -11700, 0, 0, -32274, 0, 3564, 0, 0, 12700, 22230, 0, -21789, 22590, 0, 319, -21609, 0, 27550], 'euler11': [1, 36, 15073, 527076, 214358881], 'euler13': [1, 254, 35955, 7254494, 815730721], 'euler17': [1, 0, -49430, 0, 6975757441], 'euler19': [1, -502, 323643, -65421142, 16983563041], 'euler2': [1, 9, 43, 144, 256], 'euler23': [1, -585, 393916, -163706985, 78310985281], 'euler29': [1, -1881, 1886668, -1330395561, 500246412961], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 380, -779121, 350937980, 852891037441], 'euler37': [1, 2648, 5501298, 4962778328, 3512479453921], 'euler41': [1, -5364, 12416593, -15157382004, 7984925229121], 'euler43': [1, -3586, 9440595, -12259820386, 11688200277601], 'euler47': [1, -2421, 6833428, -11813707701, 23811286661761], 'euler5': [1, -45, 1300, -28125, 390625], 'euler53': [1, 0, 9570985, 0, 62259690411361], 'euler59': [1, 3114, 15349693, 37733462154, 146830437604321], 'euler61': [1, 1826, -10511565, 25282505666, 191707312997281], 'euler67': [1, 5225, 7149504, 105289607225, 406067677556641], 'euler7': [1, 50, 99, 120050, 5764801], 'euler71': [1, 0, 37533625, 0, 645753531245761], 'euler73': [1, 6062, 65983443, 172150136942, 806460091894081], 'euler79': [1, -4360, -19940481, -169822353160, 1517108809906561], 'euler83': [1, 11700, 93088321, 555262355700, 2252292232139041], 'euler89': [1, 0, -16401782, 0, 3936588805702081], 'euler97': [1, -319, -88427520, -28240840639, 7837433594376961], 'euler_factors': [[1, 9, 43, 144, 256], [1, 0, 0, 0, 0], [1, -45, 1300, -28125, 390625], [1, 50, 99, 120050, 5764801], [1, 36, 15073, 527076, 214358881], [1, 254, 35955, 7254494, 815730721], [1, 0, -49430, 0, 6975757441], [1, -502, 323643, -65421142, 16983563041], [1, -585, 393916, -163706985, 78310985281], [1, -1881, 1886668, -1330395561, 500246412961], [1, 380, -779121, 350937980, 852891037441], [1, 2648, 5501298, 4962778328, 3512479453921], [1, -5364, 12416593, -15157382004, 7984925229121], [1, -3586, 9440595, -12259820386, 11688200277601], [1, -2421, 6833428, -11813707701, 23811286661761], [1, 0, 9570985, 0, 62259690411361], [1, 3114, 15349693, 37733462154, 146830437604321], [1, 1826, -10511565, 25282505666, 191707312997281], [1, 5225, 7149504, 105289607225, 406067677556641], [1, 0, 37533625, 0, 645753531245761], [1, 6062, 65983443, 172150136942, 806460091894081], [1, -4360, -19940481, -169822353160, 1517108809906561], [1, 11700, 93088321, 555262355700, 2252292232139041], [1, 0, -16401782, 0, 3936588805702081], [1, -319, -88427520, -28240840639, 7837433594376961]], 'id': 24079315, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/243/5/d/a'], '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': '4-3e10-1.1-c4e2-0-5', 'motivic_weight': 4, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [4, 4], 'order_of_vanishing': 0, 'prelabel': '4-3e10-1.1-c4e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.0118759990021875, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c4e2-0', 'trace_hash': 1839028874927376712, 'z1': {'__RealLiteral__': 0, 'data': '0.56535294344395599633787371388', 'prec': 103}}