LMFDB - Lfunction data - 2-3240-360.149-c0-0-5

Formats: - HTML - YAML - JSON - 2025-04-11T20:21:29.447750

Column	Type
A10	numeric
A2	numeric
A3	numeric
A4	numeric
A5	numeric
A6	numeric
A7	numeric
A8	numeric
A9	numeric
Lhash	text
a10	jsonb
a2	jsonb
a3	jsonb
a4	jsonb
a5	jsonb
a6	jsonb
a7	jsonb
a8	jsonb
a9	jsonb
accuracy	smallint
algebraic	boolean
analytic_conductor	double precision
analytic_normalization	numeric
bad_lfactors	jsonb
bad_primes	bigint[]
central_character	text
coeff_info	jsonb
coefficient_field	text
conductor	numeric
conductor_radical	integer
conjugate	text
credit	text
degree	smallint
dirichlet_coefficients	jsonb
euler_factors	jsonb
euler_factors_factorization	jsonb
gamma_factors	jsonb
group	text
index	smallint
instance_types	text[]
instance_urls	text[]
label	text
leading_term	text
load_key	text
motivic_weight	smallint
mu_imag	numeric[]
mu_real	smallint[]
nu_imag	numeric[]
nu_real_doubled	smallint[]
order_of_vanishing	smallint
origin	text
plot_delta	numeric
plot_values	jsonb
positive_zeros	jsonb
precision	smallint
prelabel	text
primitive	boolean
rational	boolean
root_analytic_conductor	double precision
root_angle	double precision
root_number	text
self_dual	boolean
sign_arg	numeric
spectral_label	text
st_group	text
symmetry_type	text
trace_hash	bigint
types	jsonb
values	jsonb
z1	numeric
z2	numeric
z3	numeric

{'Lhash': '1225516660863696102648407153100', 'a10': [-0.5, -0.8660254037844386], 'a2': [0.8660254037844386, 0.5], 'a3': [0.0, 0.0], 'a4': [0.5, 0.8660254037844386], 'a5': [-0.8660254037844386, -0.5], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [3.9689140359382235e-80, 1.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.616970640930928, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.8660254037844386, -0.5]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0.8660254037844386, 0.5]]]], 'bad_primes': [2, 3, 5], 'central_character': '3240.1349', 'coefficient_field': 'CDF', 'conductor': 3240, 'conductor_radical': 30, 'conjugate': '1774035458454606132981185645552', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.8660254037844386, -0.5]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.8660254037844386, 0.5]], [[1.0, 0], [0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [-1.7320508075688772, 0], [1.0, 0]], [[1.0, 0], [0, -1.7320508075688772], [-1.0, 0]], [[1.0, 0], [-0.8660254037844386, 1.5], [-0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [0.5, -0.8660254037844386], [-0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, -1.0], [-1.0, 0]], [[1.0, 0], [0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [-1.5, 0.8660254037844386], [0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-0.5, -0.8660254037844386], [-0.5, 0.8660254037844386]], [[1.0, 0], [0.8660254037844386, -0.5], [0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [0, 2.0], [-1.0, 0]], [[1.0, 0], [0, 1.7320508075688772], [-1.0, 0]], [[1.0, 0], [0, 0], [-0.5, -0.8660254037844386]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 5, 'label': '2-3240-360.149-c0-0-5', 'leading_term': '1.8656028912092527352001303874738', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/3240/1/bh/g/1349/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [1.8656028912092528, 1.8196048239388645, 1.7833293978536209, 1.7541479019799302, 1.7288197215468737, 1.70378033907975, 1.6754081182700615, 1.6402383321538896, 1.59511559528494, 1.5372917343818429, 1.4644829501384617, 1.374900284881274, 1.2672643409955688, 1.1408113969056584, 0.9952947948427588, 0.8309831081804496, 0.6486550844581868, 0.4495905091212232, 0.23555574576470473, 0.008782625076195951, -0.22806053222662406, -0.4719067347796422, -0.7193376405836625, -0.96664066786378, -1.2098757890385508, -1.4449514874473142, -1.6677089420775117, -1.8740131013131587, -2.059848924514414, -2.2214207219570863, -2.355252221277261, -2.4582847438503044, -2.527970698692259, -2.5623595047096273, -2.5601730431666496, -2.5208678278528556, -2.4446812649608205, -2.332659659628225, -2.1866660097744193, -2.0093661051356158, -1.8041920115392904, -1.575282655092247, -1.3274019122019713, -1.0658353400534823, -0.7962674263043837, -0.5246419720024764, -0.25700892210541393, 0.0006384032976343845, 0.2425311735917961, 0.4632930681907968, 0.6581032142088274, 0.8228486612577527, 0.9542610461704015, 1.0500323182559863, 1.1089048036472093, 1.1307314839581437, 1.1165031413619415, 1.0683399635888844, 0.9894462852998498, 0.8840283369878553, 0.7571761429213059, 0.6147120142429958, 0.4630093766064487, 0.3087869053956029, 0.1588840663345449, 0.020025126653983046, -0.1014205338132885, -0.1996734622202172, -0.26976593214865596, -0.30774197514125, -0.3108274999851025, -0.27756306370313943, -0.20789288353980062, -0.10320500093225528, 0.033680907001282206, 0.19857977147611308, 0.3860611735175225, 0.5896208712922896, 0.8018994304737767, 1.01494156603982, 1.2204879399647541, 1.4102895217030489, 1.5764332844595363, 1.7116670496236064, 1.8097107630476592, 1.8655414346381043, 1.8756394247984258, 1.8381847264831326, 1.7531933584087251, 1.622585920550494, 1.4501827135644467, 1.2416225152441935, 1.0042050473923103, 0.7466602479968345, 0.4788505670239195, 0.21141550270467988, -0.04462964036090676, -0.27832638608593624, -0.47922080436830755, -0.6378086585022973, -0.7459596557877687, -0.7973025301277891, -0.7875535043297068, -0.7147722652385096, -0.5795319073576526, -0.384992297904486, -0.13686989390408377, 0.1566989241375617, 0.4853995971860456, 0.837080330582219, 1.1981819277877213, 1.554242022993086, 1.8904554684333188, 2.1922694944827654, 2.4459899010538004, 2.6393730953192045, 2.762178367734304, 2.8066554604809673, 2.7679442499858173, 2.64436621063779, 2.437591174042886, 2.1526676231532744, 1.7979101949004166, 1.3846440008963927, 0.9268115739556259, 0.4404544467310466, -0.05691270605479759, -0.5470120522285908, -1.0115688345852907, -1.433102447951572, -1.7957086793327277, -2.0857985499629175, -2.2927598140301906, -2.4095093139394685, -2.432908032232077, -2.364015712755275, -2.208168178150073, -1.9748677145806552, -1.6774848408224232, -1.332778096748237, -0.9602468150784237, -0.5813398042872193, -0.21855009590207955, 0.10556795864857406, 0.36941823642002986, 0.5533749890700516, 0.6407423737375494, 0.6186169872792188, 0.47861188390403864, 0.21740538806869525, -0.16291533582979412, -0.6547377698516434, -1.2450469197779859, -1.9157895800021527, -2.644471230883574, -3.4049661278715693, -4.1685110158249925, -4.904843819116313, -5.583441068714348, -6.174802126485071, -6.651724773480384, -6.990515668467758, -7.172080673535427, -7.182844087064449, -7.015452302352113, -6.669226086178741, -6.150336198636788, -5.4716890094330735, -4.652521583773331, -3.717718834142396, -2.696878154550753, -1.6231588618584913, -0.5319641837609064, 0.5404880685895812, 1.5586440627875786, 2.489076506348109, 3.3018658076041563, 3.9718373304270913, 4.479598105275323, 4.812324974919682, 4.964267150681827, 4.936939045081208, 4.738993438489682, 4.385779865025087, 3.898607857459203, 3.3037486544782593, 2.631221455133993, 1.9134206756484728, 1.1836483885612512, 0.47462079272158053, -0.18298108940673324, -0.7618483648503072, -1.2392061786228492, -1.5977464236999186, -1.826288353484094, -1.920137623540596, -1.8811292256693035, -1.7173554787290006, -1.4425959137295723, -1.075480734858779, -0.6384327868395766, -0.15644392064160603, 0.34425025544663335, 0.8375284593817299, 1.2987046487292873, 1.7057441829594098, 2.040313614933338, 2.288611689671194, 2.441941087419892, 2.4969945406629592, 2.4558444337601237, 2.3256410311929363, 2.1180402108087844, 1.8483961466367815, 1.5347669930632233, 1.196791570791274, 0.854501788180219, 0.5271386655176391, 0.23203917722865522, -0.016343290143799358, -0.20723001583378195, -0.33407575984280424, -0.39486505570348984, -0.39213099509188853, -0.3326976650221192, -0.22716350040402317, -0.08915794864142065, 0.06558286787640503, 0.22026513992994137, 0.3581472519491365, 0.4636431014884314, 0.5233516637504209, 0.5269498361486432, 0.4678935802999591, 0.34388367682627474, 0.15706638480684212, -0.08604484917713391, -0.37492367954909306, -0.6956414215319154, -1.0316984165601808, -1.3650269830023902, -1.677105807070388, -1.950118221409392, -2.1680834158052447, -2.317890479796191, -2.3901702931948687, -2.3799494043203904, -2.2870426691410706, -2.116156850806715, -1.8766947022206057, -1.5822672501142947, -1.2499399746680842, -0.8992552374479342, -0.5510876182550019, -0.22639987069472353, 0.05502572718780045, 0.2758032601271939], 'positive_zeros': ['0.966762182452367038959833914728290', '2.38658944902249868862699106629410', '3.30861555030007517803080849281193', '3.74629247742254120842019771331838', '4.86588434927753064853923439151505', '5.40736776190717007796477326595975', '6.39262453117356248693827462753999', '7.24428023627683891989971176666117', '7.59728141348824773390490575469467', '8.759346748622231336065147496119132'], 'prelabel': '2-3240-360.149-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2716016046431082, 'root_angle': -0.38888888888888895, 'root_number': '0.34202014332566873304409961468239 - 0.93969262078590838405410927732446*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.19444444444444445', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.966762182452367038959833914728', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.38658944902249868862699106629', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.30861555030007517803080849281', 'prec': 103}}

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

lfunc_search • Show schema

{'algebraic': True, 'analytic_conductor': 1.616970640930928, 'bad_primes': [2, 3, 5], 'central_character': '360.149', 'conductor': 3240, 'conductor_radical': 30, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3240/1/bh/g/1349/2'], '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': '2-3240-360.149-c0-0-5', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-3240-360.149-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2716016046431082, 'root_angle': -0.19444444444444448, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.966762182452367038959833914728', 'prec': 107}}

Column	Type
Lhash	text
Lhash_array	text[]
label	text
type	text
url	text

lfunc_instances • Show schema

{'Lhash': '1225516660863696102648407153100', 'Lhash_array': ['1225516660863696102648407153100'], 'label': '2-3240-360.149-c0-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3240/1/bh/g/1349/2'}

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.