-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '757360568522162278817922900316', 'a10': [2.0413750737902774, 0.9125720837872152], 'a2': [0.5, -0.8660254037844386], 'a3': [0, 0], 'a4': [-0.5, -0.8660254037844386], 'a5': [0.23037692955090902, 2.2241687144483206], 'a6': [0, 0], 'a7': [0.4327134586813507, 0.7494816955549555], 'a8': [-1.0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.34249703648981, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.5, 0.8660254037844386]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-0.23037692955090902, -2.2241687144483206]]], [13, [[1.0, 0], [-1.354858446012866, -3.341310909099541]]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '1170.199', 'coefficient_field': 'CDF', 'conductor': 1170, 'conductor_radical': 390, 'conjugate': '2143677250064236036263634339015', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.23037692955090902, -2.2241687144483206]], [[1.0, 0], [-0.4327134586813507, -0.7494816955549555], [-3.5, 6.06217782649107]], [[1.0, 0], [0.15142959288041807, 0.08742791621278481], [5.5, 9.526279441628825]], [[1.0, 0], [-1.354858446012866, -3.341310909099541]], [[1.0, 0], [7.083387416708434, -4.089595631811022], [8.5, -14.722431864335457]], [[1.0, 0], [-5.208428636885986, 3.00708767556108], [9.5, -16.454482671904334]], [[1.0, 0], [2.5221079402463147, 1.4561396982265022], [11.5, 19.91858428704209]], [[1.0, 0], [3.2449085757641933, -5.620346519139547], [-14.5, -25.11473670974872]], [[1.0, 0], [0, -6.950571010630205], [-31.0, 0]], [[1.0, 0], [0.8795729406977635, -1.5234650222512935], [-18.5, -32.04293994002423]], [[1.0, 0], [-7.083387416708434, -4.089595631811022], [20.5, 35.50704155516198]], [[1.0, 0], [7.944759876911415, -4.5869092535817435], [21.5, -37.239092362730865]], [[1.0, 0], [-11.902095831609397, 0], [47.0, 0]], [[1.0, 0], [0, 2.487345640429154], [-53.0, 0]], [[1.0, 0], [-6.0939340377579025, 3.518334457123348], [29.5, -51.09549882328188]], [[1.0, 0], [-3.986946300666944, -6.905593559803928], [-30.5, 52.827549630850754]], [[1.0, 0], [-1.3676604990962649, 2.3688574719397395], [-33.5, -58.023702053557386]], [[1.0, 0], [12.267683112925484, -7.082750147580555], [35.5, -61.48780366869514]], [[1.0, 0], [12.870567459127171, 0], [73.0, 0]], [[1.0, 0], [-9.48960785384545, 0], [79.0, 0]], [[1.0, 0], [0.13954353860373964, 0], [83.0, 0]], [[1.0, 0], [-11.37897695342582, -6.569655407162945], [44.5, 77.07626093681505]], [[1.0, 0], [4.324107558684341, 7.4895739890339], [-48.5, 84.00446416709055]], [[1.0, 0], [-5.282761812681161, 9.150011863848432], [-50.5, -87.4685657822283]], [[1.0, 0], [0, -8.935683069325796], [-103.0, 0]], [[1.0, 0], [-0.7454549129345919, -0.4303885946515157], [53.5, 92.66471820493493]], [[1.0, 0], [0, 5.453356102220639], [-109.0, 0]], [[1.0, 0], [-10.203618544872931, 5.891061913590644], [56.5, -97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 8, 'label': '2-1170-65.4-c1-0-8', 'leading_term': '1.568741210973228379910475127198135446815145518680603338', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1170/2/bj/d/199/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.5687412109732284, 1.4547686245615767, 1.3339592387271955, 1.2056562311647627, 1.0691073050047573, 0.9235338420567458, 0.7682034979369065, 0.6025024760592587, 0.4260042292220501, 0.23853201849130354, 0.040213456319916595, -0.16847423745035878, -0.38666908836347524, -0.6130998591688951, -0.8460725497438946, -1.0834681984666066, -1.322752241343621, -1.5609956467586787, -1.7949079745568437, -2.0208823902224307, -2.2350524899286963, -2.43336055984829, -2.6116366087656564, -2.765687186350484, -2.8913926429780767, -2.9848111152675507, -3.0422871504360223, -3.06056252882404, -3.0368865245550265, -2.969122576138978, -2.855848138188203, -2.696444367405775, -2.4911722740577846, -2.241232055387616, -1.9488025281511359, -1.6170578985061668, -1.2501595498214346, -0.8532210891897409, -0.4322455635113055, 0.005965476868854869, 0.4539305424523853, 0.9036329685724396, 1.3466895163867207, 1.7745395130987551, 2.178650330813292, 2.5507341676772275, 2.882970361737206, 3.1682268721290736, 3.4002741366646636, 3.573984288993204, 3.685508716756238, 3.732427182668157, 3.7138622237780585, 3.6305532921518946, 3.4848860951821554, 3.2808738179650114, 3.0240883357559536, 2.721541113537986, 2.3815151950388866, 2.013351449774354, 1.6271940119112436, 1.2337015423168045, 0.8437325061174483, 0.4680140137284605, 0.11680485800471181, -0.20043586573544447, -0.47536279728992836, -0.7010292948860801, -0.8721321453888587, -0.9852057297124749, -1.0387567639681854, -1.0333325464582628, -0.971517820960654, -0.8578578529875159, -0.6987080261809271, -0.5020131045407131, -0.2770221651271157, -0.03394796996910983, 0.21641790336460276, 0.46312063256717734, 0.6954731025798235, 0.9034856767040106, 1.078277602294439, 1.2124529227499883, 1.3004245362495512, 1.3386715278444292, 1.3259170793146315, 1.263217073275964, 1.1539528661018612, 1.0037254911183064, 0.8201526266604533, 0.6125738598399632, 0.3916739187607354, 0.1690374487177756, -0.04334761235627552, -0.2336181220770704, -0.39057322144400636, -0.5041979176796182, -0.5661492007514796, -0.5701819175301859, -0.512493467991039, -0.39196924889506607, -0.21031456853024927, 0.027936639712860107, 0.3155407420198555, 0.6427897513461839, 0.997876054217677, 1.367363736211068, 1.7367483484600967, 2.091082210331732, 2.4156384770043893, 2.6965844363761953, 2.921633016691879, 3.080641410661778, 3.166127117999293, 3.173674572494052, 3.102209776928959, 2.954125873114036, 2.7352491112931805, 2.4546419791083256, 2.124247981386602, 1.7583903683765763, 1.3731446118994064, 0.9856112444610919, 0.6131214410212726, 0.2724121083372102, -0.021190021478747722, -0.25453492160174407, -0.41732715443019924, -0.5026789386949712, -0.5075072549954918, -0.43275061868982506, -0.28338939837042953, -0.06826292361260726, 0.20031332448505215, 0.5071168973402881, 0.8347504622823344, 1.1645042151580174, 1.477308294515448, 1.754728901099223, 1.9799580240672743, 2.138745319863651, 2.220221945782721, 2.2175700532079006, 2.1284980936859346, 1.9554908453954496, 1.7058137585434126, 1.391263359513849, 1.0276684631696882, 0.6341601696552659, 0.23224137830774916, -0.15530185322063833, -0.5055949971678155, -0.7969163047128686, -1.009920629597679, -1.1287805631281025, -1.1421817478913774, -1.0441147847571666, -0.8344149382451717, -0.5190125253102389, -0.10987091995529784, 0.3753951475977745, 0.9142116572367058, 1.4800216761594673, 2.043504118909096, 2.5739788105706314, 3.0409301612434914, 3.4155733948907, 3.672382713075253, 3.790500380720001, 3.7549496485085383, 3.557582595594002, 3.1977060731987077, 2.6823444158021874, 2.0261157206362896, 1.2507183686728798, 0.38404503864260525, -0.5410383522786304, -1.4881926741202367, -2.4193123655255824, -3.296354175193957, -4.083194780667757, -4.747420775034677, -5.2619562519571215, -5.606440151946877, -5.768277394379117, -5.7433040639950965, -5.536026741659729, -5.159418440319571, -4.6342773338339045, -3.9881782498533522, -3.2540694069447733, -2.4685868225346597, -1.6701750320067805, -0.8971142589946641, -0.18556023080261938, 0.4322969928804742, 0.929854619182351, 1.287410143916725, 1.493093512207717, 1.5433671361895318, 1.443066619309746, 1.204980942267815, 0.8489970638007117, 0.40085885698955626, -0.10938743704192366, -0.6491708401310752, -1.1852929036630422, -1.685834104446091, -2.121958283995658, -2.4695100457713557, -2.710312313562798, -2.8330891557894318, -2.8339614704609137, -2.7164888866753283, -2.4912587363771035, -2.175050523544878, -1.7896302793922807, -1.360251931155657, -0.9139608965117006, -0.47780738370216624, -0.0770825141229438, 0.2663110219191863, 0.5352504899340244, 0.7184585070937902, 0.8111746448735682, 0.8153906331154017, 0.739634482995923, 0.5983178811974789, 0.410689509126772, 0.19946268733072364, -0.010792745080862438, -0.19538856363530388, -0.331271459738369, -0.3986749840017411, -0.38255952335170573, -0.27374291643899623, -0.06964403595687514, 0.22541331858479804, 0.6003601522290959, 1.0379989852123588, 1.5160404580916016, 2.0084944619034992, 2.4873261956282944, 2.924269040114303, 3.292674641830788, 3.5692769744015793, 3.7357517304184364, 3.779964985485737, 3.6968249258212658, 3.488676296175761, 3.1652074390089457, 2.742872373347217, 2.243863127886027, 1.6946982779044828, 1.1245202244425123, 0.5632143324114616], 'positive_zeros': ['0.59745214366309307442190523738735', '2.28436956335805360819044365973596', '3.77077125730298978919274305503846', '4.51970692551565594956236615261773', '5.49545403031767987635275088073875', '6.02890106835917176538260035141057', '7.37817669203159461587560184044428', '7.80888590996714925796014417255275', '8.823689476613080481235065629895755', '9.389009274174898295030887900123674'], 'prelabel': '2-1170-65.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.0565498583353437, 'root_angle': -0.16311168644962762, 'root_number': '0.5192177283444949188076014264976357222537361082774080309 - 0.8546420014092346712387914054673867948751745435027257141*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.16311168644962762', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.59745214366309307442190523739', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.28436956335805360819044365974', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.77077125730298978919274305504', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 9.34249703648981, 'bad_primes': [2, 3, 5, 13], 'central_character': '65.4', 'conductor': 1170, 'conductor_radical': 390, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1170/2/bj/d/199/3'], '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': '2-1170-65.4-c1-0-8', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-1170-65.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.0565498583353437, 'root_angle': -0.16311168644962762, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.59745214366309307442190523739', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '757360568522162278817922900316', 'Lhash_array': ['757360568522162278817922900316'], 'factors': ['2-1170-65.4-c1-0-8'], 'label': '2-1170-65.4-c1-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1170/2/bj/d/199/3'}