-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1861072086850480199644291224009', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.5128992774059061, -0.8584487936018661], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [1.0131301485199393, -0.43303260714652714], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.8909573328664462, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [421, [[1.0, 0], [-0.9195277725514507, -0.3930250316539236]]]], 'bad_primes': [3, 421], 'central_character': '3789.379', 'coefficient_field': 'CDF', 'conductor': 3789, 'conductor_radical': 1263, 'conjugate': '1525159979759519102867623404191', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [-0.5128992774059061, 0.8584487936018661]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [-0.4738686624729987, 0.880595531856738]], [[1.0, 0], [-1.0131301485199393, 0.43303260714652714], [0.6910626489868646, -0.7227948638273916]], [[1.0, 0], [0, 0], [0.1342332658176555, 0.9909497617679347]], [[1.0, 0], [-1.6539130199349517, -0.8427107749070444], [0.5877852522924731, 0.8090169943749475]], [[1.0, 0], [0, 0], [0.9959742939952391, 0.0896393089034335]], [[1.0, 0], [-0.13250096816606863, 0.6471325432235616], [-0.9195277725514507, -0.3930250316539236]], [[1.0, 0], [0, 0], [0.17855689479863665, -0.9839295885986297]], [[1.0, 0], [0, 0], [0, 1.0]], [[1.0, 0], [1.9599371546910924, -0.3556761544701086], [0.9362348706397372, -0.3513748240813427]], [[1.0, 0], [-0.0862221305475559, -1.278847901279338], [-0.9909497617679347, 0.1342332658176555]], [[1.0, 0], [0, 0], [0.9195277725514507, 0.3930250316539236]], [[1.0, 0], [0.48703462043693585, -1.621901586635566], [-0.8345732537213026, -0.5508969814521025]], [[1.0, 0], [0, 0], [0.880595531856738, 0.4738686624729987]], [[1.0, 0], [0, 0], [-0.7227948638273916, -0.6910626489868646]], [[1.0, 0], [0, 0], [-0.6579387259397126, -0.753071466003611]], [[1.0, 0], [0.1288538901250283, 0.038693041542086394], [0.8345732537213026, 0.5508969814521025]], [[1.0, 0], [-0.6683546322092485, -0.21716158407328484], [0.8090169943749475, 0.5877852522924731]], [[1.0, 0], [0, 0], [-0.6579387259397126, 0.753071466003611]], [[1.0, 0], [-0.30901699437494745, -0.04894348370484643], [0.9510565162951535, 0.30901699437494745]], [[1.0, 0], [0.25213304835443207, -0.46854171503055025], [-0.5508969814521025, -0.8345732537213026]], [[1.0, 0], [0, 0], [0.6579387259397126, 0.753071466003611]], [[1.0, 0], [0, 0], [-0.3513748240813427, 0.9362348706397372]], [[1.0, 0], [-1.0918224650572708, 1.6540403339060301], [-0.3930250316539236, -0.9195277725514507]], [[1.0, 0], [0, 0], [0.5508969814521025, -0.8345732537213026]], [[1.0, 0], [1.5597246724984708, 0.4304566583866871], [0.8584487936018661, 0.5128992774059061]], [[1.0, 0], [0, 0], [0.30901699437494745, 0.9510565162951535]], [[1.0, 0], [1.1234898018587336, 1.4088116512993818], [-0.2225209339563144, 0.9749279121818236]], [[1.0, 0], [0, 0], [-0.1342332658176555, 0.9909497617679347]], [[1.0, 0], [0.7852945067337952, 0.5979247301140111], [0.2660368455666751, 0.9639628606958532]], [[1.0, 0], [0, 0], [-0.8584487936018661, 0.5128992774059061]], [[1.0, 0], [0, 0], [-0.9749279121818236, -0.2225209339563144]], [[1.0, 0], [0.04793655024616107, -0.35388182472546237], [-0.9639628606958532, -0.2660368455666751]], [[1.0, 0], [0, 0], [0.6234898018587335, -0.7818314824680298]], [[1.0, 0], [1.9748793503665645, 0.3127901606162921], [0.9510565162951535, 0.30901699437494745]], [[1.0, 0], [-0.3755032646825811, -0.8266963128185447], [-0.6579387259397126, 0.753071466003611]], [[1.0, 0], [0.4378898620044385, 0.079465293989864], [0.9362348706397372, 0.3513748240813427]], [[1.0, 0], [0, 0], [0.9639628606958532, 0.2660368455666751]], [[1.0, 0], [0, 0], [-0.9510565162951535, 0.30901699437494745]], [[1.0, 0], [0, 0], [-0.2660368455666751, 0.9639628606958532]], [[1.0, 0], [-1.6164047361893326, 1.1743867833108361], [0.30901699437494745, -0.9510565162951535]], [[1.0, 0], [0, 0], [0.9362348706397372, -0.3513748240813427]], [[1.0, 0], [-0.09260772269328746, -0.20388228303095873], [-0.6579387259397126, 0.753071466003611]], [[1.0, 0], [0, 0], [0.9510565162951535, 0.30901699437494745]], [[1.0, 0], [-1.689306336643348, 0.3065639018583699], [0.9362348706397372, -0.3513748240813427]], [[1.0, 0], [0.6659109178068762, -1.173577450251468], [-0.5128992774059061, -0.8584487936018661]], [[1.0, 0], [-0.7524069782255092, -1.197448846138138], [-0.4338837391175581, 0.9009688679024191]], [[1.0, 0], [0, 0], [-0.9909497617679347, -0.1342332658176555]], [[1.0, 0], [0.9242125626247362, 0.4450773125431365], [0.6234898018587335, 0.7818314824680298]], [[1.0, 0], [0, 0], [0, 1.0]], [[1.0, 0], [0, 0], [0.6234898018587335, -0.7818314824680298]], [[1.0, 0], [1.374837530375418, -1.314479270974296], [0.044864830350514924, -0.9989930665413147]], [[1.0, 0], [0, 0], [0.4338837391175581, 0.9009688679024191]], [[1.0, 0], [0, 0], [0.0896393089034335, 0.9959742939952391]], [[1.0, 0], [0, 0], [-0.9989930665413147, 0.044864830350514924]], [[1.0, 0], [0, 0], [0.9009688679024191, 0.4338837391175581]], [[1.0, 0], [-1.3701186097572953, -0.5495940438210765], [0.7227948638273916, 0.6910626489868646]], [[1.0, 0], [0.5877852522924731, 0.19098300562505258], [0.8090169943749475, 0.5877852522924731]], [[1.0, 0], [0, 0], [-0.6910626489868646, 0.7227948638273916]], [[1.0, 0], [1.2729798550708007, 1.2170933618618287], [0.044864830350514924, 0.9989930665413147]], [[1.0, 0], [0, 0], [0.5877852522924731, -0.8090169943749475]], [[1.0, 0], [-1.5000796433618122, -0.1350096115349184], [0.9839295885986297, 0.17855689479863665]], [[1.0, 0], [0, 0], [-0.7818314824680298, 0.6234898018587335]], [[1.0, 0], [1.35991397582705, 0.24678800142882953], [0.9362348706397372, 0.3513748240813427]], [[1.0, 0], [0, 0], [-0.5508969814521025, -0.8345732537213026]], [[1.0, 0], [-0.4680344470553912, -1.8574418601431808], [-0.880595531856738, 0.4738686624729987]], [[1.0, 0], [1.0000796433618122, -1.6738513801225452], [-0.4738686624729987, -0.880595531856738]], [[1.0, 0], [0, 0], [-0.3930250316539236, 0.9195277725514507]], [[1.0, 0], [0.360704591248304, -0.32969855040463547], [0.0896393089034335, -0.9959742939952391]], [[1.0, 0], [0, 0], [0.3930250316539236, 0.9195277725514507]], [[1.0, 0], [0, 0], [0.17855689479863665, -0.9839295885986297]], [[1.0, 0], [0.5300791215782952, -0.634932022335744], [-0.17855689479863665, -0.9839295885986297]], [[1.0, 0], [0.14016566753476215, 1.5573681175486942], [-0.9839295885986297, 0.17855689479863665]], [[1.0, 0], [-0.4081890417027659, -0.7193776854715139], [-0.5128992774059061, 0.8584487936018661]], [[1.0, 0], [0, 0], [-0.8090169943749475, 0.5877852522924731]], [[1.0, 0], [0, 0], [0.4338837391175581, 0.9009688679024191]], [[1.0, 0], [-1.622482868400048, -0.7369666521175149], [0.6579387259397126, 0.753071466003611]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-0.7020386370581013, 0.510060926125631], [0.30901699437494745, -0.9510565162951535]], [[1.0, 0], [0, 0], [0.5128992774059061, -0.8584487936018661]], [[1.0, 0], [-0.9195277725514507, -0.3930250316539236]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-3789-421.379-c0-0-0', 'leading_term': '1.7607901183226246221411091842513', '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/3789/1/du/a/379/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [1.7607901183226247, 1.7995094166878947, 1.8494092938290216, 1.9097753983610293, 1.9790073334949914, 2.054789830655749, 2.1342954133475036, 2.2143800811133922, 2.2917500413975858, 2.363093318795422, 2.425180142430948, 2.474940121918559, 2.509524354112029, 2.5263588625578284, 2.5231935609815905, 2.498148938513781, 2.4497611150180956, 2.377024812938861, 2.27943306131172, 2.157012001797995, 2.0103489349051418, 1.8406116758549116, 1.6495573493866749, 1.4395289183338855, 1.2134379964970907, 0.9747328303939014, 0.7273507365953982, 0.4756547411679928, 0.22435467378529636, -0.02158649167138543, -0.2570597005638784, -0.476928376091889, -0.6761560209840846, -0.8499399026606246, -0.9938474101045282, -1.1039512938488747, -1.1769597181099987, -1.2103368838294926, -1.202409938600056, -1.1524579864356315, -1.0607792555698625, -0.9287328798860993, -0.758752298075964, -0.5543279675629446, -0.3199579152187594, -0.06106558572662466, 0.21611452277024035, 0.5046818564957802, 0.797242741455875, 1.0861074543771578, 1.3635065715822032, 1.621820774877871, 1.8538174638207734, 2.0528868673808853, 2.2132699014590846, 2.330269813335126, 2.4004397147359664, 2.4217384485519666, 2.3936478676711834, 2.3172455249716934, 2.1952279671932917, 2.0318812668565776, 1.8329970790664258, 1.6057343267802906, 1.3584285422480866, 1.1003528591286889, 0.8414365884900712, 0.5919491480317903, 0.36215877192621126, 0.16197683503818053, 0.0005997112634220448, -0.11383920936548932, -0.1745944460502841, -0.17659758906544276, -0.11669867166900218, 0.0061511056964881706, 0.19078451609453007, 0.43377845296378365, 0.7294937694108319, 1.0701967365314669, 1.4462610741941337, 1.846446425909437, 2.2582460742355086, 2.6682937461889202, 3.0628166625674167, 3.4281196608516695, 3.7510833798822723, 4.019658233677012, 4.223335301017047, 4.353575373471348, 4.404178267609082, 4.3715761183749615, 4.2550367002701055, 4.056765810152216, 3.781901298859046, 3.438395339083577, 3.0367858200885385, 2.5898622023734044, 2.112235570026926, 1.61982680112465, 1.12929055381633, 0.6573959630138169, 0.2203874017938483, -0.1666497509784015, -0.4903927821976392, -0.7398296270650131, -0.9067275238286207, -0.9860012327867734, -0.975963216596218, -0.8784425454826658, -0.6987643643727129, -0.4455873472965914, -0.130602445317286, 0.23189783641946585, 0.6255646751459141, 1.0326324657632013, 1.434627893723461, 1.81312017260246, 2.150481587636925, 2.4306262742221425, 2.6396953176314653, 2.7666578248448404, 2.8038005669293757, 2.7470830328788214, 2.5963401231263576, 2.3553210355008094, 2.031559900465712, 1.636081108241243, 1.182949712303234, 0.6886844526548596, 0.1715574808632259, -0.3491895324357269, -0.8541788541752678, -1.324742747554924, -1.7437439027846044, -2.0963324877096365, -2.3706043154649694, -2.558128589467324, -2.654319221991499, -2.6586306106875903, -2.5745667054673347, -2.409500854112455, -2.1743128818070154, -1.88285871364575, -1.5512961589065208, -1.1972978240695313, -0.8391881254317736, -0.49504570354687694, -0.18181494508332052, 0.08552937486421454, 0.29472217455768307, 0.43681470233549663, 0.5066155308395702, 0.502941421994557, 0.42866268501708243, 0.29053773659555565, 0.09884215530312483, -0.13319191928600996, -0.3901001926186125, -0.6550396563209233, -0.9107289356015649, -1.140428031379294, -1.3289068655031109, -1.4633514775831316, -1.53415877712315, -1.5355753879962668, -1.4661431633094504, -1.3289230979428037, -1.1314802068469887, -0.8856239537116577, -0.6069114157609231, -0.3139329183223776, -0.027411714725667932, 0.230840210914312, 0.43905955979907313, 0.5767055327549607, 0.6256098617294, 0.571042566659755, 0.40263577874158474, 0.11511387906849198, -0.2912130474249952, -0.8102242367128275, -1.43005040936467, -2.13342731477186, -2.8983299210402556, -3.698861756265859, -4.506360147201165, -5.290666090102197, -6.02149789978943, -6.669861177759305, -7.209424433764555, -7.61779013096327, -7.87759505654337, -7.977381604800899, -7.912192461161413, -7.683854776357931, -7.300935546056267, -6.778366765099095, -6.136756126544014, -5.401415666136564, -4.601155907476765, -3.76690589882297, -2.9302293160293753, -2.1218129569523865, -1.3700060781241024, -0.6994869455371298, -0.13012673700782657, 0.3238891771522795, 0.6546360371734341, 0.8606902150143296, 0.9470230887729999, 0.9245547623154533, 0.8093927991958749, 0.6217985938910289, 0.3849392424209966, 0.12349491538573833, -0.13779994319418867, -0.375599285828551, -0.5692903308824455, -0.7021642370182074, -0.7623458595070921, -0.7434294332765636, -0.6447837625834285, -0.47150947534353305, -0.23405105383410943, 0.05251346943694029, 0.36946323283329296, 0.6956470076098521, 1.0088452454532706, 1.2872001877561514, 1.5106278597012768, 1.6621261712455508, 1.7288988430627117, 1.7032252131793273, 1.583020613706054, 1.3720501275213517, 1.0797791124545846, 0.7208657226412377, 0.3143224752163684, -0.11760560293063249, -0.5507808097689543, -0.9606509417301694, -1.3237765745970715, -1.6193138979549337, -1.8303608418376904, -1.9450811555357348, -1.9575333238155475, -1.8681480835340651, -1.6838188890073094, -1.4175927809940745, -1.0879733808372756, -0.7178717020409202, -0.3332626816757629, 0.03837560080367621, 0.3697483475962392, 0.635455075087789, 0.8136208601774444], 'positive_zeros': ['1.46812701111442731189217418730223', '2.29659286245153001197778295792821', '3.55490650472099966423895433593029', '3.80655052971180060233387936486547', '5.20767441484299494732124420633236', '5.70645696035245342808635701467282', '6.61823827076496111684080874189154', '7.54902197420845627801329284416947', '7.944404669198842538291567644758950', '8.739444029532727949731865447489779'], 'prelabel': '2-3789-421.379-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.375120843004878, 'root_angle': 0.26014362760549586, 'root_number': '0.68421811144455111629732707869405 + 0.72927743415743492256870768188907*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.1300718138027479', 'prec': 60}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.46812701111442731189217418730', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.29659286245153001197778295793', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.55490650472099966423895433593', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1.8909573328664462, 'bad_primes': [3, 421], 'central_character': '421.379', 'conductor': 3789, 'conductor_radical': 1263, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3789/1/du/a/379/1'], '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': '2-3789-421.379-c0-0-0', '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': '2-3789-421.379-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.375120843004878, 'root_angle': 0.13007181380274793, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.46812701111442731189217418730', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1861072086850480199644291224009', 'Lhash_array': ['1861072086850480199644291224009'], 'label': '2-3789-421.379-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3789/1/du/a/379/1'}