-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1221005416911856042902369297067', 'a10': [1.1242455941308076, 1.9328920932316598], 'a2': [0.8090169943749475, 0.5877852522924731], 'a3': [-0.9344883668447347, 2.876059462319829], 'a4': [0.30901699437494745, 0.9510565162951535], 'a5': [2.0456592581772806, 0.9029275715325], 'a6': [-2.4465223064908956, 1.7775025013794017], 'a7': [2.637919008493828, -0.20342886871567617], 'a8': [-0.30901699437494745, 0.9510565162951535], 'a9': [-4.97139853990644, -3.611932462905785], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.148480955638592, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.8090169943749475, -0.5877852522924731]]], [5, [[1.0, 0], [-2.0456592581772806, -0.9029275715325]]], [7, [[1.0, 0], [-2.637919008493828, 0.20342886871567617]]], [11, [[1.0, 0], [2.9641519561158924, -1.4878854730974187]]]], 'bad_primes': [2, 5, 7, 11], 'central_character': '770.139', 'coefficient_field': 'CDF', 'conductor': 770, 'conductor_radical': 770, 'conjugate': '2890279075636815242768213630965', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [0.9344883668447347, -2.876059462319829], [-2.4270509831248424, -1.7633557568774194]], [[1.0, 0], [-2.0456592581772806, -0.9029275715325]], [[1.0, 0], [-2.637919008493828, 0.20342886871567617]], [[1.0, 0], [2.9641519561158924, -1.4878854730974187]], [[1.0, 0], [0.32164184294504816, -0.44270201749659294], [-4.017220926874317, -12.363734711836996]], [[1.0, 0], [-3.5919599837063605, -4.943908780629366], [-5.253288904374106, 16.167960777017612]], [[1.0, 0], [-0.05670890069110224, 0.17453205006831168], [-15.371322893124, -11.16791979355699]], [[1.0, 0], [0, 8.001713511747427], [-23.0, 0]], [[1.0, 0], [4.80026285306819, -1.5596999480570206], [23.461492836873475, -17.04577231648172]], [[1.0, 0], [2.6397879745093755, -3.6333564419919235], [-9.57952682562337, -29.48275200514976]], [[1.0, 0], [-4.530791717742559, 1.4721434686234802], [29.933628791873055, -21.748054334821507]], [[1.0, 0], [-3.443193403853138, 10.597059654349225], [-33.16969676937284, -24.099195343991397]], [[1.0, 0], [2.2087607192842253, 0], [43.0, 0]], [[1.0, 0], [-0.017779443940385938, 0.05471950191545612], [-38.02379873562253, -27.625906857746237]], [[1.0, 0], [-7.8535007543389, 10.809416450678786], [-16.377900701872214, -50.405995363643136]], [[1.0, 0], [5.596279900251129, -1.818341565223916], [47.7320026681219, -34.67932988525592]], [[1.0, 0], [-3.981006865413423, 2.892370792004166], [18.850036656871794, -58.014447494004365]], [[1.0, 0], [0, -9.61579383103168], [-67.0, 0]], [[1.0, 0], [-0.2668373098632656, 0.1938686536742068], [21.940206600621266, -67.52501265695591]], [[1.0, 0], [6.984483260228231, -2.269396179257176], [59.05824058937116, -42.90832341735054]], [[1.0, 0], [2.2392640739726986, -3.0820825865766466], [-24.412342555620846, -75.13346478731714]], [[1.0, 0], [-3.1419175200020026, -4.324478470142383], [-25.648410533120636, 78.93769085249775]], [[1.0, 0], [0, 1.527424205688884], [-89.0, 0]], [[1.0, 0], [-8.967534827170288, -6.515295423308419], [29.974648454369902, 92.2524820806299]], [[1.0, 0], [-10.406162332859045, -7.560519488149574], [31.210716431869688, 96.05670814581052]], [[1.0, 0], [-2.5960418052560477, -7.989795125855262], [-83.32875042061958, 60.54188098612473]], [[1.0, 0], [-0.7840185424222096, 2.4129609608529727], [-86.56481839811937, -62.893021995294625]], [[1.0, 0], [0, 13.225569023166827], [-109.0, 0]], [[1.0, 0], [3.314073226771509, 1.0768076661362065], [91.41892036436906, 66.41973350904946]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 17, 'label': '2-770-385.139-c1-0-17', '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/770/2/w/b/139/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [2.0549600872017666, 1.7659018066581011, 1.489995977609124, 1.220357485733086, 0.9520934240098067, 0.683983101555671, 0.4193142331763031, 0.16588564578245046, -0.0647078341681042, -0.25837904700901904, -0.40032103949119385, -0.4771193143797974, -0.47903820531853447, -0.4022640741831347, -0.25083893080781433, -0.03798915078478531, 0.21344035400151734, 0.4716861078498796, 0.6980416550561274, 0.8501076601880649, 0.8861402188730837, 0.7701330013454474, 0.47709426926845455, -0.00215123696022362, -0.6573634750876864, -1.4571800617928534, -2.349840134408576, -3.2666203425524376, -4.1279183264588335, -4.851523946770076, -5.362228501930932, -5.601600701999248, -5.536568756844496, -5.165443039106733, -4.520223631946554, -3.6644603917239156, -2.6865318657775603, -1.6889090768441786, -0.7746672381932562, -0.033083985627026725, 0.47349851791935577, 0.7193582413998726, 0.7197945486730388, 0.5291301564522289, 0.23218441515416666, -0.06979623338688684, -0.2767070203482145, -0.30780851808422416, -0.11739406895165504, 0.2951258006889709, 0.8829859374220753, 1.5586785966683765, 2.208842524097899, 2.71523573814636, 2.9782392796948782, 2.9385327929446787, 2.592544855191757, 1.9980987777334815, 1.2682746882468414, 0.5536531358371466, 0.015421444822802588, -0.206135096068857, -0.02190658270924355, 0.5831336912496047, 1.5395912316742697, 2.699031002217144, 3.855355846661935, 4.779290778641783, 5.260231617132361, 5.147799880964482, 4.384932968329199, 3.0254465112259727, 1.2316294203861473, -0.7488607401311009, -2.623437970188131, -4.105341764039965, -4.965257132424715, -5.073743682295685, -4.425856346590891, -3.142634651907447, -1.4486789001913893, 0.37009276697454135, 2.0202376025202406, 3.255321532835464, 3.920089284781426, 3.975264748497461, 3.498071164592857, 2.6587984279513543, 1.6789732623608957, 0.7807179666333415, 0.13876405741858777, -0.1541590844128872, -0.10108440666488241, 0.20874741514255604, 0.6296160339441205, 1.0012370396773371, 1.1919976935836067, 1.1324742029343131, 0.8308180198417416, 0.366400741237167, -0.13611305103929627, -0.5448279644395075, -0.7600279493108398, -0.7436643500135198, -0.5302569219701531, -0.21563631617713705, 0.0737624219741215, 0.22256378205521532, 0.16693453331117733, -0.07862891118367789, -0.41752986260641783, -0.6935525496652667, -0.7353726308317803, -0.4120496135003623, 0.31577387418941394, 1.3644915932747572, 2.5273971581959946, 3.5095695033512864, 3.9922069624999996, 3.712225240935364, 2.5374786229736714, 0.5173838971948312, -2.106469534263918, -4.935875582336214, -7.492354498864635, -9.318049041911937, -10.077695258875027, -9.636680628616027, -8.095122144045172, -5.768241708831201, -3.1165751475183052, -0.6423202658237963, 1.2229980042156665, 2.211868664725161, 2.2721726951130683, 1.5644407352583274, 0.4069518670820514, -0.8157113787300125, -1.755574416646212, -2.187938344934054, -2.0590720570129966, -1.483444310538638, -0.6933965312251393, 0.04238766681736851, 0.5065902063030415, 0.6007572169198941, 0.37258522756908463, -0.0047096415089326205, -0.2940257128988076, -0.2775010222864782, 0.16515226234820557, 1.0082014081246264, 2.0775229577486916, 3.0964396081359338, 3.7668855406400943, 3.8616444218275476, 3.2992428010931754, 2.177596430024876, 0.7545301369800407, -0.620686993437631, -1.6054672506198924, -1.962732015606648, -1.630515675125771, -0.7406417551805188, 0.42013347032612997, 1.4956427434925015, 2.167138127697588, 2.249123614442414, 1.744791342531417, 0.8437206677878841, -0.13787527376300118, -0.856280182498034, -1.0483133997966863, -0.6147813001799525, 0.3467269780049762, 1.5700876437742497, 2.7012445654423693, 3.4060110410578375, 3.471326995817734, 2.8683255794003495, 1.7577592869569354, 0.4367735885057377, -0.7552287862801385, -1.5409099720749695, -1.7858449304907138, -1.5303458987409906, -0.9632346613263126, -0.34799568658543995, 0.0723726503637581, 0.15858203737933874, -0.08237786929236911, -0.5095831844270987, -0.9101128197357442, -1.0873392219111093, -0.9424092244925707, -0.517554198936587, 0.016869000465983483, 0.42929790070058865, 0.5249988199401174, 0.23907358728094968, -0.3125893537294844, -0.8488711910496102, -1.0075370651233053, -0.47503264794904604, 0.8797475671671974, 2.915153760643352, 5.207068580472801, 7.133016836742049, 8.033026731754521, 7.403280144297096, 5.064302525103985, 1.2492303658758854, -3.420712665737698, -8.073166553337769, -11.799022639623749, -13.884321914796857, -13.992771806617002, -12.245663175606428, -9.176322607461564, -5.573844359386777, -2.2638310391903893, 0.1082295693311121, 1.2281013249327877, 1.1579071194761292, 0.26899905362160753, -0.9085982937639266, -1.8670406383669775, -2.2726617473629225, -2.0435588098463215, -1.3350934357459383, -0.4477924812103241, 0.30261697039479873, 0.7033869304534456, 0.7096881675447083, 0.43744093150599905, 0.09336696474152602, -0.12514912281873486, -0.11795156441362059, 0.07782278311002513, 0.31055814557569034, 0.38886518262136094, 0.17585893633895705, -0.3375750377699264, -1.0129857244886447, -1.6090155799019128, -1.8749787167795857, -1.6567255620016912, -0.9710811773250997, -0.015432843702355545, 0.8966568680137857, 1.4536038486234406, 1.474478099849333, 0.9975868663801698, 0.29037077664777167, -0.2301729756996156, -0.14358381485061683, 0.8114787205808173], 'positive_zeros': ['0.963203438464845674842871508778126', '1.89480797126400022771564489385464', '2.87452851955529091297966975557387', '4.88161311987561313718130122074855', '5.59396547596942781675499032557124', '6.04272091396959416946282026988834', '7.50489731935364317477045044746691', '7.75667106361048640311384254628451', '9.077971678239625049290703390946700', '10.09925523669426204918215504509502'], 'prelabel': '2-770-385.139-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4796130657097675, 'root_angle': -0.9181364183179282, 'root_number': '-0.9671105862431091 - 0.25435627371171676*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.459068209159', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.963203438464845674842871508778', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.89480797126400022771564489385', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.87452851955529091297966975557', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 6.148480955638592, 'bad_primes': [2, 5, 7, 11], 'central_character': '385.139', 'conductor': 770, 'conductor_radical': 770, 'degree': 2, 'index': 17, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/770/2/w/b/139/2'], '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': '2-770-385.139-c1-0-17', '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': '2-770-385.139-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4796130657097675, 'root_angle': -0.4590682091589641, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.963203438464845674842871508778', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1221005416911856042902369297067', 'Lhash_array': ['1221005416911856042902369297067'], 'label': '2-770-385.139-c1-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/770/2/w/b/139/2'}