-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2666336020494147357726028261279', 'a10': [0.8320301716942639, -2.508072530876792e-61], 'a2': [0.4030317167626848, 0.4030317167626848], 'a3': [0.0, 0.0], 'a4': [0.0, -1.6751308705666461], 'a5': [1.0322142614202545, -1.0322142614202545], 'a6': [0.0, 0.0], 'a7': [-0.45074729728889706, -2.607072471947559], 'a8': [1.4811943040920157, -1.4811943040920157], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.5397479255428665, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0.45074729728889706, 2.607072471947559]]], [13, [[1.0, 0], [-3.593338407458737, 0.2965115334719825]]]], 'bad_primes': [3, 7, 13], 'central_character': '819.307', 'coefficient_field': 'CDF', 'conductor': 819, 'conductor_radical': 273, 'conjugate': '1015640431076019705746386964517', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.4030317167626848, -0.4030317167626848], [0, 2.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.0322142614202545, 1.0322142614202545], [0, -5.0]], [[1.0, 0], [0.45074729728889706, 2.607072471947559]], [[1.0, 0], [-0.5969682832373152, 0.5969682832373152], [0, -11.0]], [[1.0, 0], [-3.593338407458737, 0.2965115334719825]], [[1.0, 0], [7.348037889619157, 0], [17.0, 0]], [[1.0, 0], [3.593338407458737, -3.593338407458737], [0, -19.0]], [[1.0, 0], [0, 4.443582912276047], [-23.0, 0]], [[1.0, 0], [-3.5441983076079224, 0], [29.0, 0]], [[1.0, 0], [-1.2712213661705534, 1.2712213661705534], [0, -31.0]], [[1.0, 0], [-2.8842260208547006, 2.8842260208547006], [0, -37.0]], [[1.0, 0], [-1.2323983511462453, 1.2323983511462453], [0, -41.0]], [[1.0, 0], [0, 8.662912090450616], [-43.0, 0]], [[1.0, 0], [-2.5223011310141747, -2.5223011310141747], [0, 47.0]], [[1.0, 0], [-9.793844653409339, 0], [53.0, 0]], [[1.0, 0], [1.0897186901419385, 1.0897186901419385], [0, 59.0]], [[1.0, 0], [0, -7.1090307848688585], [-61.0, 0]], [[1.0, 0], [-8.7684520417094, -8.7684520417094], [0, 67.0]], [[1.0, 0], [-1.4660357202785916, -1.4660357202785916], [0, 71.0]], [[1.0, 0], [-0.10385664597999904, -0.10385664597999904], [0, 73.0]], [[1.0, 0], [4.798769209336249, 0], [79.0, 0]], [[1.0, 0], [-12.316454309228448, 12.316454309228448], [0, -83.0]], [[1.0, 0], [6.8901652814454915, 6.8901652814454915], [0, 89.0]], [[1.0, 0], [-6.058135109751228, 6.058135109751228], [0, -97.0]], [[1.0, 0], [-12.870654361148103, 0], [101.0, 0]], [[1.0, 0], [-6.115639538472911, 0], [103.0, 0]], [[1.0, 0], [8.869067437041277, 0], [107.0, 0]], [[1.0, 0], [4.596968283237315, 4.596968283237315], [0, 109.0]], [[1.0, 0], [1.6072023111238296, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 42, 'label': '2-819-91.34-c1-0-42', '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/819/2/y/h/307/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.7709374155378936, 1.995791917344423, 2.2176440045048706, 2.433555087159947, 2.6355174960932293, 2.8111721720939746, 2.945236850987375, 3.021356857478446, 3.0241649254701626, 2.9413949024148565, 2.765901965751942, 2.4974145590925985, 2.1438104615103635, 1.7216959975486492, 1.2560886555266744, 0.7790659717895969, 0.32734662961909683, -0.06109458791841573, -0.3511227498043978, -0.5148434921450806, -0.5357788124107511, -0.4122177407795279, -0.15914688636378596, 0.19173797686728428, 0.5942474318804543, 0.9921753255513392, 1.325741814120467, 1.5393645525268314, 1.5898171669961636, 1.4536278989507632, 1.1325128469795351, 0.6557631029737859, 0.07882390364758794, -0.5222041767628843, -1.0598014675519378, -1.4470176895236981, -1.610653192878467, -1.5036786958039046, -1.1148189567769229, -0.4734407867008156, 0.35155379098980405, 1.2592731316987804, 2.130225359336901, 2.843894878015857, 3.297952100253931, 3.425992448013149, 3.210640640866016, 2.6893563950782715, 1.9513120231197538, 1.1251511479269216, 0.35905832985513697, -0.2039119693288903, -0.4511794191972619, -0.322121624900182, 0.17849167055191856, 0.978135533427724, 1.9464135469986341, 2.9161350366824217, 3.7123222862052683, 4.18413032049329, 4.233752932260986, 3.8365792403777714, 3.048209398523733, 1.996258814847037, 0.8577830034712615, -0.1739094508280454, -0.9269233322149765, -1.2855289408627417, -1.214792662611868, -0.7695765865262381, -0.08535334683644133, 0.6480475851644928, 1.224999060354243, 1.4673400885391399, 1.2633799442306284, 0.594175504513251, -0.4590248412255294, -1.7284656190261967, -2.9924909444106293, -4.0206415606978485, -4.621820662430712, -4.685090240136525, -4.203944552690828, -3.278311738789188, -2.093376505864661, -0.8795436238714908, 0.13772366718722012, 0.7869206809020333, 0.9871211049723689, 0.763613933009553, 0.2387544939723525, -0.3999451678448397, -0.946960447557062, -1.2297873931992258, -1.1513807939682674, -0.7134321817298332, -0.014529277824165273, 0.7765306770186396, 1.465666203168153, 1.8852414320419966, 1.9391444193598395, 1.6291690666011291, 1.0552654004776434, 0.3889498455745425, -0.1736753215666506, -0.46713449276497926, -0.4051855579168261, -0.009186327924007018, 0.5924760444057009, 1.1950732337152692, 1.5713381781473472, 1.534713522361087, 0.9951178959446231, -0.00849647944488932, -1.3089634989772179, -2.646655647320049, -3.732260231536938, -4.320905114743414, -4.278107183047278, -3.6193256980423896, -2.5112615563589773, -1.2329413092894672, -0.10549881058451577, 0.5915377100627445, 0.6952738207406396, 0.20516835428572996, -0.7138816673561633, -1.7731701369791528, -2.636384643002085, -3.0104198696173388, -2.726245824689461, -1.787383084573416, -0.37198046256691275, 1.2129039040362897, 2.6128819580178617, 3.5214352683812478, 3.7622427496476445, 3.335332021690813, 2.413667672262287, 1.2907643328553575, 0.29401322987850786, -0.311448381985191, -0.4003673409276132, -0.023520978798114493, 0.6087841828573298, 1.191670376185503, 1.4204681414067937, 1.0874498885383497, 0.15149814151733246, -1.2408426833866102, -2.7904159563376925, -4.127475760398107, -4.917314015996024, -4.958582894328749, -4.2449778238898075, -2.9713500910522375, -1.4815860439190498, -0.1729131202048261, 0.6155569535125394, 0.6973160670361914, 0.08816558701343363, -1.0032958939584775, -2.241010787569646, -3.262395821997866, -3.7839958215810574, -3.6798732945714434, -3.009564061905336, -1.9884406638068384, -0.9114996896774766, -0.056153783597252364, 0.40411154364009305, 0.44741746863628384, 0.19783708719902632, -0.13031710406924654, -0.3181089836503729, -0.22716187848209118, 0.14590960383760168, 0.6657536884152209, 1.1077114230478626, 1.244172603645606, 0.9379356938466739, 0.2088849625198723, -0.7519228257810646, -1.6295724420548539, -2.0818716920913016, -1.855265233196634, -0.8816841402391589, 0.6779003330271101, 2.4615071774288375, 4.001182988530975, 4.858061252799552, 4.756024137569648, 3.671213524294875, 1.8473333574058242, -0.2703199630187752, -2.163162227572501, -3.390542817431474, -3.716431632276639, -3.1714937394471425, -2.031131954974729, -0.7173963259070737, 0.3423674493410101, 0.8530332573802346, 0.7397339876527811, 0.15764007999277366, -0.5785839798468796, -1.1201055429438793, -1.2194654683328208, -0.827988028887563, -0.11971212315760707, 0.5679614144891069, 0.8573011837167546, 0.47426203017149604, -0.6377715710909312, -2.276508705950917, -4.029283047386628, -5.398238704166719, -5.961595943272867, -5.516667883117255, -4.1551081787142055, -2.242957026849632, -0.3100740890348914, 1.1154475627649472, 1.6730861822073517, 1.2805394734505768, 0.1523147762325253, -1.2793557010800982, -2.51358665081132, -3.148478175980731, -3.0100529314138313, -2.1993181491749505, -1.0433374140043767, 0.03007280854626836, 0.6479720215186686, 0.6224252987773656, 0.009580574694130536, -0.9213785134464872, -1.7954814534410806, -2.2740362434005985, -2.17820109809748, -1.548648568578552, -0.6205876671229553, 0.27439769471473974, 0.8406179003095372, 0.9329444468467337, 0.6093245975499647, 0.10089494044088823, -0.28831038367943546, -0.31220621390935605, 0.10843748198012443, 0.8438096609057343, 1.5988952771620788, 2.0289087932192844, 1.8828386032041207, 1.1186781921491034, -0.05736516913850951, -1.247698232100022], 'positive_zeros': ['2.10336824675040336954284859999501', '2.81013640333195791431162422316661', '4.01630274708668366078168004968950', '4.94919939676390653963026701598658', '6.32240791716874737926869958179554', '6.71416477710478074417508893998946', '8.101938362468790234199919273062210', '8.764308942401454821811156414352768', '9.449912118581306677634800094240690', '10.73052360858660239225222456702446'], 'prelabel': '2-819-91.34-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.5572930855775735, 'root_angle': 0.5128817659856102, 'root_number': '-0.04045821579307418 + 0.9991812311962435*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.256440882993', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.10336824675040336954284860000', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.81013640333195791431162422317', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.01630274708668366078168004969', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 6.5397479255428665, 'bad_primes': [3, 7, 13], 'central_character': '91.34', 'conductor': 819, 'conductor_radical': 273, 'degree': 2, 'index': 42, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/819/2/y/h/307/4'], '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': '2-819-91.34-c1-0-42', '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': '2-819-91.34-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.5572930855775735, 'root_angle': 0.2564408829928051, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.10336824675040336954284860000', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2666336020494147357726028261279', 'Lhash_array': ['2666336020494147357726028261279'], 'label': '2-819-91.34-c1-0-42', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/819/2/y/h/307/4'}