-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1866297844787721944561109390296', 'a10': [0.0, 0.0], 'a2': [-0.7071067811865476, -0.7071067811865476], 'a3': [0.9659258262890683, 0.25881904510252074], 'a4': [0.0, 1.0], 'a5': [0.0, 0.0], 'a6': [-0.5, -0.8660254037844386], 'a7': [0.0, 0.0], 'a8': [0.7071067811865476, -0.7071067811865476], 'a9': [0.8660254037844386, 0.5], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.29943900757980146, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.7071067811865476, 0.7071067811865476]]], [3, [[1.0, 0], [-0.9659258262890683, -0.25881904510252074]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 5], 'central_character': '600.443', 'coefficient_field': 'CDF', 'conductor': 600, 'conductor_radical': 30, 'conjugate': '2428065110253346191503660368048', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.7071067811865476, 0.7071067811865476]], [[1.0, 0], [-0.9659258262890683, -0.25881904510252074]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [0, 1.0]], [[1.0, 0], [0, -1.7320508075688772], [-1.0, 0]], [[1.0, 0], [0, 0], [0, -1.0]], [[1.0, 0], [0.7071067811865476, 0.7071067811865476], [0, 1.0]], [[1.0, 0], [0, 1.0], [-1.0, 0]], [[1.0, 0], [0, 0], [0, 1.0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [0, 1.0]], [[1.0, 0], [0, 1.7320508075688772], [-1.0, 0]], [[1.0, 0], [0, 0], [0, 1.0]], [[1.0, 0], [0, 0], [0, -1.0]], [[1.0, 0], [0, 0], [0, 1.0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [1.224744871391589, -1.224744871391589], [0, -1.0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [1.224744871391589, 1.224744871391589], [0, 1.0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0.7071067811865476, -0.7071067811865476], [0, -1.0]], [[1.0, 0], [1.7320508075688772, 0], [1.0, 0]], [[1.0, 0], [0, 0], [0, -1.0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [0, -1.0]], [[1.0, 0], [-0.7071067811865476, -0.7071067811865476], [0, 1.0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [-0.7071067811865476, 0.7071067811865476], [0, -1.0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 2, 'label': '2-600-120.83-c0-0-2', 'leading_term': '0.88582993587141204259618418820592', '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/600/1/q/b/443/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [0.885829935871412, 0.8865664195277663, 0.898099445881895, 0.9189670934170405, 0.9471362934548259, 0.9802403563678823, 1.015782837293342, 1.051276486901247, 1.084319998294039, 1.1126313262324066, 1.1340577804704897, 1.146578014957683, 1.1483050783688291, 1.1374950965264288, 1.1125632107495518, 1.07210670247985, 1.0149343297223814, 0.9401004410897722, 0.8469422062321874, 0.7351181900575039, 0.6046464440835434, 0.4559402664739781, 0.2898397854224171, 0.10763754997701769, -0.08890362657146489, -0.29754222650343704, -0.5155605030852779, -0.7397791913689898, -0.9665855290204127, -1.1919753629605752, -1.4116097661602796, -1.620886188522849, -1.8150237226248982, -1.9891615879424465, -2.1384694373530726, -2.2582675807848287, -2.3441547185448135, -2.3921402984513227, -2.3987781749665227, -2.3612978742717674, -2.2777294758164772, -2.1470179267311202, -1.9691225275310171, -1.7450973803315208, -1.4771487858012624, -1.1686659198591614, -0.824221618639386, -0.4495407482826031, -0.05143442678983458, 0.3623007153086072, 0.7830180201850206, 1.2013897067120825, 1.6076067021017446, 1.9916057299520513, 2.3433188272012604, 2.652939372816314, 2.9111977321447813, 3.109638796781884, 3.2408930727559953, 3.298932578395983, 3.279302690544042, 3.179321249735171, 2.9982367186395447, 2.737337990225493, 2.4000095580768854, 1.99172717418842, 1.5199907998732785, 0.994193561184301, 0.4254274976707296, -0.1737709220943417, -0.7897303263864291, -1.4080016437349472, -2.013753578494966, -2.5921951274160597, -3.129012378710383, -3.610805683143631, -4.02551257746293, -4.362801628563663, -4.614422690665299, -4.774499947132233, -4.8397555422632745, -4.80965357291248, -4.686456658876613, -4.47519017580844, -4.183512425117237, -3.8214924233135363, -3.4013004946021925, -2.936820310178076, -2.44319429450612, -1.9363172712997865, -1.432295713962295, -0.9468918727050689, -0.4949732670294573, -0.08998847488558394, 0.2565102357543892, 0.5352781227728676, 0.7397057951748995, 0.8660492679096967, 0.9135514238164717, 0.8844481951196871, 0.7838573361948392, 0.6195524639688409, 0.40162989379528685, 0.14208048698108902, -0.14571696114429747, -0.4475605320391654, -0.7490249709353705, -1.0360711968263303, -1.2956393102768604, -1.5161990441658062, -1.6882329498644006, -1.8046301175545298, -1.8609718212751802, -1.8556950296890085, -1.7901250547303467, -1.6683744999654706, -1.4971118604516538, -1.2852093327284488, -1.0432853212996767, -0.7831624817721102, -0.517266641617894, -0.25799533839493843, -0.01708680711914604, 0.19497911568782916, 0.36951760691737345, 0.5000848782876428, 0.582809425025849, 0.6165895926191929, 0.6031449412415459, 0.546916111357903, 0.4548156150876359, 0.3358398188918861, 0.2005599449859322, 0.060516800328244295, -0.07245023964377395, -0.1869050537151101, -0.272509744885602, -0.3206742776814413, -0.32512349881905733, -0.2823474862463127, -0.1919063430752756, -0.056567469692071375, 0.11773828897921672, 0.3221458017386366, 0.5452642761773852, 0.7737494089807457, 0.9930134741084801, 1.1880391123844616, 1.3442554432700533, 1.4484299340747706, 1.4895265986285802, 1.4594808120517913, 1.3538434478946582, 1.1722521546263571, 0.9186952294565415, 0.601543413234744, 0.23333658046553685, -0.16967482369894674, -0.5882202908842095, -1.00090506593051, -1.385272173062654, -1.7189806695532706, -1.9810415054915225, -2.153046541862919, -2.22032370500092, -2.1729522138109774, -2.00657640552776, -1.7229648096844266, -1.3302724839254676, -0.8429787445145979, -0.28148864261833856, 0.328595943940299, 0.9575118174363184, 1.5726354263971416, 2.1399923304876425, 2.6259048355467485, 2.998697378791296, 3.2303731031701717, 3.298173350722737, 3.1859347825001056, 2.885166502622675, 2.3957816727229204, 1.7264341421754845, 0.8944298455964041, -0.07479581359496924, -1.1486207681261564, -2.288562910596253, -3.4519329213995746, -4.59373694504999, -5.668737623566195, -6.633571400085266, -7.4488146588300435, -8.080891604135216, -8.503722930237718, -8.700026100808095, -8.66219492714694, -8.392707289688751, -7.904034208928215, -7.218049750615819, -6.364968017481155, -5.381859245743973, -4.310820322112634, -3.1968945071464865, -2.085849625071905, -1.0219325523152791, -0.04571992280952469, 0.8078196533869045, 1.5109477267307259, 2.044375530063557, 2.398016166385881, 2.5712308625621274, 2.572559208509378, 2.418952587167023, 2.1345583472913394, 1.749128003086191, 1.2961443167291065, 0.8107782130196887, 0.3277960807505583, -0.12045949913560258, -0.5058974032050789, -0.8062077406017302, -1.0060058753038603, -1.0975265540065673, -1.0808316862095373, -0.9635252912495096, -0.759999542899218, -0.4902648243028076, -0.17844244071204993, 0.1489805063805331, 0.46501994552885356, 0.744065776429354, 0.9636336012619713, 1.1058839284155118, 1.1588108265203108, 1.1170236631140544, 0.9820722315750902, 0.7622955658418465, 0.4722061439667603, 0.1314519543211659, -0.2365729749112623, -0.6063753694696858, -0.9521551079495277, -1.2496213234369542, -1.4777081845884117, -1.6200724950541787, -1.6662693674175528, -1.6125234387169751, -1.4620400529900228, -1.2248317935858646, -0.9170686639666455, -0.559992890598369, -0.1784695414506491, 0.20073016038197625, 0.5507965977573233, 0.8467727470476016, 1.0673375502962614, 1.1963567778714326], 'positive_zeros': ['1.47224940725126572218738898426327', '3.00787396981305638761693367607587', '4.29461748777089127943875183278022', '5.82769030661011163315792003107587', '6.46893148745807972454904486371936', '7.62970450650671747037675368682355', '8.340207736389128160026029759172467', '8.834226499925666687571611685444078', '9.786658380750722333654077956877889', '10.65427956932928628926149291077877'], 'prelabel': '2-600-120.83-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5472102041992651, 'root_angle': 0.04158863293260416, 'root_number': '0.99147683010412155443109500825090 + 0.13028313538859464578482793936498*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.02079431646630208', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.47224940725126572218738898426', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.00787396981305638761693367608', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.29461748777089127943875183278', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.29943900757980146, 'bad_primes': [2, 3, 5], 'central_character': '120.83', 'conductor': 600, 'conductor_radical': 30, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/600/1/q/b/443/2'], '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': '2-600-120.83-c0-0-2', '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': '2-600-120.83-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5472102041992651, 'root_angle': 0.02079431646630208, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.47224940725126572218738898426', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1866297844787721944561109390296', 'Lhash_array': ['1866297844787721944561109390296'], 'label': '2-600-120.83-c0-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/600/1/q/b/443/2'}