-
lfunc_lfunctions • Show schema
Hide schema
{'A10': 0, 'A2': 0, 'A3': 1, 'A4': -2, 'A5': -2, 'A6': 0, 'A7': -2, 'A8': 0, 'A9': 1, 'Lhash': '434983000008113389', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.010309278350515464, 0.0], 'a4': [-0.020618556701030927, 0.0], 'a5': [-0.020618556701030927, 0.0], 'a6': [0.0, 0.0], 'a7': [-0.020618556701030927, 0.0], 'a8': [0.0, 0.0], 'a9': [0.010309278350515464, 0.0], 'algebraic': True, 'analytic_conductor': 2.065852091759074, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.500000000000000', 'prec': 57}, 'bad_lfactors': [[2, [1, 0, 2]], [3, [1, -1]], [5, [1, 2, 5]]], 'bad_primes': [2, 3, 5], 'central_character': '32400.1', 'coefficient_field': '1.1.1.1', 'conductor': 32400, 'conductor_radical': 30, 'degree': 4, 'euler_factors': [[1, 0, 2], [1, -1], [1, 2, 5], [1, 2, 11, 14, 49], [1, -2, -2, -22, 121], [1, 4, 9, 52, 169], [1, -2, 10, -34, 289], [1, 0, 1, 0, 361], [1, 10, 58, 230, 529], [1, 0, 22, 0, 841], [1, 3, 22, 93, 961], [1, 5, 44, 185, 1369], [1, 6, 46, 246, 1681], [1, 3, 58, 129, 1849], [1, 0, -26, 0, 2209], [1, 2, -38, 106, 2809], [1, -8, 22, -472, 3481], [1, 6, -17, 366, 3721], [1, -8, 33, -536, 4489], [1, 2, 22, 142, 5041], [1, 25, 288, 1825, 5329], [1, -1, 30, -79, 6241], [1, 2, -110, 166, 6889], [1, -18, 202, -1602, 7921], [1, 0, 133, 0, 9409]], 'gamma_factors': [[], [0, 0]], 'index': 10, 'label': '4-180e2-1.1-c1e2-0-10', 'leading_term': '1.58708503178', 'load_key': 'G2Q', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 1, 'origin': 'Genus2Curve/Q/32400/b', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.1875', 'prec': 20}, 'plot_values': [0.0, 0.304854796945382, 0.6503453971345318, 1.061768709319229, 1.533311448823737, 2.013974384185684, 2.401239520881363, 2.55141240458441, 2.314274547048897, 1.591661932289108, 0.4051711306858335, -1.057321245987515, -2.453077360392699, -3.377073164289037, -3.521924423136105, -2.842766918348916, -1.632831925698898, -0.4327535522033276, 0.2241889953050334, 0.1166791245973573, -0.4991415101348973, -1.015241532364507, -0.8734419811261657, -0.01321321473684137, 0.9710008021924059, 1.167568188074389, 0.03987379625878268, -2.005404588988825, -3.686438594440068, -3.664735365945785, -1.614262798433821, 1.303022577808797, 3.088234638160192, 2.355900434389923, -0.505254687966606, -3.489934715834061, -4.479629119363998, -2.927381455687464, -0.2679563304307213, 1.372774127942514, 1.050228364611656, -0.2748773413556173, -0.8517242553390657, 0.0209722602426786, 1.319531337590063, 1.502663198026479, 0.3019476936758037, -0.9123638233311818, -0.677305943470374, 0.8222963036276426, 1.895387426596097, 1.328566615946182, -0.1201435844252169, -0.6891605277169744, -0.08672505388494804, -0.3747014923992053, -3.704164939582407, -9.196162327568297, -12.85267385686141, -11.27878436448515, -5.39086944960056, 0.2279449503616466, 1.916302573108546, 0.3906357995717142, -0.8070111586940161, 0.1979176544526909, 1.721376057386773, 1.336609601443378, -0.5693103048815248, -1.302508296300119, 0.3283354513556716, 2.21438949598261, 1.746264851189703, -0.6114592409264641, -1.974022803603037, -1.017527692624884, 0.3796231991199281, 0.1710552794842733, -0.6756732636454095, 0.2751480618845884, 2.831644431808246, 3.872171257447119, 1.795666667378756, -0.7346928862023636, -0.2806686994439966, 2.34641105076027, 3.089588956404381, 0.6450933042719658, -1.369813638976784, 0.2921869754461609, 3.372089430117315, 3.063782551574396, -0.9111602233487665, -3.645958095660688, -2.071235476093908, 0.6827497237866705, 0.09580855194301666, -3.051951272261378, -4.120722984558187, -1.634122009804629, 0.9595854392363473, 0.9210983332479538, -0.1170878563712057, 0.1839306605072152, 0.8215819491768671, -0.05052730727049762, -1.06317361662733, 0.06984667614319373, 1.605850837946418, -0.2227639398014599, -4.204654684443975, -4.175335590275782, 2.063914983269288, 8.376096063515146, 8.205720312950731, 3.284045196532902, 0.06011016691288902, 0.160625420836577, -0.07020040033015913, -1.817119395298113, -1.94037010297735, 0.4141253951897681, 1.488345722823492, -0.478786885971517, -1.771914608331702, 0.3184079392244593, 2.499047818524033, 1.329324922292885, -0.4149828802523788, 1.196020158080165, 3.524891625408745, 1.539872894280318, -2.67772471918004, -2.349417771774891, 2.763908700158472, 5.557969955438502, 2.907927526589137, -0.09551163062282221, 0.5335638378802185, 1.738541815620438, 0.3387511448649517, -1.112160568228659, 0.07080138106370223, 1.351972647248337, 0.1567924592361887, -1.089089136734047, -0.04364174142316394, 0.8833073318923726, -0.01421788906927751, 0.447258110108431, 3.398628481221286, 3.330787032253464, -2.560659698300351, -7.096885803068292, -3.70624912526933, 1.943470577082952, 0.8363319983612701, -4.380654097435605, -4.552797386572643, 0.1226975359646027, 1.610894609427871], 'positive_zeros': [1.928952515466692, 3.284698289069039, 3.606118808070785, 4.314819084336015, 4.879260932801101, 5.727698013001537, 6.346387810140871, 7.145995224913475, 7.647466603429066, 8.059610910159881, 8.662600313956734, 9.093364537555837, 9.7327239046654, 10.15480180288728, 10.24720393877257, 11.42697668343865, 11.85149024676409, 12.16587880701116, 12.69464671673192, 13.09786957236355, 13.64084652068701, 14.18212805883447, 14.46942727199144, 14.78652987287662, 15.49169353790968, 15.77327928596515, 16.35327420726574, 16.66992357113909, 17.21120702258858, 17.75148092812948, 18.00694061101302, 18.66202618480868, 19.0918742955978, 19.27050373689284, 19.68092019454556], 'prelabel': '4-180e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.198877490147783, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'USp(4)', 'trace_hash': 434983000008113389, 'z1': {'__RealLiteral__': 0, 'data': '1.92895251547', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.28469828907', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.60611880807', 'prec': 44}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 2.065852091759074, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 32400, 'conductor_radical': 30, 'degree': 4, 'dirichlet_coefficients': [1, 0, 1, -2, -2, 0, -2, 0, 1, 0, 2, -2, -4, 0, -2, 4, 2, 0, 0, 4, -2, 0, -10, 0, -1, 0, 1, 4, 0, 0, -3, 0, 2, 0, 4, -2, -5, 0, -4, 0, -6, 0, -3, -4, -2, 0, 0, 4, -7, 0, 2, 8, -2, 0, -4, 0, 0, 0, 8, 4, -6, 0, -2, -8, 8, 0, 8, -4, -10, 0, -2, 0, -25, 0, -1, 0, -4, 0, 1, -8, 1, 0, -2, 4, -4, 0, 0, 0, 18, 0, 8, 20, -3, 0, 0, 0, 0, 0, 2, 2], 'euler11': [1, -2, -2, -22, 121], 'euler13': [1, 4, 9, 52, 169], 'euler17': [1, -2, 10, -34, 289], 'euler19': [1, 0, 1, 0, 361], 'euler2': [1, 0, 2, 0, 0], 'euler23': [1, 10, 58, 230, 529], 'euler29': [1, 0, 22, 0, 841], 'euler3': [1, -1, 0, 0, 0], 'euler31': [1, 3, 22, 93, 961], 'euler37': [1, 5, 44, 185, 1369], 'euler41': [1, 6, 46, 246, 1681], 'euler43': [1, 3, 58, 129, 1849], 'euler47': [1, 0, -26, 0, 2209], 'euler5': [1, 2, 5, 0, 0], 'euler53': [1, 2, -38, 106, 2809], 'euler59': [1, -8, 22, -472, 3481], 'euler61': [1, 6, -17, 366, 3721], 'euler67': [1, -8, 33, -536, 4489], 'euler7': [1, 2, 11, 14, 49], 'euler71': [1, 2, 22, 142, 5041], 'euler73': [1, 25, 288, 1825, 5329], 'euler79': [1, -1, 30, -79, 6241], 'euler83': [1, 2, -110, 166, 6889], 'euler89': [1, -18, 202, -1602, 7921], 'euler97': [1, 0, 133, 0, 9409], 'euler_factors': [[1, 0, 2, 0, 0], [1, -1, 0, 0, 0], [1, 2, 5, 0, 0], [1, 2, 11, 14, 49], [1, -2, -2, -22, 121], [1, 4, 9, 52, 169], [1, -2, 10, -34, 289], [1, 0, 1, 0, 361], [1, 10, 58, 230, 529], [1, 0, 22, 0, 841], [1, 3, 22, 93, 961], [1, 5, 44, 185, 1369], [1, 6, 46, 246, 1681], [1, 3, 58, 129, 1849], [1, 0, -26, 0, 2209], [1, 2, -38, 106, 2809], [1, -8, 22, -472, 3481], [1, 6, -17, 366, 3721], [1, -8, 33, -536, 4489], [1, 2, 22, 142, 5041], [1, 25, 288, 1825, 5329], [1, -1, 30, -79, 6241], [1, 2, -110, 166, 6889], [1, -18, 202, -1602, 7921], [1, 0, 133, 0, 9409]], 'index': 10, 'instance_types': ['G2Q'], 'instance_urls': ['Genus2Curve/Q/32400/b'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': True, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-180e2-1.1-c1e2-0-10', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 1, 'prelabel': '4-180e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.198877490147783, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 434983000008113389, 'z1': {'__RealLiteral__': 0, 'data': '1.92895251547', 'prec': 44}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '434983000008113389', 'Lhash_array': ['434983000008113389'], 'label': '4-180e2-1.1-c1e2-0-10', 'type': 'G2Q', 'url': 'Genus2Curve/Q/32400/b'}