Table lfunc_lfunctions
L-functions
{'Lhash': '2787507282518924007146742806222', 'a10': [-28.043915526641623, 0.0], 'a2': [5.608783105328325, 0.0], 'a3': [-1.895195850627857, 0.0], 'a4': [23.458447922616443, 0.0], 'a5': [-5.0, 0.0], 'a6': [-10.629742468289868, 0.0], 'a7': [11.442558079426966, 0.0], 'a8': [86.70308154296885, 0.0], 'a9': [-23.408232687762954, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.785219650660173, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 7}, 'bad_lfactors': [[5, [[1.0, 0], [5.0, 0]]], [23, [[1.0, 0], [23.0, 0]]]], 'bad_primes': [5, 23], 'central_character': '115.1', 'coefficient_field': 'CDF', 'conductor': 115, 'conductor_radical': 115, 'conjugate': '2787507282518924007146742806222', 'degree': 2, 'euler_factors': [[[1.0, 0], [-5.608783105328325, 0], [8.0, 0]], [[1.0, 0], [1.895195850627857, 0], [27.0, 0]], [[1.0, 0], [5.0, 0]], [[1.0, 0], [-11.442558079426966, 0], [343.0, 0]], [[1.0, 0], [-37.72446692588809, 0], [1331.0, 0]], [[1.0, 0], [8.69345594632207, 0], [2197.0, 0]], [[1.0, 0], [105.68664808717834, 0], [4913.0, 0]], [[1.0, 0], [128.27929960433744, 0], [6859.0, 0]], [[1.0, 0], [23.0, 0]], [[1.0, 0], [133.3833682628651, 0], [24389.0, 0]], [[1.0, 0], [-106.00779244783575, 0], [29791.0, 0]], [[1.0, 0], [248.83504173801865, 0], [50653.0, 0]], [[1.0, 0], [-134.2326269693546, 0], [68921.0, 0]], [[1.0, 0], [-108.68370720100475, 0], [79507.0, 0]], [[1.0, 0], [76.20001074363506, 0], [103823.0, 0]], [[1.0, 0], [-476.2070642591012, 0], [148877.0, 0]], [[1.0, 0], [-607.9997267456858, 0], [205379.0, 0]], [[1.0, 0], [366.2726505176139, 0], [226981.0, 0]], [[1.0, 0], [-136.0407813652837, 0], [300763.0, 0]], [[1.0, 0], [152.87425858969107, 0], [357911.0, 0]], [[1.0, 0], [-1228.1593703535502, 0], [389017.0, 0]], [[1.0, 0], [364.63709221330737, 0], [493039.0, 0]], [[1.0, 0], [762.7444805118602, 0], [571787.0, 0]], [[1.0, 0], [-271.2222079115198, 0], [704969.0, 0]], [[1.0, 0], [-574.509582200327, 0], [912673.0, 0]], [[1.0, 0], [-1372.2450014554972, 0], [1030301.0, 0]], [[1.0, 0], [242.42789006131932, 0], [1092727.0, 0]], [[1.0, 0], [-650.8955856667773, 0], [1225043.0, 0]], [[1.0, 0], [1230.4285482299374, 0], [1295029.0, 0]], [[1.0, 0], [-238.95886019886422, 0], [1442897.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 10530656, 'index': 11, 'label': '2-115-1.1-c3-0-11', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/115/4/a/e/1/5', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 10}, 'plot_values': [4.387217660591302, 4.374721533171737, 4.336862195345858, 4.272569149028689, 4.180196452098089, 4.057719893716397, 3.902993924813795, 3.7140516154581413, 3.489428696279143, 3.2284914177506336, 2.931747194818371, 2.6011165985096714, 2.240145234708195, 1.8541346460899941, 1.4501729518812483, 1.0370488977953196, 0.625037653153725, 0.22555324271202185, -0.14932909118419108, -0.4874673061017548, -0.7773394142500878, -1.0087870979065425, -1.17376978411811, -1.2670741068756, -1.2869179815515834, -1.2353870476079043, -1.1186449929986564, -0.9468689319019707, -0.7338767863497293, -0.4964351688955863, -0.25326256991646073, -0.023772029545066256, 0.1733724099932926, 0.32178317109315796, 0.4088354991220009, 0.42697343972330776, 0.37469329911177673, 0.2570731940557362, 0.08574282415111448, -0.12177228410967232, -0.3433448949075775, -0.5541291375296112, -0.7289166536091866, -0.8447856066330861, -0.8838073861432464, -0.8355376168550006, -0.6990032993569532, -0.4839117324859639, -0.21085208678546302, 0.0896631837276603, 0.3793663320258611, 0.6155376312942263, 0.7552377319148734, 0.7601351836224469, 0.6014871537682057, 0.2647575932659872, -0.2466694308054184, -0.9091935317717934, -1.678540735451814, -2.4914184706934157, -3.2693592629507156, -3.9246007954434967, -4.367611637684771, -4.515650196591687, -4.301566736609382, -3.6819500889554257, -2.6437020603983536, -1.2082052803460586, 0.5675648253730415, 2.5933573801603544, 4.751422844456125, 6.905402608618641, 8.911616019653573, 10.631713236159666, 11.945440755120607, 12.76217390924714, 13.029928425864881, 12.740775658368552, 11.931938686221798, 10.682305618700797, 9.104612508015268, 7.33406069201465, 5.5145776876668675, 3.7842468628838786, 2.2615716868309117, 1.0341781241696362, 0.15129164655024982, -0.37912137565601584, -0.588233529824194, -0.5395758695995679, -0.3185226137207397, -0.019464262050971747, 0.2675921312511711, 0.46917401518681157, 0.5375939633476914, 0.4560546674760552, 0.2389556335999135, -0.07255313585230765, -0.41902156557777576, -0.7338008376448606, -0.9550320285071274, -1.0366109563297115, -0.9563649519003814, -0.7201052309805526, -0.3608696210194012, 0.06655157426938267, 0.4949297502729474, 0.8562129267844623, 1.0934750585816042, 1.1711223172038498, 1.081516139066718, 0.8467339732560285, 0.5149935773331956, 0.15218958077038136, -0.17012109598398278, -0.38825124336606986, -0.45902467918417955, -0.3691512302432347, -0.13941753834107143, 0.17739559462232082, 0.504882426390213, 0.7565321527423686, 0.8522411229701314, 0.7349540113835601, 0.38433079638034917, -0.1753620669771767, -0.8751095187390434, -1.6094816912605758, -2.2526969793978506, -2.6802119139965113, -2.7924568053350693, -2.536664115217886, -1.9227273983705866, -1.0297329697727582, -0.0011526048726125996, 0.9715159793137682, 1.6749054264672605, 1.9061683931504132, 1.5067144316397858, 0.3918312190958543, -1.4289570080299356, -3.8447329853432266, -6.651226739211438, -9.573659686045005, -12.301554113496358, -14.530582494544909, -16.00517596256106, -16.555251775938427, -16.121157257462084, -14.76267668091778, -12.65044195466015, -10.040921724174247, -7.238857748022465, -4.55310331363971, -2.2529219192392573, -0.5317163273503294, 0.5161231221242847, 0.901824418970821, 0.7317189782959344, 0.18196717022381997, -0.5366194336800522, -1.2171996696014216, -1.6920875416877552, -1.858452431911874, -1.6904124665462756, -1.236048201101368, -0.6007305996514155, 0.07930728176081414, 0.6675060064873605, 1.055395335411443, 1.1833241917131916, 1.0496952751616853, 0.7073777775356821, 0.24866907753765358, -0.21746876960065506, -0.590645630460411, -0.8011172671757366, -0.8238945898890547, -0.681953307682665, -0.4381037596803346, -0.17765772965086132, 0.013880380609480353, 0.0727359865592001, -0.026874984604155876, -0.2661161866527336, -0.5862501632646939, -0.9037256796907152, -1.1321145572098028, -1.2055983160835773, -1.098121785800477, -0.8331297581773524, -0.48085750237510355, -0.1430350460576865, 0.07204597803271952, 0.07857884696071753, -0.16055033171976724, -0.6172202671378257, -1.1962745134210728, -1.7504614872800985, -2.110322538842713, -2.1235564457302623, -1.6956673056023523, -0.8226270188626776, 0.39278452041938633, 1.7464225863235932, 2.9611465982373524, 3.734349105149296, 3.79641787800086, 2.9688927021078384, 1.2102621194042318, -1.360964527131939, -4.472291957895305, -7.733207966081762, -10.695880318862155, -12.930112108420674, -14.098733776164446, -14.018950160667275, -12.69743350823801, -10.331785051312643, -7.277450860708653, -3.98597206984145, -0.9261712401257776, 1.4966831037297128, 3.008281496222051, 3.506533175481171, 3.0692999756458437, 1.9280462763097712, 0.4137212037848257, -1.1133364474288643, -2.334758169767149, -3.0322864008894745, -3.121499926176424, -2.655516978048574, -1.7996992687916253, -0.7845750726052535, 0.151402441260156, 0.8159827736511464, 1.1022304285753757, 1.0047450412670154, 0.610786830627717, 0.07006836105678428, -0.4481785867659125, -0.799636198206237, -0.8997899372941587, -0.7410918374478417, -0.38899466166692204, 0.04107037497798877, 0.4189026577001059, 0.6371308026592233, 0.6410562601672155, 0.4428842153907469, 0.11678986978647357, -0.2235374707235428, -0.4585058779180474, -0.4980074530829451, -0.3086976391910966, 0.07455567399088801], 'positive_zeros': ['2.19895551819804108901185471354270', '3.88885640964164232945636930315256', '4.80359286017242429493817590715888', '6.08800160953761094023893853907586', '6.94472487130905508025393066757118', '8.462236193289258324322650966332523', '10.77847380511645222129874223625759', '11.38293641615412936303278623971113', '12.09797136599461961746010360502937', '13.10606026286804760985171368022583'], 'prelabel': '2-115-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.6048454178050897, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.19895551819804108901185471354', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '3.88885640964164232945636930315', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '4.80359286017242429493817590716', 'prec': 100}}