-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1367017010337585284539280840266', 'a10': [0.0, 0.0], 'a2': [1.1791472355911317, 0.7807764064044151], 'a3': [-1.5102239590221098, -0.8480705121601534], 'a4': [0.7807764064044151, 1.841300682453088], 'a5': [0.0, 0.0], 'a6': [-1.1186229595424588, -2.1791472355911314], 'a7': [0.0, 3.0204479180442196], 'a8': [-0.5169937887291752, 2.780776406404415], 'a9': [1.5615528128088303, 2.5615528128088303], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.3955120606384126, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.1791472355911317, -0.7807764064044151]]], [3, [[1.0, 0], [1.5102239590221098, 0.8480705121601534]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 5], 'central_character': '300.251', 'coefficient_field': 'CDF', 'conductor': 300, 'conductor_radical': 30, 'conjugate': '2758361101230489955959755035114', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.1791472355911317, -0.7807764064044151]], [[1.0, 0], [1.5102239590221098, 0.8480705121601534]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -3.0204479180442196], [-7.0, 0]], [[1.0, 0], [1.3243068937239129, 0], [11.0, 0]], [[1.0, 0], [-5.123105625617661, 0], [13.0, 0]], [[1.0, 0], [0, -2.0], [-17.0, 0]], [[1.0, 0], [0, -1.3243068937239129], [-19.0, 0]], [[1.0, 0], [-0.371834130596394, 0], [23.0, 0]], [[1.0, 0], [0, 3.1231056256176606], [-29.0, 0]], [[1.0, 0], [0, 4.716588942364527], [-31.0, 0]], [[1.0, 0], [5.123105625617661, 0], [37.0, 0]], [[1.0, 0], [0, -1.1231056256176606], [-41.0, 0]], [[1.0, 0], [0, 7.737036860408746], [-43.0, 0]], [[1.0, 0], [-3.0204479180442196, 0], [47.0, 0]], [[1.0, 0], [0, 12.246211251235321], [-53.0, 0]], [[1.0, 0], [-14.149766827093579, 0], [59.0, 0]], [[1.0, 0], [-3.1231056256176606, 0], [61.0, 0]], [[1.0, 0], [0, -4.344754811768133], [-67.0, 0]], [[1.0, 0], [3.3922820486406136, 0], [71.0, 0]], [[1.0, 0], [8.246211251235321, 0], [73.0, 0]], [[1.0, 0], [0, -8.10887099100514], [-79.0, 0]], [[1.0, 0], [-15.102239590221098, 0], [83.0, 0]], [[1.0, 0], [0, 10.246211251235321], [-89.0, 0]], [[1.0, 0], [-6.0, 0], [97.0, 0]], [[1.0, 0], [0, -0.8768943743823394], [-101.0, 0]], [[1.0, 0], [0, -9.805012015325447], [-103.0, 0]], [[1.0, 0], [3.0204479180442196, 0], [107.0, 0]], [[1.0, 0], [0.8768943743823394, 0], [109.0, 0]], [[1.0, 0], [0, -14.0], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 7, 'label': '2-300-12.11-c1-0-7', '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/300/2/e/c/251/8', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.5489888317501541, 1.4276182633663879, 1.3071567110574458, 1.180050321488066, 1.037969680363967, 0.8729379079174936, 0.6782886048847874, 0.4494163021076788, 0.18434594639730195, -0.11584664366861151, -0.44675665185714153, -0.8005361939498451, -1.1659837210952866, -1.5288797177461353, -1.872601674859513, -2.1790305942873673, -2.4297323190652844, -2.6073627305747973, -2.697209769954008, -2.6887514050962165, -2.577081640400485, -2.364041155872725, -2.0588894760898935, -1.6783749859616022, -1.246099203070107, -0.7911317549551852, -0.3459090377776345, 0.05646376731189266, 0.3852997147803604, 0.6155202969300345, 0.7306061920375221, 0.7249418447729657, 0.6052047983191766, 0.39051513263037074, 0.11117129674113022, -0.19405063808110437, -0.48188008161829665, -0.7094788611076995, -0.8398057645791491, -0.8467868070240362, -0.719599567700299, -0.46540459043398863, -0.10997548743854549, 0.3041102017980041, 0.7217708961555248, 1.081929723083836, 1.3256102968230739, 1.4046985595639627, 1.290239922272537, 0.9790629942485117, 0.49760434927204056, -0.0979373407039325, -0.7255792010845242, -1.2855983529311945, -1.6719949681839257, -1.7861689983952616, -1.551156679624946, -0.9245124822465163, 0.09208951651275067, 1.4481939075516135, 3.0459644595495656, 4.748014859363726, 6.3911556415686865, 7.804653908919273, 8.830839649920257, 9.345384062037287, 9.274422000186734, 8.605947073208595, 7.393568976309804, 5.751718671472584, 3.8425888021273074, 1.8563311833953942, -0.01289201687617234, -1.5916731444424685, -2.749356517717608, -3.413982616636792, -3.5797254252968953, -3.304629827469941, -2.6989590953053333, -1.9059699794734983, -1.078191192616602, -0.3530648277074424, 0.1680360510158862, 0.4339301853038514, 0.4485562170317832, 0.2659592165720104, -0.02365068833923691, -0.3141331757771809, -0.5061326406207134, -0.527957042864742, -0.3505976534640627, 0.006069777817176048, 0.47720120085565854, 0.9663552680630899, 1.3657640364770873, 1.5794982826264214, 1.544820318063872, 1.2472352831551834, 0.7258871519562913, 0.06781049062770299, -0.6082017218661134, -1.1751618334104752, -1.5242491993057892, -1.5885388808675598, -1.3589638352257085, -0.8887641338701961, -0.284920732677048, 0.312253271844581, 0.7576246162487845, 0.9322069331021351, 0.7701240986115848, 0.2756313234462578, -0.4739309210772479, -1.3405843410400216, -2.1516721632411646, -2.7344529688424615, -2.9523556910121274, -2.73521972973383, -2.0967623808460405, -1.1349434070170694, -0.014386809758955545, 1.0661313423461163, 1.91473470837374, 2.3874874217893725, 2.4204833748453787, 2.0455976906804474, 1.385768975375902, 0.6300039098845646, -0.007216964122023628, -0.33378967821719435, -0.22476648901136548, 0.34604269006933164, 1.2952729608943532, 2.443339919589412, 3.5500002184349526, 4.365184318264631, 4.684436248936016, 4.39681025676288, 3.514248794736693, 2.175149925640978, 0.6202989132506078, -0.8545732409778434, -1.9599835364952243, -2.4746333414485155, -2.2944960424565215, -1.45791799022508, -0.14062468245126192, 1.3789341002185447, 2.7768591647245047, 3.751488294233454, 4.08677439176477, 3.6974149032793964, 2.645748655127178, 1.1267148239299516, -0.5756464871744558, -2.1502374124886408, -3.325397607195509, -3.9248403114323653, -3.900595420558041, -3.3360094041738746, -2.4189468612478295, -1.3923487956438791, -0.49453833489913235, 0.09614406554963333, 0.2991773518096755, 0.14357815644409092, -0.24841117389988093, -0.7005065593874898, -1.0336040323231612, -1.1153634334615363, -0.8951915893807939, -0.4157400941107052, 0.20159290010945488, 0.792672576508265, 1.1979033769325294, 1.3075426327946686, 1.092439679988927, 0.6116654211597188, -0.005042063833029543, -0.5949928248864639, -1.0096206100975913, -1.1572974994956964, -1.0292624274436228, -0.7006721871647826, -0.3058535907714976, 0.005584374970240265, 0.11917105328054449, -0.0026286978491346824, -0.30066056988465684, -0.6290543117623714, -0.7943023010089526, -0.6141707355805696, 0.019380438808013694, 1.0915603984259323, 2.446117943418472, 3.8052466749951623, 4.82643978171068, 5.184307161292808, 4.657529523329694, 3.198159562775311, 0.9634907399565004, -1.700770072371522, -4.325259106131356, -6.416369980706998, -7.567390076035788, -7.554298788212662, -6.391911257298097, -4.33520712181015, -1.8240672389574595, 0.6161327490326935, 2.494266532223182, 3.464294900955684, 3.399978250032669, 2.415322135010237, 0.8264421531557913, -0.9344933099023384, -2.4304244129205084, -3.326738724996589, -3.467431756854055, -2.9015387760046027, -1.8549143075994534, -0.65715156236093, 0.35478736359930624, 0.929021456725086, 0.9620575876509907, 0.5166850293858977, -0.20850055373534046, -0.9470628335473285, -1.448885731565358, -1.5551915517034811, -1.2424924336414591, -0.6233366917971969, 0.09507566771434547, 0.6806353568481274, 0.9522458987340217, 0.8381320242382632, 0.3983823474263248, -0.1952424975882354, -0.7158751207672683, -0.9567076067969214, -0.801005571893798, -0.26455332498349443, 0.5035656865942956, 1.2631231917898609, 1.7556734064876165, 1.7861984259656734, 1.2881838270927333, 0.3513841043989982, -0.7973968479920428, -1.8559013858246998, -2.5326368495601965, -2.6320471190189787, -2.1128229214039758, -1.1013508951825517, 0.1442093550242422, 1.3086566778515871, 2.1107253665376433], 'positive_zeros': ['1.07838627622742878055959292716232', '3.35621918157467965496976573047163', '4.29584253173765608915211451173546', '5.28431288016760838679428698689799', '6.35538263924068519824575907287306', '7.24028958102532479004651994047374', '8.999079707261716256282494779965926', '10.20287699958123065425384378148028', '10.74039560232277892652826018184744', '11.37322350519567213477611741103369'], 'prelabel': '2-300-12.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.5477441844951034, 'root_angle': -0.46478969766159123, 'root_number': '0.1103909814731262 - 0.9938882387921691*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.232394848831', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.07838627622742878055959292716', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.35621918157467965496976573047', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.29584253173765608915211451174', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 2.3955120606384126, 'bad_primes': [2, 3, 5], 'central_character': '12.11', 'conductor': 300, 'conductor_radical': 30, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/300/2/e/c/251/8'], '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': '2-300-12.11-c1-0-7', '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': '2-300-12.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.5477441844951034, 'root_angle': -0.23239484883079561, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.07838627622742878055959292716', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1367017010337585284539280840266', 'Lhash_array': ['1367017010337585284539280840266'], 'label': '2-300-12.11-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/300/2/e/c/251/8'}