data: - - Lhash: '2131828983585735045518801708143' a10: 0 a2: 0 a3: -1 a4: 0 a5: 0 a6: 0 a7: -1 a8: 0 a9: -2 accuracy: 100 algebraic: true analytic_conductor: 9.7098088857877 analytic_normalization: __RealLiteral__: 0 data: '0.5' prec: 10 bad_lfactors: - - 2 - - 1 - - 19 - - 1 - 1 bad_primes: - 2 - 19 central_character: '1216.1' coefficient_field: 1.1.1.1 conductor: 1216 conductor_radical: 38 degree: 2 euler_factors: - - 1 - - 1 - 1 - 3 - - 1 - 0 - 5 - - 1 - 1 - 7 - - 1 - -6 - 11 - - 1 - 5 - 13 - - 1 - -3 - 17 - - 1 - 1 - - 1 - -3 - 23 - - 1 - 9 - 29 - - 1 - 4 - 31 - - 1 - 2 - 37 - - 1 - 0 - 41 - - 1 - 8 - 43 - - 1 - 0 - 47 - - 1 - -3 - 53 - - 1 - 9 - 59 - - 1 - -10 - 61 - - 1 - 5 - 67 - - 1 - 6 - 71 - - 1 - 7 - 73 - - 1 - 10 - 79 - - 1 - -6 - 83 - - 1 - 12 - 89 - - 1 - 10 - 97 - - 1 - 18 - 101 - - 1 - -14 - 103 - - 1 - -9 - 107 - - 1 - 11 - 109 - - 1 - -6 - 113 euler_factors_factorization: - - 1 - - - - 1 - 1 - 3 - 1 - - - - 1 - 0 - 5 - 1 - - - - 1 - 1 - 7 - 1 - - - - 1 - -6 - 11 - 1 - - - - 1 - 5 - 13 - 1 - - - - 1 - -3 - 17 - 1 - - - - 1 - 1 - 1 - - - - 1 - -3 - 23 - 1 - - - - 1 - 9 - 29 - 1 - - - - 1 - 4 - 31 - 1 - - - - 1 - 2 - 37 - 1 - - - - 1 - 0 - 41 - 1 - - - - 1 - 8 - 43 - 1 - - - - 1 - 0 - 47 - 1 - - - - 1 - -3 - 53 - 1 - - - - 1 - 9 - 59 - 1 - - - - 1 - -10 - 61 - 1 - - - - 1 - 5 - 67 - 1 - - - - 1 - 6 - 71 - 1 - - - - 1 - 7 - 73 - 1 - - - - 1 - 10 - 79 - 1 - - - - 1 - -6 - 83 - 1 - - - - 1 - 12 - 89 - 1 - - - - 1 - 10 - 97 - 1 - - - - 1 - 18 - 101 - 1 - - - - 1 - -14 - 103 - 1 - - - - 1 - -9 - 107 - 1 - - - - 1 - 11 - 109 - 1 - - - - 1 - -6 - 113 - 1 gamma_factors: - [] - - 0 group: GL2 id: 20373777 index: 24 label: 2-1216-1.1-c1-0-24 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: 1 origin: ModularForm/GL2/Q/holomorphic/1216/2/a/e plot_delta: __RealLiteral__: 0 data: '0.05859375' prec: 34 plot_values: - -1.367361755389411e-60 - 0.13078614286547313 - 0.2615929376869216 - 0.3923790922270763 - 0.5229832392386073 - 0.6530730296143359 - 0.782104144672942 - 0.9092910436339435 - 1.0335903793300962 - 1.153697255078288 - 1.2680539275428782 - 1.3748701944640436 - 1.4721545086795724 - 1.557754775491261 - 1.629407761363704 - 1.6847960208831871 - 1.7216112044781338 - 1.7376225262887997 - 1.7307490476519107 - 1.699134274199834 - 1.6412213866337695 - 1.5558272428660542 - 1.4422131194660055 - 1.3001500198728746 - 1.129976281158798 - 0.9326451739958111 - 0.7097602235293338 - 0.46359609124801077 - 0.19710305606667194 - -0.08610657993788087 - -0.3817914593251075 - -0.6851343467509954 - -0.9908158116116628 - -1.2931081031111538 - -1.5859882436035702 - -1.8632686696336693 - -2.1187430399022857 - -2.3463441293894727 - -2.5403100651368047 - -2.695354559080632 - -2.806836284587586 - -2.87092215307942 - -2.8847390007016633 - -2.8465081148340343 - -2.755657134730514 - -2.6129041628894565 - -2.4203094308454873 - -2.181290574803855 - -1.9005984849863486 - -1.5842517816013744 - -1.2394292155194995 - -0.874320660403595 - -0.4979388149676202 - -0.1198952222665893 - 0.24985431494699414 - 0.6012884439649733 - 0.9246153488204488 - 1.2105753848920981 - 1.4507415951743747 - 1.6378078987326175 - 1.7658545352915322 - 1.8305805128215706 - 1.8294933581533377 - 1.7620474209369004 - 1.6297233202436205 - 1.4360428261783844 - 1.186515494981512 - 0.8885156681710741 - 0.5510909323219673 - 0.18470573106404717 - -0.19907357070903117 - -0.5879433513765661 - -0.969265983393951 - -1.3304985055715899 - -1.659631931084335 - -1.9456252761874389 - -2.1788178328613887 - -2.3513032714951154 - -2.4572498818697417 - -2.493152651214613 - -2.4580049183955586 - -2.353379986049728 - -2.1834162417914476 - -1.954702932390272 - -1.6760676235317724 - -1.3582704144525435 - -1.0136139982177885 - -0.6554824925442002 - -0.2978254388400679 - 0.04539368973282437 - 0.3607628715166818 - 0.6359777699404592 - 0.8603652571610375 - 1.0253511396856083 - 1.124850490568082 - 1.1555614908558756 - 1.1171471254175498 - 1.0122933582163374 - 0.8466373790468614 - 0.6285649781382094 - 0.36888184469570545 - 0.08036935416989728 - -0.2227590533976612 - -0.5254797579873528 - -0.8126336647560065 - -1.06962496925471 - -1.283113079730597 - -1.4416659785699064 - -1.5363439147133617 - -1.5611843883215273 - -1.513562885866325 - -1.3944086468884482 - -1.2082607238780303 - -0.9631565020860695 - -0.6703523895692048 - -0.34388423862199746 - 1.7142724650179756e-05 - 0.34363266073575144 - 0.6685544878469113 - 0.9565437723147306 - 1.1904078122255952 - 1.354855736814059 - 1.4372913583184301 - 1.4285034552783813 - 1.32321732351221 - 1.120476886749003 - 0.823833800723443 - 0.4413285264781259 - -0.014742076724290558 - -0.5282659149651274 - -1.0799505647771712 - -1.64812700285417 - -2.2096882374818345 - -2.7411212907630813 - -3.2195851614972897 - -3.6239837440893425 - -3.9359814486065217 - -4.140910606883913 - -4.228523679411035 - -4.19354968573979 - -4.036022924141052 - -3.7613625571635994 - -3.3801935420333895 - -2.9079121130292513 - -2.3640119490066165 - -1.7711996230287577 - -1.1543392740786884 - -0.539276040928906 - 0.04840489602839659 - 0.5846222568011907 - 1.047982679298541 - 1.4208436331025283 - 1.6901990099059323 - 1.8483391903012096 - 1.8932481262176852 - 1.8287129428220696 - 1.664136123193717 - 1.4140557587963 - 1.0973948255986832 - 0.7364751498045377 - 0.35584484647060877 - -0.0190212003249481 - -0.36308043868121315 - -0.6530696209598025 - -0.8687673989240897 - -0.9941036734780843 - -1.0180540341524675 - -0.9352683442926971 - -0.7463962551090269 - -0.4580884733328279 - -0.0826701235401358 - 0.3624994069728803 - 0.8559481739546148 - 1.3732468522628323 - 1.888335593522419 - 2.374950300243847 - 2.8080694700550093 - 3.1653005347997882 - 3.4281269615685823 - 3.5829442577139345 - 3.6218241287627517 - 3.5429608240903203 - 3.350771390863185 - 3.0556411754246966 - 2.6733263606199453 - 2.22404543053326 - 1.731310026385518 - 1.2205615768915286 - 0.7176923615564312 - 0.24753749715720963 - -0.16757282784332322 - -0.5091139782147561 - -0.7634411231389712 - -0.9225704152656578 - -0.9846171556239323 - -0.9538610579644378 - -0.8404309381185642 - -0.6596242227279331 - -0.43089921551638655 - -0.1765986963215644 - 0.07951913936778965 - 0.3138532968507025 - 0.5045391853037605 - 0.6329353956394536 - 0.684923071196103 - 0.651932872882947 - 0.531629988535281 - 0.328207710584702 - 0.05226366215175529 - -0.2797415981552653 - -0.6464176683356717 - -1.022718050038769 - -1.381481059030754 - -1.6951460880244142 - -1.9375404592154715 - -2.085625450701027 - -2.1210902831218834 - -2.031690049355104 - -1.8122374628079065 - -1.4651781616925794 - -1.0007040167962231 - -0.4363869955398823 - 0.20365406594828378 - 0.8900117862700786 - 1.5896040508465923 - 2.2675499233779615 - 2.889195903453016 - 3.4221691126808045 - 3.8383299091488055 - 4.115500346970285 - 4.238856729581242 - 4.201893659209407 - 4.0068923854245915 - 3.664856403908948 - 3.1949103167900477 - 2.623191876486027 - 1.9812997369305272 - 1.3043886103408404 - 0.6290273338874866 - -0.00904784340342157 - -0.577143848414813 - -1.0476446597119524 - -1.3997372528375969 - -1.6207163648723097 - -1.7067803777666863 - -1.6632622190118318 - -1.5042748708218219 - -1.2517886060106833 - -0.9341940103702507 - -0.5844387836106218 - -0.23785496566424058 - 0.07018534689718788 - 0.3066350631640687 - 0.4430042542181653 - 0.45731281207048763 - 0.3356338326273103 - 0.0731234981311671 positive_zeros: - '1.68171654176783246558951167350312' - '3.12424893607844884324162519174929' - '4.07138629192131545636061302537983' - '5.20686401818851827647471141246289' - '5.93366234401884381484558908153572' - '6.79687210361750407728091466083682' - '7.49822591496797438401690336538278' - '8.666881218945426773456780708719223' - '9.430534638052368973397733045259035' prelabel: 2-1216-1.1-c1-0 primitive: true rational: true root_analytic_conductor: 3.11605662429098 root_angle: 1.0 root_number: '-1' self_dual: true sign_arg: __RealLiteral__: 0 data: '0.5' prec: 10 spectral_label: c1-0 trace_hash: 1980463916705955596 types: - CMF z1: __RealLiteral__: 0 data: '1.68171654176783246558951167350' prec: 103 z2: __RealLiteral__: 0 data: '3.12424893607844884324162519175' prec: 103 z3: __RealLiteral__: 0 data: '4.07138629192131545636061302538' prec: 103 - - algebraic: true analytic_conductor: 9.7098088857877 bad_primes: - 2 - 19 central_character: '1.1' conductor: 1216 conductor_radical: 38 degree: 2 dirichlet_coefficients: - 1 - 0 - -1 - 0 - 0 - 0 - -1 - 0 - -2 - 0 - 6 - 0 - -5 - 0 - 0 - 0 - 3 - 0 - -1 - 0 - 1 - 0 - 3 - 0 - -5 - 0 - 5 - 0 - -9 - 0 - -4 - 0 - -6 - 0 - 0 - 0 - -2 - 0 - 5 - 0 - 0 - 0 - -8 - 0 - 0 - 0 - 0 - 0 - -6 - 0 - -3 - 0 - 3 - 0 - 0 - 0 - 1 - 0 - -9 - 0 - 10 - 0 - 2 - 0 - 0 - 0 - -5 - 0 - -3 - 0 - -6 - 0 - -7 - 0 - 5 - 0 - -6 - 0 - -10 - 0 - 1 - 0 - 6 - 0 - 0 - 0 - 9 - 0 - -12 - 0 - 5 - 0 - 4 - 0 - 0 - 0 - -10 - 0 - -12 - 0 euler11: - 1 - -6 - 11 euler13: - 1 - 5 - 13 euler17: - 1 - -3 - 17 euler19: - 1 - 1 - 0 euler2: - 1 - 0 - 0 euler23: - 1 - -3 - 23 euler29: - 1 - 9 - 29 euler3: - 1 - 1 - 3 euler31: - 1 - 4 - 31 euler37: - 1 - 2 - 37 euler41: - 1 - 0 - 41 euler43: - 1 - 8 - 43 euler47: - 1 - 0 - 47 euler5: - 1 - 0 - 5 euler53: - 1 - -3 - 53 euler59: - 1 - 9 - 59 euler61: - 1 - -10 - 61 euler67: - 1 - 5 - 67 euler7: - 1 - 1 - 7 euler71: - 1 - 6 - 71 euler73: - 1 - 7 - 73 euler79: - 1 - 10 - 79 euler83: - 1 - -6 - 83 euler89: - 1 - 12 - 89 euler97: - 1 - 10 - 97 euler_factors: - - 1 - 0 - 0 - - 1 - 1 - 3 - - 1 - 0 - 5 - - 1 - 1 - 7 - - 1 - -6 - 11 - - 1 - 5 - 13 - - 1 - -3 - 17 - - 1 - 1 - 0 - - 1 - -3 - 23 - - 1 - 9 - 29 - - 1 - 4 - 31 - - 1 - 2 - 37 - - 1 - 0 - 41 - - 1 - 8 - 43 - - 1 - 0 - 47 - - 1 - -3 - 53 - - 1 - 9 - 59 - - 1 - -10 - 61 - - 1 - 5 - 67 - - 1 - 6 - 71 - - 1 - 7 - 73 - - 1 - 10 - 79 - - 1 - -6 - 83 - - 1 - 12 - 89 - - 1 - 10 - 97 id: 20373777 index: 24 instance_types: - ECQ - CMF - CMF instance_urls: - EllipticCurve/Q/1216/e - ModularForm/GL2/Q/holomorphic/1216/2/a/e/1/1 - ModularForm/GL2/Q/holomorphic/1216/2/a/e is_instance_Artin: false is_instance_BMF: false is_instance_CMF: true is_instance_DIR: false is_instance_ECNF: false is_instance_ECQ: true 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: 2-1216-1.1-c1-0-24 motivic_weight: 1 mu_imag: [] mu_real: [] nu_imag: - __RealLiteral__: 0 data: '0.0' prec: 10 nu_real_doubled: - 1 order_of_vanishing: 1 prelabel: 2-1216-1.1-c1-0 primitive: true rational: true root_analytic_conductor: 3.11605662429098 root_angle: 0.5 self_dual: true spectral_label: c1-0 trace_hash: 1980463916705955596 z1: __RealLiteral__: 0 data: '1.68171654176783246558951167350' prec: 103 - - Lhash: '2131828983585735045518801708143' Lhash_array: - '2131828983585735045518801708143' id: 20709641 label: 2-1216-1.1-c1-0-24 type: CMF url: ModularForm/GL2/Q/holomorphic/1216/2/a/e - Lhash: '2131828983585735045518801708143' Lhash_array: - '2131828983585735045518801708143' id: 24552226 label: 2-1216-1.1-c1-0-24 type: CMF url: ModularForm/GL2/Q/holomorphic/1216/2/a/e/1/1 - Lhash: '1980463916705955596' Lhash_array: - '1980463916705955596' id: 101321 label: 2-1216-1.1-c1-0-24 type: ECQ url: EllipticCurve/Q/1216/e label_cols: - label - label - label labels: - 2-1216-1.1-c1-0-24 - 2-1216-1.1-c1-0-24 - 2-1216-1.1-c1-0-24 tables: - lfunc_lfunctions - lfunc_search - lfunc_instances timestamp: '2024-04-23T06:41:46.674747'