data: - - Lhash: '3647582925568777525320191164416' a10: - 0.0 - 0.0 a2: - -0.43139055754696165 - -0.7471903635768031 a3: - -1.5395680228570532 - -2.666610037296779 a4: - 0.6278043737186432 - -1.0873890724946491 a5: - 0.0 - 0.0 a6: - -1.328310215523555 - 2.3007007814995633 a7: - 0.5665197076922784 - 0.0 a8: - -2.8088777454234726 - 0.0 a9: - -3.2405393940079517 - 5.612778874350234 accuracy: 100 algebraic: true analytic_conductor: 3.79289409601082 analytic_normalization: __RealLiteral__: 0 data: '0.5' prec: 10 bad_lfactors: - - 5 - - - 1.0 - 0 - - 0 - 0 - - 19 - - - 1.0 - 0 - - 2.368343767726595 - -3.6593643980711454 bad_primes: - 5 - 19 central_character: '475.26' coefficient_field: CDF conductor: 475 conductor_radical: 95 conjugate: '408755577797167456643501287810' degree: 2 euler_factors: - - - 1.0 - 0 - - 0.43139055754696165 - 0.7471903635768031 - - -1.0 - 1.7320508075688772 - - - 1.0 - 0 - - 1.5395680228570532 - 2.666610037296779 - - -1.5 - 2.598076211353316 - - - 1.0 - 0 - - 0 - 0 - - - 1.0 - 0 - - -0.5665197076922784 - 0 - - 7.0 - 0 - - - 1.0 - 0 - - 1.9122291784843966 - 0 - - 11.0 - 0 - - - 1.0 - 0 - - 0.0972656465153458 - -0.16846904159561366 - - -6.5 - -11.258330249197702 - - - 1.0 - 0 - - 2.647745488167145 - 4.586029711016755 - - -8.5 - 14.722431864335457 - - - 1.0 - 0 - - 2.368343767726595 - -3.6593643980711454 - - - 1.0 - 0 - - 1.6876987265578756 - -2.9231799422675344 - - -11.5 - -19.91858428704209 - - - 1.0 - 0 - - -4.368343767726595 - 7.566193350629321 - - -14.5 - -25.11473670974872 - - - 1.0 - 0 - - -5.65662043104711 - 0 - - 31.0 - 0 - - - 1.0 - 0 - - -0.9555822937536617 - 0 - - 37.0 - 0 - - - 1.0 - 0 - - 5.024964198773706 - 8.703493298490693 - - -20.5 - 35.50704155516198 - - - 1.0 - 0 - - -2.4662157486919587 - -4.27161097916099 - - -21.5 - 37.239092362730865 - - - 1.0 - 0 - - 4.419708307684861 - -7.6551593435444385 - - -23.5 - -40.703193977868615 - - - 1.0 - 0 - - -4.103049418064358 - 7.106690058053383 - - -26.5 - -45.89934640057525 - - - 1.0 - 0 - - 1.8571262728520224 - 3.2166370606507244 - - -29.5 - 51.09549882328188 - - - 1.0 - 0 - - -1.7556087474372863 - 3.0408035487737366 - - -30.5 - -52.827549630850754 - - - 1.0 - 0 - - 2.0218236375894914 - -3.501901264248724 - - -33.5 - -58.023702053557386 - - - 1.0 - 0 - - 2.597665666859974 - 4.499288916078765 - - -35.5 - 61.48780366869514 - - - 1.0 - 0 - - 4.302045178950657 - 7.451360826399281 - - -36.5 - 63.21985447626402 - - - 1.0 - 0 - - 3.313240862094221 - 5.738701510860499 - - -39.5 - 68.41600689897065 - - - 1.0 - 0 - - 4.517365804211523 - 0 - - 83.0 - 0 - - - 1.0 - 0 - - 1.6867591379057794 - -2.9215525269838882 - - -44.5 - -77.07626093681505 - - - 1.0 - 0 - - 7.5961099999143125 - 13.15684845973361 - - -48.5 - 84.00446416709055 - - - 1.0 - 0 - - 1.7706781008666208 - -3.0669044345505565 - - -50.5 - -87.4685657822283 - - - 1.0 - 0 - - -15.691941635972176 - 0 - - 103.0 - 0 - - - 1.0 - 0 - - -1.057312408124615 - 0 - - 107.0 - 0 - - - 1.0 - 0 - - -3.372195626281357 - -5.84081415778086 - - -54.5 - 94.39676901250381 - - - 1.0 - 0 - - 7.900908493015856 - 0 - - 113.0 - 0 gamma_factors: - [] - - 0 group: GL2 id: 10631924 index: 27 label: 2-475-19.7-c1-0-27 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/475/2/e/g/26/2 plot_delta: __RealLiteral__: 0 data: '0.125' prec: 17 plot_values: - 0.4510922290181146 - 0.664906805069093 - 0.9093786172558481 - 1.1901630392826803 - 1.511018495345839 - 1.872689580186941 - 2.272087716331516 - 2.7017661082555855 - 3.149679862568558 - 3.599250909505862 - 4.029783711261283 - 4.417283088148746 - 4.735706834590856 - 4.958647186671849 - 5.061382779856243 - 5.023183293482045 - 4.829689959768056 - 4.475144677643189 - 3.9642071533535277 - 3.31309141654877 - 2.549776819712059 - 1.7131079896145895 - 0.8506929001907297 - 0.015633074039024048 - -0.7377356256150589 - -1.3587645669997337 - -1.8056157895385407 - -2.0500294901912133 - -2.0811365043365435 - -1.907747343192168 - -1.5586601398317572 - -1.0807190281167438 - -0.5346084534865375 - 0.011337806560691466 - 0.48873723921678636 - 0.8373348266579712 - 1.012744513519275 - 0.992688862539232 - 0.7807585118186069 - 0.4069542129519853 - -0.07534738470135624 - -0.5958862977471546 - -1.0768369738058454 - -1.4438387194958502 - -1.6372616116355407 - -1.622052015976871 - -1.3945597386596291 - -0.9850621559914372 - -0.45524887639870143 - 0.10934817168544586 - 0.6111978707142421 - 0.9553556395335718 - 1.0646878453980932 - 0.8933476030687446 - 0.4361986220556329 - -0.2676418155022288 - -1.1381465154983397 - -2.0645493205305248 - -2.921137154052264 - -3.5864195196226154 - -3.9626947983880765 - -3.9927525147775826 - -3.6707170758599856 - -3.0448508947050534 - -2.2113936082082963 - -1.3000288873242414 - -0.453086512198568 - 0.19817232020093364 - 0.5561238462031003 - 0.5741254303409374 - 0.26529078175910387 - -0.2992418933518871 - -1.002632669245169 - -1.703355613174541 - -2.261273121597667 - -2.5639971297718542 - -2.5484891677104056 - -2.213547451234931 - -1.6204235238619156 - -0.8810432304142625 - -0.1357689411985807 - 0.4751524084425751 - 0.8408248903550753 - 0.9035798413725905 - 0.6722659257993558 - 0.2216804018851092 - -0.3223735314372615 - -0.8098857806766742 - -1.100093279177128 - -1.0946460647439589 - -0.763179572833398 - -0.15517289339340534 - 0.6054425369369701 - 1.3429376768291292 - 1.8659564943577498 - 2.0102515475753897 - 1.6791203591018913 - 0.8725567786664888 - -0.30205331889609593 - -1.641378434444883 - -2.878912876653626 - -3.733647535706661 - -3.965494617802181 - -3.4263494940445143 - -2.09597552797639 - -0.09453063350639572 - 2.331936157541929 - 4.851194036737504 - 7.102591168350764 - 8.761715686765355 - 9.599066313864284 - 9.520818618937225 - 8.583335754952238 - 6.978507436474618 - 4.993149546325894 - 2.9512050759741473 - 1.1511104956785005 - -0.18841333588167664 - -0.962953375633415 - -1.1907668087271464 - -0.9943486024855244 - -0.5607487307235167 - -0.09091392446015732 - 0.24944855334518526 - 0.3658067844262383 - 0.24951798307650472 - -0.03111611526333845 - -0.3597757233797091 - -0.6122668814862071 - -0.6963676570353824 - -0.5801781506107136 - -0.3011032551960923 - 0.04691440010591327 - 0.34408837197474373 - 0.48433900560041104 - 0.41181017559139255 - 0.14292885657344778 - -0.23366437351158198 - -0.58085405539215 - -0.7550861264955816 - -0.6555330632707458 - -0.2662249251512565 - 0.32219876635013295 - 0.9198131335688912 - 1.2750599908408513 - 1.13560238050618 - 0.31818112592447884 - -1.230479919987934 - -3.3988601361481763 - -5.913595242621872 - -8.38291797340868 - -10.373029502112436 - -11.5008882920517 - -11.52170376186311 - -10.389544459983561 - -8.275144371202298 - -5.534987239685756 - -2.6376414828486645 - -0.06408236006058254 - 1.7944655071983773 - 2.716689179505179 - 2.6901793493313915 - 1.9003754409421 - 0.6732567118444159 - -0.6126907166537763 - -1.6220219290802023 - -2.140651783436703 - -2.1172598623325616 - -1.6584148582531397 - -0.9808265163331983 - -0.33585554004301144 - 0.07117632930900464 - 0.14331986689430534 - -0.08188893500678958 - -0.44959510730546953 - -0.7422784458344361 - -0.7549113253755685 - -0.3673799513345264 - 0.40849618962507894 - 1.422665920752847 - 2.424519123502943 - 3.134468925661932 - 3.328754199297333 - 2.91206012692617 - 1.9553178815091243 - 0.6856721251749848 - -0.5705679247236968 - -1.4771378013273895 - -1.7842407549950343 - -1.404206563492087 - -0.44354101797663326 - 0.8194677485313966 - 2.0068877071028717 - 2.7437624655392554 - 2.76266239440374 - 1.9804616705285178 - 0.5251136689059526 - -1.295734068274668 - -3.075820342622944 - -4.418264055545943 - -5.039925121219173 - -4.842724719948319 - -3.9322725647780783 - -2.5796520879429923 - -1.138846332362154 - 0.054939211185390746 - 0.775725104276427 - 0.9597750315661412 - 0.7070019167653034 - 0.23275576582980265 - -0.21273008340093327 - -0.4303288409539597 - -0.33556555993985404 - 0.020216906935779565 - 0.4767129821017145 - 0.8291563392714417 - 0.9075705271905342 - 0.6429667202658299 - 0.09709141292364626 - -0.5553105132176963 - -1.0864357210681572 - -1.297417165849272 - -1.0938626864254426 - -0.5275903957555873 - 0.2121677228764271 - 0.8579942754701843 - 1.1562584292267997 - 0.9617169675636889 - 0.30181262534407216 - -0.6140415715186011 - -1.4478343003722087 - -1.835949665406892 - -1.5111562908465406 - -0.40446074771605467 - 1.308420408243825 - 3.2355433061067127 - 4.8687747327922875 - 5.728790844329711 - 5.51250216356294 - 4.197153899294556 - 2.066465373502947 - -0.3533027649578815 - -2.432207475019696 - -3.611694206476726 - -3.5648121375707422 - -2.29356435561744 - -0.1332906919615855 - 2.3385237686911533 - 4.462924923374311 - 5.682566593648901 - 5.69340602485788 - 4.520988424594371 - 2.5004758524891493 - 0.16892535856302984 - -1.8953772567958693 - -3.236677733835153 - -3.6395386167668904 positive_zeros: - '2.87743556853289236613669667394308' - '4.12229232275385861023371375830213' - '4.98156739590223893994444172315573' - '6.10038654298557615937351209811343' - '6.83167891063163961448092741056628' - '8.331344481220509837029653326746534' - '8.814370355136126178962758883699976' - '10.02475564979755108825668644122495' - '10.67661375662914938523166022850055' - '11.40172181660714741497514595355320' prelabel: 2-475-19.7-c1-0 primitive: true rational: false root_analytic_conductor: 1.9475353901818626 root_angle: -0.5827412746231437 root_number: -0.25702196934712657 - 0.9664055604521968*I self_dual: false sign_arg: __RealLiteral__: 0 data: '-0.291370637312' prec: 50 spectral_label: c1-0 types: - CMF z1: __RealLiteral__: 0 data: '2.87743556853289236613669667394' prec: 103 z2: __RealLiteral__: 0 data: '4.12229232275385861023371375830' prec: 103 z3: __RealLiteral__: 0 data: '4.98156739590223893994444172316' prec: 103 - - algebraic: true analytic_conductor: 3.79289409601082 bad_primes: - 5 - 19 central_character: '19.7' conductor: 475 conductor_radical: 95 degree: 2 id: 10631924 index: 27 instance_types: - CMF instance_urls: - ModularForm/GL2/Q/holomorphic/475/2/e/g/26/2 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: 2-475-19.7-c1-0-27 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: 2-475-19.7-c1-0 primitive: true rational: false root_analytic_conductor: 1.9475353901818626 root_angle: -0.29137063731157187 self_dual: false spectral_label: c1-0 z1: __RealLiteral__: 0 data: '2.87743556853289236613669667394' prec: 103 - - Lhash: '3647582925568777525320191164416' Lhash_array: - '3647582925568777525320191164416' id: 10997987 label: 2-475-19.7-c1-0-27 type: CMF url: ModularForm/GL2/Q/holomorphic/475/2/e/g/26/2 label_cols: - label - label - label labels: - 2-475-19.7-c1-0-27 - 2-475-19.7-c1-0-27 - 2-475-19.7-c1-0-27 tables: - lfunc_lfunctions - lfunc_search - lfunc_instances timestamp: '2024-04-25T01:49:32.726744'