Properties

Level $29$
Weight $0$
Character 29.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 29 \)
Weight: \( 0 \)
Character: 29.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 1.0172665508 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.060201485\) \(a_{3}=-1.200807413\) \(a_{4}=+0.124027189\) \(a_{5}=+1.424694582\)
\(a_{6}=+1.273097804\) \(a_{7}=-0.909725968\) \(a_{8}=+0.928707677\) \(a_{9}=+0.441938447\) \(a_{10}=-1.510463314\)
\(a_{11}=+0.105922854\) \(a_{12}=-0.148932767\) \(a_{13}=+0.388921957\) \(a_{14}=+0.964492817\) \(a_{15}=-1.710783817\)
\(a_{16}=-1.108644439\) \(a_{17}=-0.369797010\) \(a_{18}=-0.468543802\) \(a_{19}=+0.736861471\) \(a_{20}=+0.176700884\)
\(a_{21}=+1.092405708\) \(a_{22}=-0.112299567\) \(a_{23}=+0.741345354\) \(a_{24}=-1.115199049\) \(a_{25}=+1.029754692\)
\(a_{26}=-0.412335681\) \(a_{27}=+0.670124392\) \(a_{28}=-0.112830673\) \(a_{29}=-0.185695331\) \(a_{30}=+1.813775453\)
\(a_{31}=-0.607786892\) \(a_{32}=+0.246678779\) \(a_{33}=-0.127192986\) \(a_{34}=+0.392059340\) \(a_{35}=-1.296081655\)
\(a_{36}=+0.054812415\) \(a_{37}=-1.608161526\) \(a_{38}=-0.781221648\) \(a_{39}=-0.467020373\) \(a_{40}=+1.323124749\)
\(a_{41}=+1.332305449\) \(a_{42}=-1.158170132\) \(a_{43}=+0.586819857\) \(a_{44}=+0.013137347\) \(a_{45}=+0.629627300\)
\(a_{46}=-0.785975608\) \(a_{47}=-1.229665613\) \(a_{48}=+1.331268420\) \(a_{49}=-0.172398692\) \(a_{50}=-1.091747456\)
\(a_{51}=+0.444054999\) \(a_{52}=+0.048236916\) \(a_{53}=+1.708949370\) \(a_{54}=-0.710466849\) \(a_{55}=+0.150907691\)
\(a_{56}=-0.844869452\) \(a_{57}=-0.884828671\) \(a_{58}=+0.196874533\) \(a_{59}=-0.060360486\) \(a_{60}=-0.212183769\)
\(a_{61}=-0.231004382\) \(a_{62}=+0.644376476\) \(a_{63}=-0.402042977\) \(a_{64}=+0.847115169\) \(a_{65}=+0.554095062\)
\(a_{66}=+0.134850154\) \(a_{67}=+0.180895970\) \(a_{68}=-0.045864922\) \(a_{69}=-0.890212922\) \(a_{70}=+1.374107723\)
\(a_{71}=+1.463141640\) \(a_{72}=+0.410431645\) \(a_{73}=+0.261774740\) \(a_{74}=+1.704975189\) \(a_{75}=-1.236536952\)
\(a_{76}=+0.091390770\) \(a_{77}=-0.096360843\) \(a_{78}=+0.495135714\) \(a_{79}=+0.768960807\) \(a_{80}=-1.579479750\)
\(a_{81}=-1.246628882\) \(a_{82}=-1.412512145\) \(a_{83}=-1.884317709\) \(a_{84}=+0.135488040\) \(a_{85}=-0.526847762\)
\(a_{86}=-0.622147293\) \(a_{87}=+0.222984377\) \(a_{88}=+0.098371337\) \(a_{89}=-0.689140591\) \(a_{90}=-0.667531843\)
\(a_{91}=-0.353812415\) \(a_{92}=+0.091946980\) \(a_{93}=+0.729834911\) \(a_{94}=+1.303693350\) \(a_{95}=+1.049802552\)
\(a_{96}=-0.296213683\) \(a_{97}=-0.096621047\) \(a_{98}=+0.182777342\) \(a_{99}=+0.046811349\) \(a_{100}=+0.127717624\)

Showing 100 of 1500 available coefficients

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