Properties

Level $7$
Weight $0$
Character 7.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 7 \)
Weight: \( 0 \)
Character: 7.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 11.2763113507 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.691952662\) \(a_{3}=+0.553714916\) \(a_{4}=-0.521201514\) \(a_{5}=+0.437096326\)
\(a_{6}=+0.383144510\) \(a_{7}=-0.377964473\) \(a_{8}=-1.052599436\) \(a_{9}=-0.693399792\) \(a_{10}=+0.302449966\)
\(a_{11}=+0.148627858\) \(a_{12}=-0.288597053\) \(a_{13}=+0.109763389\) \(a_{14}=-0.261533523\) \(a_{15}=+0.242026755\)
\(a_{16}=-0.207147467\) \(a_{17}=-0.740698613\) \(a_{18}=-0.479799831\) \(a_{19}=-1.922623784\) \(a_{20}=-0.227815267\)
\(a_{21}=-0.209284566\) \(a_{22}=+0.102843442\) \(a_{23}=+0.412156935\) \(a_{24}=-0.582840009\) \(a_{25}=-0.808946802\)
\(a_{26}=+0.075951069\) \(a_{27}=-0.937660724\) \(a_{28}=+0.196995656\) \(a_{29}=-0.904472851\) \(a_{30}=+0.167471058\)
\(a_{31}=+0.365250301\) \(a_{32}=+0.909263195\) \(a_{33}=+0.082297462\) \(a_{34}=-0.512528376\) \(a_{35}=-0.165206882\)
\(a_{36}=+0.361401021\) \(a_{37}=+0.324684508\) \(a_{38}=-1.330364645\) \(a_{39}=+0.060777626\) \(a_{40}=-0.460087346\)
\(a_{41}=-0.036696137\) \(a_{42}=-0.144815013\) \(a_{43}=+1.420307255\) \(a_{44}=-0.077465065\) \(a_{45}=-0.303082501\)
\(a_{46}=+0.285193088\) \(a_{47}=+0.239716542\) \(a_{48}=-0.114700643\) \(a_{49}=+0.142857143\) \(a_{50}=-0.559752893\)
\(a_{51}=-0.410135870\) \(a_{52}=-0.057208844\) \(a_{53}=+1.177594995\) \(a_{54}=-0.648816833\) \(a_{55}=+0.064964691\)
\(a_{56}=+0.397845191\) \(a_{57}=-1.064585468\) \(a_{58}=-0.625852396\) \(a_{59}=-0.501902076\) \(a_{60}=-0.126144711\)
\(a_{61}=+1.679580086\) \(a_{62}=+0.252735918\) \(a_{63}=+0.262080487\) \(a_{64}=+0.836314555\) \(a_{65}=+0.047977174\)
\(a_{66}=+0.056945948\) \(a_{67}=-1.058887115\) \(a_{68}=+0.386053238\) \(a_{69}=+0.228217443\) \(a_{70}=-0.114315342\)
\(a_{71}=-1.567478005\) \(a_{72}=+0.729872230\) \(a_{73}=-1.501541071\) \(a_{74}=+0.224666309\) \(a_{75}=-0.447925911\)
\(a_{76}=+1.002074428\) \(a_{77}=-0.056176050\) \(a_{78}=+0.042055240\) \(a_{79}=+0.955513315\) \(a_{80}=-0.090543397\)
\(a_{81}=+0.174203063\) \(a_{82}=-0.025391990\) \(a_{83}=+0.703403988\) \(a_{84}=+0.109079433\) \(a_{85}=-0.323756642\)
\(a_{86}=+0.982785385\) \(a_{87}=-0.500820109\) \(a_{88}=-0.156445600\) \(a_{89}=-1.297818952\) \(a_{90}=-0.209718743\)
\(a_{91}=-0.041486661\) \(a_{92}=-0.214816818\) \(a_{93}=+0.202244540\) \(a_{94}=+0.165872499\) \(a_{95}=-0.840371792\)
\(a_{96}=+0.503472594\) \(a_{97}=+0.093281990\) \(a_{98}=+0.098850380\) \(a_{99}=-0.103058526\) \(a_{100}=+0.421624298\)

Showing 100 of 1228 available coefficients

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