Properties

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

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Maass form invariants

Level: \( 7 \)
Weight: \( 0 \)
Character: 7.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 10.175062328 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.550222568\) \(a_{3}=+0.392480455\) \(a_{4}=+1.403190011\) \(a_{5}=+1.841194645\)
\(a_{6}=-0.608432060\) \(a_{7}=-0.377964473\) \(a_{8}=-0.625034255\) \(a_{9}=-0.845959092\) \(a_{10}=-2.854261491\)
\(a_{11}=+1.345232449\) \(a_{12}=+0.550724655\) \(a_{13}=+0.087476285\) \(a_{14}=+0.585929056\) \(a_{15}=+0.722632913\)
\(a_{16}=-0.434247803\) \(a_{17}=+0.204676444\) \(a_{18}=+1.311424876\) \(a_{19}=-0.254582973\) \(a_{20}=+2.583545935\)
\(a_{21}=-0.148343668\) \(a_{22}=-2.085409702\) \(a_{23}=+0.044956913\) \(a_{24}=-0.245313729\) \(a_{25}=+2.389997721\)
\(a_{26}=-0.135607711\) \(a_{27}=-0.724502865\) \(a_{28}=-0.530355973\) \(a_{29}=+0.614514619\) \(a_{30}=-1.120241850\)
\(a_{31}=+0.609888828\) \(a_{32}=+1.298215000\) \(a_{33}=+0.527977444\) \(a_{34}=-0.317294042\) \(a_{35}=-0.695906164\)
\(a_{36}=-1.187041348\) \(a_{37}=+0.369258102\) \(a_{38}=+0.394660270\) \(a_{39}=+0.034332732\) \(a_{40}=-1.150809723\)
\(a_{41}=+0.262560898\) \(a_{42}=+0.229965703\) \(a_{43}=+0.721867426\) \(a_{44}=+1.887616735\) \(a_{45}=-1.557575350\)
\(a_{46}=-0.069693221\) \(a_{47}=+1.747629495\) \(a_{48}=-0.170433776\) \(a_{49}=+0.142857143\) \(a_{50}=-3.705028405\)
\(a_{51}=+0.080331504\) \(a_{52}=+0.122745849\) \(a_{53}=-1.327992840\) \(a_{54}=+1.123140692\) \(a_{55}=+2.476834781\)
\(a_{56}=+0.236240743\) \(a_{57}=-0.099918841\) \(a_{58}=-0.952634431\) \(a_{59}=-0.024955240\) \(a_{60}=+1.013991285\)
\(a_{61}=+1.095373065\) \(a_{62}=-0.945463425\) \(a_{63}=+0.319742482\) \(a_{64}=-1.578274388\) \(a_{65}=+0.161060867\)
\(a_{66}=-0.818482549\) \(a_{67}=-0.185313593\) \(a_{68}=+0.287199941\) \(a_{69}=+0.017644710\) \(a_{70}=+1.078809440\)
\(a_{71}=-1.474671713\) \(a_{72}=+0.528753411\) \(a_{73}=+0.917865972\) \(a_{74}=-0.572432243\) \(a_{75}=+0.938027394\)
\(a_{76}=-0.357228285\) \(a_{77}=-0.508450074\) \(a_{78}=-0.053223376\) \(a_{79}=+0.832460463\) \(a_{80}=-0.799534730\)
\(a_{81}=+0.561605878\) \(a_{82}=-0.407027830\) \(a_{83}=+0.937970007\) \(a_{84}=-0.208154354\) \(a_{85}=+0.376849172\)
\(a_{86}=-1.119055176\) \(a_{87}=+0.241184977\) \(a_{88}=-0.840816361\) \(a_{89}=-0.553664037\) \(a_{90}=+2.414588460\)
\(a_{91}=-0.033062928\) \(a_{92}=+0.063083091\) \(a_{93}=+0.239369445\) \(a_{94}=-2.709214685\) \(a_{95}=-0.468736806\)
\(a_{96}=+0.509524014\) \(a_{97}=-1.192040951\) \(a_{98}=-0.221460367\) \(a_{99}=-1.138011621\) \(a_{100}=+3.353620929\)

Showing 100 of 1228 available coefficients

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