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: \( 10.6716858394 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.137850772\) \(a_{3}=-0.630317014\) \(a_{4}=-0.980997165\) \(a_{5}=-1.803143564\)
\(a_{6}=-0.086889687\) \(a_{7}=+0.377964472\) \(a_{8}=-0.273081988\) \(a_{9}=-0.602700462\) \(a_{10}=-0.248564732\)
\(a_{11}=-0.093718305\) \(a_{12}=+0.618339204\) \(a_{13}=-0.857268969\) \(a_{14}=+0.052102694\) \(a_{15}=+1.136552067\)
\(a_{16}=+0.943352602\) \(a_{17}=+0.857799749\) \(a_{18}=-0.083082724\) \(a_{19}=+0.075884744\) \(a_{20}=+1.768878724\)
\(a_{21}=-0.238237438\) \(a_{22}=-0.012919141\) \(a_{23}=-1.221799811\) \(a_{24}=+0.172128223\) \(a_{25}=+2.251326713\)
\(a_{26}=-0.118175189\) \(a_{27}=+1.010209370\) \(a_{28}=-0.370782076\) \(a_{29}=-1.510874515\) \(a_{30}=+0.156674580\)
\(a_{31}=-0.120554037\) \(a_{32}=+0.403123872\) \(a_{33}=+0.059072242\) \(a_{34}=+0.118248358\) \(a_{35}=-0.681524206\)
\(a_{36}=+0.591247444\) \(a_{37}=+0.325097524\) \(a_{38}=+0.010460770\) \(a_{39}=+0.540351217\) \(a_{40}=+0.492406030\)
\(a_{41}=-0.405998488\) \(a_{42}=-0.032841215\) \(a_{43}=-1.905747459\) \(a_{44}=+0.091937392\) \(a_{45}=+1.086755459\)
\(a_{46}=-0.168426047\) \(a_{47}=+0.064373527\) \(a_{48}=-0.594611195\) \(a_{49}=+0.142857142\) \(a_{50}=+0.310347125\)
\(a_{51}=-0.540685777\) \(a_{52}=+0.840978428\) \(a_{53}=+0.715681006\) \(a_{54}=+0.139258141\) \(a_{55}=+0.168987559\)
\(a_{56}=-0.103215290\) \(a_{57}=-0.047831445\) \(a_{58}=-0.208275218\) \(a_{59}=-1.146984894\) \(a_{60}=-1.114954356\)
\(a_{61}=+1.147517396\) \(a_{62}=-0.016618467\) \(a_{63}=-0.227799362\) \(a_{64}=-0.887781665\) \(a_{65}=+1.545779024\)
\(a_{66}=+0.008143154\) \(a_{67}=-0.055137367\) \(a_{68}=-0.841499122\) \(a_{69}=+0.770121209\) \(a_{70}=-0.093948638\)
\(a_{71}=+0.976440383\) \(a_{72}=+0.164586640\) \(a_{73}=+0.517558602\) \(a_{74}=+0.044814945\) \(a_{75}=-1.419049532\)
\(a_{76}=-0.074442718\) \(a_{77}=-0.035422190\) \(a_{78}=+0.074487832\) \(a_{79}=+1.046249809\) \(a_{80}=-1.701000173\)
\(a_{81}=-0.034051692\) \(a_{82}=-0.055967205\) \(a_{83}=+0.196018764\) \(a_{84}=+0.233710251\) \(a_{85}=-1.546736097\)
\(a_{86}=-0.262708758\) \(a_{87}=+0.952329913\) \(a_{88}=+0.025592781\) \(a_{89}=+1.584466700\) \(a_{90}=+0.149810079\)
\(a_{91}=-0.324017214\) \(a_{92}=+1.198582151\) \(a_{93}=+0.075987260\) \(a_{94}=+0.008873940\) \(a_{95}=-0.136831087\)
\(a_{96}=-0.254095836\) \(a_{97}=-1.001340170\) \(a_{98}=+0.019692967\) \(a_{99}=+0.056484066\) \(a_{100}=-2.208545122\)

Showing 100 of 1228 available coefficients

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