Properties

Level $14$
Weight $0$
Character 14.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 14 = 2 \cdot 7 \)
Weight: \( 0 \)
Character: 14.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 9.5264015474 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-1.248690549\) \(a_{4}=+0.500000000\) \(a_{5}=+1.728922109\)
\(a_{6}=+0.882957555\) \(a_{7}=+0.377964473\) \(a_{8}=-0.353553391\) \(a_{9}=+0.559228087\) \(a_{10}=-1.222532547\)
\(a_{11}=+1.042503831\) \(a_{12}=-0.624345274\) \(a_{13}=-1.214818008\) \(a_{14}=-0.267261242\) \(a_{15}=-2.158888697\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.291147713\) \(a_{18}=-0.395433973\) \(a_{19}=+1.346612230\) \(a_{20}=+0.864461054\)
\(a_{21}=-0.471960665\) \(a_{22}=-0.737161528\) \(a_{23}=-1.673897726\) \(a_{24}=+0.441478777\) \(a_{25}=+1.989171658\)
\(a_{26}=+0.859006052\) \(a_{27}=+0.550387722\) \(a_{28}=+0.188982237\) \(a_{29}=+0.556034000\) \(a_{30}=+1.526564838\)
\(a_{31}=+0.259330240\) \(a_{32}=-0.176776695\) \(a_{33}=-1.301764681\) \(a_{34}=+0.205872522\) \(a_{35}=+0.653471134\)
\(a_{36}=+0.279614044\) \(a_{37}=+0.446768723\) \(a_{38}=-0.952198639\) \(a_{39}=+1.516931766\) \(a_{40}=-0.611266274\)
\(a_{41}=-0.460716436\) \(a_{42}=+0.333726587\) \(a_{43}=-0.318714832\) \(a_{44}=+0.521251915\) \(a_{45}=+0.966861804\)
\(a_{46}=+1.183624433\) \(a_{47}=-0.379498902\) \(a_{48}=-0.312172637\) \(a_{49}=+0.142857143\) \(a_{50}=-1.406556769\)
\(a_{51}=+0.363553397\) \(a_{52}=-0.607409004\) \(a_{53}=+0.916713787\) \(a_{54}=-0.389182890\) \(a_{55}=+1.802407922\)
\(a_{56}=-0.133630621\) \(a_{57}=-1.681501964\) \(a_{58}=-0.393175412\) \(a_{59}=+0.936482375\) \(a_{60}=-1.079444349\)
\(a_{61}=+0.137761666\) \(a_{62}=-0.183374172\) \(a_{63}=+0.211368349\) \(a_{64}=+0.125000000\) \(a_{65}=-2.100325713\)
\(a_{66}=+0.920486633\) \(a_{67}=+1.919977019\) \(a_{68}=-0.145573856\) \(a_{69}=+2.090180270\) \(a_{70}=-0.462073870\)
\(a_{71}=+1.094891228\) \(a_{72}=-0.197716986\) \(a_{73}=-1.112975064\) \(a_{74}=-0.315913193\) \(a_{75}=-2.483859850\)
\(a_{76}=+0.673306115\) \(a_{77}=+0.394029411\) \(a_{78}=-1.072632738\) \(a_{79}=+1.626863835\) \(a_{80}=+0.432230527\)
\(a_{81}=-1.246492033\) \(a_{82}=+0.325775716\) \(a_{83}=+1.314821149\) \(a_{84}=-0.235980333\) \(a_{85}=-0.503371717\)
\(a_{86}=+0.225365419\) \(a_{87}=-0.694314402\) \(a_{88}=-0.368580764\) \(a_{89}=+0.014256749\) \(a_{90}=-0.683674538\)
\(a_{91}=-0.459158048\) \(a_{92}=-0.836948863\) \(a_{93}=-0.323823217\) \(a_{94}=+0.268346247\) \(a_{95}=+2.328187650\)
\(a_{96}=+0.220739389\) \(a_{97}=+0.282594689\) \(a_{98}=-0.101015254\) \(a_{99}=+0.582997427\) \(a_{100}=+0.994585829\)

Showing 100 of 196 available coefficients

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