Properties

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

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Maass form invariants

Level: \( 14 = 2 \cdot 7 \)
Weight: \( 0 \)
Character: 14.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 3.62819352869 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+0.230887210\) \(a_{4}=+0.500000000\) \(a_{5}=-1.900208032\)
\(a_{6}=-0.163261912\) \(a_{7}=+0.377964473\) \(a_{8}=-0.353553391\) \(a_{9}=-0.946691096\) \(a_{10}=+1.343649985\)
\(a_{11}=+0.411456462\) \(a_{12}=+0.115443605\) \(a_{13}=-0.462546744\) \(a_{14}=-0.267261242\) \(a_{15}=-0.438733731\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.627990890\) \(a_{18}=+0.669411694\) \(a_{19}=+0.443971788\) \(a_{20}=-0.950104016\)
\(a_{21}=+0.087267163\) \(a_{22}=-0.290943654\) \(a_{23}=-0.753780895\) \(a_{24}=-0.081630956\) \(a_{25}=+2.610790565\)
\(a_{26}=+0.327069939\) \(a_{27}=-0.449466076\) \(a_{28}=+0.188982237\) \(a_{29}=-0.146978268\) \(a_{30}=+0.310231596\)
\(a_{31}=-1.355122333\) \(a_{32}=-0.176776696\) \(a_{33}=+0.095000035\) \(a_{34}=+0.444056618\) \(a_{35}=-0.718211128\)
\(a_{36}=-0.473345548\) \(a_{37}=+0.231561458\) \(a_{38}=-0.313935462\) \(a_{39}=-0.106796120\) \(a_{40}=+0.671824976\)
\(a_{41}=-1.404114456\) \(a_{42}=-0.061707178\) \(a_{43}=+0.814507977\) \(a_{44}=+0.205728256\) \(a_{45}=+1.798910003\)
\(a_{46}=+0.533003583\) \(a_{47}=+0.749255888\) \(a_{48}=+0.057721802\) \(a_{49}=+0.142857143\) \(a_{50}=-1.846107713\)
\(a_{51}=-0.144995064\) \(a_{52}=-0.231273373\) \(a_{53}=+0.106729835\) \(a_{54}=+0.317820510\) \(a_{55}=-0.781852874\)
\(a_{56}=-0.133630622\) \(a_{57}=+0.102507409\) \(a_{58}=+0.103929328\) \(a_{59}=-0.461240197\) \(a_{60}=-0.219366868\)
\(a_{61}=-1.492281003\) \(a_{62}=+0.958216189\) \(a_{63}=-0.357815606\) \(a_{64}=+0.124999997\) \(a_{65}=+0.878935040\)
\(a_{66}=-0.067175171\) \(a_{67}=+0.948457250\) \(a_{68}=-0.313995440\) \(a_{69}=-0.174038398\) \(a_{70}=+0.507851954\)
\(a_{71}=+0.510633420\) \(a_{72}=+0.334705782\) \(a_{73}=-0.801109981\) \(a_{74}=-0.163738618\) \(a_{75}=+0.602798218\)
\(a_{76}=+0.221986142\) \(a_{77}=+0.155515736\) \(a_{78}=+0.075516737\) \(a_{79}=-1.882113016\) \(a_{80}=-0.475052009\)
\(a_{81}=+0.842915128\) \(a_{82}=+0.992858856\) \(a_{83}=+0.033085448\) \(a_{84}=+0.043633581\) \(a_{85}=+1.193313319\)
\(a_{86}=-0.575944128\) \(a_{87}=-0.033935402\) \(a_{88}=-0.145471821\) \(a_{89}=-0.305356190\) \(a_{90}=-1.272021463\)
\(a_{91}=-0.174826227\) \(a_{92}=-0.376890452\) \(a_{93}=-0.312880491\) \(a_{94}=-0.529803933\) \(a_{95}=-0.843638781\)
\(a_{96}=-0.040815317\) \(a_{97}=+1.499701270\) \(a_{98}=-0.101015258\) \(a_{99}=-0.389521643\) \(a_{100}=+1.305394999\)

Showing 100 of 2000 available coefficients

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