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: \( 6.59193983828 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-1.869942120\) \(a_{4}=+0.500000000\) \(a_{5}=-0.639802368\)
\(a_{6}=-1.322248753\) \(a_{7}=-0.377964473\) \(a_{8}=+0.353553391\) \(a_{9}=+2.496683532\) \(a_{10}=-0.452408593\)
\(a_{11}=+0.403856608\) \(a_{12}=-0.934971060\) \(a_{13}=+1.508407999\) \(a_{14}=-0.267261242\) \(a_{15}=+1.196393397\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.465756624\) \(a_{18}=+1.765421856\) \(a_{19}=-0.730586173\) \(a_{20}=-0.319901184\)
\(a_{21}=+0.706771688\) \(a_{22}=+0.285569746\) \(a_{23}=+0.769829777\) \(a_{24}=-0.661124377\) \(a_{25}=-0.590652929\)
\(a_{26}=+1.066605525\) \(a_{27}=-2.798711577\) \(a_{28}=-0.188982237\) \(a_{29}=+1.448189054\) \(a_{30}=+0.845977884\)
\(a_{31}=+0.506074759\) \(a_{32}=+0.176776695\) \(a_{33}=-0.755188481\) \(a_{34}=-0.329339667\) \(a_{35}=+0.241822565\)
\(a_{36}=+1.248341766\) \(a_{37}=+1.314338996\) \(a_{38}=-0.516602437\) \(a_{39}=-2.820635651\) \(a_{40}=-0.226204297\)
\(a_{41}=+0.579126904\) \(a_{42}=+0.499763053\) \(a_{43}=+0.376968023\) \(a_{44}=+0.201928304\) \(a_{45}=-1.597384037\)
\(a_{46}=+0.544351855\) \(a_{47}=+0.450805544\) \(a_{48}=-0.467485530\) \(a_{49}=+0.142857143\) \(a_{50}=-0.417654692\)
\(a_{51}=+0.870937928\) \(a_{52}=+0.754203999\) \(a_{53}=-0.217264351\) \(a_{54}=-1.978987935\) \(a_{55}=-0.258388414\)
\(a_{56}=-0.133630621\) \(a_{57}=+1.366153858\) \(a_{58}=+1.024024301\) \(a_{59}=+0.092002189\) \(a_{60}=+0.598196699\)
\(a_{61}=+1.517882724\) \(a_{62}=+0.357848894\) \(a_{63}=-0.943657676\) \(a_{64}=+0.125000000\) \(a_{65}=-0.965083010\)
\(a_{66}=-0.533998896\) \(a_{67}=-1.480757427\) \(a_{68}=-0.232878312\) \(a_{69}=-1.439537125\) \(a_{70}=+0.170994376\)
\(a_{71}=-0.674389347\) \(a_{72}=+0.882710928\) \(a_{73}=-0.171164460\) \(a_{74}=+0.929378017\) \(a_{75}=+1.104486791\)
\(a_{76}=-0.365293087\) \(a_{77}=-0.152643450\) \(a_{78}=-1.994490596\) \(a_{79}=+1.421063170\) \(a_{80}=-0.159950592\)
\(a_{81}=+2.736745128\) \(a_{82}=+0.409504561\) \(a_{83}=+0.557594200\) \(a_{84}=+0.353385844\) \(a_{85}=+0.297992191\)
\(a_{86}=+0.266556645\) \(a_{87}=-2.708029710\) \(a_{88}=+0.142784873\) \(a_{89}=+0.301899600\) \(a_{90}=-1.129521085\)
\(a_{91}=-0.570124634\) \(a_{92}=+0.384914888\) \(a_{93}=-0.946330507\) \(a_{94}=+0.318767658\) \(a_{95}=+0.467430764\)
\(a_{96}=-0.330562188\) \(a_{97}=-0.026382000\) \(a_{98}=+0.101015254\) \(a_{99}=+1.008302142\) \(a_{100}=-0.295326465\)

Showing 100 of 156 available coefficients

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