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: \( 8.56497336757 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-1.389761354\) \(a_{4}=+0.500000000\) \(a_{5}=-1.071229538\)
\(a_{6}=+0.982709678\) \(a_{7}=+0.377964473\) \(a_{8}=-0.353553391\) \(a_{9}=+0.931436621\) \(a_{10}=+0.757473670\)
\(a_{11}=+1.965017848\) \(a_{12}=-0.694880677\) \(a_{13}=+0.285619768\) \(a_{14}=-0.267261242\) \(a_{15}=+1.488753413\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.008363218\) \(a_{18}=-0.658625151\) \(a_{19}=-1.395013507\) \(a_{20}=-0.535614769\)
\(a_{21}=-0.525280418\) \(a_{22}=-1.389477446\) \(a_{23}=+0.264347604\) \(a_{24}=+0.491354839\) \(a_{25}=+0.147532723\)
\(a_{26}=-0.201963675\) \(a_{27}=+0.095286734\) \(a_{28}=+0.188982237\) \(a_{29}=-0.790726920\) \(a_{30}=-1.052707634\)
\(a_{31}=+0.840209631\) \(a_{32}=-0.176776695\) \(a_{33}=-2.730905865\) \(a_{34}=+0.005913688\) \(a_{35}=-0.404886708\)
\(a_{36}=+0.465718311\) \(a_{37}=+1.747979480\) \(a_{38}=+0.986423510\) \(a_{39}=-0.396943316\) \(a_{40}=+0.378736835\)
\(a_{41}=-1.846917643\) \(a_{42}=+0.371429345\) \(a_{43}=+0.212640822\) \(a_{44}=+0.982508924\) \(a_{45}=-0.997782421\)
\(a_{46}=-0.186921983\) \(a_{47}=+0.380923143\) \(a_{48}=-0.347440339\) \(a_{49}=+0.142857143\) \(a_{50}=-0.104321389\)
\(a_{51}=+0.011622877\) \(a_{52}=+0.142809884\) \(a_{53}=-0.006482472\) \(a_{54}=-0.067377896\) \(a_{55}=-2.104985161\)
\(a_{56}=-0.133630621\) \(a_{57}=+1.938735860\) \(a_{58}=+0.559128367\) \(a_{59}=-1.718602167\) \(a_{60}=+0.744376707\)
\(a_{61}=+0.614507360\) \(a_{62}=-0.594117928\) \(a_{63}=+0.352049952\) \(a_{64}=+0.125000000\) \(a_{65}=-0.305964333\)
\(a_{66}=+1.931042056\) \(a_{67}=-0.114737154\) \(a_{68}=-0.004181609\) \(a_{69}=-0.367380084\) \(a_{70}=+0.286298137\)
\(a_{71}=-1.054190888\) \(a_{72}=-0.329312576\) \(a_{73}=+1.011376825\) \(a_{74}=-1.236008143\) \(a_{75}=-0.205035277\)
\(a_{76}=-0.697506753\) \(a_{77}=+0.742706935\) \(a_{78}=+0.280681311\) \(a_{79}=-0.250324896\) \(a_{80}=-0.267807384\)
\(a_{81}=-1.063862441\) \(a_{82}=+1.305967990\) \(a_{83}=-0.064812796\) \(a_{84}=-0.262640209\) \(a_{85}=+0.008958924\)
\(a_{86}=-0.150359767\) \(a_{87}=+1.098921715\) \(a_{88}=-0.694738723\) \(a_{89}=-0.291353272\) \(a_{90}=+0.705538716\)
\(a_{91}=+0.107954125\) \(a_{92}=+0.132173802\) \(a_{93}=-1.167690874\) \(a_{94}=-0.269353337\) \(a_{95}=+1.494379668\)
\(a_{96}=+0.245677419\) \(a_{97}=+0.040959748\) \(a_{98}=-0.101015254\) \(a_{99}=+1.830289603\) \(a_{100}=+0.073766361\)

Showing 100 of 192 available coefficients

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