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: \( 7.87382712891 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+1.369997723\) \(a_{4}=+0.500000000\) \(a_{5}=-1.170547885\)
\(a_{6}=-0.968734680\) \(a_{7}=+0.377964473\) \(a_{8}=-0.353553391\) \(a_{9}=+0.876893762\) \(a_{10}=+0.827702347\)
\(a_{11}=-1.504127944\) \(a_{12}=+0.684998862\) \(a_{13}=+1.599846895\) \(a_{14}=-0.267261242\) \(a_{15}=-1.603647937\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.157923403\) \(a_{18}=-0.620057526\) \(a_{19}=-0.938931550\) \(a_{20}=-0.585273942\)
\(a_{21}=+0.517810468\) \(a_{22}=+1.063579069\) \(a_{23}=-0.651067366\) \(a_{24}=-0.484367340\) \(a_{25}=+0.370182351\)
\(a_{26}=-1.131262588\) \(a_{27}=-0.168655266\) \(a_{28}=+0.188982237\) \(a_{29}=-1.118163170\) \(a_{30}=+1.133950331\)
\(a_{31}=+0.026598829\) \(a_{32}=-0.176776695\) \(a_{33}=-2.060651859\) \(a_{34}=+0.818775490\) \(a_{35}=-0.442425514\)
\(a_{36}=+0.438446881\) \(a_{37}=-0.825372143\) \(a_{38}=+0.663924866\) \(a_{39}=+2.191786604\) \(a_{40}=+0.413851174\)
\(a_{41}=+0.286663746\) \(a_{42}=-0.366147293\) \(a_{43}=-0.451066852\) \(a_{44}=-0.752063972\) \(a_{45}=-1.026446139\)
\(a_{46}=+0.460374150\) \(a_{47}=-0.866090841\) \(a_{48}=+0.342499431\) \(a_{49}=+0.142857143\) \(a_{50}=-0.261758450\)
\(a_{51}=-1.586352426\) \(a_{52}=+0.799923447\) \(a_{53}=+0.428786212\) \(a_{54}=+0.119257282\) \(a_{55}=+1.760653784\)
\(a_{56}=-0.133630621\) \(a_{57}=-1.286334086\) \(a_{58}=+0.790660760\) \(a_{59}=+1.115554333\) \(a_{60}=-0.801823969\)
\(a_{61}=-0.123895798\) \(a_{62}=-0.018808212\) \(a_{63}=+0.331434689\) \(a_{64}=+0.125000000\) \(a_{65}=-1.872697399\)
\(a_{66}=+1.457100903\) \(a_{67}=-0.087978881\) \(a_{68}=-0.578961701\) \(a_{69}=-0.891960810\) \(a_{70}=+0.312842081\)
\(a_{71}=+1.201185177\) \(a_{72}=-0.310028763\) \(a_{73}=+0.782890265\) \(a_{74}=+0.583626239\) \(a_{75}=+0.507148978\)
\(a_{76}=-0.469465775\) \(a_{77}=-0.568506926\) \(a_{78}=-1.549827171\) \(a_{79}=-1.290807891\) \(a_{80}=-0.292636971\)
\(a_{81}=-1.107951092\) \(a_{82}=-0.202701879\) \(a_{83}=+1.967419026\) \(a_{84}=+0.258905234\) \(a_{85}=+1.355404790\)
\(a_{86}=+0.318952430\) \(a_{87}=-1.531880997\) \(a_{88}=+0.531789535\) \(a_{89}=+0.913790950\) \(a_{90}=+0.725807025\)
\(a_{91}=+0.604685289\) \(a_{92}=-0.325533683\) \(a_{93}=+0.036440335\) \(a_{94}=+0.612418707\) \(a_{95}=+1.099064340\)
\(a_{96}=-0.242183670\) \(a_{97}=-1.872083080\) \(a_{98}=-0.101015254\) \(a_{99}=-1.318960412\) \(a_{100}=+0.185091175\)

Showing 100 of 178 available coefficients

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