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: \( 5.24897949499 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+0.805726291\) \(a_{4}=+0.500000000\) \(a_{5}=-0.560822769\)
\(a_{6}=-0.569734524\) \(a_{7}=-0.377964473\) \(a_{8}=-0.353553391\) \(a_{9}=-0.350805144\) \(a_{10}=+0.396561583\)
\(a_{11}=-1.120683861\) \(a_{12}=+0.402863145\) \(a_{13}=-0.589077184\) \(a_{14}=+0.267261242\) \(a_{15}=-0.451869649\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.287805707\) \(a_{18}=+0.248056697\) \(a_{19}=+0.574225109\) \(a_{20}=-0.280411384\)
\(a_{21}=-0.304535913\) \(a_{22}=+0.792443158\) \(a_{23}=+1.473626310\) \(a_{24}=-0.284867262\) \(a_{25}=-0.685477822\)
\(a_{26}=+0.416540472\) \(a_{27}=-1.088379219\) \(a_{28}=-0.188982237\) \(a_{29}=-0.604868426\) \(a_{30}=+0.319520093\)
\(a_{31}=+0.051592588\) \(a_{32}=-0.176776695\) \(a_{33}=-0.902964450\) \(a_{34}=+0.910616149\) \(a_{35}=+0.211971082\)
\(a_{36}=-0.175402572\) \(a_{37}=+1.025096682\) \(a_{38}=-0.406038468\) \(a_{39}=-0.474634975\) \(a_{40}=+0.198280793\)
\(a_{41}=+0.906932225\) \(a_{42}=+0.215339412\) \(a_{43}=+1.547556668\) \(a_{44}=-0.560341928\) \(a_{45}=+0.196739515\)
\(a_{46}=-1.042011163\) \(a_{47}=-1.822254321\) \(a_{48}=+0.201431574\) \(a_{49}=+0.142857210\) \(a_{50}=+0.484706014\)
\(a_{51}=-1.037618916\) \(a_{52}=-0.294538592\) \(a_{53}=-1.271745681\) \(a_{54}=+0.769600326\) \(a_{55}=+0.628505026\)
\(a_{56}=+0.133630621\) \(a_{57}=+0.462668267\) \(a_{58}=+0.427706566\) \(a_{59}=+0.934890445\) \(a_{60}=-0.225934825\)
\(a_{61}=-0.052455956\) \(a_{62}=-0.036481469\) \(a_{63}=+0.132591882\) \(a_{64}=+0.124999999\) \(a_{65}=+0.330367899\)
\(a_{66}=+0.638492285\) \(a_{67}=-1.225380783\) \(a_{68}=-0.643902856\) \(a_{69}=+1.187339463\) \(a_{70}=-0.149886193\)
\(a_{71}=-1.642433817\) \(a_{72}=+0.124028348\) \(a_{73}=+1.321760492\) \(a_{74}=-0.724852826\) \(a_{75}=-0.552307492\)
\(a_{76}=+0.287112552\) \(a_{77}=+0.423578688\) \(a_{78}=+0.335617602\) \(a_{79}=+0.648278990\) \(a_{80}=-0.140205682\)
\(a_{81}=-0.526130602\) \(a_{82}=-0.641297955\) \(a_{83}=-1.028529326\) \(a_{84}=-0.152267931\) \(a_{85}=+0.722230791\)
\(a_{86}=-1.094287818\) \(a_{87}=-0.487358390\) \(a_{88}=+0.396221575\) \(a_{89}=+0.649074182\) \(a_{90}=-0.139115847\)
\(a_{91}=+0.222650251\) \(a_{92}=+0.736813153\) \(a_{93}=+0.041569507\) \(a_{94}=+1.288528374\) \(a_{95}=-0.322038515\)
\(a_{96}=-0.142433631\) \(a_{97}=+1.221741333\) \(a_{98}=-0.101015246\) \(a_{99}=+0.393141654\) \(a_{100}=-0.342738893\)

Showing 100 of 2000 available coefficients

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