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: \( 3.01504959328 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-0.988494934\) \(a_{4}=+0.500000000\) \(a_{5}=-0.323295271\)
\(a_{6}=+0.698971471\) \(a_{7}=-0.377964473\) \(a_{8}=-0.353553391\) \(a_{9}=-0.022877765\) \(a_{10}=+0.228604278\)
\(a_{11}=-1.541479929\) \(a_{12}=-0.494247467\) \(a_{13}=+1.727283206\) \(a_{14}=+0.267261242\) \(a_{15}=+0.319575737\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.250270454\) \(a_{18}=+0.016177023\) \(a_{19}=-0.906930401\) \(a_{20}=-0.161647635\)
\(a_{21}=+0.373615967\) \(a_{22}=+1.089990911\) \(a_{23}=-0.733760149\) \(a_{24}=+0.349485736\) \(a_{25}=-0.895480168\)
\(a_{26}=-1.221373668\) \(a_{27}=+1.011109489\) \(a_{28}=-0.188982237\) \(a_{29}=-0.251921604\) \(a_{30}=-0.225974171\)
\(a_{31}=+0.319491422\) \(a_{32}=-0.176776695\) \(a_{33}=+1.523745101\) \(a_{34}=+0.176967936\) \(a_{35}=+0.122194124\)
\(a_{36}=-0.011438880\) \(a_{37}=+1.231343040\) \(a_{38}=+0.641296641\) \(a_{39}=-1.707410701\) \(a_{40}=+0.114302127\)
\(a_{41}=-0.428992821\) \(a_{42}=-0.264186441\) \(a_{43}=-1.195096311\) \(a_{44}=-0.770740076\) \(a_{45}=+0.007396273\)
\(a_{46}=+0.518846777\) \(a_{47}=-0.383559947\) \(a_{48}=-0.247123734\) \(a_{49}=+0.142857143\) \(a_{50}=+0.633200099\)
\(a_{51}=+0.247391076\) \(a_{52}=+0.863641603\) \(a_{53}=+0.073347915\) \(a_{54}=-0.714962376\) \(a_{55}=+0.498353171\)
\(a_{56}=+0.133630622\) \(a_{57}=+0.896496110\) \(a_{58}=+0.178135473\) \(a_{59}=-0.047912958\) \(a_{60}=+0.159787874\)
\(a_{61}=-0.570980563\) \(a_{62}=-0.225914534\) \(a_{63}=+0.008646983\) \(a_{64}=+0.125000001\) \(a_{65}=-0.558422664\)
\(a_{66}=-1.077450424\) \(a_{67}=+1.461123750\) \(a_{68}=-0.125135211\) \(a_{69}=+0.725317726\) \(a_{70}=-0.086404570\)
\(a_{71}=-0.971274178\) \(a_{72}=+0.008088629\) \(a_{73}=-1.304086678\) \(a_{74}=-0.870694047\) \(a_{75}=+0.885179138\)
\(a_{76}=-0.453459958\) \(a_{77}=+0.582636460\) \(a_{78}=+1.207328011\) \(a_{79}=-0.859494676\) \(a_{80}=-0.080827131\)
\(a_{81}=-0.976601587\) \(a_{82}=+0.303343203\) \(a_{83}=+0.764044133\) \(a_{84}=+0.186840703\) \(a_{85}=+0.080911271\)
\(a_{86}=+0.845060769\) \(a_{87}=+0.249023229\) \(a_{88}=+0.544995476\) \(a_{89}=+0.247966875\) \(a_{90}=-0.005229948\)
\(a_{91}=-0.652851682\) \(a_{92}=-0.366880139\) \(a_{93}=-0.315815833\) \(a_{94}=+0.271217894\) \(a_{95}=+0.293206141\)
\(a_{96}=+0.174742861\) \(a_{97}=+0.077857560\) \(a_{98}=-0.101015215\) \(a_{99}=+0.035266019\) \(a_{100}=-0.447740137\)

Showing 100 of 2000 available coefficients

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