Properties

Level $10$
Weight $0$
Character 10.1
Symmetry even
Fricke sign $-1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 21.738972733 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+0.193491072\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=-0.136818849\) \(a_{7}=+1.567745783\) \(a_{8}=-0.353553391\) \(a_{9}=-0.962561205\) \(a_{10}=-0.316227766\)
\(a_{11}=+0.958167774\) \(a_{12}=+0.096745536\) \(a_{13}=+0.901049348\) \(a_{14}=-1.108563675\) \(a_{15}=+0.086531838\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.578850567\) \(a_{18}=+0.680633556\) \(a_{19}=-0.532825120\) \(a_{20}=+0.223606798\)
\(a_{21}=+0.303344811\) \(a_{22}=-0.677526931\) \(a_{23}=-0.637724731\) \(a_{24}=-0.068409424\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.637138104\) \(a_{27}=-0.379738071\) \(a_{28}=+0.783872892\) \(a_{29}=-0.569526991\) \(a_{30}=-0.061187249\)
\(a_{31}=-1.189313411\) \(a_{32}=-0.176776695\) \(a_{33}=+0.185396909\) \(a_{34}=+1.116415943\) \(a_{35}=+0.701117229\)
\(a_{36}=-0.481280603\) \(a_{37}=-1.531700124\) \(a_{38}=+0.376764256\) \(a_{39}=+0.174345004\) \(a_{40}=-0.158113883\)
\(a_{41}=-1.138279543\) \(a_{42}=-0.214497173\) \(a_{43}=-0.828740266\) \(a_{44}=+0.479083887\) \(a_{45}=-0.430470457\)
\(a_{46}=+0.450939482\) \(a_{47}=+0.265205168\) \(a_{48}=+0.048372768\) \(a_{49}=+1.457826841\) \(a_{50}=-0.141421356\)
\(a_{51}=-0.305493488\) \(a_{52}=+0.450524674\) \(a_{53}=+1.372355424\) \(a_{54}=+0.268515365\) \(a_{55}=+0.428505655\)
\(a_{56}=-0.554281837\) \(a_{57}=-0.103096903\) \(a_{58}=+0.402716397\) \(a_{59}=+1.313864291\) \(a_{60}=+0.043265919\)
\(a_{61}=-1.129614810\) \(a_{62}=+0.840971578\) \(a_{63}=-1.509051271\) \(a_{64}=+0.125000000\) \(a_{65}=+0.402961518\)
\(a_{66}=-0.131095412\) \(a_{67}=-0.322527971\) \(a_{68}=-0.789425284\) \(a_{69}=-0.123394041\) \(a_{70}=-0.495764747\)
\(a_{71}=+1.956178516\) \(a_{72}=+0.340316778\) \(a_{73}=-0.179123210\) \(a_{74}=+1.083075544\) \(a_{75}=+0.038698214\)
\(a_{76}=-0.266412560\) \(a_{77}=+1.502163488\) \(a_{78}=-0.123280534\) \(a_{79}=-0.114120143\) \(a_{80}=+0.111803399\)
\(a_{81}=+0.889085279\) \(a_{82}=+0.804885184\) \(a_{83}=-1.430493835\) \(a_{84}=+0.151672406\) \(a_{85}=-0.706083439\)
\(a_{86}=+0.586007862\) \(a_{87}=-0.110198388\) \(a_{88}=-0.338763465\) \(a_{89}=+0.368697716\) \(a_{90}=+0.304388580\)
\(a_{91}=+1.412616315\) \(a_{92}=-0.318862365\) \(a_{93}=-0.230121526\) \(a_{94}=-0.187528373\) \(a_{95}=-0.238286638\)
\(a_{96}=-0.034204712\) \(a_{97}=-0.408563046\) \(a_{98}=-1.030839245\) \(a_{99}=-0.922295128\) \(a_{100}=+0.099975586\)

Showing 100 of 209 available coefficients

Rows: Cols: