Properties

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

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Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 25.759928588 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+1.120715402\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+0.792465460\) \(a_{7}=+1.440466612\) \(a_{8}=+0.353553391\) \(a_{9}=+0.256003011\) \(a_{10}=-0.316227766\)
\(a_{11}=+1.144545430\) \(a_{12}=+0.560357701\) \(a_{13}=+1.361356914\) \(a_{14}=+1.018563710\) \(a_{15}=-0.501199164\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.912915796\) \(a_{18}=+0.181021465\) \(a_{19}=-1.121690746\) \(a_{20}=-0.223606798\)
\(a_{21}=+1.614353118\) \(a_{22}=+0.809315835\) \(a_{23}=+1.449541481\) \(a_{24}=+0.396232730\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.962624705\) \(a_{27}=-0.833808884\) \(a_{28}=+0.720233306\) \(a_{29}=+0.124316968\) \(a_{30}=-0.354401328\)
\(a_{31}=-0.764694112\) \(a_{32}=+0.176776695\) \(a_{33}=+1.282709692\) \(a_{34}=+0.645528950\) \(a_{35}=-0.644196253\)
\(a_{36}=+0.128001506\) \(a_{37}=-0.705354750\) \(a_{38}=-0.793155133\) \(a_{39}=+1.525693661\) \(a_{40}=-0.158113883\)
\(a_{41}=-1.644298029\) \(a_{42}=+1.141520037\) \(a_{43}=-1.060639040\) \(a_{44}=+0.572272715\) \(a_{45}=-0.114488027\)
\(a_{46}=+1.024980611\) \(a_{47}=+0.752390315\) \(a_{48}=+0.280178850\) \(a_{49}=+1.074944061\) \(a_{50}=+0.141421356\)
\(a_{51}=+1.023118793\) \(a_{52}=+0.680678457\) \(a_{53}=+1.169473565\) \(a_{54}=-0.589591916\) \(a_{55}=-0.511856277\)
\(a_{56}=+0.509281855\) \(a_{57}=-1.257096095\) \(a_{58}=+0.087905371\) \(a_{59}=+0.881948629\) \(a_{60}=-0.250599582\)
\(a_{61}=-0.433559801\) \(a_{62}=-0.540720392\) \(a_{63}=+0.368763791\) \(a_{64}=+0.125000000\) \(a_{65}=-0.608817320\)
\(a_{66}=+0.907012721\) \(a_{67}=+1.540086414\) \(a_{68}=+0.456457898\) \(a_{69}=+1.624523464\) \(a_{70}=-0.455515539\)
\(a_{71}=+0.492043598\) \(a_{72}=+0.090510733\) \(a_{73}=-1.225344158\) \(a_{74}=-0.498761127\) \(a_{75}=+0.224143080\)
\(a_{76}=-0.560845373\) \(a_{77}=+1.648679479\) \(a_{78}=+1.078828333\) \(a_{79}=+0.359147881\) \(a_{80}=-0.111803399\)
\(a_{81}=-1.190465470\) \(a_{82}=-1.162694287\) \(a_{83}=+1.905781738\) \(a_{84}=+0.807176559\) \(a_{85}=-0.408268355\)
\(a_{86}=-0.749985058\) \(a_{87}=+0.139323941\) \(a_{88}=+0.404657918\) \(a_{89}=-0.599856981\) \(a_{90}=-0.080955260\)
\(a_{91}=+1.960989182\) \(a_{92}=+0.724770741\) \(a_{93}=-0.857004469\) \(a_{94}=+0.532020294\) \(a_{95}=+0.501635352\)
\(a_{96}=+0.198116365\) \(a_{97}=-0.185324290\) \(a_{98}=+0.760100235\) \(a_{99}=+0.293007077\) \(a_{100}=+0.099975586\)

Showing 100 of 222 available coefficients

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