Properties

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

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 21.7875095659 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+1.392322571\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=-0.984520731\) \(a_{7}=+0.286359809\) \(a_{8}=-0.353553391\) \(a_{9}=+0.938562141\) \(a_{10}=-0.316227766\)
\(a_{11}=-0.186449671\) \(a_{12}=+0.696161285\) \(a_{13}=+0.360908310\) \(a_{14}=-0.202486963\) \(a_{15}=+0.622665583\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.210191302\) \(a_{18}=-0.663663655\) \(a_{19}=-0.273789162\) \(a_{20}=+0.223606798\)
\(a_{21}=+0.398705225\) \(a_{22}=+0.131839827\) \(a_{23}=+0.379959778\) \(a_{24}=-0.492260366\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.255200713\) \(a_{27}=-0.085541318\) \(a_{28}=+0.143179904\) \(a_{29}=+0.067891234\) \(a_{30}=-0.440291056\)
\(a_{31}=+1.740684315\) \(a_{32}=-0.176776695\) \(a_{33}=-0.259598085\) \(a_{34}=+0.855734476\) \(a_{35}=+0.128064000\)
\(a_{36}=+0.469281071\) \(a_{37}=+1.442688961\) \(a_{38}=+0.193598173\) \(a_{39}=+0.502500786\) \(a_{40}=-0.158113883\)
\(a_{41}=+1.521298930\) \(a_{42}=-0.281927169\) \(a_{43}=+1.591722157\) \(a_{44}=-0.093224836\) \(a_{45}=+0.419737750\)
\(a_{46}=-0.268672135\) \(a_{47}=+0.483982483\) \(a_{48}=+0.348080643\) \(a_{49}=-0.917998060\) \(a_{50}=-0.141421356\)
\(a_{51}=-1.684976665\) \(a_{52}=+0.180454155\) \(a_{53}=-1.544566082\) \(a_{54}=+0.060486846\) \(a_{55}=-0.083382828\)
\(a_{56}=-0.101243481\) \(a_{57}=-0.381202831\) \(a_{58}=-0.048006352\) \(a_{59}=+1.044111127\) \(a_{60}=+0.311332791\)
\(a_{61}=+0.049492030\) \(a_{62}=-1.230849683\) \(a_{63}=+0.268766475\) \(a_{64}=+0.125000000\) \(a_{65}=+0.161403103\)
\(a_{66}=+0.183563567\) \(a_{67}=+0.386293270\) \(a_{68}=-0.605095651\) \(a_{69}=+0.529026575\) \(a_{70}=-0.090554923\)
\(a_{71}=-0.414097588\) \(a_{72}=-0.331831827\) \(a_{73}=+0.015468443\) \(a_{74}=-1.020135147\) \(a_{75}=+0.278464514\)
\(a_{76}=-0.136894581\) \(a_{77}=-0.053391692\) \(a_{78}=-0.355321713\) \(a_{79}=+0.699914013\) \(a_{80}=+0.111803399\)
\(a_{81}=-1.057663248\) \(a_{82}=-1.075720790\) \(a_{83}=-0.829457107\) \(a_{84}=+0.199352613\) \(a_{85}=-0.541214003\)
\(a_{86}=-1.125517531\) \(a_{87}=+0.094526497\) \(a_{88}=+0.065919913\) \(a_{89}=+1.257898301\) \(a_{90}=-0.296799409\)
\(a_{91}=+0.103349635\) \(a_{92}=+0.189979889\) \(a_{93}=+2.423594060\) \(a_{94}=-0.342227296\) \(a_{95}=-0.122442236\)
\(a_{96}=-0.246130183\) \(a_{97}=+1.405632912\) \(a_{98}=+0.649122653\) \(a_{99}=-0.174994603\) \(a_{100}=+0.099975586\)

Showing 100 of 209 available coefficients

Rows: Cols: